text:
using Rubin
using Tests
using Elliptic
using HypergeometricFunctions
using Polylogarithms
using SpecialFunctions

@test integrate(x^2*(a*c+-1*b*c*x)^3*(a+b*x), x) == :(-1//7*b^4*c^3*x^7+1//3*a^4*c^3*x^3+-1//2*b*a^3*c^3*x^4+1//3*a*b^3*c^3*x^6)
@test integrate(x*(a*c+-1*b*c*x)^3*(a+b*x), x) == :((1/2)*a^4*c^3*x^2+-1//6*b^4*c^3*x^6+-2//3*b*a^3*c^3*x^3+2//5*a*b^3*c^3*x^5)
@test integrate((a*c+-1*b*c*x)^3*(a+b*x), x) == :(1//5*b^-1*c^3*(a+-1*b*x)^5+-1//2*a*b^-1*c^3*(a+-1*b*x)^4)
@test integrate(x^-1*(a*c+-1*b*c*x)^3*(a+b*x), x) == :(a^4*c^3*log(x)+-1//4*b^4*c^3*x^4+-2*b*x*a^3*c^3+2//3*a*b^3*c^3*x^3)
@test integrate(x^-2*(a*c+-1*b*c*x)^3*(a+b*x), x) == :(-1*a^4*c^3*x^-1+-1//3*b^4*c^3*x^3+a*b^3*c^3*x^2+-2*b*a^3*c^3*log(x))
@test integrate(x^-3*(a*c+-1*b*c*x)^3*(a+b*x), x) == :(-1//2*c^3*x^-2*(a+-1*b*x)^4)
@test integrate(x^-4*(a*c+-1*b*c*x)^3*(a+b*x), x) == :(-1*x*b^4*c^3+-1//3*a^4*c^3*x^-3+b*a^3*c^3*x^-2+2*a*b^3*c^3*log(x))
@test integrate(x^-5*(a*c+-1*b*c*x)^3*(a+b*x), x) == :(-1*b^4*c^3*log(x)+-1//4*a^4*c^3*x^-4+-2*a*b^3*c^3*x^-1+2//3*b*a^3*c^3*x^-3)
@test integrate(x^-6*(a*c+-1*b*c*x)^3*(a+b*x), x) == :(b^4*c^3*x^-1+-1//5*a^4*c^3*x^-5+(1/2)*b*a^3*c^3*x^-4+-1*a*b^3*c^3*x^-2)
@test integrate(x^-7*(a*c+-1*b*c*x)^3*(a+b*x), x) == :((1/2)*b^4*c^3*x^-2+-1//6*a^4*c^3*x^-6+-2//3*a*b^3*c^3*x^-3+2//5*b*a^3*c^3*x^-5)
@test integrate(x^-8*(a*c+-1*b*c*x)^3*(a+b*x), x) == :(-1//7*a^4*c^3*x^-7+1//3*b^4*c^3*x^-3+-1//2*a*b^3*c^3*x^-4+1//3*b*a^3*c^3*x^-6)
@test integrate(x^4*(a*c+-1*b*c*x)^4*(a+b*x), x) == :(1//5*a^5*c^4*x^5+1//10*b^5*c^4*x^10+-1//2*b*a^4*c^4*x^6+-1//3*a*b^4*c^4*x^9+1//4*a^2*b^3*c^4*x^8+2//7*a^3*b^2*c^4*x^7)
@test integrate(x^3*(a*c+-1*b*c*x)^4*(a+b*x), x) == :(1//4*a^5*c^4*x^4+1//9*b^5*c^4*x^9+-3//5*b*a^4*c^4*x^5+-3//8*a*b^4*c^4*x^8+1//3*a^3*b^2*c^4*x^6+2//7*a^2*b^3*c^4*x^7)
@test integrate(x^2*(a*c+-1*b*c*x)^4*(a+b*x), x) == :(1//8*b^-3*c^4*(a+-1*b*x)^8+-4//7*a*b^-3*c^4*(a+-1*b*x)^7+-2//5*a^3*b^-3*c^4*(a+-1*b*x)^5+5//6*a^2*b^-3*c^4*(a+-1*b*x)^6)
@test integrate(x*(a*c+-1*b*c*x)^4*(a+b*x), x) == :(-1//7*b^-2*c^4*(a+-1*b*x)^7+(1/2)*a*b^-2*c^4*(a+-1*b*x)^6+-2//5*a^2*b^-2*c^4*(a+-1*b*x)^5)
@test integrate((a*c+-1*b*c*x)^4*(a+b*x), x) == :(1//6*b^-1*c^4*(a+-1*b*x)^6+-2//5*a*b^-1*c^4*(a+-1*b*x)^5)
@test integrate(x^-1*(a*c+-1*b*c*x)^4*(a+b*x), x) == :(a^5*c^4*log(x)+1//5*b^5*c^4*x^5+a^3*b^2*c^4*x^2+-3*b*x*a^4*c^4+-3//4*a*b^4*c^4*x^4+2//3*a^2*b^3*c^4*x^3)
@test integrate(x^-2*(a*c+-1*b*c*x)^4*(a+b*x), x) == :(-1*a^5*c^4*x^-1+1//4*b^5*c^4*x^4+a^2*b^3*c^4*x^2+-1*a*b^4*c^4*x^3+-3*b*a^4*c^4*log(x)+2*x*a^3*b^2*c^4)
@test integrate(x^-3*(a*c+-1*b*c*x)^4*(a+b*x), x) == :(-1//2*a^5*c^4*x^-2+1//3*b^5*c^4*x^3+2*x*a^2*b^3*c^4+2*a^3*b^2*c^4*log(x)+3*b*a^4*c^4*x^-1+-3//2*a*b^4*c^4*x^2)
@test integrate(x^-4*(a*c+-1*b*c*x)^4*(a+b*x), x) == :((1/2)*b^5*c^4*x^2+-1//3*a^5*c^4*x^-3+-3*a*x*b^4*c^4+-2*a^3*b^2*c^4*x^-1+2*a^2*b^3*c^4*log(x)+3//2*b*a^4*c^4*x^-2)
@test integrate(x^-5*(a*c+-1*b*c*x)^4*(a+b*x), x) == :(x*b^5*c^4+-1//4*a^5*c^4*x^-4+b*a^4*c^4*x^-3+-1*a^3*b^2*c^4*x^-2+-3*a*b^4*c^4*log(x)+-2*a^2*b^3*c^4*x^-1)
@test integrate(x^-6*(a*c+-1*b*c*x)^4*(a+b*x), x) == :(b^5*c^4*log(x)+-1//5*a^5*c^4*x^-5+-1*a^2*b^3*c^4*x^-2+3*a*b^4*c^4*x^-1+-2//3*a^3*b^2*c^4*x^-3+3//4*b*a^4*c^4*x^-4)
@test integrate(x^-7*(a*c+-1*b*c*x)^4*(a+b*x), x) == :(-1//6*c^4*x^-6*(a+-1*b*x)^5+-7//30*b*a^-1*c^4*x^-5*(a+-1*b*x)^5)
@test integrate(x^-8*(a*c+-1*b*c*x)^4*(a+b*x), x) == :(-1//2*b^5*c^4*x^-2+-1//7*a^5*c^4*x^-7+a*b^4*c^4*x^-3+(1/2)*b*a^4*c^4*x^-6+-2//5*a^3*b^2*c^4*x^-5+-1//2*a^2*b^3*c^4*x^-4)
@test integrate(x^-9*(a*c+-1*b*c*x)^4*(a+b*x), x) == :(-1//3*b^5*c^4*x^-3+-1//8*a^5*c^4*x^-8+-2//5*a^2*b^3*c^4*x^-5+-1//3*a^3*b^2*c^4*x^-6+3//4*a*b^4*c^4*x^-4+3//7*b*a^4*c^4*x^-7)
@test integrate(x^4*(a*c+-1*b*c*x)^5*(a+b*x), x) == :(-1//11*b^6*c^5*x^11+1//5*a^6*c^5*x^5+-5//9*a^2*b^4*c^5*x^9+-2//3*b*a^5*c^5*x^6+2//5*a*b^5*c^5*x^10+5//7*a^4*b^2*c^5*x^7)
@test integrate(x^3*(a*c+-1*b*c*x)^5*(a+b*x), x) == :(-1//10*b^6*c^5*x^10+1//4*a^6*c^5*x^4+-5//8*a^2*b^4*c^5*x^8+-4//5*b*a^5*c^5*x^5+4//9*a*b^5*c^5*x^9+5//6*a^4*b^2*c^5*x^6)
@test integrate(x^2*(a*c+-1*b*c*x)^5*(a+b*x), x) == :(1//9*b^-3*c^5*(a+-1*b*x)^9+-1//2*a*b^-3*c^5*(a+-1*b*x)^8+-1//3*a^3*b^-3*c^5*(a+-1*b*x)^6+5//7*a^2*b^-3*c^5*(a+-1*b*x)^7)
@test integrate(x*(a*c+-1*b*c*x)^5*(a+b*x), x) == :(-1//8*b^-2*c^5*(a+-1*b*x)^8+-1//3*a^2*b^-2*c^5*(a+-1*b*x)^6+3//7*a*b^-2*c^5*(a+-1*b*x)^7)
@test integrate((a*c+-1*b*c*x)^5*(a+b*x), x) == :(1//7*b^-1*c^5*(a+-1*b*x)^7+-1//3*a*b^-1*c^5*(a+-1*b*x)^6)
@test integrate(x^-1*(a*c+-1*b*c*x)^5*(a+b*x), x) == :(a^6*c^5*log(x)+-1//6*b^6*c^5*x^6+-4*b*x*a^5*c^5+-5//4*a^2*b^4*c^5*x^4+4//5*a*b^5*c^5*x^5+5//2*a^4*b^2*c^5*x^2)
@test integrate(x^-2*(a*c+-1*b*c*x)^5*(a+b*x), x) == :(-1*a^6*c^5*x^-1+-1//5*b^6*c^5*x^5+a*b^5*c^5*x^4+-4*b*a^5*c^5*log(x)+5*x*a^4*b^2*c^5+-5//3*a^2*b^4*c^5*x^3)
@test integrate(x^-3*(a*c+-1*b*c*x)^5*(a+b*x), x) == :(-1//2*a^6*c^5*x^-2+-1//4*b^6*c^5*x^4+4*b*a^5*c^5*x^-1+5*a^4*b^2*c^5*log(x)+-5//2*a^2*b^4*c^5*x^2+4//3*a*b^5*c^5*x^3)
@test integrate(x^-4*(a*c+-1*b*c*x)^5*(a+b*x), x) == :(-1//3*c^5*x^-3*(a+-1*b*x)^6)
@test integrate(x^-5*(a*c+-1*b*c*x)^5*(a+b*x), x) == :(-1//2*b^6*c^5*x^2+-1//4*a^6*c^5*x^-4+-5*a^2*b^4*c^5*log(x)+4*a*x*b^5*c^5+-5//2*a^4*b^2*c^5*x^-2+4//3*b*a^5*c^5*x^-3)
@test integrate(x^-6*(a*c+-1*b*c*x)^5*(a+b*x), x) == :(-1*x*b^6*c^5+-1//5*a^6*c^5*x^-5+b*a^5*c^5*x^-4+4*a*b^5*c^5*log(x)+5*a^2*b^4*c^5*x^-1+-5//3*a^4*b^2*c^5*x^-3)
@test integrate(x^-7*(a*c+-1*b*c*x)^5*(a+b*x), x) == :(-1*b^6*c^5*log(x)+-1//6*a^6*c^5*x^-6+-4*a*b^5*c^5*x^-1+-5//4*a^4*b^2*c^5*x^-4+4//5*b*a^5*c^5*x^-5+5//2*a^2*b^4*c^5*x^-2)
@test integrate(x^-8*(a*c+-1*b*c*x)^5*(a+b*x), x) == :(-1//7*c^5*x^-7*(a+-1*b*x)^6+-4//21*b*a^-1*c^5*x^-6*(a+-1*b*x)^6)
@test integrate(x^-9*(a*c+-1*b*c*x)^5*(a+b*x), x) == :(-1//8*c^5*x^-8*(a+-1*b*x)^6+-5//28*b*a^-1*c^5*x^-7*(a+-1*b*x)^6+-5//168*a^-2*b^2*c^5*x^-6*(a+-1*b*x)^6)
@test integrate(x^-10*(a*c+-1*b*c*x)^5*(a+b*x), x) == :(-1//9*a^6*c^5*x^-9+1//3*b^6*c^5*x^-3+a^2*b^4*c^5*x^-5+(1/2)*b*a^5*c^5*x^-8+-1*a*b^5*c^5*x^-4+-5//7*a^4*b^2*c^5*x^-7)
@test integrate(x^-11*(a*c+-1*b*c*x)^5*(a+b*x), x) == :(-1//10*a^6*c^5*x^-10+1//4*b^6*c^5*x^-4+-5//8*a^4*b^2*c^5*x^-8+-4//5*a*b^5*c^5*x^-5+4//9*b*a^5*c^5*x^-9+5//6*a^2*b^4*c^5*x^-6)
@test integrate(x^-12*(a*c+-1*b*c*x)^5*(a+b*x), x) == :(-1//11*a^6*c^5*x^-11+1//5*b^6*c^5*x^-5+-5//9*a^4*b^2*c^5*x^-9+-2//3*a*b^5*c^5*x^-6+2//5*b*a^5*c^5*x^-10+5//7*a^2*b^4*c^5*x^-7)
@test integrate(x^-8*(a*c+-1*b*c*x)^6*(a+b*x), x) == :(b^7*c^6*log(x)+-1//7*a^7*c^6*x^-7+5*a*b^6*c^6*x^-1+-9//2*a^2*b^5*c^6*x^-2+-9//5*a^5*b^2*c^6*x^-5+5//3*a^3*b^4*c^6*x^-3+5//4*a^4*b^3*c^6*x^-4+5//6*b*a^6*c^6*x^-6)
@test integrate(x^-9*(a*c+-1*b*c*x)^6*(a+b*x), x) == :(-1//8*c^6*x^-8*(a+-1*b*x)^7+-9//56*b*a^-1*c^6*x^-7*(a+-1*b*x)^7)
@test integrate(x^-10*(a*c+-1*b*c*x)^6*(a+b*x), x) == :(-1//9*c^6*x^-9*(a+-1*b*x)^7+-11//72*b*a^-1*c^6*x^-8*(a+-1*b*x)^7+-11//504*a^-2*b^2*c^6*x^-7*(a+-1*b*x)^7)
@test integrate(x^-11*(a*c+-1*b*c*x)^6*(a+b*x), x) == :(-1//10*c^6*x^-10*(a+-1*b*x)^7+-13//90*b*a^-1*c^6*x^-9*(a+-1*b*x)^7+-13//360*a^-2*b^2*c^6*x^-8*(a+-1*b*x)^7+-13//2520*a^-3*b^3*c^6*x^-7*(a+-1*b*x)^7)
@test integrate(x^-12*(a*c+-1*b*c*x)^6*(a+b*x), x) == :(-1//4*b^7*c^6*x^-4+-1//11*a^7*c^6*x^-11+a*b^6*c^6*x^-5+(1/2)*b*a^6*c^6*x^-10+-1*a^5*b^2*c^6*x^-9+-3//2*a^2*b^5*c^6*x^-6+5//7*a^3*b^4*c^6*x^-7+5//8*a^4*b^3*c^6*x^-8)
@test integrate(x^-13*(a*c+-1*b*c*x)^6*(a+b*x), x) == :(-1//5*b^7*c^6*x^-5+-1//12*a^7*c^6*x^-12+-9//7*a^2*b^5*c^6*x^-7+-9//10*a^5*b^2*c^6*x^-10+5//6*a*b^6*c^6*x^-6+5//8*a^3*b^4*c^6*x^-8+5//9*a^4*b^3*c^6*x^-9+5//11*b*a^6*c^6*x^-11)
@test integrate(x^4*(A+B*x)*(a+b*x), x) == :(x^6*(1//6*A*b+1//6*B*a)+1//5*A*a*x^5+1//7*B*b*x^7)
@test integrate(x^3*(A+B*x)*(a+b*x), x) == :(x^5*(1//5*A*b+1//5*B*a)+1//4*A*a*x^4+1//6*B*b*x^6)
@test integrate(x^2*(A+B*x)*(a+b*x), x) == :(x^4*(1//4*A*b+1//4*B*a)+1//3*A*a*x^3+1//5*B*b*x^5)
@test integrate(x*(A+B*x)*(a+b*x), x) == :(x^3*(1//3*A*b+1//3*B*a)+(1/2)*A*a*x^2+1//4*B*b*x^4)
@test integrate((A+B*x)*(a+b*x), x) == :((1/2)*x^2*(A*b+B*a)+A*a*x+1//3*B*b*x^3)
@test integrate(x^-1*(A+B*x)*(a+b*x), x) == :(x*(A*b+B*a)+A*a*log(x)+(1/2)*B*b*x^2)
@test integrate(x^-2*(A+B*x)*(a+b*x), x) == :((A*b+B*a)*log(x)+B*b*x+-1*A*a*x^-1)
@test integrate(x^-3*(A+B*x)*(a+b*x), x) == :(-1*x^-1*(A*b+B*a)+B*b*log(x)+-1//2*A*a*x^-2)
@test integrate(x^-4*(A+B*x)*(a+b*x), x) == :(-1//2*x^-2*(A*b+B*a)+-1*B*b*x^-1+-1//3*A*a*x^-3)
@test integrate(x^-5*(A+B*x)*(a+b*x), x) == :(-1//3*x^-3*(A*b+B*a)+-1//2*B*b*x^-2+-1//4*A*a*x^-4)
@test integrate(x^-6*(A+B*x)*(a+b*x), x) == :(-1//4*x^-4*(A*b+B*a)+-1//3*B*b*x^-3+-1//5*A*a*x^-5)
@test integrate(x^4*(a+b*x)^2*(A+B*x), x) == :(1//5*A*a^2*x^5+1//6*a*x^6*(B*a+2*A*b)+1//7*b*x^7*(A*b+2*B*a)+1//8*B*b^2*x^8)
@test integrate(x^3*(a+b*x)^2*(A+B*x), x) == :(1//4*A*a^2*x^4+1//5*a*x^5*(B*a+2*A*b)+1//6*b*x^6*(A*b+2*B*a)+1//7*B*b^2*x^7)
@test integrate(x^2*(a+b*x)^2*(A+B*x), x) == :(1//3*A*a^2*x^3+1//4*a*x^4*(B*a+2*A*b)+1//5*b*x^5*(A*b+2*B*a)+1//6*B*b^2*x^6)
@test integrate(x*(a+b*x)^2*(A+B*x), x) == :((1/2)*A*a^2*x^2+1//3*a*x^3*(B*a+2*A*b)+1//4*b*x^4*(A*b+2*B*a)+1//5*B*b^2*x^5)
@test integrate((a+b*x)^2*(A+B*x), x) == :(1//3*b^-2*(a+b*x)^3*(A*b+-1*B*a)+1//4*B*b^-2*(a+b*x)^4)
@test integrate(x^-1*(a+b*x)^2*(A+B*x), x) == :(A*a^2*log(x)+(1/2)*A*b^2*x^2+1//3*B*b^-1*(a+b*x)^3+2*A*a*b*x)
@test integrate(x^-2*(a+b*x)^2*(A+B*x), x) == :(a*(B*a+2*A*b)*log(x)+b*x*(A*b+2*B*a)+(1/2)*B*b^2*x^2+-1*A*a^2*x^-1)
@test integrate(x^-3*(a+b*x)^2*(A+B*x), x) == :(B*x*b^2+b*(A*b+2*B*a)*log(x)+-1*a*x^-1*(B*a+2*A*b)+-1//2*A*a^2*x^-2)
@test integrate(x^-4*(a+b*x)^2*(A+B*x), x) == :(B*b^2*log(x)+-1*b*x^-1*(A*b+2*B*a)+-1//2*a*x^-2*(B*a+2*A*b)+-1//3*A*a^2*x^-3)
@test integrate(x^-5*(a+b*x)^2*(A+B*x), x) == :(-1//4*A*a^-1*x^-4*(a+b*x)^3+1//12*a^-2*x^-3*(a+b*x)^3*(A*b+-4*B*a))
@test integrate(x^-6*(a+b*x)^2*(A+B*x), x) == :(-1//2*B*b^2*x^-2+-1//3*b*x^-3*(A*b+2*B*a)+-1//4*a*x^-4*(B*a+2*A*b)+-1//5*A*a^2*x^-5)
@test integrate(x^-7*(a+b*x)^2*(A+B*x), x) == :(-1//3*B*b^2*x^-3+-1//4*b*x^-4*(A*b+2*B*a)+-1//5*a*x^-5*(B*a+2*A*b)+-1//6*A*a^2*x^-6)
@test integrate(x^-8*(a+b*x)^2*(A+B*x), x) == :(-1//4*B*b^2*x^-4+-1//5*b*x^-5*(A*b+2*B*a)+-1//6*a*x^-6*(B*a+2*A*b)+-1//7*A*a^2*x^-7)
@test integrate(x^4*(a+b*x)^3*(A+B*x), x) == :(1//5*A*a^3*x^5+1//6*a^2*x^6*(B*a+3*A*b)+1//8*b^2*x^8*(A*b+3*B*a)+1//9*B*b^3*x^9+3//7*a*b*x^7*(A*b+B*a))
@test integrate(x^3*(a+b*x)^3*(A+B*x), x) == :(1//4*A*a^3*x^4+1//5*a^2*x^5*(B*a+3*A*b)+1//7*b^2*x^7*(A*b+3*B*a)+1//8*B*b^3*x^8+(1/2)*a*b*x^6*(A*b+B*a))
@test integrate(x^2*(a+b*x)^3*(A+B*x), x) == :(1//3*A*a^3*x^3+1//4*a^2*x^4*(B*a+3*A*b)+1//6*b^2*x^6*(A*b+3*B*a)+1//7*B*b^3*x^7+3//5*a*b*x^5*(A*b+B*a))
@test integrate(x*(a+b*x)^3*(A+B*x), x) == :(1//5*b^-3*(a+b*x)^5*(A*b+-2*B*a)+1//6*B*b^-3*(a+b*x)^6+-1//4*a*b^-3*(a+b*x)^4*(A*b+-1*B*a))
@test integrate((a+b*x)^3*(A+B*x), x) == :(1//4*b^-2*(a+b*x)^4*(A*b+-1*B*a)+1//5*B*b^-2*(a+b*x)^5)
@test integrate(x^-1*(a+b*x)^3*(A+B*x), x) == :(A*a^3*log(x)+1//3*A*b^3*x^3+1//4*B*b^-1*(a+b*x)^4+3*A*b*x*a^2+3//2*A*a*b^2*x^2)
@test integrate(x^-2*(a+b*x)^3*(A+B*x), x) == :(a^2*(B*a+3*A*b)*log(x)+(1/2)*b^2*x^2*(A*b+3*B*a)+-1*A*a^3*x^-1+1//3*B*b^3*x^3+3*a*b*x*(A*b+B*a))
@test integrate(x^-3*(a+b*x)^3*(A+B*x), x) == :(x*b^2*(A*b+3*B*a)+(1/2)*B*b^3*x^2+-1*a^2*x^-1*(B*a+3*A*b)+-1//2*A*a^3*x^-2+3*a*b*(A*b+B*a)*log(x))
@test integrate(x^-4*(a+b*x)^3*(A+B*x), x) == :(B*x*b^3+b^2*(A*b+3*B*a)*log(x)+-1//2*a^2*x^-2*(B*a+3*A*b)+-1//3*A*a^3*x^-3+-3*a*b*x^-1*(A*b+B*a))
@test integrate(x^-5*(a+b*x)^3*(A+B*x), x) == :(B*b^3*log(x)+-1//3*B*a^3*x^-3+-3*B*a*b^2*x^-1+-3//2*B*b*a^2*x^-2+-1//4*A*a^-1*x^-4*(a+b*x)^4)
@test integrate(x^-6*(a+b*x)^3*(A+B*x), x) == :(-1//5*A*a^-1*x^-5*(a+b*x)^4+1//20*a^-2*x^-4*(a+b*x)^4*(A*b+-5*B*a))
@test integrate(x^-7*(a+b*x)^3*(A+B*x), x) == :(-1//2*B*b^3*x^-2+-1//3*b^2*x^-3*(A*b+3*B*a)+-1//5*a^2*x^-5*(B*a+3*A*b)+-1//6*A*a^3*x^-6+-3//4*a*b*x^-4*(A*b+B*a))
@test integrate(x^-8*(a+b*x)^3*(A+B*x), x) == :(-1//3*B*b^3*x^-3+-1//4*b^2*x^-4*(A*b+3*B*a)+-1//6*a^2*x^-6*(B*a+3*A*b)+-1//7*A*a^3*x^-7+-3//5*a*b*x^-5*(A*b+B*a))
@test integrate(x^-9*(a+b*x)^3*(A+B*x), x) == :(-1//4*B*b^3*x^-4+-1//5*b^2*x^-5*(A*b+3*B*a)+-1//7*a^2*x^-7*(B*a+3*A*b)+-1//8*A*a^3*x^-8+-1//2*a*b*x^-6*(A*b+B*a))
@test integrate(x^-10*(a+b*x)^3*(A+B*x), x) == :(-1//5*B*b^3*x^-5+-1//6*b^2*x^-6*(A*b+3*B*a)+-1//8*a^2*x^-8*(B*a+3*A*b)+-1//9*A*a^3*x^-9+-3//7*a*b*x^-7*(A*b+B*a))
@test integrate(x^5*(a+b*x)^5*(A+B*x), x) == :(1//6*A*a^5*x^6+1//7*a^4*x^7*(B*a+5*A*b)+1//11*b^4*x^11*(A*b+5*B*a)+1//12*B*b^5*x^12+(1/2)*a*b^3*x^10*(A*b+2*B*a)+5//8*b*a^3*x^8*(B*a+2*A*b)+10//9*a^2*b^2*x^9*(A*b+B*a))
@test integrate(x^4*(a+b*x)^5*(A+B*x), x) == :(1//5*A*a^5*x^5+1//6*a^4*x^6*(B*a+5*A*b)+1//10*b^4*x^10*(A*b+5*B*a)+1//11*B*b^5*x^11+5//4*a^2*b^2*x^8*(A*b+B*a)+5//7*b*a^3*x^7*(B*a+2*A*b)+5//9*a*b^3*x^9*(A*b+2*B*a))
@test integrate(x^3*(a+b*x)^5*(A+B*x), x) == :(1//9*b^-5*(a+b*x)^9*(A*b+-4*B*a)+1//10*B*b^-5*(a+b*x)^10+-3//8*a*b^-5*(a+b*x)^8*(A*b+-2*B*a)+-1//6*a^3*b^-5*(a+b*x)^6*(A*b+-1*B*a)+1//7*a^2*b^-5*(a+b*x)^7*(-4*B*a+3*A*b))
@test integrate(x^2*(a+b*x)^5*(A+B*x), x) == :(1//8*b^-4*(a+b*x)^8*(A*b+-3*B*a)+1//9*B*b^-4*(a+b*x)^9+-1//7*a*b^-4*(a+b*x)^7*(-3*B*a+2*A*b)+1//6*a^2*b^-4*(a+b*x)^6*(A*b+-1*B*a))
@test integrate(x*(a+b*x)^5*(A+B*x), x) == :(1//7*b^-3*(a+b*x)^7*(A*b+-2*B*a)+1//8*B*b^-3*(a+b*x)^8+-1//6*a*b^-3*(a+b*x)^6*(A*b+-1*B*a))
@test integrate((a+b*x)^5*(A+B*x), x) == :(1//6*b^-2*(a+b*x)^6*(A*b+-1*B*a)+1//7*B*b^-2*(a+b*x)^7)
@test integrate(x^-1*(a+b*x)^5*(A+B*x), x) == :(A*a^5*log(x)+1//5*A*b^5*x^5+1//6*B*b^-1*(a+b*x)^6+5*A*b*x*a^4+5*A*a^3*b^2*x^2+5//4*A*a*b^4*x^4+10//3*A*a^2*b^3*x^3)
@test integrate(x^-2*(a+b*x)^5*(A+B*x), x) == :(a^4*(B*a+5*A*b)*log(x)+-1*A*a^5*x^-1+1//4*b^4*x^4*(A*b+5*B*a)+1//5*B*b^5*x^5+5*b*x*a^3*(B*a+2*A*b)+5*a^2*b^2*x^2*(A*b+B*a)+5//3*a*b^3*x^3*(A*b+2*B*a))
@test integrate(x^-3*(a+b*x)^5*(A+B*x), x) == :(-1*a^4*x^-1*(B*a+5*A*b)+-1//2*A*a^5*x^-2+1//3*b^4*x^3*(A*b+5*B*a)+1//4*B*b^5*x^4+5*b*a^3*(B*a+2*A*b)*log(x)+10*x*a^2*b^2*(A*b+B*a)+5//2*a*b^3*x^2*(A*b+2*B*a))
@test integrate(x^-4*(a+b*x)^5*(A+B*x), x) == :((1/2)*b^4*x^2*(A*b+5*B*a)+-1//2*a^4*x^-2*(B*a+5*A*b)+-1//3*A*a^5*x^-3+1//3*B*b^5*x^3+-5*b*a^3*x^-1*(B*a+2*A*b)+5*a*x*b^3*(A*b+2*B*a)+10*a^2*b^2*(A*b+B*a)*log(x))
@test integrate(x^-5*(a+b*x)^5*(A+B*x), x) == :(x*b^4*(A*b+5*B*a)+(1/2)*B*b^5*x^2+-1//3*a^4*x^-3*(B*a+5*A*b)+-1//4*A*a^5*x^-4+-10*a^2*b^2*x^-1*(A*b+B*a)+5*a*b^3*(A*b+2*B*a)*log(x)+-5//2*b*a^3*x^-2*(B*a+2*A*b))
@test integrate(x^-6*(a+b*x)^5*(A+B*x), x) == :(B*x*b^5+b^4*(A*b+5*B*a)*log(x)+-1//4*a^4*x^-4*(B*a+5*A*b)+-1//5*A*a^5*x^-5+-5*a*b^3*x^-1*(A*b+2*B*a)+-5*a^2*b^2*x^-2*(A*b+B*a)+-5//3*b*a^3*x^-3*(B*a+2*A*b))
@test integrate(x^-7*(a+b*x)^5*(A+B*x), x) == :(B*b^5*log(x)+-1//5*B*a^5*x^-5+-5*B*a*b^4*x^-1+-5*B*a^2*b^3*x^-2+-10//3*B*a^3*b^2*x^-3+-5//4*B*b*a^4*x^-4+-1//6*A*a^-1*x^-6*(a+b*x)^6)
@test integrate(x^-8*(a+b*x)^5*(A+B*x), x) == :(-1//7*A*a^-1*x^-7*(a+b*x)^6+1//42*a^-2*x^-6*(a+b*x)^6*(A*b+-7*B*a))
@test integrate(x^-9*(a+b*x)^5*(A+B*x), x) == :(-1//8*A*a^-1*x^-8*(a+b*x)^6+1//28*a^-2*x^-7*(a+b*x)^6*(A*b+-4*B*a)+-1//168*b*a^-3*x^-6*(a+b*x)^6*(A*b+-4*B*a))
@test integrate(x^-10*(a+b*x)^5*(A+B*x), x) == :(-1//3*B*b^5*x^-3+-1//4*b^4*x^-4*(A*b+5*B*a)+-1//8*a^4*x^-8*(B*a+5*A*b)+-1//9*A*a^5*x^-9+-1*a*b^3*x^-5*(A*b+2*B*a)+-5//3*a^2*b^2*x^-6*(A*b+B*a)+-5//7*b*a^3*x^-7*(B*a+2*A*b))
@test integrate(x^-11*(a+b*x)^5*(A+B*x), x) == :(-1//4*B*b^5*x^-4+-1//5*b^4*x^-5*(A*b+5*B*a)+-1//9*a^4*x^-9*(B*a+5*A*b)+-1//10*A*a^5*x^-10+-10//7*a^2*b^2*x^-7*(A*b+B*a)+-5//6*a*b^3*x^-6*(A*b+2*B*a)+-5//8*b*a^3*x^-8*(B*a+2*A*b))
@test integrate(x^-12*(a+b*x)^5*(A+B*x), x) == :(-1//5*B*b^5*x^-5+-1//6*b^4*x^-6*(A*b+5*B*a)+-1//10*a^4*x^-10*(B*a+5*A*b)+-1//11*A*a^5*x^-11+-5//4*a^2*b^2*x^-8*(A*b+B*a)+-5//7*a*b^3*x^-7*(A*b+2*B*a)+-5//9*b*a^3*x^-9*(B*a+2*A*b))
@test integrate(x^10*(a+b*x)^10*(A+B*x), x) == :(1//11*A*a^10*x^11+1//12*a^9*x^12*(B*a+10*A*b)+1//21*b^9*x^21*(A*b+10*B*a)+1//22*B*b^10*x^22+2*a^6*b^3*x^15*(4*B*a+7*A*b)+1//4*a*b^8*x^20*(2*A*b+9*B*a)+5//3*a^3*b^6*x^18*(4*A*b+7*B*a)+5//13*b*a^8*x^13*(2*B*a+9*A*b)+15//14*a^7*b^2*x^14*(3*B*a+8*A*b)+15//19*a^2*b^7*x^19*(3*A*b+8*B*a)+21//8*a^5*b^4*x^16*(5*B*a+6*A*b)+42//17*a^4*b^5*x^17*(5*A*b+6*B*a))
@test integrate(x^9*(a+b*x)^10*(A+B*x), x) == :(1//10*A*a^10*x^10+1//11*a^9*x^11*(B*a+10*A*b)+1//20*b^9*x^20*(A*b+10*B*a)+1//21*B*b^10*x^21+5//6*a^2*b^7*x^18*(3*A*b+8*B*a)+5//12*b*a^8*x^12*(2*B*a+9*A*b)+5//19*a*b^8*x^19*(2*A*b+9*B*a)+14//5*a^5*b^4*x^15*(5*B*a+6*A*b)+15//7*a^6*b^3*x^14*(4*B*a+7*A*b)+15//13*a^7*b^2*x^13*(3*B*a+8*A*b)+21//8*a^4*b^5*x^16*(5*A*b+6*B*a)+30//17*a^3*b^6*x^17*(4*A*b+7*B*a))
@test integrate(x^8*(a+b*x)^10*(A+B*x), x) == :(1//19*b^-10*(a+b*x)^19*(A*b+-9*B*a)+1//20*B*b^-10*(a+b*x)^20+-2*a^5*b^-10*(a+b*x)^14*(-3*B*a+2*A*b)+-7//8*a^3*b^-10*(a+b*x)^16*(-9*B*a+4*A*b)+-2//9*a*b^-10*(a+b*x)^18*(-9*B*a+2*A*b)+-1//12*a^7*b^-10*(a+b*x)^12*(-9*B*a+8*A*b)+1//11*a^8*b^-10*(a+b*x)^11*(A*b+-1*B*a)+4//13*a^6*b^-10*(a+b*x)^13*(-9*B*a+7*A*b)+14//15*a^4*b^-10*(a+b*x)^15*(-9*B*a+5*A*b)+28//17*a^2*b^-10*(a+b*x)^17*(A*b+-3*B*a))
@test integrate(x^7*(a+b*x)^10*(A+B*x), x) == :(1//18*b^-9*(a+b*x)^18*(A*b+-8*B*a)+1//19*B*b^-9*(a+b*x)^19+(1/2)*a^4*b^-9*(a+b*x)^14*(-8*B*a+5*A*b)+-7//3*a^3*b^-9*(a+b*x)^15*(A*b+-2*B*a)+-7//13*a^5*b^-9*(a+b*x)^13*(-4*B*a+3*A*b)+-7//17*a*b^-9*(a+b*x)^17*(A*b+-4*B*a)+-1//11*a^7*b^-9*(a+b*x)^11*(A*b+-1*B*a)+1//12*a^6*b^-9*(a+b*x)^12*(-8*B*a+7*A*b)+7//16*a^2*b^-9*(a+b*x)^16*(-8*B*a+3*A*b))
@test integrate(x^6*(a+b*x)^10*(A+B*x), x) == :(1//17*b^-8*(a+b*x)^17*(A*b+-7*B*a)+1//18*B*b^-8*(a+b*x)^18+-5//14*a^3*b^-8*(a+b*x)^14*(-7*B*a+4*A*b)+-3//16*a*b^-8*(a+b*x)^16*(-7*B*a+2*A*b)+-1//12*a^5*b^-8*(a+b*x)^12*(-7*B*a+6*A*b)+1//3*a^2*b^-8*(a+b*x)^15*(-7*B*a+3*A*b)+1//11*a^6*b^-8*(a+b*x)^11*(A*b+-1*B*a)+3//13*a^4*b^-8*(a+b*x)^13*(-7*B*a+5*A*b))
@test integrate(x^5*(a+b*x)^10*(A+B*x), x) == :(1//16*b^-7*(a+b*x)^16*(A*b+-6*B*a)+1//17*B*b^-7*(a+b*x)^17+-5//13*a^3*b^-7*(a+b*x)^13*(-3*B*a+2*A*b)+-1//3*a*b^-7*(a+b*x)^15*(A*b+-3*B*a)+-1//11*a^5*b^-7*(a+b*x)^11*(A*b+-1*B*a)+1//12*a^4*b^-7*(a+b*x)^12*(-6*B*a+5*A*b)+5//7*a^2*b^-7*(a+b*x)^14*(A*b+-2*B*a))
@test integrate(x^4*(a+b*x)^10*(A+B*x), x) == :(1//15*b^-6*(a+b*x)^15*(A*b+-5*B*a)+1//16*B*b^-6*(a+b*x)^16+-1//7*a*b^-6*(a+b*x)^14*(-5*B*a+2*A*b)+-1//12*a^3*b^-6*(a+b*x)^12*(-5*B*a+4*A*b)+1//11*a^4*b^-6*(a+b*x)^11*(A*b+-1*B*a)+2//13*a^2*b^-6*(a+b*x)^13*(-5*B*a+3*A*b))
@test integrate(x^3*(a+b*x)^10*(A+B*x), x) == :(1//14*b^-5*(a+b*x)^14*(A*b+-4*B*a)+1//15*B*b^-5*(a+b*x)^15+-3//13*a*b^-5*(a+b*x)^13*(A*b+-2*B*a)+-1//11*a^3*b^-5*(a+b*x)^11*(A*b+-1*B*a)+1//12*a^2*b^-5*(a+b*x)^12*(-4*B*a+3*A*b))
@test integrate(x^2*(a+b*x)^10*(A+B*x), x) == :(1//13*b^-4*(a+b*x)^13*(A*b+-3*B*a)+1//14*B*b^-4*(a+b*x)^14+-1//12*a*b^-4*(a+b*x)^12*(-3*B*a+2*A*b)+1//11*a^2*b^-4*(a+b*x)^11*(A*b+-1*B*a))
@test integrate(x*(a+b*x)^10*(A+B*x), x) == :(1//12*b^-3*(a+b*x)^12*(A*b+-2*B*a)+1//13*B*b^-3*(a+b*x)^13+-1//11*a*b^-3*(a+b*x)^11*(A*b+-1*B*a))
@test integrate((a+b*x)^10*(A+B*x), x) == :(1//11*b^-2*(a+b*x)^11*(A*b+-1*B*a)+1//12*B*b^-2*(a+b*x)^12)
@test integrate(x^-1*(a+b*x)^10*(A+B*x), x) == :(A*a^10*log(x)+1//10*A*b^10*x^10+1//11*B*b^-1*(a+b*x)^11+10*A*b*x*a^9+35*A*a^4*b^6*x^6+40*A*a^7*b^3*x^3+10//9*A*a*b^9*x^9+45//2*A*a^8*b^2*x^2+45//8*A*a^2*b^8*x^8+105//2*A*a^6*b^4*x^4+120//7*A*a^3*b^7*x^7+252//5*A*a^5*b^5*x^5)
@test integrate(x^-2*(a+b*x)^10*(A+B*x), x) == :(a^9*(B*a+10*A*b)*log(x)+-1*A*a^10*x^-1+1//9*b^9*x^9*(A*b+10*B*a)+1//10*B*b^10*x^10+5*b*x*a^8*(2*B*a+9*A*b)+5*a^3*b^6*x^6*(4*A*b+7*B*a)+10*a^6*b^3*x^3*(4*B*a+7*A*b)+5//8*a*b^8*x^8*(2*A*b+9*B*a)+15//2*a^7*b^2*x^2*(3*B*a+8*A*b)+15//7*a^2*b^7*x^7*(3*A*b+8*B*a)+21//2*a^5*b^4*x^4*(5*B*a+6*A*b)+42//5*a^4*b^5*x^5*(5*A*b+6*B*a))
@test integrate(x^-3*(a+b*x)^10*(A+B*x), x) == :(-1*a^9*x^-1*(B*a+10*A*b)+-1//2*A*a^10*x^-2+1//8*b^9*x^8*(A*b+10*B*a)+1//9*B*b^10*x^9+5*b*a^8*(2*B*a+9*A*b)*log(x)+6*a^3*b^6*x^5*(4*A*b+7*B*a)+14*a^5*b^4*x^3*(5*B*a+6*A*b)+15*x*a^7*b^2*(3*B*a+8*A*b)+15*a^6*b^3*x^2*(4*B*a+7*A*b)+5//2*a^2*b^7*x^6*(3*A*b+8*B*a)+5//7*a*b^8*x^7*(2*A*b+9*B*a)+21//2*a^4*b^5*x^4*(5*A*b+6*B*a))
@test integrate(x^-4*(a+b*x)^10*(A+B*x), x) == :(-1//2*a^9*x^-2*(B*a+10*A*b)+-1//3*A*a^10*x^-3+1//7*b^9*x^7*(A*b+10*B*a)+1//8*B*b^10*x^8+-5*b*a^8*x^-1*(2*B*a+9*A*b)+3*a^2*b^7*x^5*(3*A*b+8*B*a)+14*a^4*b^5*x^3*(5*A*b+6*B*a)+15*a^7*b^2*(3*B*a+8*A*b)*log(x)+21*a^5*b^4*x^2*(5*B*a+6*A*b)+30*x*a^6*b^3*(4*B*a+7*A*b)+5//6*a*b^8*x^6*(2*A*b+9*B*a)+15//2*a^3*b^6*x^4*(4*A*b+7*B*a))
@test integrate(x^-5*(a+b*x)^10*(A+B*x), x) == :(-1//3*a^9*x^-3*(B*a+10*A*b)+-1//4*A*a^10*x^-4+1//6*b^9*x^6*(A*b+10*B*a)+1//7*B*b^10*x^7+a*b^8*x^5*(2*A*b+9*B*a)+-15*a^7*b^2*x^-1*(3*B*a+8*A*b)+10*a^3*b^6*x^3*(4*A*b+7*B*a)+21*a^4*b^5*x^2*(5*A*b+6*B*a)+30*a^6*b^3*(4*B*a+7*A*b)*log(x)+42*x*a^5*b^4*(5*B*a+6*A*b)+-5//2*b*a^8*x^-2*(2*B*a+9*A*b)+15//4*a^2*b^7*x^4*(3*A*b+8*B*a))
@test integrate(x^-6*(a+b*x)^10*(A+B*x), x) == :(-1//4*a^9*x^-4*(B*a+10*A*b)+-1//5*A*a^10*x^-5+1//5*b^9*x^5*(A*b+10*B*a)+1//6*B*b^10*x^6+-30*a^6*b^3*x^-1*(4*B*a+7*A*b)+5*a^2*b^7*x^3*(3*A*b+8*B*a)+15*a^3*b^6*x^2*(4*A*b+7*B*a)+42*x*a^4*b^5*(5*A*b+6*B*a)+42*a^5*b^4*(5*B*a+6*A*b)*log(x)+-15//2*a^7*b^2*x^-2*(3*B*a+8*A*b)+-5//3*b*a^8*x^-3*(2*B*a+9*A*b)+5//4*a*b^8*x^4*(2*A*b+9*B*a))
@test integrate(x^-7*(a+b*x)^10*(A+B*x), x) == :(-1//5*a^9*x^-5*(B*a+10*A*b)+-1//6*A*a^10*x^-6+1//4*b^9*x^4*(A*b+10*B*a)+1//5*B*b^10*x^5+-42*a^5*b^4*x^-1*(5*B*a+6*A*b)+-15*a^6*b^3*x^-2*(4*B*a+7*A*b)+-5*a^7*b^2*x^-3*(3*B*a+8*A*b)+30*x*a^3*b^6*(4*A*b+7*B*a)+42*a^4*b^5*(5*A*b+6*B*a)*log(x)+-5//4*b*a^8*x^-4*(2*B*a+9*A*b)+5//3*a*b^8*x^3*(2*A*b+9*B*a)+15//2*a^2*b^7*x^2*(3*A*b+8*B*a))
@test integrate(x^-8*(a+b*x)^10*(A+B*x), x) == :(-1//6*a^9*x^-6*(B*a+10*A*b)+-1//7*A*a^10*x^-7+1//3*b^9*x^3*(A*b+10*B*a)+1//4*B*b^10*x^4+-1*b*a^8*x^-5*(2*B*a+9*A*b)+-42*a^4*b^5*x^-1*(5*A*b+6*B*a)+-21*a^5*b^4*x^-2*(5*B*a+6*A*b)+-10*a^6*b^3*x^-3*(4*B*a+7*A*b)+15*x*a^2*b^7*(3*A*b+8*B*a)+30*a^3*b^6*(4*A*b+7*B*a)*log(x)+-15//4*a^7*b^2*x^-4*(3*B*a+8*A*b)+5//2*a*b^8*x^2*(2*A*b+9*B*a))
@test integrate(x^-9*(a+b*x)^10*(A+B*x), x) == :((1/2)*b^9*x^2*(A*b+10*B*a)+-1//7*a^9*x^-7*(B*a+10*A*b)+-1//8*A*a^10*x^-8+1//3*B*b^10*x^3+-30*a^3*b^6*x^-1*(4*A*b+7*B*a)+-21*a^4*b^5*x^-2*(5*A*b+6*B*a)+-14*a^5*b^4*x^-3*(5*B*a+6*A*b)+-3*a^7*b^2*x^-5*(3*B*a+8*A*b)+5*a*x*b^8*(2*A*b+9*B*a)+15*a^2*b^7*(3*A*b+8*B*a)*log(x)+-15//2*a^6*b^3*x^-4*(4*B*a+7*A*b)+-5//6*b*a^8*x^-6*(2*B*a+9*A*b))
@test integrate(x^-10*(a+b*x)^10*(A+B*x), x) == :(x*b^9*(A*b+10*B*a)+(1/2)*B*b^10*x^2+-1//8*a^9*x^-8*(B*a+10*A*b)+-1//9*A*a^10*x^-9+-15*a^2*b^7*x^-1*(3*A*b+8*B*a)+-15*a^3*b^6*x^-2*(4*A*b+7*B*a)+-14*a^4*b^5*x^-3*(5*A*b+6*B*a)+-6*a^6*b^3*x^-5*(4*B*a+7*A*b)+5*a*b^8*(2*A*b+9*B*a)*log(x)+-21//2*a^5*b^4*x^-4*(5*B*a+6*A*b)+-5//2*a^7*b^2*x^-6*(3*B*a+8*A*b)+-5//7*b*a^8*x^-7*(2*B*a+9*A*b))
@test integrate(x^-11*(a+b*x)^10*(A+B*x), x) == :(B*x*b^10+b^9*(A*b+10*B*a)*log(x)+-1//9*a^9*x^-9*(B*a+10*A*b)+-1//10*A*a^10*x^-10+-10*a^3*b^6*x^-3*(4*A*b+7*B*a)+-5*a*b^8*x^-1*(2*A*b+9*B*a)+-5*a^6*b^3*x^-6*(4*B*a+7*A*b)+-42//5*a^5*b^4*x^-5*(5*B*a+6*A*b)+-21//2*a^4*b^5*x^-4*(5*A*b+6*B*a)+-15//2*a^2*b^7*x^-2*(3*A*b+8*B*a)+-15//7*a^7*b^2*x^-7*(3*B*a+8*A*b)+-5//8*b*a^8*x^-8*(2*B*a+9*A*b))
@test integrate(x^-12*(a+b*x)^10*(A+B*x), x) == :(B*b^10*log(x)+-1//10*B*a^10*x^-10+-40*B*a^3*b^7*x^-3+-35*B*a^6*b^4*x^-6+-10*B*a*b^9*x^-1+-252//5*B*a^5*b^5*x^-5+-120//7*B*a^7*b^3*x^-7+-105//2*B*a^4*b^6*x^-4+-45//2*B*a^2*b^8*x^-2+-45//8*B*a^8*b^2*x^-8+-10//9*B*b*a^9*x^-9+-1//11*A*a^-1*x^-11*(a+b*x)^11)
@test integrate(x^-13*(a+b*x)^10*(A+B*x), x) == :(-1//12*A*a^-1*x^-12*(a+b*x)^11+1//132*a^-2*x^-11*(a+b*x)^11*(A*b+-12*B*a))
@test integrate(x^-14*(a+b*x)^10*(A+B*x), x) == :(-1//13*A*a^-1*x^-13*(a+b*x)^11+1//156*a^-2*x^-12*(a+b*x)^11*(-13*B*a+2*A*b)+-1//1716*b*a^-3*x^-11*(a+b*x)^11*(-13*B*a+2*A*b))
@test integrate(x^-15*(a+b*x)^10*(A+B*x), x) == :(-1//14*A*a^-1*x^-14*(a+b*x)^11+1//182*a^-2*x^-13*(a+b*x)^11*(-14*B*a+3*A*b)+-1//1092*b*a^-3*x^-12*(a+b*x)^11*(-14*B*a+3*A*b)+1//12012*a^-4*b^2*x^-11*(a+b*x)^11*(-14*B*a+3*A*b))
@test integrate(x^-16*(a+b*x)^10*(A+B*x), x) == :(-1//15*A*a^-1*x^-15*(a+b*x)^11+1//210*a^-2*x^-14*(a+b*x)^11*(-15*B*a+4*A*b)+-1//910*b*a^-3*x^-13*(a+b*x)^11*(-15*B*a+4*A*b)+-1//60060*a^-5*b^3*x^-11*(a+b*x)^11*(-15*B*a+4*A*b)+1//5460*a^-4*b^2*x^-12*(a+b*x)^11*(-15*B*a+4*A*b))
@test integrate(x^-17*(a+b*x)^10*(A+B*x), x) == :(-1//16*A*a^-1*x^-16*(a+b*x)^11+1//240*a^-2*x^-15*(a+b*x)^11*(-16*B*a+5*A*b)+-1//840*b*a^-3*x^-14*(a+b*x)^11*(-16*B*a+5*A*b)+-1//21840*a^-5*b^3*x^-12*(a+b*x)^11*(-16*B*a+5*A*b)+1//3640*a^-4*b^2*x^-13*(a+b*x)^11*(-16*B*a+5*A*b)+1//240240*a^-6*b^4*x^-11*(a+b*x)^11*(-16*B*a+5*A*b))
@test integrate(x^-18*(a+b*x)^10*(A+B*x), x) == :(-1//17*A*a^-1*x^-17*(a+b*x)^11+1//272*a^-2*x^-16*(a+b*x)^11*(-17*B*a+6*A*b)+-1//816*b*a^-3*x^-15*(a+b*x)^11*(-17*B*a+6*A*b)+-1//12376*a^-5*b^3*x^-13*(a+b*x)^11*(-17*B*a+6*A*b)+-1//816816*a^-7*b^5*x^-11*(a+b*x)^11*(-17*B*a+6*A*b)+1//2856*a^-4*b^2*x^-14*(a+b*x)^11*(-17*B*a+6*A*b)+1//74256*a^-6*b^4*x^-12*(a+b*x)^11*(-17*B*a+6*A*b))
@test integrate(x^-19*(a+b*x)^10*(A+B*x), x) == :(-1//7*B*b^10*x^-7+-1//8*b^9*x^-8*(A*b+10*B*a)+-1//17*a^9*x^-17*(B*a+10*A*b)+-1//18*A*a^10*x^-18+-1*a^7*b^2*x^-15*(3*B*a+8*A*b)+-42//13*a^5*b^4*x^-13*(5*B*a+6*A*b)+-30//11*a^3*b^6*x^-11*(4*A*b+7*B*a)+-15//7*a^6*b^3*x^-14*(4*B*a+7*A*b)+-7//2*a^4*b^5*x^-12*(5*A*b+6*B*a)+-5//9*a*b^8*x^-9*(2*A*b+9*B*a)+-5//16*b*a^8*x^-16*(2*B*a+9*A*b)+-3//2*a^2*b^7*x^-10*(3*A*b+8*B*a))
@test integrate(x^-20*(a+b*x)^10*(A+B*x), x) == :(-1//8*B*b^10*x^-8+-1//9*b^9*x^-9*(A*b+10*B*a)+-1//18*a^9*x^-18*(B*a+10*A*b)+-1//19*A*a^10*x^-19+-3*a^5*b^4*x^-14*(5*B*a+6*A*b)+-2*a^6*b^3*x^-15*(4*B*a+7*A*b)+-42//13*a^4*b^5*x^-13*(5*A*b+6*B*a)+-15//11*a^2*b^7*x^-11*(3*A*b+8*B*a)+-15//16*a^7*b^2*x^-16*(3*B*a+8*A*b)+-5//2*a^3*b^6*x^-12*(4*A*b+7*B*a)+-5//17*b*a^8*x^-17*(2*B*a+9*A*b)+-1//2*a*b^8*x^-10*(2*A*b+9*B*a))
@test integrate(x^-21*(a+b*x)^10*(A+B*x), x) == :(-1//9*B*b^10*x^-9+-1//10*b^9*x^-10*(A*b+10*B*a)+-1//19*a^9*x^-19*(B*a+10*A*b)+-1//20*A*a^10*x^-20+-3*a^4*b^5*x^-14*(5*A*b+6*B*a)+-30//13*a^3*b^6*x^-13*(4*A*b+7*B*a)+-15//8*a^6*b^3*x^-16*(4*B*a+7*A*b)+-15//17*a^7*b^2*x^-17*(3*B*a+8*A*b)+-14//5*a^5*b^4*x^-15*(5*B*a+6*A*b)+-5//4*a^2*b^7*x^-12*(3*A*b+8*B*a)+-5//11*a*b^8*x^-11*(2*A*b+9*B*a)+-5//18*b*a^8*x^-18*(2*B*a+9*A*b))
@test integrate(x^13*(a+b*x)^15*(A+B*x), x) == :(1//14*A*a^15*x^14+1//15*a^14*x^15*(B*a+15*A*b)+1//29*b^14*x^29*(A*b+15*B*a)+1//30*B*b^15*x^30+15//16*b*a^13*x^16*(B*a+7*A*b)+15//28*a*b^13*x^28*(A*b+7*B*a)+35//2*a^3*b^11*x^26*(A*b+3*B*a)+35//17*a^12*b^2*x^17*(3*B*a+13*A*b)+35//27*a^2*b^12*x^27*(3*A*b+13*B*a)+273//19*a^10*b^4*x^19*(5*B*a+11*A*b)+273//25*a^4*b^10*x^25*(5*A*b+11*B*a)+455//18*a^11*b^3*x^18*(B*a+3*A*b)+585//2*a^7*b^7*x^22*(A*b+B*a)+715//21*a^8*b^6*x^21*(7*B*a+9*A*b)+715//23*a^6*b^8*x^23*(7*A*b+9*B*a)+1001//20*a^9*b^5*x^20*(3*B*a+5*A*b)+1001//24*a^5*b^9*x^24*(3*A*b+5*B*a))
@test integrate(x^12*(a+b*x)^15*(A+B*x), x) == :(1//13*A*a^15*x^13+1//14*a^14*x^14*(B*a+15*A*b)+1//28*b^14*x^28*(A*b+15*B*a)+1//29*B*b^15*x^29+b*a^13*x^15*(B*a+7*A*b)+5//9*a*b^13*x^27*(A*b+7*B*a)+35//16*a^12*b^2*x^16*(3*B*a+13*A*b)+35//26*a^2*b^12*x^26*(3*A*b+13*B*a)+65//2*a^6*b^8*x^22*(7*A*b+9*B*a)+91//5*a^3*b^11*x^25*(A*b+3*B*a)+91//6*a^10*b^4*x^18*(5*B*a+11*A*b)+91//8*a^4*b^10*x^24*(5*A*b+11*B*a)+143//4*a^8*b^6*x^20*(7*B*a+9*A*b)+455//17*a^11*b^3*x^17*(B*a+3*A*b)+1001//19*a^9*b^5*x^19*(3*B*a+5*A*b)+1001//23*a^5*b^9*x^23*(3*A*b+5*B*a)+2145//7*a^7*b^7*x^21*(A*b+B*a))
@test integrate(x^11*(a+b*x)^15*(A+B*x), x) == :(1//27*b^-13*(a+b*x)^27*(A*b+-12*B*a)+1//28*B*b^-13*(a+b*x)^28+-21*a^5*b^-13*(a+b*x)^22*(A*b+-2*B*a)+-55//8*a^3*b^-13*(a+b*x)^24*(A*b+-3*B*a)+-33//4*a^7*b^-13*(a+b*x)^20*(-3*B*a+2*A*b)+-11//18*a^9*b^-13*(a+b*x)^18*(-6*B*a+5*A*b)+-11//26*a*b^-13*(a+b*x)^26*(A*b+-6*B*a)+-1//16*a^11*b^-13*(a+b*x)^16*(A*b+-1*B*a)+1//17*a^10*b^-13*(a+b*x)^17*(-12*B*a+11*A*b)+11//5*a^2*b^-13*(a+b*x)^25*(A*b+-4*B*a)+22//7*a^6*b^-13*(a+b*x)^21*(-12*B*a+7*A*b)+55//19*a^8*b^-13*(a+b*x)^19*(-4*B*a+3*A*b)+66//23*a^4*b^-13*(a+b*x)^23*(-12*B*a+5*A*b))
@test integrate(x^10*(a+b*x)^15*(A+B*x), x) == :(1//26*b^-12*(a+b*x)^26*(A*b+-11*B*a)+1//27*B*b^-12*(a+b*x)^27+-2*a^5*b^-12*(a+b*x)^21*(-11*B*a+6*A*b)+-30//23*a^3*b^-12*(a+b*x)^23*(-11*B*a+4*A*b)+-15//19*a^7*b^-12*(a+b*x)^19*(-11*B*a+8*A*b)+-1//5*a*b^-12*(a+b*x)^25*(-11*B*a+2*A*b)+-1//17*a^9*b^-12*(a+b*x)^17*(-11*B*a+10*A*b)+1//16*a^10*b^-12*(a+b*x)^16*(A*b+-1*B*a)+3//2*a^6*b^-12*(a+b*x)^20*(-11*B*a+7*A*b)+5//8*a^2*b^-12*(a+b*x)^24*(-11*B*a+3*A*b)+5//18*a^8*b^-12*(a+b*x)^18*(-11*B*a+9*A*b)+21//11*a^4*b^-12*(a+b*x)^22*(-11*B*a+5*A*b))
@test integrate(x^9*(a+b*x)^15*(A+B*x), x) == :(1//25*b^-11*(a+b*x)^25*(A*b+-10*B*a)+1//26*B*b^-11*(a+b*x)^26+6*a^4*b^-11*(a+b*x)^21*(A*b+-2*B*a)+-21//10*a^5*b^-11*(a+b*x)^20*(-5*B*a+3*A*b)+-21//11*a^3*b^-11*(a+b*x)^22*(-5*B*a+2*A*b)+-3//8*a*b^-11*(a+b*x)^24*(A*b+-5*B*a)+-1//2*a^7*b^-11*(a+b*x)^18*(-5*B*a+4*A*b)+-1//16*a^9*b^-11*(a+b*x)^16*(A*b+-1*B*a)+1//17*a^8*b^-11*(a+b*x)^17*(-10*B*a+9*A*b)+12//19*a^6*b^-11*(a+b*x)^19*(-10*B*a+7*A*b)+12//23*a^2*b^-11*(a+b*x)^23*(-10*B*a+3*A*b))
@test integrate(x^8*(a+b*x)^15*(A+B*x), x) == :(1//24*b^-10*(a+b*x)^24*(A*b+-9*B*a)+1//25*B*b^-10*(a+b*x)^25+-28//19*a^5*b^-10*(a+b*x)^19*(-3*B*a+2*A*b)+-4//23*a*b^-10*(a+b*x)^23*(-9*B*a+2*A*b)+-2//3*a^3*b^-10*(a+b*x)^21*(-9*B*a+4*A*b)+-1//17*a^7*b^-10*(a+b*x)^17*(-9*B*a+8*A*b)+1//16*a^8*b^-10*(a+b*x)^16*(A*b+-1*B*a)+2//9*a^6*b^-10*(a+b*x)^18*(-9*B*a+7*A*b)+7//10*a^4*b^-10*(a+b*x)^20*(-9*B*a+5*A*b)+14//11*a^2*b^-10*(a+b*x)^22*(A*b+-3*B*a))
@test integrate(x^7*(a+b*x)^15*(A+B*x), x) == :(1//23*b^-9*(a+b*x)^23*(A*b+-8*B*a)+1//24*B*b^-9*(a+b*x)^24+-7//4*a^3*b^-9*(a+b*x)^20*(A*b+-2*B*a)+-7//18*a^5*b^-9*(a+b*x)^18*(-4*B*a+3*A*b)+-7//22*a*b^-9*(a+b*x)^22*(A*b+-4*B*a)+-1//16*a^7*b^-9*(a+b*x)^16*(A*b+-1*B*a)+1//3*a^2*b^-9*(a+b*x)^21*(-8*B*a+3*A*b)+1//17*a^6*b^-9*(a+b*x)^17*(-8*B*a+7*A*b)+7//19*a^4*b^-9*(a+b*x)^19*(-8*B*a+5*A*b))
@test integrate(x^6*(a+b*x)^15*(A+B*x), x) == :(1//22*b^-8*(a+b*x)^22*(A*b+-7*B*a)+1//23*B*b^-8*(a+b*x)^23+-5//19*a^3*b^-8*(a+b*x)^19*(-7*B*a+4*A*b)+-1//7*a*b^-8*(a+b*x)^21*(-7*B*a+2*A*b)+-1//17*a^5*b^-8*(a+b*x)^17*(-7*B*a+6*A*b)+1//4*a^2*b^-8*(a+b*x)^20*(-7*B*a+3*A*b)+1//6*a^4*b^-8*(a+b*x)^18*(-7*B*a+5*A*b)+1//16*a^6*b^-8*(a+b*x)^16*(A*b+-1*B*a))
@test integrate(x^5*(a+b*x)^15*(A+B*x), x) == :(1//21*b^-7*(a+b*x)^21*(A*b+-6*B*a)+1//22*B*b^-7*(a+b*x)^22+-5//18*a^3*b^-7*(a+b*x)^18*(-3*B*a+2*A*b)+-1//4*a*b^-7*(a+b*x)^20*(A*b+-3*B*a)+-1//16*a^5*b^-7*(a+b*x)^16*(A*b+-1*B*a)+1//17*a^4*b^-7*(a+b*x)^17*(-6*B*a+5*A*b)+10//19*a^2*b^-7*(a+b*x)^19*(A*b+-2*B*a))
@test integrate(x^4*(a+b*x)^15*(A+B*x), x) == :(1//20*b^-6*(a+b*x)^20*(A*b+-5*B*a)+1//21*B*b^-6*(a+b*x)^21+-2//19*a*b^-6*(a+b*x)^19*(-5*B*a+2*A*b)+-1//17*a^3*b^-6*(a+b*x)^17*(-5*B*a+4*A*b)+1//9*a^2*b^-6*(a+b*x)^18*(-5*B*a+3*A*b)+1//16*a^4*b^-6*(a+b*x)^16*(A*b+-1*B*a))
@test integrate(x^3*(a+b*x)^15*(A+B*x), x) == :(1//19*b^-5*(a+b*x)^19*(A*b+-4*B*a)+1//20*B*b^-5*(a+b*x)^20+-1//6*a*b^-5*(a+b*x)^18*(A*b+-2*B*a)+-1//16*a^3*b^-5*(a+b*x)^16*(A*b+-1*B*a)+1//17*a^2*b^-5*(a+b*x)^17*(-4*B*a+3*A*b))
@test integrate(x^2*(a+b*x)^15*(A+B*x), x) == :(1//18*b^-4*(a+b*x)^18*(A*b+-3*B*a)+1//19*B*b^-4*(a+b*x)^19+-1//17*a*b^-4*(a+b*x)^17*(-3*B*a+2*A*b)+1//16*a^2*b^-4*(a+b*x)^16*(A*b+-1*B*a))
@test integrate(x*(a+b*x)^15*(A+B*x), x) == :(1//17*b^-3*(a+b*x)^17*(A*b+-2*B*a)+1//18*B*b^-3*(a+b*x)^18+-1//16*a*b^-3*(a+b*x)^16*(A*b+-1*B*a))
@test integrate((a+b*x)^15*(A+B*x), x) == :(1//16*b^-2*(a+b*x)^16*(A*b+-1*B*a)+1//17*B*b^-2*(a+b*x)^17)
@test integrate(x^-1*(a+b*x)^15*(A+B*x), x) == :(A*a^15*log(x)+1//15*A*b^15*x^15+1//16*B*b^-1*(a+b*x)^16+15*A*b*x*a^14+15//14*A*a*b^14*x^14+105//2*A*a^13*b^2*x^2+105//13*A*a^2*b^13*x^13+455//3*A*a^12*b^3*x^3+455//12*A*a^3*b^12*x^12+1365//4*A*a^11*b^4*x^4+1365//11*A*a^4*b^11*x^11+3003//5*A*a^10*b^5*x^5+3003//10*A*a^5*b^10*x^10+5005//6*A*a^9*b^6*x^6+5005//9*A*a^6*b^9*x^9+6435//7*A*a^8*b^7*x^7+6435//8*A*a^7*b^8*x^8)
@test integrate(x^-2*(a+b*x)^15*(A+B*x), x) == :(a^14*(B*a+15*A*b)*log(x)+-1*A*a^15*x^-1+1//14*b^14*x^14*(A*b+15*B*a)+1//15*B*b^15*x^15+15*b*x*a^13*(B*a+7*A*b)+15//13*a*b^13*x^13*(A*b+7*B*a)+35//2*a^12*b^2*x^2*(3*B*a+13*A*b)+35//12*a^2*b^12*x^12*(3*A*b+13*B*a)+273//4*a^10*b^4*x^4*(5*B*a+11*A*b)+273//10*a^4*b^10*x^10*(5*A*b+11*B*a)+455//3*a^11*b^3*x^3*(B*a+3*A*b)+455//11*a^3*b^11*x^11*(A*b+3*B*a)+715//6*a^8*b^6*x^6*(7*B*a+9*A*b)+715//8*a^6*b^8*x^8*(7*A*b+9*B*a)+1001//5*a^9*b^5*x^5*(3*B*a+5*A*b)+1001//9*a^5*b^9*x^9*(3*A*b+5*B*a)+6435//7*a^7*b^7*x^7*(A*b+B*a))
@test integrate(x^-3*(a+b*x)^15*(A+B*x), x) == :(-1*a^14*x^-1*(B*a+15*A*b)+-1//2*A*a^15*x^-2+1//13*b^14*x^13*(A*b+15*B*a)+1//14*B*b^15*x^14+15*b*a^13*(B*a+7*A*b)*log(x)+35*x*a^12*b^2*(3*B*a+13*A*b)+91*a^10*b^4*x^3*(5*B*a+11*A*b)+143*a^8*b^6*x^5*(7*B*a+9*A*b)+5//4*a*b^13*x^12*(A*b+7*B*a)+35//11*a^2*b^12*x^11*(3*A*b+13*B*a)+91//2*a^3*b^11*x^10*(A*b+3*B*a)+91//3*a^4*b^10*x^9*(5*A*b+11*B*a)+455//2*a^11*b^3*x^2*(B*a+3*A*b)+715//7*a^6*b^8*x^7*(7*A*b+9*B*a)+1001//4*a^9*b^5*x^4*(3*B*a+5*A*b)+1001//8*a^5*b^9*x^8*(3*A*b+5*B*a)+2145//2*a^7*b^7*x^6*(A*b+B*a))
@test integrate(x^-4*(a+b*x)^15*(A+B*x), x) == :(-1//2*a^14*x^-2*(B*a+15*A*b)+-1//3*A*a^15*x^-3+1//12*b^14*x^12*(A*b+15*B*a)+1//13*B*b^15*x^13+-15*b*a^13*x^-1*(B*a+7*A*b)+35*a^12*b^2*(3*B*a+13*A*b)*log(x)+143*a^5*b^9*x^7*(3*A*b+5*B*a)+455*x*a^11*b^3*(B*a+3*A*b)+1287*a^7*b^7*x^5*(A*b+B*a)+7//2*a^2*b^12*x^10*(3*A*b+13*B*a)+15//11*a*b^13*x^11*(A*b+7*B*a)+273//2*a^10*b^4*x^2*(5*B*a+11*A*b)+273//8*a^4*b^10*x^8*(5*A*b+11*B*a)+455//9*a^3*b^11*x^9*(A*b+3*B*a)+715//4*a^8*b^6*x^4*(7*B*a+9*A*b)+715//6*a^6*b^8*x^6*(7*A*b+9*B*a)+1001//3*a^9*b^5*x^3*(3*B*a+5*A*b))
@test integrate(x^-5*(a+b*x)^15*(A+B*x), x) == :(-1//3*a^14*x^-3*(B*a+15*A*b)+-1//4*A*a^15*x^-4+1//11*b^14*x^11*(A*b+15*B*a)+1//12*B*b^15*x^12+-35*a^12*b^2*x^-1*(3*B*a+13*A*b)+39*a^4*b^10*x^7*(5*A*b+11*B*a)+143*a^6*b^8*x^5*(7*A*b+9*B*a)+273*x*a^10*b^4*(5*B*a+11*A*b)+455*a^11*b^3*(B*a+3*A*b)*log(x)+-15//2*b*a^13*x^-2*(B*a+7*A*b)+3//2*a*b^13*x^10*(A*b+7*B*a)+35//9*a^2*b^12*x^9*(3*A*b+13*B*a)+455//8*a^3*b^11*x^8*(A*b+3*B*a)+715//3*a^8*b^6*x^3*(7*B*a+9*A*b)+1001//2*a^9*b^5*x^2*(3*B*a+5*A*b)+1001//6*a^5*b^9*x^6*(3*A*b+5*B*a)+6435//4*a^7*b^7*x^4*(A*b+B*a))
@test integrate(x^-6*(a+b*x)^15*(A+B*x), x) == :(-1//4*a^14*x^-4*(B*a+15*A*b)+-1//5*A*a^15*x^-5+1//10*b^14*x^10*(A*b+15*B*a)+1//11*B*b^15*x^11+-455*a^11*b^3*x^-1*(B*a+3*A*b)+-5*b*a^13*x^-3*(B*a+7*A*b)+65*a^3*b^11*x^7*(A*b+3*B*a)+273*a^10*b^4*(5*B*a+11*A*b)*log(x)+1001*x*a^9*b^5*(3*B*a+5*A*b)+2145*a^7*b^7*x^3*(A*b+B*a)+-35//2*a^12*b^2*x^-2*(3*B*a+13*A*b)+5//3*a*b^13*x^9*(A*b+7*B*a)+35//8*a^2*b^12*x^8*(3*A*b+13*B*a)+91//2*a^4*b^10*x^6*(5*A*b+11*B*a)+715//2*a^8*b^6*x^2*(7*B*a+9*A*b)+715//4*a^6*b^8*x^4*(7*A*b+9*B*a)+1001//5*a^5*b^9*x^5*(3*A*b+5*B*a))
@test integrate(x^-7*(a+b*x)^15*(A+B*x), x) == :(-1//5*a^14*x^-5*(B*a+15*A*b)+-1//6*A*a^15*x^-6+1//9*b^14*x^9*(A*b+15*B*a)+1//10*B*b^15*x^10+-273*a^10*b^4*x^-1*(5*B*a+11*A*b)+5*a^2*b^12*x^7*(3*A*b+13*B*a)+715*x*a^8*b^6*(7*B*a+9*A*b)+1001*a^9*b^5*(3*B*a+5*A*b)*log(x)+-455//2*a^11*b^3*x^-2*(B*a+3*A*b)+-35//3*a^12*b^2*x^-3*(3*B*a+13*A*b)+-15//4*b*a^13*x^-4*(B*a+7*A*b)+15//8*a*b^13*x^8*(A*b+7*B*a)+273//5*a^4*b^10*x^5*(5*A*b+11*B*a)+455//6*a^3*b^11*x^6*(A*b+3*B*a)+715//3*a^6*b^8*x^3*(7*A*b+9*B*a)+1001//4*a^5*b^9*x^4*(3*A*b+5*B*a)+6435//2*a^7*b^7*x^2*(A*b+B*a))
@test integrate(x^-8*(a+b*x)^15*(A+B*x), x) == :(-1//6*a^14*x^-6*(B*a+15*A*b)+-1//7*A*a^15*x^-7+1//8*b^14*x^8*(A*b+15*B*a)+1//9*B*b^15*x^9+-1001*a^9*b^5*x^-1*(3*B*a+5*A*b)+-3*b*a^13*x^-5*(B*a+7*A*b)+91*a^3*b^11*x^5*(A*b+3*B*a)+715*a^8*b^6*(7*B*a+9*A*b)*log(x)+6435*x*a^7*b^7*(A*b+B*a)+-455//3*a^11*b^3*x^-3*(B*a+3*A*b)+-273//2*a^10*b^4*x^-2*(5*B*a+11*A*b)+-35//4*a^12*b^2*x^-4*(3*B*a+13*A*b)+15//7*a*b^13*x^7*(A*b+7*B*a)+35//6*a^2*b^12*x^6*(3*A*b+13*B*a)+273//4*a^4*b^10*x^4*(5*A*b+11*B*a)+715//2*a^6*b^8*x^2*(7*A*b+9*B*a)+1001//3*a^5*b^9*x^3*(3*A*b+5*B*a))
@test integrate(x^-9*(a+b*x)^15*(A+B*x), x) == :(-1//7*a^14*x^-7*(B*a+15*A*b)+-1//8*A*a^15*x^-8+1//7*b^14*x^7*(A*b+15*B*a)+1//8*B*b^15*x^8+-715*a^8*b^6*x^-1*(7*B*a+9*A*b)+-91*a^10*b^4*x^-3*(5*B*a+11*A*b)+-7*a^12*b^2*x^-5*(3*B*a+13*A*b)+7*a^2*b^12*x^5*(3*A*b+13*B*a)+91*a^4*b^10*x^3*(5*A*b+11*B*a)+715*x*a^6*b^8*(7*A*b+9*B*a)+6435*a^7*b^7*(A*b+B*a)*log(x)+-1001//2*a^9*b^5*x^-2*(3*B*a+5*A*b)+-455//4*a^11*b^3*x^-4*(B*a+3*A*b)+-5//2*b*a^13*x^-6*(B*a+7*A*b)+5//2*a*b^13*x^6*(A*b+7*B*a)+455//4*a^3*b^11*x^4*(A*b+3*B*a)+1001//2*a^5*b^9*x^2*(3*A*b+5*B*a))
@test integrate(x^-10*(a+b*x)^15*(A+B*x), x) == :(-1//8*a^14*x^-8*(B*a+15*A*b)+-1//9*A*a^15*x^-9+1//6*b^14*x^6*(A*b+15*B*a)+1//7*B*b^15*x^7+-6435*a^7*b^7*x^-1*(A*b+B*a)+-91*a^11*b^3*x^-5*(B*a+3*A*b)+3*a*b^13*x^5*(A*b+7*B*a)+715*a^6*b^8*(7*A*b+9*B*a)*log(x)+1001*x*a^5*b^9*(3*A*b+5*B*a)+-1001//3*a^9*b^5*x^-3*(3*B*a+5*A*b)+-715//2*a^8*b^6*x^-2*(7*B*a+9*A*b)+-273//4*a^10*b^4*x^-4*(5*B*a+11*A*b)+-35//6*a^12*b^2*x^-6*(3*B*a+13*A*b)+-15//7*b*a^13*x^-7*(B*a+7*A*b)+35//4*a^2*b^12*x^4*(3*A*b+13*B*a)+273//2*a^4*b^10*x^2*(5*A*b+11*B*a)+455//3*a^3*b^11*x^3*(A*b+3*B*a))
@test integrate(x^-11*(a+b*x)^15*(A+B*x), x) == :(-1//9*a^14*x^-9*(B*a+15*A*b)+-1//10*A*a^15*x^-10+1//5*b^14*x^5*(A*b+15*B*a)+1//6*B*b^15*x^6+-715*a^6*b^8*x^-1*(7*A*b+9*B*a)+-5*a^12*b^2*x^-7*(3*B*a+13*A*b)+273*x*a^4*b^10*(5*A*b+11*B*a)+1001*a^5*b^9*(3*A*b+5*B*a)*log(x)+-6435//2*a^7*b^7*x^-2*(A*b+B*a)+-1001//4*a^9*b^5*x^-4*(3*B*a+5*A*b)+-715//3*a^8*b^6*x^-3*(7*B*a+9*A*b)+-455//6*a^11*b^3*x^-6*(B*a+3*A*b)+-273//5*a^10*b^4*x^-5*(5*B*a+11*A*b)+-15//8*b*a^13*x^-8*(B*a+7*A*b)+15//4*a*b^13*x^4*(A*b+7*B*a)+35//3*a^2*b^12*x^3*(3*A*b+13*B*a)+455//2*a^3*b^11*x^2*(A*b+3*B*a))
@test integrate(x^-12*(a+b*x)^15*(A+B*x), x) == :(-1//10*a^14*x^-10*(B*a+15*A*b)+-1//11*A*a^15*x^-11+1//4*b^14*x^4*(A*b+15*B*a)+1//5*B*b^15*x^5+-2145*a^7*b^7*x^-3*(A*b+B*a)+-1001*a^5*b^9*x^-1*(3*A*b+5*B*a)+-65*a^11*b^3*x^-7*(B*a+3*A*b)+5*a*b^13*x^3*(A*b+7*B*a)+273*a^4*b^10*(5*A*b+11*B*a)*log(x)+455*x*a^3*b^11*(A*b+3*B*a)+-1001//5*a^9*b^5*x^-5*(3*B*a+5*A*b)+-715//2*a^6*b^8*x^-2*(7*A*b+9*B*a)+-715//4*a^8*b^6*x^-4*(7*B*a+9*A*b)+-91//2*a^10*b^4*x^-6*(5*B*a+11*A*b)+-35//8*a^12*b^2*x^-8*(3*B*a+13*A*b)+-5//3*b*a^13*x^-9*(B*a+7*A*b)+35//2*a^2*b^12*x^2*(3*A*b+13*B*a))
@test integrate(x^-13*(a+b*x)^15*(A+B*x), x) == :(-1//11*a^14*x^-11*(B*a+15*A*b)+-1//12*A*a^15*x^-12+1//3*b^14*x^3*(A*b+15*B*a)+1//4*B*b^15*x^4+-273*a^4*b^10*x^-1*(5*A*b+11*B*a)+-143*a^8*b^6*x^-5*(7*B*a+9*A*b)+-39*a^10*b^4*x^-7*(5*B*a+11*A*b)+35*x*a^2*b^12*(3*A*b+13*B*a)+455*a^3*b^11*(A*b+3*B*a)*log(x)+-6435//4*a^7*b^7*x^-4*(A*b+B*a)+-1001//2*a^5*b^9*x^-2*(3*A*b+5*B*a)+-1001//6*a^9*b^5*x^-6*(3*B*a+5*A*b)+-715//3*a^6*b^8*x^-3*(7*A*b+9*B*a)+-455//8*a^11*b^3*x^-8*(B*a+3*A*b)+-35//9*a^12*b^2*x^-9*(3*B*a+13*A*b)+-3//2*b*a^13*x^-10*(B*a+7*A*b)+15//2*a*b^13*x^2*(A*b+7*B*a))
@test integrate(x^-14*(a+b*x)^15*(A+B*x), x) == :((1/2)*b^14*x^2*(A*b+15*B*a)+-1//12*a^14*x^-12*(B*a+15*A*b)+-1//13*A*a^15*x^-13+1//3*B*b^15*x^3+-1287*a^7*b^7*x^-5*(A*b+B*a)+-455*a^3*b^11*x^-1*(A*b+3*B*a)+-143*a^9*b^5*x^-7*(3*B*a+5*A*b)+15*a*x*b^13*(A*b+7*B*a)+35*a^2*b^12*(3*A*b+13*B*a)*log(x)+-1001//3*a^5*b^9*x^-3*(3*A*b+5*B*a)+-715//4*a^6*b^8*x^-4*(7*A*b+9*B*a)+-715//6*a^8*b^6*x^-6*(7*B*a+9*A*b)+-455//9*a^11*b^3*x^-9*(B*a+3*A*b)+-273//2*a^4*b^10*x^-2*(5*A*b+11*B*a)+-273//8*a^10*b^4*x^-8*(5*B*a+11*A*b)+-15//11*b*a^13*x^-11*(B*a+7*A*b)+-7//2*a^12*b^2*x^-10*(3*B*a+13*A*b))
@test integrate(x^-15*(a+b*x)^15*(A+B*x), x) == :(x*b^14*(A*b+15*B*a)+(1/2)*B*b^15*x^2+-1//13*a^14*x^-13*(B*a+15*A*b)+-1//14*A*a^15*x^-14+-143*a^6*b^8*x^-5*(7*A*b+9*B*a)+-91*a^4*b^10*x^-3*(5*A*b+11*B*a)+-35*a^2*b^12*x^-1*(3*A*b+13*B*a)+15*a*b^13*(A*b+7*B*a)*log(x)+-2145//2*a^7*b^7*x^-6*(A*b+B*a)+-1001//4*a^5*b^9*x^-4*(3*A*b+5*B*a)+-1001//8*a^9*b^5*x^-8*(3*B*a+5*A*b)+-715//7*a^8*b^6*x^-7*(7*B*a+9*A*b)+-455//2*a^3*b^11*x^-2*(A*b+3*B*a)+-91//2*a^11*b^3*x^-10*(B*a+3*A*b)+-91//3*a^10*b^4*x^-9*(5*B*a+11*A*b)+-35//11*a^12*b^2*x^-11*(3*B*a+13*A*b)+-5//4*b*a^13*x^-12*(B*a+7*A*b))
@test integrate(x^-16*(a+b*x)^15*(A+B*x), x) == :(B*x*b^15+b^14*(A*b+15*B*a)*log(x)+-1//14*a^14*x^-14*(B*a+15*A*b)+-1//15*A*a^15*x^-15+-15*a*b^13*x^-1*(A*b+7*B*a)+-6435//7*a^7*b^7*x^-7*(A*b+B*a)+-1001//5*a^5*b^9*x^-5*(3*A*b+5*B*a)+-1001//9*a^9*b^5*x^-9*(3*B*a+5*A*b)+-715//6*a^6*b^8*x^-6*(7*A*b+9*B*a)+-715//8*a^8*b^6*x^-8*(7*B*a+9*A*b)+-455//3*a^3*b^11*x^-3*(A*b+3*B*a)+-455//11*a^11*b^3*x^-11*(B*a+3*A*b)+-273//4*a^4*b^10*x^-4*(5*A*b+11*B*a)+-273//10*a^10*b^4*x^-10*(5*B*a+11*A*b)+-35//2*a^2*b^12*x^-2*(3*A*b+13*B*a)+-35//12*a^12*b^2*x^-12*(3*B*a+13*A*b)+-15//13*b*a^13*x^-13*(B*a+7*A*b))
@test integrate(x^-17*(a+b*x)^15*(A+B*x), x) == :(B*b^15*log(x)+-1//15*B*a^15*x^-15+-15*B*a*b^14*x^-1+-6435//7*B*a^7*b^8*x^-7+-6435//8*B*a^8*b^7*x^-8+-5005//6*B*a^6*b^9*x^-6+-5005//9*B*a^9*b^6*x^-9+-3003//5*B*a^5*b^10*x^-5+-3003//10*B*a^10*b^5*x^-10+-1365//4*B*a^4*b^11*x^-4+-1365//11*B*a^11*b^4*x^-11+-455//3*B*a^3*b^12*x^-3+-455//12*B*a^12*b^3*x^-12+-105//2*B*a^2*b^13*x^-2+-105//13*B*a^13*b^2*x^-13+-15//14*B*b*a^14*x^-14+-1//16*A*a^-1*x^-16*(a+b*x)^16)
@test integrate(x^-18*(a+b*x)^15*(A+B*x), x) == :(-1//17*A*a^-1*x^-17*(a+b*x)^16+1//272*a^-2*x^-16*(a+b*x)^16*(A*b+-17*B*a))
@test integrate(x^-19*(a+b*x)^15*(A+B*x), x) == :(-1//18*A*a^-1*x^-18*(a+b*x)^16+1//153*a^-2*x^-17*(a+b*x)^16*(A*b+-9*B*a)+-1//2448*b*a^-3*x^-16*(a+b*x)^16*(A*b+-9*B*a))
@test integrate(x^-20*(a+b*x)^15*(A+B*x), x) == :(-1//19*A*a^-1*x^-19*(a+b*x)^16+1//342*a^-2*x^-18*(a+b*x)^16*(-19*B*a+3*A*b)+-1//2907*b*a^-3*x^-17*(a+b*x)^16*(-19*B*a+3*A*b)+1//46512*a^-4*b^2*x^-16*(a+b*x)^16*(-19*B*a+3*A*b))
@test integrate(x^-21*(a+b*x)^15*(A+B*x), x) == :(-1//20*A*a^-1*x^-20*(a+b*x)^16+1//95*a^-2*x^-19*(a+b*x)^16*(A*b+-5*B*a)+-1//570*b*a^-3*x^-18*(a+b*x)^16*(A*b+-5*B*a)+-1//77520*a^-5*b^3*x^-16*(a+b*x)^16*(A*b+-5*B*a)+1//4845*a^-4*b^2*x^-17*(a+b*x)^16*(A*b+-5*B*a))
@test integrate(x^-22*(a+b*x)^15*(A+B*x), x) == :(-1//21*A*a^-1*x^-21*(a+b*x)^16+1//420*a^-2*x^-20*(a+b*x)^16*(-21*B*a+5*A*b)+-1//1995*b*a^-3*x^-19*(a+b*x)^16*(-21*B*a+5*A*b)+-1//101745*a^-5*b^3*x^-17*(a+b*x)^16*(-21*B*a+5*A*b)+1//11970*a^-4*b^2*x^-18*(a+b*x)^16*(-21*B*a+5*A*b)+1//1627920*a^-6*b^4*x^-16*(a+b*x)^16*(-21*B*a+5*A*b))
@test integrate(x^-23*(a+b*x)^15*(A+B*x), x) == :(-1//22*A*a^-1*x^-22*(a+b*x)^16+1//231*a^-2*x^-21*(a+b*x)^16*(-11*B*a+3*A*b)+-1//924*b*a^-3*x^-20*(a+b*x)^16*(-11*B*a+3*A*b)+-1//26334*a^-5*b^3*x^-18*(a+b*x)^16*(-11*B*a+3*A*b)+-1//3581424*a^-7*b^5*x^-16*(a+b*x)^16*(-11*B*a+3*A*b)+1//4389*a^-4*b^2*x^-19*(a+b*x)^16*(-11*B*a+3*A*b)+1//223839*a^-6*b^4*x^-17*(a+b*x)^16*(-11*B*a+3*A*b))
@test integrate(x^-24*(a+b*x)^15*(A+B*x), x) == :(-1//23*A*a^-1*x^-23*(a+b*x)^16+1//506*a^-2*x^-22*(a+b*x)^16*(-23*B*a+7*A*b)+-1//1771*b*a^-3*x^-21*(a+b*x)^16*(-23*B*a+7*A*b)+-1//33649*a^-5*b^3*x^-19*(a+b*x)^16*(-23*B*a+7*A*b)+-1//1716099*a^-7*b^5*x^-17*(a+b*x)^16*(-23*B*a+7*A*b)+1//7084*a^-4*b^2*x^-20*(a+b*x)^16*(-23*B*a+7*A*b)+1//201894*a^-6*b^4*x^-18*(a+b*x)^16*(-23*B*a+7*A*b)+1//27457584*a^-8*b^6*x^-16*(a+b*x)^16*(-23*B*a+7*A*b))
@test integrate(x^-25*(a+b*x)^15*(A+B*x), x) == :(-1//24*A*a^-1*x^-24*(a+b*x)^16+1//69*a^-2*x^-23*(a+b*x)^16*(A*b+-3*B*a)+-7//1518*b*a^-3*x^-22*(a+b*x)^16*(A*b+-3*B*a)+-1//3036*a^-5*b^3*x^-20*(a+b*x)^16*(A*b+-3*B*a)+-1//86526*a^-7*b^5*x^-18*(a+b*x)^16*(A*b+-3*B*a)+-1//11767536*a^-9*b^7*x^-16*(a+b*x)^16*(A*b+-3*B*a)+1//759*a^-4*b^2*x^-21*(a+b*x)^16*(A*b+-3*B*a)+1//14421*a^-6*b^4*x^-19*(a+b*x)^16*(A*b+-3*B*a)+1//735471*a^-8*b^6*x^-17*(a+b*x)^16*(A*b+-3*B*a))
@test integrate(x^-26*(a+b*x)^15*(A+B*x), x) == :(-1//25*A*a^-1*x^-25*(a+b*x)^16+1//600*a^-2*x^-24*(a+b*x)^16*(-25*B*a+9*A*b)+-1//1725*b*a^-3*x^-23*(a+b*x)^16*(-25*B*a+9*A*b)+-1//18975*a^-5*b^3*x^-21*(a+b*x)^16*(-25*B*a+9*A*b)+-1//360525*a^-7*b^5*x^-19*(a+b*x)^16*(-25*B*a+9*A*b)+-1//18386775*a^-9*b^7*x^-17*(a+b*x)^16*(-25*B*a+9*A*b)+1//75900*a^-6*b^4*x^-20*(a+b*x)^16*(-25*B*a+9*A*b)+1//2163150*a^-8*b^6*x^-18*(a+b*x)^16*(-25*B*a+9*A*b)+1//294188400*a^-10*b^8*x^-16*(a+b*x)^16*(-25*B*a+9*A*b)+7//37950*a^-4*b^2*x^-22*(a+b*x)^16*(-25*B*a+9*A*b))
@test integrate(x^-27*(a+b*x)^15*(A+B*x), x) == :(-1//26*A*a^-1*x^-26*(a+b*x)^16+1//325*a^-2*x^-25*(a+b*x)^16*(-13*B*a+5*A*b)+-21//164450*a^-5*b^3*x^-22*(a+b*x)^16*(-13*B*a+5*A*b)+-3//2600*b*a^-3*x^-24*(a+b*x)^16*(-13*B*a+5*A*b)+-3//328900*a^-7*b^5*x^-20*(a+b*x)^16*(-13*B*a+5*A*b)+-1//3124550*a^-9*b^7*x^-18*(a+b*x)^16*(-13*B*a+5*A*b)+-1//424938800*a^-11*b^9*x^-16*(a+b*x)^16*(-13*B*a+5*A*b)+1//26558675*a^-10*b^8*x^-17*(a+b*x)^16*(-13*B*a+5*A*b)+3//7475*a^-4*b^2*x^-23*(a+b*x)^16*(-13*B*a+5*A*b)+3//82225*a^-6*b^4*x^-21*(a+b*x)^16*(-13*B*a+5*A*b)+3//1562275*a^-8*b^6*x^-19*(a+b*x)^16*(-13*B*a+5*A*b))
@test integrate(x^-28*(a+b*x)^15*(A+B*x), x) == :(-1//11*B*b^15*x^-11+-1//12*b^14*x^-12*(A*b+15*B*a)+-1//26*a^14*x^-26*(B*a+15*A*b)+-1//27*A*a^15*x^-27+-6435//19*a^7*b^7*x^-19*(A*b+B*a)+-1001//17*a^5*b^9*x^-17*(3*A*b+5*B*a)+-715//18*a^6*b^8*x^-18*(7*A*b+9*B*a)+-455//23*a^11*b^3*x^-23*(B*a+3*A*b)+-273//16*a^4*b^10*x^-16*(5*A*b+11*B*a)+-273//22*a^10*b^4*x^-22*(5*B*a+11*A*b)+-143//3*a^9*b^5*x^-21*(3*B*a+5*A*b)+-143//4*a^8*b^6*x^-20*(7*B*a+9*A*b)+-91//3*a^3*b^11*x^-15*(A*b+3*B*a)+-35//24*a^12*b^2*x^-24*(3*B*a+13*A*b)+-15//13*a*b^13*x^-13*(A*b+7*B*a)+-5//2*a^2*b^12*x^-14*(3*A*b+13*B*a)+-3//5*b*a^13*x^-25*(B*a+7*A*b))
@test integrate(x^-29*(a+b*x)^15*(A+B*x), x) == :(-1//12*B*b^15*x^-12+-1//13*b^14*x^-13*(A*b+15*B*a)+-1//27*a^14*x^-27*(B*a+15*A*b)+-1//28*A*a^15*x^-28+-1287//4*a^7*b^7*x^-20*(A*b+B*a)+-1001//18*a^5*b^9*x^-18*(3*A*b+5*B*a)+-715//19*a^6*b^8*x^-19*(7*A*b+9*B*a)+-715//21*a^8*b^6*x^-21*(7*B*a+9*A*b)+-455//16*a^3*b^11*x^-16*(A*b+3*B*a)+-455//24*a^11*b^3*x^-24*(B*a+3*A*b)+-273//17*a^4*b^10*x^-17*(5*A*b+11*B*a)+-273//23*a^10*b^4*x^-23*(5*B*a+11*A*b)+-91//2*a^9*b^5*x^-22*(3*B*a+5*A*b)+-15//14*a*b^13*x^-14*(A*b+7*B*a)+-15//26*b*a^13*x^-26*(B*a+7*A*b)+-7//3*a^2*b^12*x^-15*(3*A*b+13*B*a)+-7//5*a^12*b^2*x^-25*(3*B*a+13*A*b))
@test integrate(x^-30*(a+b*x)^15*(A+B*x), x) == :(-1//13*B*b^15*x^-13+-1//14*b^14*x^-14*(A*b+15*B*a)+-1//28*a^14*x^-28*(B*a+15*A*b)+-1//29*A*a^15*x^-29+-1*a*b^13*x^-15*(A*b+7*B*a)+-2145//7*a^7*b^7*x^-21*(A*b+B*a)+-1001//19*a^5*b^9*x^-19*(3*A*b+5*B*a)+-1001//23*a^9*b^5*x^-23*(3*B*a+5*A*b)+-455//17*a^3*b^11*x^-17*(A*b+3*B*a)+-143//4*a^6*b^8*x^-20*(7*A*b+9*B*a)+-91//5*a^11*b^3*x^-25*(B*a+3*A*b)+-91//6*a^4*b^10*x^-18*(5*A*b+11*B*a)+-91//8*a^10*b^4*x^-24*(5*B*a+11*A*b)+-65//2*a^8*b^6*x^-22*(7*B*a+9*A*b)+-35//16*a^2*b^12*x^-16*(3*A*b+13*B*a)+-35//26*a^12*b^2*x^-26*(3*B*a+13*A*b)+-5//9*b*a^13*x^-27*(B*a+7*A*b))
@test integrate(x^3*(c+d*x)^16*(a+b*x), x) == :(-1//20*d^-5*(c+d*x)^20*(-1*a*d+4*b*c)+1//21*b*d^-5*(c+d*x)^21+-1//18*c^2*d^-5*(c+d*x)^18*(-3*a*d+4*b*c)+1//17*c^3*d^-5*(c+d*x)^17*(b*c+-1*a*d)+3//19*c*d^-5*(c+d*x)^19*(-1*a*d+2*b*c))
@test integrate(x^2*(c+d*x)^16*(a+b*x), x) == :(-1//19*d^-4*(c+d*x)^19*(-1*a*d+3*b*c)+1//20*b*d^-4*(c+d*x)^20+-1//17*c^2*d^-4*(c+d*x)^17*(b*c+-1*a*d)+1//18*c*d^-4*(c+d*x)^18*(-2*a*d+3*b*c))
@test integrate(x*(c+d*x)^16*(a+b*x), x) == :(-1//18*d^-3*(c+d*x)^18*(-1*a*d+2*b*c)+1//19*b*d^-3*(c+d*x)^19+1//17*c*d^-3*(c+d*x)^17*(b*c+-1*a*d))
@test integrate((c+d*x)^16*(a+b*x), x) == :(-1//17*d^-2*(c+d*x)^17*(b*c+-1*a*d)+1//18*b*d^-2*(c+d*x)^18)
@test integrate(x^2*(2+x)^5*(2+3x), x) == :(1//3*x^3*(2+x)^6)
@test integrate(x^4*(a+b*x)^-1*(A+B*x), x) == :(1//4*b^-2*x^4*(A*b+-1*B*a)+1//5*B*b^-1*x^5+a^4*b^-6*(A*b+-1*B*a)*log(a+b*x)+(1/2)*a^2*b^-4*x^2*(A*b+-1*B*a)+-1*x*a^3*b^-5*(A*b+-1*B*a)+-1//3*a*b^-3*x^3*(A*b+-1*B*a))
@test integrate(x^3*(a+b*x)^-1*(A+B*x), x) == :(1//3*b^-2*x^3*(A*b+-1*B*a)+1//4*B*b^-1*x^4+x*a^2*b^-4*(A*b+-1*B*a)+-1*a^3*b^-5*(A*b+-1*B*a)*log(a+b*x)+-1//2*a*b^-3*x^2*(A*b+-1*B*a))
@test integrate(x^2*(a+b*x)^-1*(A+B*x), x) == :((1/2)*b^-2*x^2*(A*b+-1*B*a)+1//3*B*b^-1*x^3+a^2*b^-4*(A*b+-1*B*a)*log(a+b*x)+-1*a*x*b^-3*(A*b+-1*B*a))
@test integrate(x*(a+b*x)^-1*(A+B*x), x) == :(x*b^-2*(A*b+-1*B*a)+(1/2)*B*b^-1*x^2+-1*a*b^-3*(A*b+-1*B*a)*log(a+b*x))
@test integrate((a+b*x)^-1*(A+B*x), x) == :(B*x*b^-1+b^-2*(A*b+-1*B*a)*log(a+b*x))
@test integrate(x^-1*(a+b*x)^-1*(A+B*x), x) == :(A*a^-1*log(x)+-1*a^-1*b^-1*(A*b+-1*B*a)*log(a+b*x))
@test integrate(x^-2*(a+b*x)^-1*(A+B*x), x) == :(a^-2*(A*b+-1*B*a)*log(a+b*x)+-1*A*a^-1*x^-1+-1*a^-2*(A*b+-1*B*a)*log(x))
@test integrate(x^-3*(a+b*x)^-1*(A+B*x), x) == :(a^-2*x^-1*(A*b+-1*B*a)+-1//2*A*a^-1*x^-2+b*a^-3*(A*b+-1*B*a)*log(x)+-1*b*a^-3*(A*b+-1*B*a)*log(a+b*x))
@test integrate(x^-4*(a+b*x)^-1*(A+B*x), x) == :((1/2)*a^-2*x^-2*(A*b+-1*B*a)+-1//3*A*a^-1*x^-3+a^-4*b^2*(A*b+-1*B*a)*log(a+b*x)+-1*b*a^-3*x^-1*(A*b+-1*B*a)+-1*a^-4*b^2*(A*b+-1*B*a)*log(x))
@test integrate(x^-5*(a+b*x)^-1*(A+B*x), x) == :(-1//4*A*a^-1*x^-4+1//3*a^-2*x^-3*(A*b+-1*B*a)+a^-5*b^3*(A*b+-1*B*a)*log(x)+a^-4*b^2*x^-1*(A*b+-1*B*a)+-1*a^-5*b^3*(A*b+-1*B*a)*log(a+b*x)+-1//2*b*a^-3*x^-2*(A*b+-1*B*a))
@test integrate(x^4*(a+b*x)^-2*(A+B*x), x) == :(1//3*b^-3*x^3*(A*b+-2*B*a)+1//4*B*b^-2*x^4+x*a^2*b^-5*(-4*B*a+3*A*b)+-1*a^3*b^-6*(-5*B*a+4*A*b)*log(a+b*x)+-1*a^4*b^-6*(a+b*x)^-1*(A*b+-1*B*a)+-1//2*a*b^-4*x^2*(-3*B*a+2*A*b))
@test integrate(x^3*(a+b*x)^-2*(A+B*x), x) == :((1/2)*b^-3*x^2*(A*b+-2*B*a)+1//3*B*b^-2*x^3+a^2*b^-5*(-4*B*a+3*A*b)*log(a+b*x)+a^3*b^-5*(a+b*x)^-1*(A*b+-1*B*a)+-1*a*x*b^-4*(-3*B*a+2*A*b))
@test integrate(x^2*(a+b*x)^-2*(A+B*x), x) == :(x*b^-3*(A*b+-2*B*a)+(1/2)*B*b^-2*x^2+-1*a*b^-4*(-3*B*a+2*A*b)*log(a+b*x)+-1*a^2*b^-4*(a+b*x)^-1*(A*b+-1*B*a))
@test integrate(x*(a+b*x)^-2*(A+B*x), x) == :(B*x*b^-2+b^-3*(A*b+-2*B*a)*log(a+b*x)+a*b^-3*(a+b*x)^-1*(A*b+-1*B*a))
@test integrate((a+b*x)^-2*(A+B*x), x) == :(B*b^-2*log(a+b*x)+-1*b^-2*(a+b*x)^-1*(A*b+-1*B*a))
@test integrate(x^-1*(a+b*x)^-2*(A+B*x), x) == :(A*a^-2*log(x)+-1*A*a^-2*log(a+b*x)+a^-1*b^-1*(a+b*x)^-1*(A*b+-1*B*a))
@test integrate(x^-2*(a+b*x)^-2*(A+B*x), x) == :(a^-3*(-1*B*a+2*A*b)*log(a+b*x)+-1*A*a^-2*x^-1+-1*a^-3*(-1*B*a+2*A*b)*log(x)+-1*a^-2*(a+b*x)^-1*(A*b+-1*B*a))
@test integrate(x^-3*(a+b*x)^-2*(A+B*x), x) == :(a^-3*x^-1*(-1*B*a+2*A*b)+-1//2*A*a^-2*x^-2+b*a^-4*(-2*B*a+3*A*b)*log(x)+b*a^-3*(a+b*x)^-1*(A*b+-1*B*a)+-1*b*a^-4*(-2*B*a+3*A*b)*log(a+b*x))
@test integrate(x^-4*(a+b*x)^-2*(A+B*x), x) == :((1/2)*a^-3*x^-2*(-1*B*a+2*A*b)+-1//3*A*a^-2*x^-3+a^-5*b^2*(-3*B*a+4*A*b)*log(a+b*x)+-1*b*a^-4*x^-1*(-2*B*a+3*A*b)+-1*a^-5*b^2*(-3*B*a+4*A*b)*log(x)+-1*a^-4*b^2*(a+b*x)^-1*(A*b+-1*B*a))
@test integrate(x^4*(a+b*x)^-3*(A+B*x), x) == :((1/2)*b^-4*x^2*(A*b+-3*B*a)+1//3*B*b^-3*x^3+a^3*b^-6*(a+b*x)^-1*(-5*B*a+4*A*b)+-3*a*x*b^-5*(A*b+-2*B*a)+2*a^2*b^-6*(-5*B*a+3*A*b)*log(a+b*x)+-1//2*a^4*b^-6*(a+b*x)^-2*(A*b+-1*B*a))
@test integrate(x^3*(a+b*x)^-3*(A+B*x), x) == :(x*b^-4*(A*b+-3*B*a)+(1/2)*B*b^-3*x^2+(1/2)*a^3*b^-5*(a+b*x)^-2*(A*b+-1*B*a)+-1*a^2*b^-5*(a+b*x)^-1*(-4*B*a+3*A*b)+-3*a*b^-5*(A*b+-2*B*a)*log(a+b*x))
@test integrate(x^2*(a+b*x)^-3*(A+B*x), x) == :(B*x*b^-3+b^-4*(A*b+-3*B*a)*log(a+b*x)+a*b^-4*(a+b*x)^-1*(-3*B*a+2*A*b)+-1//2*a^2*b^-4*(a+b*x)^-2*(A*b+-1*B*a))
@test integrate(x*(a+b*x)^-3*(A+B*x), x) == :(B*b^-3*log(a+b*x)+-1*b^-3*(a+b*x)^-1*(A*b+-2*B*a)+(1/2)*a*b^-3*(a+b*x)^-2*(A*b+-1*B*a))
@test integrate((a+b*x)^-3*(A+B*x), x) == :(-1*(A+B*x)^2*(a+b*x)^-2*(-2*B*a+2*A*b)^-1)
@test integrate(x^-1*(a+b*x)^-3*(A+B*x), x) == :(A*a^-3*log(x)+A*a^-2*(a+b*x)^-1+-1*A*a^-3*log(a+b*x)+(1/2)*a^-1*b^-1*(a+b*x)^-2*(A*b+-1*B*a))
@test integrate(x^-2*(a+b*x)^-3*(A+B*x), x) == :(a^-4*(-1*B*a+3*A*b)*log(a+b*x)+-1*A*a^-3*x^-1+-1*a^-4*(-1*B*a+3*A*b)*log(x)+-1*a^-3*(a+b*x)^-1*(-1*B*a+2*A*b)+-1//2*a^-2*(a+b*x)^-2*(A*b+-1*B*a))
@test integrate(x^-3*(a+b*x)^-3*(A+B*x), x) == :(a^-4*x^-1*(-1*B*a+3*A*b)+-1//2*A*a^-3*x^-2+b*a^-4*(a+b*x)^-1*(-2*B*a+3*A*b)+(1/2)*b*a^-3*(a+b*x)^-2*(A*b+-1*B*a)+-3*b*a^-5*(-1*B*a+2*A*b)*log(a+b*x)+3*b*a^-5*(-1*B*a+2*A*b)*log(x))
@test integrate(x^-4*(a+b*x)^-3*(A+B*x), x) == :((1/2)*a^-4*x^-2*(-1*B*a+3*A*b)+-1//3*A*a^-3*x^-3+-1*a^-5*b^2*(a+b*x)^-1*(-3*B*a+4*A*b)+-3*b*a^-5*x^-1*(-1*B*a+2*A*b)+-2*a^-6*b^2*(-3*B*a+5*A*b)*log(x)+2*a^-6*b^2*(-3*B*a+5*A*b)*log(a+b*x)+-1//2*a^-4*b^2*(a+b*x)^-2*(A*b+-1*B*a))
@test integrate(x^3*(a+b*x)^2*(c+d*x)^16, x) == :(1//20*d^-6*(c+d*x)^20*(a^2*d^2+10*b^2*c^2+-8*a*b*c*d)+1//22*b^2*d^-6*(c+d*x)^22+-1//17*c^3*d^-6*(c+d*x)^17*(b*c+-1*a*d)^2+-1//19*c*d^-6*(c+d*x)^19*(3*a^2*d^2+10*b^2*c^2+-12*a*b*c*d)+-1//21*b*d^-6*(c+d*x)^21*(-2*a*d+5*b*c)+1//18*c^2*d^-6*(c+d*x)^18*(b*c+-1*a*d)*(-3*a*d+5*b*c))
@test integrate(x^2*(a+b*x)^2*(c+d*x)^16, x) == :(1//19*d^-5*(c+d*x)^19*(a^2*d^2+6*b^2*c^2+-6*a*b*c*d)+1//21*b^2*d^-5*(c+d*x)^21+-1//10*b*d^-5*(c+d*x)^20*(-1*a*d+2*b*c)+1//17*c^2*d^-5*(c+d*x)^17*(b*c+-1*a*d)^2+-1//9*c*d^-5*(c+d*x)^18*(b*c+-1*a*d)*(-1*a*d+2*b*c))
@test integrate(x*(a+b*x)^2*(c+d*x)^16, x) == :(1//20*b^2*d^-4*(c+d*x)^20+-1//17*c*d^-4*(c+d*x)^17*(b*c+-1*a*d)^2+-1//19*b*d^-4*(c+d*x)^19*(-2*a*d+3*b*c)+1//18*d^-4*(c+d*x)^18*(b*c+-1*a*d)*(-1*a*d+3*b*c))
@test integrate(x^3*(a+b*x)^-1*(c+d*x), x) == :(1//3*b^-2*x^3*(b*c+-1*a*d)+1//4*d*b^-1*x^4+x*a^2*b^-4*(b*c+-1*a*d)+-1*a^3*b^-5*(b*c+-1*a*d)*log(a+b*x)+-1//2*a*b^-3*x^2*(b*c+-1*a*d))
@test integrate(x^2*(a+b*x)^-1*(c+d*x), x) == :((1/2)*b^-2*x^2*(b*c+-1*a*d)+1//3*d*b^-1*x^3+a^2*b^-4*(b*c+-1*a*d)*log(a+b*x)+-1*a*x*b^-3*(b*c+-1*a*d))
@test integrate(x*(a+b*x)^-1*(c+d*x), x) == :(x*b^-2*(b*c+-1*a*d)+(1/2)*d*b^-1*x^2+-1*a*b^-3*(b*c+-1*a*d)*log(a+b*x))
@test integrate((a+b*x)^-1*(c+d*x), x) == :(d*x*b^-1+b^-2*(b*c+-1*a*d)*log(a+b*x))
@test integrate(x^-1*(a+b*x)^-1*(c+d*x), x) == :(c*a^-1*log(x)+-1*a^-1*b^-1*(b*c+-1*a*d)*log(a+b*x))
@test integrate(x^-2*(a+b*x)^-1*(c+d*x), x) == :(a^-2*(b*c+-1*a*d)*log(a+b*x)+-1*c*a^-1*x^-1+-1*a^-2*(b*c+-1*a*d)*log(x))
@test integrate(x^-3*(a+b*x)^-1*(c+d*x), x) == :(a^-2*x^-1*(b*c+-1*a*d)+-1//2*c*a^-1*x^-2+b*a^-3*(b*c+-1*a*d)*log(x)+-1*b*a^-3*(b*c+-1*a*d)*log(a+b*x))
@test integrate(x^-4*(a+b*x)^-1*(c+d*x), x) == :((1/2)*a^-2*x^-2*(b*c+-1*a*d)+-1//3*c*a^-1*x^-3+a^-4*b^2*(b*c+-1*a*d)*log(a+b*x)+-1*b*a^-3*x^-1*(b*c+-1*a*d)+-1*a^-4*b^2*(b*c+-1*a*d)*log(x))
@test integrate(x^3*(a+b*x)^-1*(c+d*x)^2, x) == :(1//3*b^-3*x^3*(b*c+-1*a*d)^2+1//5*b^-1*d^2*x^5+x*a^2*b^-5*(b*c+-1*a*d)^2+-1*a^3*b^-6*(b*c+-1*a*d)^2*log(a+b*x)+-1//2*a*b^-4*x^2*(b*c+-1*a*d)^2+1//4*d*b^-2*x^4*(-1*a*d+2*b*c))
@test integrate(x^2*(a+b*x)^-1*(c+d*x)^2, x) == :((1/2)*b^-3*x^2*(b*c+-1*a*d)^2+1//4*b^-1*d^2*x^4+a^2*b^-5*(b*c+-1*a*d)^2*log(a+b*x)+-1*a*x*b^-4*(b*c+-1*a*d)^2+1//3*d*b^-2*x^3*(-1*a*d+2*b*c))
@test integrate(x*(a+b*x)^-1*(c+d*x)^2, x) == :(x*b^-3*(b*c+-1*a*d)^2+1//3*b^-1*d^2*x^3+(1/2)*d*b^-2*x^2*(-1*a*d+2*b*c)+-1*a*b^-4*(b*c+-1*a*d)^2*log(a+b*x))
@test integrate((a+b*x)^-1*(c+d*x)^2, x) == :((1/2)*b^-1*(c+d*x)^2+b^-3*(b*c+-1*a*d)^2*log(a+b*x)+d*x*b^-2*(b*c+-1*a*d))
@test integrate(x^-1*(a+b*x)^-1*(c+d*x)^2, x) == :(x*b^-1*d^2+a^-1*c^2*log(x)+-1*a^-1*b^-2*(b*c+-1*a*d)^2*log(a+b*x))
@test integrate(x^-2*(a+b*x)^-1*(c+d*x)^2, x) == :(-1*a^-1*c^2*x^-1+a^-2*b^-1*(b*c+-1*a*d)^2*log(a+b*x)+-1*c*a^-2*(b*c+-2*a*d)*log(x))
@test integrate(x^-3*(a+b*x)^-1*(c+d*x)^2, x) == :(a^-3*(b*c+-1*a*d)^2*log(x)+-1*a^-3*(b*c+-1*a*d)^2*log(a+b*x)+-1//2*a^-1*c^2*x^-2+c*a^-2*x^-1*(b*c+-2*a*d))
@test integrate(x^-4*(a+b*x)^-1*(c+d*x)^2, x) == :(-1*a^-3*x^-1*(b*c+-1*a*d)^2+-1//3*a^-1*c^2*x^-3+b*a^-4*(b*c+-1*a*d)^2*log(a+b*x)+(1/2)*c*a^-2*x^-2*(b*c+-2*a*d)+-1*b*a^-4*(b*c+-1*a*d)^2*log(x))
@test integrate(x^-5*(a+b*x)^-1*(c+d*x)^2, x) == :(-1//2*a^-3*x^-2*(b*c+-1*a*d)^2+-1//4*a^-1*c^2*x^-4+b*a^-4*x^-1*(b*c+-1*a*d)^2+a^-5*b^2*(b*c+-1*a*d)^2*log(x)+-1*a^-5*b^2*(b*c+-1*a*d)^2*log(a+b*x)+1//3*c*a^-2*x^-3*(b*c+-2*a*d))
@test integrate(x^3*(a+b*x)^-1*(c+d*x)^3, x) == :(1//3*b^-4*x^3*(b*c+-1*a*d)^3+1//6*b^-1*d^3*x^6+x*a^2*b^-6*(b*c+-1*a*d)^3+-1*a^3*b^-7*(b*c+-1*a*d)^3*log(a+b*x)+-1//2*a*b^-5*x^2*(b*c+-1*a*d)^3+1//4*d*b^-3*x^4*(a^2*d^2+3*b^2*c^2+-3*a*b*c*d)+1//5*b^-2*d^2*x^5*(-1*a*d+3*b*c))
@test integrate(x^2*(a+b*x)^-1*(c+d*x)^3, x) == :((1/2)*b^-4*x^2*(b*c+-1*a*d)^3+1//5*b^-1*d^3*x^5+a^2*b^-6*(b*c+-1*a*d)^3*log(a+b*x)+-1*a*x*b^-5*(b*c+-1*a*d)^3+1//3*d*b^-3*x^3*(a^2*d^2+3*b^2*c^2+-3*a*b*c*d)+1//4*b^-2*d^2*x^4*(-1*a*d+3*b*c))
@test integrate(x*(a+b*x)^-1*(c+d*x)^3, x) == :(x*b^-4*(b*c+-1*a*d)^3+1//4*b^-1*d^3*x^4+(1/2)*d*b^-3*x^2*(a^2*d^2+3*b^2*c^2+-3*a*b*c*d)+-1*a*b^-5*(b*c+-1*a*d)^3*log(a+b*x)+1//3*b^-2*d^2*x^3*(-1*a*d+3*b*c))
@test integrate((a+b*x)^-1*(c+d*x)^3, x) == :(1//3*b^-1*(c+d*x)^3+b^-4*(b*c+-1*a*d)^3*log(a+b*x)+(1/2)*b^-2*(c+d*x)^2*(b*c+-1*a*d)+d*x*b^-3*(b*c+-1*a*d)^2)
@test integrate(x^-1*(a+b*x)^-1*(c+d*x)^3, x) == :(a^-1*c^3*log(x)+(1/2)*b^-1*d^3*x^2+x*b^-2*d^2*(-1*a*d+3*b*c)+-1*a^-1*b^-3*(b*c+-1*a*d)^3*log(a+b*x))
@test integrate(x^-2*(a+b*x)^-1*(c+d*x)^3, x) == :(x*b^-1*d^3+-1*a^-1*c^3*x^-1+a^-2*b^-2*(b*c+-1*a*d)^3*log(a+b*x)+-1*a^-2*c^2*(b*c+-3*a*d)*log(x))
@test integrate(x^-3*(a+b*x)^-1*(c+d*x)^3, x) == :(-1//2*a^-1*c^3*x^-2+c*a^-3*(b^2*c^2+3*a^2*d^2+-3*a*b*c*d)*log(x)+a^-2*c^2*x^-1*(b*c+-3*a*d)+-1*a^-3*b^-1*(b*c+-1*a*d)^3*log(a+b*x))
@test integrate(x^-4*(a+b*x)^-1*(c+d*x)^3, x) == :(a^-4*(b*c+-1*a*d)^3*log(a+b*x)+-1*a^-4*(b*c+-1*a*d)^3*log(x)+-1//3*a^-1*c^3*x^-3+(1/2)*a^-2*c^2*x^-2*(b*c+-3*a*d)+-1*c*a^-3*x^-1*(b^2*c^2+3*a^2*d^2+-3*a*b*c*d))
@test integrate(x^-5*(a+b*x)^-1*(c+d*x)^3, x) == :(a^-4*x^-1*(b*c+-1*a*d)^3+-1//4*a^-1*c^3*x^-4+b*a^-5*(b*c+-1*a*d)^3*log(x)+-1*b*a^-5*(b*c+-1*a*d)^3*log(a+b*x)+-1//2*c*a^-3*x^-2*(b^2*c^2+3*a^2*d^2+-3*a*b*c*d)+1//3*a^-2*c^2*x^-3*(b*c+-3*a*d))
@test integrate(x^-6*(a+b*x)^-1*(c+d*x)^3, x) == :((1/2)*a^-4*x^-2*(b*c+-1*a*d)^3+-1//5*a^-1*c^3*x^-5+a^-6*b^2*(b*c+-1*a*d)^3*log(a+b*x)+-1*b*a^-5*x^-1*(b*c+-1*a*d)^3+-1*a^-6*b^2*(b*c+-1*a*d)^3*log(x)+-1//3*c*a^-3*x^-3*(b^2*c^2+3*a^2*d^2+-3*a*b*c*d)+1//4*a^-2*c^2*x^-4*(b*c+-3*a*d))
@test integrate(x^5*(a+b*x)^-1*(c+d*x)^-1, x) == :(1//4*b^-1*d^-1*x^4+c^5*d^-5*(b*c+-1*a*d)^-1*log(c+d*x)+(1/2)*b^-3*d^-3*x^2*(a^2*d^2+b^2*c^2+a*b*c*d)+-1*a^5*b^-5*(b*c+-1*a*d)^-1*log(a+b*x)+-1//3*b^-2*d^-2*x^3*(a*d+b*c)+-1*x*b^-4*d^-4*(a*d+b*c)*(a^2*d^2+b^2*c^2))
@test integrate(x^4*(a+b*x)^-1*(c+d*x)^-1, x) == :(1//3*b^-1*d^-1*x^3+x*b^-3*d^-3*(a^2*d^2+b^2*c^2+a*b*c*d)+a^4*b^-4*(b*c+-1*a*d)^-1*log(a+b*x)+-1*c^4*d^-4*(b*c+-1*a*d)^-1*log(c+d*x)+-1//2*b^-2*d^-2*x^2*(a*d+b*c))
@test integrate(x^3*(a+b*x)^-1*(c+d*x)^-1, x) == :((1/2)*b^-1*d^-1*x^2+c^3*d^-3*(b*c+-1*a*d)^-1*log(c+d*x)+-1*x*b^-2*d^-2*(a*d+b*c)+-1*a^3*b^-3*(b*c+-1*a*d)^-1*log(a+b*x))
@test integrate(x^2*(a+b*x)^-1*(c+d*x)^-1, x) == :(x*b^-1*d^-1+a^2*b^-2*(b*c+-1*a*d)^-1*log(a+b*x)+-1*c^2*d^-2*(b*c+-1*a*d)^-1*log(c+d*x))
@test integrate(x*(a+b*x)^-1*(c+d*x)^-1, x) == :(c*d^-1*(b*c+-1*a*d)^-1*log(c+d*x)+-1*a*b^-1*(b*c+-1*a*d)^-1*log(a+b*x))
@test integrate((a+b*x)^-1*(c+d*x)^-1, x) == :((b*c+-1*a*d)^-1*log(a+b*x)+-1*(b*c+-1*a*d)^-1*log(c+d*x))
@test integrate(x^-1*(a+b*x)^-1*(c+d*x)^-1, x) == :(a^-1*c^-1*log(x)+d*c^-1*(b*c+-1*a*d)^-1*log(c+d*x)+-1*b*a^-1*(b*c+-1*a*d)^-1*log(a+b*x))
@test integrate(x^-2*(a+b*x)^-1*(c+d*x)^-1, x) == :(-1*a^-1*c^-1*x^-1+a^-2*b^2*(b*c+-1*a*d)^-1*log(a+b*x)+-1*a^-2*c^-2*(a*d+b*c)*log(x)+-1*c^-2*d^2*(b*c+-1*a*d)^-1*log(c+d*x))
@test integrate(x^-3*(a+b*x)^-1*(c+d*x)^-1, x) == :(-1//2*a^-1*c^-1*x^-2+a^-3*c^-3*(a^2*d^2+b^2*c^2+a*b*c*d)*log(x)+a^-2*c^-2*x^-1*(a*d+b*c)+c^-3*d^3*(b*c+-1*a*d)^-1*log(c+d*x)+-1*a^-3*b^3*(b*c+-1*a*d)^-1*log(a+b*x))
@test integrate(x^-4*(a+b*x)^-1*(c+d*x)^-1, x) == :(-1//3*a^-1*c^-1*x^-3+a^-4*b^4*(b*c+-1*a*d)^-1*log(a+b*x)+(1/2)*a^-2*c^-2*x^-2*(a*d+b*c)+-1*a^-3*c^-3*x^-1*(a^2*d^2+b^2*c^2+a*b*c*d)+-1*c^-4*d^4*(b*c+-1*a*d)^-1*log(c+d*x)+-1*a^-4*c^-4*(a*d+b*c)*(a^2*d^2+b^2*c^2)*log(x))
@test integrate(x^5*(a+b*x)^-1*(c+d*x)^-2, x) == :(1//3*b^-1*d^-2*x^3+x*b^-3*d^-4*(a^2*d^2+3*b^2*c^2+2*a*b*c*d)+-1*a^5*b^-4*(b*c+-1*a*d)^-2*log(a+b*x)+-1*c^5*d^-5*(c+d*x)^-1*(b*c+-1*a*d)^-1+-1//2*b^-2*d^-3*x^2*(a*d+2*b*c)+-1*c^4*d^-5*(b*c+-1*a*d)^-2*(-5*a*d+4*b*c)*log(c+d*x))
@test integrate(x^4*(a+b*x)^-1*(c+d*x)^-2, x) == :((1/2)*b^-1*d^-2*x^2+a^4*b^-3*(b*c+-1*a*d)^-2*log(a+b*x)+c^4*d^-4*(c+d*x)^-1*(b*c+-1*a*d)^-1+-1*x*b^-2*d^-3*(a*d+2*b*c)+c^3*d^-4*(b*c+-1*a*d)^-2*(-4*a*d+3*b*c)*log(c+d*x))
@test integrate(x^3*(a+b*x)^-1*(c+d*x)^-2, x) == :(x*b^-1*d^-2+-1*a^3*b^-2*(b*c+-1*a*d)^-2*log(a+b*x)+-1*c^3*d^-3*(c+d*x)^-1*(b*c+-1*a*d)^-1+-1*c^2*d^-3*(b*c+-1*a*d)^-2*(-3*a*d+2*b*c)*log(c+d*x))
@test integrate(x^2*(a+b*x)^-1*(c+d*x)^-2, x) == :(a^2*b^-1*(b*c+-1*a*d)^-2*log(a+b*x)+c^2*d^-2*(c+d*x)^-1*(b*c+-1*a*d)^-1+c*d^-2*(b*c+-1*a*d)^-2*(b*c+-2*a*d)*log(c+d*x))
@test integrate(x*(a+b*x)^-1*(c+d*x)^-2, x) == :(a*(b*c+-1*a*d)^-2*log(c+d*x)+-1*a*(b*c+-1*a*d)^-2*log(a+b*x)+-1*c*d^-1*(c+d*x)^-1*(b*c+-1*a*d)^-1)
@test integrate((a+b*x)^-1*(c+d*x)^-2, x) == :((c+d*x)^-1*(b*c+-1*a*d)^-1+b*(b*c+-1*a*d)^-2*log(a+b*x)+-1*b*(b*c+-1*a*d)^-2*log(c+d*x))
@test integrate(x^-1*(a+b*x)^-1*(c+d*x)^-2, x) == :(a^-1*c^-2*log(x)+-1*d*c^-1*(c+d*x)^-1*(b*c+-1*a*d)^-1+-1*a^-1*b^2*(b*c+-1*a*d)^-2*log(a+b*x)+d*c^-2*(b*c+-1*a*d)^-2*(-1*a*d+2*b*c)*log(c+d*x))
@test integrate(x^-2*(a+b*x)^-1*(c+d*x)^-2, x) == :(-1*a^-1*c^-2*x^-1+a^-2*b^3*(b*c+-1*a*d)^-2*log(a+b*x)+c^-2*d^2*(c+d*x)^-1*(b*c+-1*a*d)^-1+-1*a^-2*c^-3*(b*c+2*a*d)*log(x)+-1*c^-3*d^2*(b*c+-1*a*d)^-2*(-2*a*d+3*b*c)*log(c+d*x))
@test integrate(x^-3*(a+b*x)^-1*(c+d*x)^-2, x) == :(-1//2*a^-1*c^-2*x^-2+a^-3*c^-4*(b^2*c^2+3*a^2*d^2+2*a*b*c*d)*log(x)+a^-2*c^-3*x^-1*(b*c+2*a*d)+-1*a^-3*b^4*(b*c+-1*a*d)^-2*log(a+b*x)+-1*c^-3*d^3*(c+d*x)^-1*(b*c+-1*a*d)^-1+c^-4*d^3*(b*c+-1*a*d)^-2*(-3*a*d+4*b*c)*log(c+d*x))
@test integrate(x^5*(a+b*x)^-1*(c+d*x)^-3, x) == :((1/2)*b^-1*d^-3*x^2+-1*x*b^-2*d^-4*(a*d+3*b*c)+-1*a^5*b^-3*(b*c+-1*a*d)^-3*log(a+b*x)+-1//2*c^5*d^-5*(c+d*x)^-2*(b*c+-1*a*d)^-1+c^3*d^-5*(b*c+-1*a*d)^-3*(6*b^2*c^2+10*a^2*d^2+-15*a*b*c*d)*log(c+d*x)+c^4*d^-5*(c+d*x)^-1*(b*c+-1*a*d)^-2*(-5*a*d+4*b*c))
@test integrate(x^4*(a+b*x)^-1*(c+d*x)^-3, x) == :(x*b^-1*d^-3+a^4*b^-2*(b*c+-1*a*d)^-3*log(a+b*x)+(1/2)*c^4*d^-4*(c+d*x)^-2*(b*c+-1*a*d)^-1+-1*c^2*d^-4*(b*c+-1*a*d)^-3*(3*b^2*c^2+6*a^2*d^2+-8*a*b*c*d)*log(c+d*x)+-1*c^3*d^-4*(c+d*x)^-1*(b*c+-1*a*d)^-2*(-4*a*d+3*b*c))
@test integrate(x^3*(a+b*x)^-1*(c+d*x)^-3, x) == :(-1*a^3*b^-1*(b*c+-1*a*d)^-3*log(a+b*x)+-1//2*c^3*d^-3*(c+d*x)^-2*(b*c+-1*a*d)^-1+c*d^-3*(b*c+-1*a*d)^-3*(b^2*c^2+3*a^2*d^2+-3*a*b*c*d)*log(c+d*x)+c^2*d^-3*(c+d*x)^-1*(b*c+-1*a*d)^-2*(-3*a*d+2*b*c))
@test integrate(x^2*(a+b*x)^-1*(c+d*x)^-3, x) == :(a^2*(b*c+-1*a*d)^-3*log(a+b*x)+-1*a^2*(b*c+-1*a*d)^-3*log(c+d*x)+(1/2)*c^2*d^-2*(c+d*x)^-2*(b*c+-1*a*d)^-1+-1*c*d^-2*(c+d*x)^-1*(b*c+-1*a*d)^-2*(b*c+-2*a*d))
@test integrate(x*(a+b*x)^-1*(c+d*x)^-3, x) == :(-1*a*(c+d*x)^-1*(b*c+-1*a*d)^-2+a*b*(b*c+-1*a*d)^-3*log(c+d*x)+-1*a*b*(b*c+-1*a*d)^-3*log(a+b*x)+-1//2*c*d^-1*(c+d*x)^-2*(b*c+-1*a*d)^-1)
@test integrate((a+b*x)^-1*(c+d*x)^-3, x) == :((c+d*x)^-2*(-2*a*d+2*b*c)^-1+b*(c+d*x)^-1*(b*c+-1*a*d)^-2+b^2*(b*c+-1*a*d)^-3*log(a+b*x)+-1*b^2*(b*c+-1*a*d)^-3*log(c+d*x))
@test integrate(x^-1*(a+b*x)^-1*(c+d*x)^-3, x) == :(a^-1*c^-3*log(x)+-1*a^-1*b^3*(b*c+-1*a*d)^-3*log(a+b*x)+-1//2*d*c^-1*(c+d*x)^-2*(b*c+-1*a*d)^-1+d*c^-3*(b*c+-1*a*d)^-3*(a^2*d^2+3*b^2*c^2+-3*a*b*c*d)*log(c+d*x)+-1*d*c^-2*(c+d*x)^-1*(b*c+-1*a*d)^-2*(-1*a*d+2*b*c))
@test integrate(x^-2*(a+b*x)^-1*(c+d*x)^-3, x) == :(-1*a^-1*c^-3*x^-1+a^-2*b^4*(b*c+-1*a*d)^-3*log(a+b*x)+(1/2)*c^-2*d^2*(c+d*x)^-2*(b*c+-1*a*d)^-1+-1*a^-2*c^-4*(b*c+3*a*d)*log(x)+c^-3*d^2*(c+d*x)^-1*(b*c+-1*a*d)^-2*(-2*a*d+3*b*c)+-1*c^-4*d^2*(b*c+-1*a*d)^-3*(3*a^2*d^2+6*b^2*c^2+-8*a*b*c*d)*log(c+d*x))
@test integrate(x^4*(a+b*x)^-2*(c+d*x)^2, x) == :(1//5*b^-2*d^2*x^5+(1/2)*d*b^-3*x^4*(b*c+-1*a*d)+-1*a^4*b^-7*(a+b*x)^-1*(b*c+-1*a*d)^2+1//3*b^-4*x^3*(b*c+-1*a*d)*(b*c+-3*a*d)+x*a^2*b^-6*(b*c+-1*a*d)*(-5*a*d+3*b*c)+-1*a*b^-5*x^2*(b*c+-1*a*d)*(b*c+-2*a*d)+-2*a^3*b^-7*(b*c+-1*a*d)*(-3*a*d+2*b*c)*log(a+b*x))
@test integrate(x^3*(a+b*x)^-2*(c+d*x)^2, x) == :(1//4*b^-2*d^2*x^4+a^3*b^-6*(a+b*x)^-1*(b*c+-1*a*d)^2+(1/2)*b^-4*x^2*(b*c+-1*a*d)*(b*c+-3*a*d)+2//3*d*b^-3*x^3*(b*c+-1*a*d)+a^2*b^-6*(b*c+-1*a*d)*(-5*a*d+3*b*c)*log(a+b*x)+-2*a*x*b^-5*(b*c+-1*a*d)*(b*c+-2*a*d))
@test integrate(x^2*(a+b*x)^-2*(c+d*x)^2, x) == :(1//3*b^-2*d^2*x^3+d*b^-3*x^2*(b*c+-1*a*d)+x*b^-4*(b*c+-1*a*d)*(b*c+-3*a*d)+-1*a^2*b^-5*(a+b*x)^-1*(b*c+-1*a*d)^2+-2*a*b^-5*(b*c+-1*a*d)*(b*c+-2*a*d)*log(a+b*x))
@test integrate(x*(a+b*x)^-2*(c+d*x)^2, x) == :((1/2)*b^-2*d^2*x^2+a*b^-4*(a+b*x)^-1*(b*c+-1*a*d)^2+b^-4*(b*c+-1*a*d)*(b*c+-3*a*d)*log(a+b*x)+2*d*x*b^-3*(b*c+-1*a*d))
@test integrate((a+b*x)^-2*(c+d*x)^2, x) == :(x*b^-2*d^2+-1*b^-3*(a+b*x)^-1*(b*c+-1*a*d)^2+2*d*b^-3*(b*c+-1*a*d)*log(a+b*x))
@test integrate(x^-1*(a+b*x)^-2*(c+d*x)^2, x) == :(-1*(a^-2*c^2+-1*b^-2*d^2)*log(a+b*x)+a^-2*c^2*log(x)+a^-1*b^-2*(a+b*x)^-1*(b*c+-1*a*d)^2)
@test integrate(x^-2*(a+b*x)^-2*(c+d*x)^2, x) == :(-1*a^-2*c^2*x^-1+-1*a^-2*b^-1*(a+b*x)^-1*(b*c+-1*a*d)^2+-2*c*a^-3*(b*c+-1*a*d)*log(x)+2*c*a^-3*(b*c+-1*a*d)*log(a+b*x))
@test integrate(x^-3*(a+b*x)^-2*(c+d*x)^2, x) == :(a^-3*(a+b*x)^-1*(b*c+-1*a*d)^2+-1//2*a^-2*c^2*x^-2+a^-4*(b*c+-1*a*d)*(-1*a*d+3*b*c)*log(x)+-1*a^-4*(b*c+-1*a*d)*(-1*a*d+3*b*c)*log(a+b*x)+2*c*a^-3*x^-1*(b*c+-1*a*d))
@test integrate(x^-4*(a+b*x)^-2*(c+d*x)^2, x) == :(-1//3*a^-2*c^2*x^-3+c*a^-3*x^-2*(b*c+-1*a*d)+-1*b*a^-4*(a+b*x)^-1*(b*c+-1*a*d)^2+-1*a^-4*x^-1*(b*c+-1*a*d)*(-1*a*d+3*b*c)+-2*b*a^-5*(b*c+-1*a*d)*(-1*a*d+2*b*c)*log(x)+2*b*a^-5*(b*c+-1*a*d)*(-1*a*d+2*b*c)*log(a+b*x))
@test integrate(x^-5*(a+b*x)^-2*(c+d*x)^2, x) == :(-1//4*a^-2*c^2*x^-4+a^-5*b^2*(a+b*x)^-1*(b*c+-1*a*d)^2+-1//2*a^-4*x^-2*(b*c+-1*a*d)*(-1*a*d+3*b*c)+2//3*c*a^-3*x^-3*(b*c+-1*a*d)+a^-6*b^2*(b*c+-1*a*d)*(-3*a*d+5*b*c)*log(x)+-1*a^-6*b^2*(b*c+-1*a*d)*(-3*a*d+5*b*c)*log(a+b*x)+2*b*a^-5*x^-1*(b*c+-1*a*d)*(-1*a*d+2*b*c))
@test integrate(x^4*(a+b*x)^-2*(c+d*x)^3, x) == :(1//6*b^-2*d^3*x^6+-1*a^4*b^-8*(a+b*x)^-1*(b*c+-1*a*d)^3+1//3*b^-5*x^3*(b*c+-1*a*d)^2*(b*c+-4*a*d)+1//5*b^-3*d^2*x^5*(-2*a*d+3*b*c)+3//4*d*b^-4*x^4*(b*c+-1*a*d)^2+-1*a^3*b^-8*(b*c+-1*a*d)^2*(-7*a*d+4*b*c)*log(a+b*x)+3*x*a^2*b^-7*(b*c+-1*a*d)^2*(b*c+-2*a*d)+-1//2*a*b^-6*x^2*(b*c+-1*a*d)^2*(-5*a*d+2*b*c))
@test integrate(x^3*(a+b*x)^-2*(c+d*x)^3, x) == :(1//5*b^-2*d^3*x^5+d*b^-4*x^3*(b*c+-1*a*d)^2+a^3*b^-7*(a+b*x)^-1*(b*c+-1*a*d)^3+(1/2)*b^-5*x^2*(b*c+-1*a*d)^2*(b*c+-4*a*d)+1//4*b^-3*d^2*x^4*(-2*a*d+3*b*c)+-1*a*x*b^-6*(b*c+-1*a*d)^2*(-5*a*d+2*b*c)+3*a^2*b^-7*(b*c+-1*a*d)^2*(b*c+-2*a*d)*log(a+b*x))
@test integrate(x^2*(a+b*x)^-2*(c+d*x)^3, x) == :(1//4*b^-2*d^3*x^4+x*b^-5*(b*c+-1*a*d)^2*(b*c+-4*a*d)+-1*a^2*b^-6*(a+b*x)^-1*(b*c+-1*a*d)^3+1//3*b^-3*d^2*x^3*(-2*a*d+3*b*c)+3//2*d*b^-4*x^2*(b*c+-1*a*d)^2+-1*a*b^-6*(b*c+-1*a*d)^2*(-5*a*d+2*b*c)*log(a+b*x))
@test integrate(x*(a+b*x)^-2*(c+d*x)^3, x) == :(1//3*b^-2*d^3*x^3+a*b^-5*(a+b*x)^-1*(b*c+-1*a*d)^3+b^-5*(b*c+-1*a*d)^2*(b*c+-4*a*d)*log(a+b*x)+(1/2)*b^-3*d^2*x^2*(-2*a*d+3*b*c)+3*d*x*b^-4*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^-2*(c+d*x)^3, x) == :((1/2)*b^-2*d^3*x^2+-1*b^-4*(a+b*x)^-1*(b*c+-1*a*d)^3+x*b^-3*d^2*(-2*a*d+3*b*c)+3*d*b^-4*(b*c+-1*a*d)^2*log(a+b*x))
@test integrate(x^-1*(a+b*x)^-2*(c+d*x)^3, x) == :(x*b^-2*d^3+a^-2*c^3*log(x)+a^-1*b^-3*(a+b*x)^-1*(b*c+-1*a*d)^3+-1*a^-2*b^-3*(b*c+-1*a*d)^2*(b*c+2*a*d)*log(a+b*x))
@test integrate(x^-2*(a+b*x)^-2*(c+d*x)^3, x) == :(-1*a^-2*c^3*x^-1+-1*a^-3*c^2*(-3*a*d+2*b*c)*log(x)+-1*a^-2*b^-2*(a+b*x)^-1*(b*c+-1*a*d)^3+a^-3*b^-2*(b*c+-1*a*d)^2*(a*d+2*b*c)*log(a+b*x))
@test integrate(x^-3*(a+b*x)^-2*(c+d*x)^3, x) == :(-1//2*a^-2*c^3*x^-2+a^-3*b^-1*(a+b*x)^-1*(b*c+-1*a*d)^3+a^-3*c^2*x^-1*(-3*a*d+2*b*c)+-3*c*a^-4*(b*c+-1*a*d)^2*log(a+b*x)+3*c*a^-4*(b*c+-1*a*d)^2*log(x))
@test integrate(x^-4*(a+b*x)^-2*(c+d*x)^3, x) == :(-1*a^-4*(a+b*x)^-1*(b*c+-1*a*d)^3+-1//3*a^-2*c^3*x^-3+a^-5*(b*c+-1*a*d)^2*(-1*a*d+4*b*c)*log(a+b*x)+(1/2)*a^-3*c^2*x^-2*(-3*a*d+2*b*c)+-1*a^-5*(b*c+-1*a*d)^2*(-1*a*d+4*b*c)*log(x)+-3*c*a^-4*x^-1*(b*c+-1*a*d)^2)
@test integrate(x^-5*(a+b*x)^-2*(c+d*x)^3, x) == :(-1//4*a^-2*c^3*x^-4+b*a^-5*(a+b*x)^-1*(b*c+-1*a*d)^3+a^-5*x^-1*(b*c+-1*a*d)^2*(-1*a*d+4*b*c)+-3//2*c*a^-4*x^-2*(b*c+-1*a*d)^2+1//3*a^-3*c^2*x^-3*(-3*a*d+2*b*c)+b*a^-6*(b*c+-1*a*d)^2*(-2*a*d+5*b*c)*log(x)+-1*b*a^-6*(b*c+-1*a*d)^2*(-2*a*d+5*b*c)*log(a+b*x))
@test integrate(x^-6*(a+b*x)^-2*(c+d*x)^3, x) == :(-1//5*a^-2*c^3*x^-5+(1/2)*a^-5*x^-2*(b*c+-1*a*d)^2*(-1*a*d+4*b*c)+-1*c*a^-4*x^-3*(b*c+-1*a*d)^2+-1*a^-6*b^2*(a+b*x)^-1*(b*c+-1*a*d)^3+1//4*a^-3*c^2*x^-4*(-3*a*d+2*b*c)+-1*b*a^-6*x^-1*(b*c+-1*a*d)^2*(-2*a*d+5*b*c)+-3*a^-7*b^2*(b*c+-1*a*d)^2*(-1*a*d+2*b*c)*log(x)+3*a^-7*b^2*(b*c+-1*a*d)^2*(-1*a*d+2*b*c)*log(a+b*x))
@test integrate(x^6*(a+b*x)^-2*(c+d*x)^-2, x) == :(1//3*b^-2*d^-2*x^3+x*b^-4*d^-4*(3*a^2*d^2+3*b^2*c^2+4*a*b*c*d)+-1*a^6*b^-5*(a+b*x)^-1*(b*c+-1*a*d)^-2+-1*b^-3*d^-3*x^2*(a*d+b*c)+-1*c^6*d^-5*(c+d*x)^-1*(b*c+-1*a*d)^-2+-2*a^5*b^-5*(b*c+-1*a*d)^-3*(-2*a*d+3*b*c)*log(a+b*x)+-2*c^5*d^-5*(b*c+-1*a*d)^-3*(-3*a*d+2*b*c)*log(c+d*x))
@test integrate(x^5*(a+b*x)^-2*(c+d*x)^-2, x) == :((1/2)*b^-2*d^-2*x^2+a^5*b^-4*(a+b*x)^-1*(b*c+-1*a*d)^-2+c^5*d^-4*(c+d*x)^-1*(b*c+-1*a*d)^-2+-1*x*b^-3*d^-3*(2*a*d+2*b*c)+a^4*b^-4*(b*c+-1*a*d)^-3*(-3*a*d+5*b*c)*log(a+b*x)+c^4*d^-4*(b*c+-1*a*d)^-3*(-5*a*d+3*b*c)*log(c+d*x))
@test integrate(x^4*(a+b*x)^-2*(c+d*x)^-2, x) == :(x*b^-2*d^-2+-1*a^4*b^-3*(a+b*x)^-1*(b*c+-1*a*d)^-2+-1*c^4*d^-3*(c+d*x)^-1*(b*c+-1*a*d)^-2+-2*a^3*b^-3*(b*c+-1*a*d)^-3*(-1*a*d+2*b*c)*log(a+b*x)+-2*c^3*d^-3*(b*c+-1*a*d)^-3*(b*c+-2*a*d)*log(c+d*x))
@test integrate(x^3*(a+b*x)^-2*(c+d*x)^-2, x) == :(a^3*b^-2*(a+b*x)^-1*(b*c+-1*a*d)^-2+c^3*d^-2*(c+d*x)^-1*(b*c+-1*a*d)^-2+a^2*b^-2*(b*c+-1*a*d)^-3*(-1*a*d+3*b*c)*log(a+b*x)+c^2*d^-2*(b*c+-1*a*d)^-3*(b*c+-3*a*d)*log(c+d*x))
@test integrate(x^2*(a+b*x)^-2*(c+d*x)^-2, x) == :(-1*a^2*b^-1*(a+b*x)^-1*(b*c+-1*a*d)^-2+-1*c^2*d^-1*(c+d*x)^-1*(b*c+-1*a*d)^-2+-2*a*c*(b*c+-1*a*d)^-3*log(a+b*x)+2*a*c*(b*c+-1*a*d)^-3*log(c+d*x))
@test integrate(x*(a+b*x)^-2*(c+d*x)^-2, x) == :(a*(a+b*x)^-1*(b*c+-1*a*d)^-2+c*(c+d*x)^-1*(b*c+-1*a*d)^-2+(b*c+-1*a*d)^-3*(a*d+b*c)*log(a+b*x)+-1*(b*c+-1*a*d)^-3*(a*d+b*c)*log(c+d*x))
@test integrate((a+b*x)^-2*(c+d*x)^-2, x) == :(-1*b*(a+b*x)^-1*(b*c+-1*a*d)^-2+-1*d*(c+d*x)^-1*(b*c+-1*a*d)^-2+-2*b*d*(b*c+-1*a*d)^-3*log(a+b*x)+2*b*d*(b*c+-1*a*d)^-3*log(c+d*x))
@test integrate(x^-1*(a+b*x)^-2*(c+d*x)^-2, x) == :(a^-2*c^-2*log(x)+a^-1*b^2*(a+b*x)^-1*(b*c+-1*a*d)^-2+c^-1*d^2*(c+d*x)^-1*(b*c+-1*a*d)^-2+-1*a^-2*b^2*(b*c+-1*a*d)^-3*(b*c+-3*a*d)*log(a+b*x)+-1*c^-2*d^2*(b*c+-1*a*d)^-3*(-1*a*d+3*b*c)*log(c+d*x))
@test integrate(x^-2*(a+b*x)^-2*(c+d*x)^-2, x) == :(-1*a^-2*c^-2*x^-1+-1*a^-3*c^-3*(2*a*d+2*b*c)*log(x)+-1*a^-2*b^3*(a+b*x)^-1*(b*c+-1*a*d)^-2+-1*c^-2*d^3*(c+d*x)^-1*(b*c+-1*a*d)^-2+2*a^-3*b^3*(b*c+-1*a*d)^-3*(b*c+-2*a*d)*log(a+b*x)+2*c^-3*d^3*(b*c+-1*a*d)^-3*(-1*a*d+2*b*c)*log(c+d*x))
@test integrate(x^-3*(a+b*x)^-2*(c+d*x)^-2, x) == :(-1//2*a^-2*c^-2*x^-2+a^-4*c^-4*(3*a^2*d^2+3*b^2*c^2+4*a*b*c*d)*log(x)+a^-3*b^4*(a+b*x)^-1*(b*c+-1*a*d)^-2+a^-3*c^-3*x^-1*(2*a*d+2*b*c)+c^-3*d^4*(c+d*x)^-1*(b*c+-1*a*d)^-2+-1*a^-4*b^4*(b*c+-1*a*d)^-3*(-5*a*d+3*b*c)*log(a+b*x)+-1*c^-4*d^4*(b*c+-1*a*d)^-3*(-3*a*d+5*b*c)*log(c+d*x))
@test integrate(x^7*(a+b*x)^-2*(c+d*x)^-3, x) == :(1//3*b^-2*d^-3*x^3+x*b^-4*d^-5*(3*a^2*d^2+6*b^2*c^2+6*a*b*c*d)+a^7*b^-5*(a+b*x)^-1*(b*c+-1*a*d)^-3+(1/2)*c^7*d^-6*(c+d*x)^-2*(b*c+-1*a*d)^-2+-1//2*b^-3*d^-4*x^2*(2*a*d+3*b*c)+a^6*b^-5*(b*c+-1*a*d)^-4*(-4*a*d+7*b*c)*log(a+b*x)+-1*c^5*d^-6*(b*c+-1*a*d)^-4*(10*b^2*c^2+21*a^2*d^2+-28*a*b*c*d)*log(c+d*x)+-1*c^6*d^-6*(c+d*x)^-1*(b*c+-1*a*d)^-3*(-7*a*d+5*b*c))
@test integrate(x^6*(a+b*x)^-2*(c+d*x)^-3, x) == :((1/2)*b^-2*d^-3*x^2+-1*x*b^-3*d^-4*(2*a*d+3*b*c)+-1*a^6*b^-4*(a+b*x)^-1*(b*c+-1*a*d)^-3+-1//2*c^6*d^-5*(c+d*x)^-2*(b*c+-1*a*d)^-2+-3*a^5*b^-4*(b*c+-1*a*d)^-4*(-1*a*d+2*b*c)*log(a+b*x)+2*c^5*d^-5*(c+d*x)^-1*(b*c+-1*a*d)^-3*(-3*a*d+2*b*c)+3*c^4*d^-5*(b*c+-1*a*d)^-4*(2*b^2*c^2+5*a^2*d^2+-6*a*b*c*d)*log(c+d*x))
@test integrate(x^5*(a+b*x)^-2*(c+d*x)^-3, x) == :(x*b^-2*d^-3+a^5*b^-3*(a+b*x)^-1*(b*c+-1*a*d)^-3+(1/2)*c^5*d^-4*(c+d*x)^-2*(b*c+-1*a*d)^-2+a^4*b^-3*(b*c+-1*a*d)^-4*(-2*a*d+5*b*c)*log(a+b*x)+-1*c^3*d^-4*(b*c+-1*a*d)^-4*(3*b^2*c^2+10*a^2*d^2+-10*a*b*c*d)*log(c+d*x)+-1*c^4*d^-4*(c+d*x)^-1*(b*c+-1*a*d)^-3*(-5*a*d+3*b*c))
@test integrate(x^4*(a+b*x)^-2*(c+d*x)^-3, x) == :(-1*a^4*b^-2*(a+b*x)^-1*(b*c+-1*a*d)^-3+-1//2*c^4*d^-3*(c+d*x)^-2*(b*c+-1*a*d)^-2+c^2*d^-3*(b*c+-1*a*d)^-4*(b^2*c^2+6*a^2*d^2+-4*a*b*c*d)*log(c+d*x)+-1*a^3*b^-2*(b*c+-1*a*d)^-4*(-1*a*d+4*b*c)*log(a+b*x)+2*c^3*d^-3*(c+d*x)^-1*(b*c+-1*a*d)^-3*(b*c+-2*a*d))
@test integrate(x^3*(a+b*x)^-2*(c+d*x)^-3, x) == :(a^3*b^-1*(a+b*x)^-1*(b*c+-1*a*d)^-3+(1/2)*c^3*d^-2*(c+d*x)^-2*(b*c+-1*a*d)^-2+-3*c*a^2*(b*c+-1*a*d)^-4*log(c+d*x)+3*c*a^2*(b*c+-1*a*d)^-4*log(a+b*x)+-1*c^2*d^-2*(c+d*x)^-1*(b*c+-1*a*d)^-3*(b*c+-3*a*d))
@test integrate(x^2*(a+b*x)^-2*(c+d*x)^-3, x) == :(-1*a^2*(a+b*x)^-1*(b*c+-1*a*d)^-3+a*(b*c+-1*a*d)^-4*(a*d+2*b*c)*log(c+d*x)+-1*a*(b*c+-1*a*d)^-4*(a*d+2*b*c)*log(a+b*x)+-2*a*c*(c+d*x)^-1*(b*c+-1*a*d)^-3+-1//2*c^2*d^-1*(c+d*x)^-2*(b*c+-1*a*d)^-2)
@test integrate(x*(a+b*x)^-2*(c+d*x)^-3, x) == :((c+d*x)^-1*(b*c+-1*a*d)^-3*(a*d+b*c)+(1/2)*c*(c+d*x)^-2*(b*c+-1*a*d)^-2+a*b*(a+b*x)^-1*(b*c+-1*a*d)^-3+b*(b*c+-1*a*d)^-4*(b*c+2*a*d)*log(a+b*x)+-1*b*(b*c+-1*a*d)^-4*(b*c+2*a*d)*log(c+d*x))
@test integrate((a+b*x)^-2*(c+d*x)^-3, x) == :(-1*b^2*(a+b*x)^-1*(b*c+-1*a*d)^-3+-1//2*d*(c+d*x)^-2*(b*c+-1*a*d)^-2+-3*d*b^2*(b*c+-1*a*d)^-4*log(a+b*x)+-2*b*d*(c+d*x)^-1*(b*c+-1*a*d)^-3+3*d*b^2*(b*c+-1*a*d)^-4*log(c+d*x))
@test integrate(x^-1*(a+b*x)^-2*(c+d*x)^-3, x) == :(a^-2*c^-3*log(x)+a^-1*b^3*(a+b*x)^-1*(b*c+-1*a*d)^-3+(1/2)*c^-1*d^2*(c+d*x)^-2*(b*c+-1*a*d)^-2+c^-2*d^2*(c+d*x)^-1*(b*c+-1*a*d)^-3*(-1*a*d+3*b*c)+-1*a^-2*b^3*(b*c+-1*a*d)^-4*(b*c+-4*a*d)*log(a+b*x)+-1*c^-3*d^2*(b*c+-1*a*d)^-4*(a^2*d^2+6*b^2*c^2+-4*a*b*c*d)*log(c+d*x))
@test integrate(x^-2*(a+b*x)^-2*(c+d*x)^-3, x) == :(-1*a^-2*c^-3*x^-1+-1*a^-3*c^-4*(2*b*c+3*a*d)*log(x)+-1*a^-2*b^4*(a+b*x)^-1*(b*c+-1*a*d)^-3+-1//2*c^-2*d^3*(c+d*x)^-2*(b*c+-1*a*d)^-2+a^-3*b^4*(b*c+-1*a*d)^-4*(-5*a*d+2*b*c)*log(a+b*x)+c^-4*d^3*(b*c+-1*a*d)^-4*(3*a^2*d^2+10*b^2*c^2+-10*a*b*c*d)*log(c+d*x)+-2*c^-3*d^3*(c+d*x)^-1*(b*c+-1*a*d)^-3*(-1*a*d+2*b*c))
@test integrate(x^-3*(a+b*x)^-2*(c+d*x)^-3, x) == :(-1//2*a^-2*c^-3*x^-2+a^-4*c^-5*(3*b^2*c^2+6*a^2*d^2+6*a*b*c*d)*log(x)+a^-3*b^5*(a+b*x)^-1*(b*c+-1*a*d)^-3+a^-3*c^-4*x^-1*(2*b*c+3*a*d)+(1/2)*c^-3*d^4*(c+d*x)^-2*(b*c+-1*a*d)^-2+c^-4*d^4*(c+d*x)^-1*(b*c+-1*a*d)^-3*(-3*a*d+5*b*c)+-3*a^-4*b^5*(b*c+-1*a*d)^-4*(b*c+-2*a*d)*log(a+b*x)+-3*c^-5*d^4*(b*c+-1*a*d)^-4*(2*a^2*d^2+5*b^2*c^2+-6*a*b*c*d)*log(c+d*x))
@test integrate(x^2*(1+x)^-2*(-1+x)^-2, x) == :(-1//2*arctanh(x)+x*(2+-2*x^2)^-1)
@test integrate(x^3*(a+b*x)^-3*(c+d*x)^3, x) == :(1//4*b^-3*d^3*x^4+x*b^-6*(b*c+-1*a*d)*(b^2*c^2+10*a^2*d^2+-8*a*b*c*d)+b^-4*d^2*x^3*(b*c+-1*a*d)+(1/2)*a^3*b^-7*(a+b*x)^-2*(b*c+-1*a*d)^3+-3*a*b^-7*(b*c+-1*a*d)*(b^2*c^2+5*a^2*d^2+-5*a*b*c*d)*log(a+b*x)+-3*a^2*b^-7*(a+b*x)^-1*(b*c+-1*a*d)^2*(b*c+-2*a*d)+3//2*d*b^-5*x^2*(b*c+-1*a*d)*(b*c+-2*a*d))
@test integrate(x^2*(a+b*x)^-3*(c+d*x)^3, x) == :(1//3*b^-3*d^3*x^3+b^-6*(b*c+-1*a*d)*(b^2*c^2+10*a^2*d^2+-8*a*b*c*d)*log(a+b*x)+-1//2*a^2*b^-6*(a+b*x)^-2*(b*c+-1*a*d)^3+3//2*b^-4*d^2*x^2*(b*c+-1*a*d)+a*b^-6*(a+b*x)^-1*(b*c+-1*a*d)^2*(-5*a*d+2*b*c)+3*d*x*b^-5*(b*c+-1*a*d)*(b*c+-2*a*d))
@test integrate(x*(a+b*x)^-3*(c+d*x)^3, x) == :((1/2)*b^-3*d^3*x^2+(1/2)*a*b^-5*(a+b*x)^-2*(b*c+-1*a*d)^3+-1*b^-5*(a+b*x)^-1*(b*c+-1*a*d)^2*(b*c+-4*a*d)+3*x*b^-4*d^2*(b*c+-1*a*d)+3*d*b^-5*(b*c+-1*a*d)*(b*c+-2*a*d)*log(a+b*x))
@test integrate((a+b*x)^-3*(c+d*x)^3, x) == :(x*b^-3*d^3+-1//2*b^-4*(a+b*x)^-2*(b*c+-1*a*d)^3+-3*d*b^-4*(a+b*x)^-1*(b*c+-1*a*d)^2+3*b^-4*d^2*(b*c+-1*a*d)*log(a+b*x))
@test integrate(x^-1*(a+b*x)^-3*(c+d*x)^3, x) == :(-1*(a^-3*c^3+-1*b^-3*d^3)*log(a+b*x)+a^-3*c^3*log(x)+(1/2)*a^-1*b^-3*(a+b*x)^-2*(b*c+-1*a*d)^3+a^-2*b^-3*(a+b*x)^-1*(b*c+-1*a*d)^2*(b*c+2*a*d))
@test integrate(x^-2*(a+b*x)^-3*(c+d*x)^3, x) == :(-1*a^-3*c^3*x^-1+-3*a^-4*c^2*(b*c+-1*a*d)*log(x)+3*a^-4*c^2*(b*c+-1*a*d)*log(a+b*x)+-1//2*a^-2*b^-2*(a+b*x)^-2*(b*c+-1*a*d)^3+-1*a^-3*b^-2*(a+b*x)^-1*(b*c+-1*a*d)^2*(a*d+2*b*c))
@test integrate(x^-3*(a+b*x)^-3*(c+d*x)^3, x) == :(-1//2*a^-3*c^3*x^-2+(1/2)*a^-3*b^-1*(a+b*x)^-2*(b*c+-1*a*d)^3+3*c*a^-4*(a+b*x)^-1*(b*c+-1*a*d)^2+3*a^-4*c^2*x^-1*(b*c+-1*a*d)+-3*c*a^-5*(b*c+-1*a*d)*(-1*a*d+2*b*c)*log(a+b*x)+3*c*a^-5*(b*c+-1*a*d)*(-1*a*d+2*b*c)*log(x))
@test integrate(x^-4*(a+b*x)^-3*(c+d*x)^3, x) == :(-1//2*a^-4*(a+b*x)^-2*(b*c+-1*a*d)^3+-1//3*a^-3*c^3*x^-3+a^-6*(b*c+-1*a*d)*(a^2*d^2+10*b^2*c^2+-8*a*b*c*d)*log(a+b*x)+-1*a^-6*(b*c+-1*a*d)*(a^2*d^2+10*b^2*c^2+-8*a*b*c*d)*log(x)+-1*a^-5*(a+b*x)^-1*(b*c+-1*a*d)^2*(-1*a*d+4*b*c)+3//2*a^-4*c^2*x^-2*(b*c+-1*a*d)+-3*c*a^-5*x^-1*(b*c+-1*a*d)*(-1*a*d+2*b*c))
@test integrate(x^7*(a+b*x)^-3*(c+d*x)^-3, x) == :((1/2)*b^-3*d^-3*x^2+(1/2)*a^7*b^-5*(a+b*x)^-2*(b*c+-1*a*d)^-3+-1*x*b^-4*d^-4*(3*a*d+3*b*c)+-1//2*c^7*d^-5*(c+d*x)^-2*(b*c+-1*a*d)^-3+c^6*d^-5*(c+d*x)^-1*(b*c+-1*a*d)^-4*(-7*a*d+4*b*c)+-1*a^6*b^-5*(a+b*x)^-1*(b*c+-1*a*d)^-4*(-4*a*d+7*b*c)+-3*a^5*b^-5*(b*c+-1*a*d)^-5*(2*a^2*d^2+7*b^2*c^2+-7*a*b*c*d)*log(a+b*x)+3*c^5*d^-5*(b*c+-1*a*d)^-5*(2*b^2*c^2+7*a^2*d^2+-7*a*b*c*d)*log(c+d*x))
@test integrate(x^6*(a+b*x)^-3*(c+d*x)^-3, x) == :(x*b^-3*d^-3+(1/2)*c^6*d^-4*(c+d*x)^-2*(b*c+-1*a*d)^-3+-1//2*a^6*b^-4*(a+b*x)^-2*(b*c+-1*a*d)^-3+-3*c^4*d^-4*(b*c+-1*a*d)^-5*(b^2*c^2+5*a^2*d^2+-4*a*b*c*d)*log(c+d*x)+-3*c^5*d^-4*(c+d*x)^-1*(b*c+-1*a*d)^-4*(b*c+-2*a*d)+3*a^4*b^-4*(b*c+-1*a*d)^-5*(a^2*d^2+5*b^2*c^2+-4*a*b*c*d)*log(a+b*x)+3*a^5*b^-4*(a+b*x)^-1*(b*c+-1*a*d)^-4*(-1*a*d+2*b*c))
@test integrate(x^5*(a+b*x)^-3*(c+d*x)^-3, x) == :((1/2)*a^5*b^-3*(a+b*x)^-2*(b*c+-1*a*d)^-3+-1//2*c^5*d^-3*(c+d*x)^-2*(b*c+-1*a*d)^-3+c^3*d^-3*(b*c+-1*a*d)^-5*(b^2*c^2+10*a^2*d^2+-5*a*b*c*d)*log(c+d*x)+c^4*d^-3*(c+d*x)^-1*(b*c+-1*a*d)^-4*(-5*a*d+2*b*c)+-1*a^3*b^-3*(b*c+-1*a*d)^-5*(a^2*d^2+10*b^2*c^2+-5*a*b*c*d)*log(a+b*x)+-1*a^4*b^-3*(a+b*x)^-1*(b*c+-1*a*d)^-4*(-2*a*d+5*b*c))
@test integrate(x^4*(a+b*x)^-3*(c+d*x)^-3, x) == :((1/2)*c^4*d^-2*(c+d*x)^-2*(b*c+-1*a*d)^-3+-6*a^2*c^2*(b*c+-1*a*d)^-5*log(c+d*x)+6*a^2*c^2*(b*c+-1*a*d)^-5*log(a+b*x)+-1//2*a^4*b^-2*(a+b*x)^-2*(b*c+-1*a*d)^-3+a^3*b^-2*(a+b*x)^-1*(b*c+-1*a*d)^-4*(-1*a*d+4*b*c)+-1*c^3*d^-2*(c+d*x)^-1*(b*c+-1*a*d)^-4*(b*c+-4*a*d))
@test integrate(x^3*(a+b*x)^-3*(c+d*x)^-3, x) == :((1/2)*a^3*b^-1*(a+b*x)^-2*(b*c+-1*a*d)^-3+-3*a*c^2*(c+d*x)^-1*(b*c+-1*a*d)^-4+-3*c*a^2*(a+b*x)^-1*(b*c+-1*a*d)^-4+-1//2*c^3*d^-1*(c+d*x)^-2*(b*c+-1*a*d)^-3+-3*a*c*(b*c+-1*a*d)^-5*(a*d+b*c)*log(a+b*x)+3*a*c*(b*c+-1*a*d)^-5*(a*d+b*c)*log(c+d*x))
@test integrate(x^2*(a+b*x)^-3*(c+d*x)^-3, x) == :((b*c+-1*a*d)^-5*(a^2*d^2+b^2*c^2+4*a*b*c*d)*log(a+b*x)+(1/2)*c^2*(c+d*x)^-2*(b*c+-1*a*d)^-3+-1*(b*c+-1*a*d)^-5*(a^2*d^2+b^2*c^2+4*a*b*c*d)*log(c+d*x)+-1//2*a^2*(a+b*x)^-2*(b*c+-1*a*d)^-3+a*(a+b*x)^-1*(b*c+-1*a*d)^-4*(a*d+2*b*c)+c*(c+d*x)^-1*(b*c+-1*a*d)^-4*(b*c+2*a*d))
@test integrate(x*(a+b*x)^-3*(c+d*x)^-3, x) == :((1/2)*a*b*(a+b*x)^-2*(b*c+-1*a*d)^-3+-1*b*(a+b*x)^-1*(b*c+-1*a*d)^-4*(b*c+2*a*d)+-1*d*(c+d*x)^-1*(b*c+-1*a*d)^-4*(a*d+2*b*c)+-1//2*c*d*(c+d*x)^-2*(b*c+-1*a*d)^-3+-3*b*d*(b*c+-1*a*d)^-5*(a*d+b*c)*log(a+b*x)+3*b*d*(b*c+-1*a*d)^-5*(a*d+b*c)*log(c+d*x))
@test integrate((a+b*x)^-3*(c+d*x)^-3, x) == :((1/2)*d^2*(c+d*x)^-2*(b*c+-1*a*d)^-3+-1//2*b^2*(a+b*x)^-2*(b*c+-1*a*d)^-3+-6*b^2*d^2*(b*c+-1*a*d)^-5*log(c+d*x)+3*b*d^2*(c+d*x)^-1*(b*c+-1*a*d)^-4+3*d*b^2*(a+b*x)^-1*(b*c+-1*a*d)^-4+6*b^2*d^2*(b*c+-1*a*d)^-5*log(a+b*x))
@test integrate(x^-1*(a+b*x)^-3*(c+d*x)^-3, x) == :(a^-3*c^-3*log(x)+(1/2)*a^-1*b^3*(a+b*x)^-2*(b*c+-1*a*d)^-3+-1//2*c^-1*d^3*(c+d*x)^-2*(b*c+-1*a*d)^-3+a^-2*b^3*(a+b*x)^-1*(b*c+-1*a*d)^-4*(b*c+-4*a*d)+c^-3*d^3*(b*c+-1*a*d)^-5*(a^2*d^2+10*b^2*c^2+-5*a*b*c*d)*log(c+d*x)+-1*a^-3*b^3*(b*c+-1*a*d)^-5*(b^2*c^2+10*a^2*d^2+-5*a*b*c*d)*log(a+b*x)+-1*c^-2*d^3*(c+d*x)^-1*(b*c+-1*a*d)^-4*(-1*a*d+4*b*c))
@test integrate(x^-2*(a+b*x)^-3*(c+d*x)^-3, x) == :(-1*a^-3*c^-3*x^-1+(1/2)*c^-2*d^4*(c+d*x)^-2*(b*c+-1*a*d)^-3+-1*a^-4*c^-4*(3*a*d+3*b*c)*log(x)+-1//2*a^-2*b^4*(a+b*x)^-2*(b*c+-1*a*d)^-3+c^-3*d^4*(c+d*x)^-1*(b*c+-1*a*d)^-4*(-2*a*d+5*b*c)+-1*a^-3*b^4*(a+b*x)^-1*(b*c+-1*a*d)^-4*(-5*a*d+2*b*c)+-3*c^-4*d^4*(b*c+-1*a*d)^-5*(a^2*d^2+5*b^2*c^2+-4*a*b*c*d)*log(c+d*x)+3*a^-4*b^4*(b*c+-1*a*d)^-5*(b^2*c^2+5*a^2*d^2+-4*a*b*c*d)*log(a+b*x))
@test integrate(x^7//2*(A+B*x)*(a+b*x), x) == :(1//11*x^11//2*(2*A*b+2*B*a)+2//9*A*a*x^9//2+2//13*B*b*x^13//2)
@test integrate(x^5//2*(A+B*x)*(a+b*x), x) == :(1//9*x^9//2*(2*A*b+2*B*a)+2//7*A*a*x^7//2+2//11*B*b*x^11//2)
@test integrate(x^3//2*(A+B*x)*(a+b*x), x) == :(1//7*x^7//2*(2*A*b+2*B*a)+2//5*A*a*x^5//2+2//9*B*b*x^9//2)
@test integrate(x^(1/2)*(A+B*x)*(a+b*x), x) == :(1//5*x^5//2*(2*A*b+2*B*a)+2//3*A*a*x^3//2+2//7*B*b*x^7//2)
@test integrate(x^-1//2*(A+B*x)*(a+b*x), x) == :(1//3*x^3//2*(2*A*b+2*B*a)+2*A*a*x^(1/2)+2//5*B*b*x^5//2)
@test integrate(x^-3//2*(A+B*x)*(a+b*x), x) == :(x^(1/2)*(2*A*b+2*B*a)+-2*A*a*x^-1//2+2//3*B*b*x^3//2)
@test integrate(x^-5//2*(A+B*x)*(a+b*x), x) == :(-1*x^-1//2*(2*A*b+2*B*a)+2*B*b*x^(1/2)+-2//3*A*a*x^-3//2)
@test integrate(x^-7//2*(A+B*x)*(a+b*x), x) == :(-1//3*x^-3//2*(2*A*b+2*B*a)+-2*B*b*x^-1//2+-2//5*A*a*x^-5//2)
@test integrate(x^7//2*(a+b*x)^2*(A+B*x), x) == :(2//9*A*a^2*x^9//2+2//11*a*x^11//2*(B*a+2*A*b)+2//13*b*x^13//2*(A*b+2*B*a)+2//15*B*b^2*x^15//2)
@test integrate(x^5//2*(a+b*x)^2*(A+B*x), x) == :(2//7*A*a^2*x^7//2+2//9*a*x^9//2*(B*a+2*A*b)+2//11*b*x^11//2*(A*b+2*B*a)+2//13*B*b^2*x^13//2)
@test integrate(x^3//2*(a+b*x)^2*(A+B*x), x) == :(2//5*A*a^2*x^5//2+2//7*a*x^7//2*(B*a+2*A*b)+2//9*b*x^9//2*(A*b+2*B*a)+2//11*B*b^2*x^11//2)
@test integrate(x^(1/2)*(a+b*x)^2*(A+B*x), x) == :(2//3*A*a^2*x^3//2+2//5*a*x^5//2*(B*a+2*A*b)+2//7*b*x^7//2*(A*b+2*B*a)+2//9*B*b^2*x^9//2)
@test integrate(x^-1//2*(a+b*x)^2*(A+B*x), x) == :(2*A*a^2*x^(1/2)+2//3*a*x^3//2*(B*a+2*A*b)+2//5*b*x^5//2*(A*b+2*B*a)+2//7*B*b^2*x^7//2)
@test integrate(x^-3//2*(a+b*x)^2*(A+B*x), x) == :(-2*A*a^2*x^-1//2+2*a*x^(1/2)*(B*a+2*A*b)+2//3*b*x^3//2*(A*b+2*B*a)+2//5*B*b^2*x^5//2)
@test integrate(x^-5//2*(a+b*x)^2*(A+B*x), x) == :(-2*a*x^-1//2*(B*a+2*A*b)+2*b*x^(1/2)*(A*b+2*B*a)+-2//3*A*a^2*x^-3//2+2//3*B*b^2*x^3//2)
@test integrate(x^-7//2*(a+b*x)^2*(A+B*x), x) == :(-2*b*x^-1//2*(A*b+2*B*a)+2*B*b^2*x^(1/2)+-2//3*a*x^-3//2*(B*a+2*A*b)+-2//5*A*a^2*x^-5//2)
@test integrate(x^7//2*(a+b*x)^3*(A+B*x), x) == :(2//9*A*a^3*x^9//2+2//11*a^2*x^11//2*(B*a+3*A*b)+2//15*b^2*x^15//2*(A*b+3*B*a)+2//17*B*b^3*x^17//2+6//13*a*b*x^13//2*(A*b+B*a))
@test integrate(x^5//2*(a+b*x)^3*(A+B*x), x) == :(2//7*A*a^3*x^7//2+2//9*a^2*x^9//2*(B*a+3*A*b)+2//13*b^2*x^13//2*(A*b+3*B*a)+2//15*B*b^3*x^15//2+6//11*a*b*x^11//2*(A*b+B*a))
@test integrate(x^3//2*(a+b*x)^3*(A+B*x), x) == :(2//5*A*a^3*x^5//2+2//7*a^2*x^7//2*(B*a+3*A*b)+2//11*b^2*x^11//2*(A*b+3*B*a)+2//13*B*b^3*x^13//2+2//3*a*b*x^9//2*(A*b+B*a))
@test integrate(x^(1/2)*(a+b*x)^3*(A+B*x), x) == :(2//3*A*a^3*x^3//2+2//5*a^2*x^5//2*(B*a+3*A*b)+2//9*b^2*x^9//2*(A*b+3*B*a)+2//11*B*b^3*x^11//2+6//7*a*b*x^7//2*(A*b+B*a))
@test integrate(x^-1//2*(a+b*x)^3*(A+B*x), x) == :(2*A*a^3*x^(1/2)+2//3*a^2*x^3//2*(B*a+3*A*b)+2//7*b^2*x^7//2*(A*b+3*B*a)+2//9*B*b^3*x^9//2+6//5*a*b*x^5//2*(A*b+B*a))
@test integrate(x^-3//2*(a+b*x)^3*(A+B*x), x) == :(-2*A*a^3*x^-1//2+2*a^2*x^(1/2)*(B*a+3*A*b)+2//5*b^2*x^5//2*(A*b+3*B*a)+2//7*B*b^3*x^7//2+2*a*b*x^3//2*(A*b+B*a))
@test integrate(x^-5//2*(a+b*x)^3*(A+B*x), x) == :(-2*a^2*x^-1//2*(B*a+3*A*b)+-2//3*A*a^3*x^-3//2+2//3*b^2*x^3//2*(A*b+3*B*a)+2//5*B*b^3*x^5//2+6*a*b*x^(1/2)*(A*b+B*a))
@test integrate(x^-7//2*(a+b*x)^3*(A+B*x), x) == :(2*b^2*x^(1/2)*(A*b+3*B*a)+-2//3*a^2*x^-3//2*(B*a+3*A*b)+-2//5*A*a^3*x^-5//2+2//3*B*b^3*x^3//2+-6*a*b*x^-1//2*(A*b+B*a))
@test integrate(x^7//2*(a+b*x)^-1*(A+B*x), x) == :(1//7*b^-2*x^7//2*(-2*B*a+2*A*b)+2//9*B*b^-1*x^9//2+-2*a^3*b^-5*x^(1/2)*(A*b+-1*B*a)+2*a^7//2*b^-11//2*(A*b+-1*B*a)*arctan(a^-1//2*b^(1/2)*x^(1/2))+-2//5*a*b^-3*x^5//2*(A*b+-1*B*a)+2//3*a^2*b^-4*x^3//2*(A*b+-1*B*a))
@test integrate(x^5//2*(a+b*x)^-1*(A+B*x), x) == :(1//5*b^-2*x^5//2*(-2*B*a+2*A*b)+2//7*B*b^-1*x^7//2+-2*a^5//2*b^-9//2*(A*b+-1*B*a)*arctan(a^-1//2*b^(1/2)*x^(1/2))+2*a^2*b^-4*x^(1/2)*(A*b+-1*B*a)+-2//3*a*b^-3*x^3//2*(A*b+-1*B*a))
@test integrate(x^3//2*(a+b*x)^-1*(A+B*x), x) == :(1//3*b^-2*x^3//2*(-2*B*a+2*A*b)+2//5*B*b^-1*x^5//2+-2*a*b^-3*x^(1/2)*(A*b+-1*B*a)+2*a^3//2*b^-7//2*(A*b+-1*B*a)*arctan(a^-1//2*b^(1/2)*x^(1/2)))
@test integrate(x^(1/2)*(a+b*x)^-1*(A+B*x), x) == :(b^-2*x^(1/2)*(-2*B*a+2*A*b)+2//3*B*b^-1*x^3//2+-2*a^(1/2)*b^-5//2*(A*b+-1*B*a)*arctan(a^-1//2*b^(1/2)*x^(1/2)))
@test integrate(x^-1//2*(a+b*x)^-1*(A+B*x), x) == :(2*B*b^-1*x^(1/2)+a^-1//2*b^-3//2*(-2*B*a+2*A*b)*arctan(a^-1//2*b^(1/2)*x^(1/2)))
@test integrate(x^-3//2*(a+b*x)^-1*(A+B*x), x) == :(-2*A*a^-1*x^-1//2+-1*a^-3//2*b^-1//2*(-2*B*a+2*A*b)*arctan(a^-1//2*b^(1/2)*x^(1/2)))
@test integrate(x^-5//2*(a+b*x)^-1*(A+B*x), x) == :(a^-2*x^-1//2*(-2*B*a+2*A*b)+-2//3*A*a^-1*x^-3//2+2*a^-5//2*b^(1/2)*(A*b+-1*B*a)*arctan(a^-1//2*b^(1/2)*x^(1/2)))
@test integrate(x^-7//2*(a+b*x)^-1*(A+B*x), x) == :(-2//5*A*a^-1*x^-5//2+1//3*a^-2*x^-3//2*(-2*B*a+2*A*b)+-2*b*a^-3*x^-1//2*(A*b+-1*B*a)+-2*a^-7//2*b^3//2*(A*b+-1*B*a)*arctan(a^-1//2*b^(1/2)*x^(1/2)))
@test integrate(x^-9//2*(a+b*x)^-1*(A+B*x), x) == :(-2//7*A*a^-1*x^-7//2+1//5*a^-2*x^-5//2*(-2*B*a+2*A*b)+2*a^-4*b^2*x^-1//2*(A*b+-1*B*a)+2*a^-9//2*b^5//2*(A*b+-1*B*a)*arctan(a^-1//2*b^(1/2)*x^(1/2))+-2//3*b*a^-3*x^-3//2*(A*b+-1*B*a))
@test integrate(x^-11//2*(a+b*x)^-1*(A+B*x), x) == :(-2//9*A*a^-1*x^-9//2+1//7*a^-2*x^-7//2*(-2*B*a+2*A*b)+-2*a^-5*b^3*x^-1//2*(A*b+-1*B*a)+-2*a^-11//2*b^7//2*(A*b+-1*B*a)*arctan(a^-1//2*b^(1/2)*x^(1/2))+-2//5*b*a^-3*x^-5//2*(A*b+-1*B*a)+2//3*a^-4*b^2*x^-3//2*(A*b+-1*B*a))
@test integrate(x^7//2*(a+b*x)^-2*(A+B*x), x) == :(1//5*b^-3*x^5//2*(-9*B*a+7*A*b)+a^2*b^-5*x^(1/2)*(-9*B*a+7*A*b)+-1*a^5//2*b^-11//2*(-9*B*a+7*A*b)*arctan(a^-1//2*b^(1/2)*x^(1/2))+-1//3*a*b^-4*x^3//2*(-9*B*a+7*A*b)+-1//7*a^-1*b^-2*x^7//2*(-9*B*a+7*A*b)+a^-1*b^-1*x^9//2*(a+b*x)^-1*(A*b+-1*B*a))
@test integrate(x^5//2*(a+b*x)^-2*(A+B*x), x) == :(1//3*b^-3*x^3//2*(-7*B*a+5*A*b)+a^3//2*b^-9//2*(-7*B*a+5*A*b)*arctan(a^-1//2*b^(1/2)*x^(1/2))+-1*a*b^-4*x^(1/2)*(-7*B*a+5*A*b)+-1//5*a^-1*b^-2*x^5//2*(-7*B*a+5*A*b)+a^-1*b^-1*x^7//2*(a+b*x)^-1*(A*b+-1*B*a))
@test integrate(x^3//2*(a+b*x)^-2*(A+B*x), x) == :(b^-3*x^(1/2)*(-5*B*a+3*A*b)+-1*a^(1/2)*b^-7//2*(-5*B*a+3*A*b)*arctan(a^-1//2*b^(1/2)*x^(1/2))+-1//3*a^-1*b^-2*x^3//2*(-5*B*a+3*A*b)+a^-1*b^-1*x^5//2*(a+b*x)^-1*(A*b+-1*B*a))
@test integrate(x^(1/2)*(a+b*x)^-2*(A+B*x), x) == :(a^-1//2*b^-5//2*(A*b+-3*B*a)*arctan(a^-1//2*b^(1/2)*x^(1/2))+-1*a^-1*b^-2*x^(1/2)*(A*b+-3*B*a)+a^-1*b^-1*x^3//2*(a+b*x)^-1*(A*b+-1*B*a))
@test integrate(x^-1//2*(a+b*x)^-2*(A+B*x), x) == :(a^-3//2*b^-3//2*(A*b+B*a)*arctan(a^-1//2*b^(1/2)*x^(1/2))+a^-1*b^-1*x^(1/2)*(a+b*x)^-1*(A*b+-1*B*a))
@test integrate(x^-3//2*(a+b*x)^-2*(A+B*x), x) == :(-1*a^-2*b^-1*x^-1//2*(-1*B*a+3*A*b)+-1*a^-5//2*b^-1//2*(-1*B*a+3*A*b)*arctan(a^-1//2*b^(1/2)*x^(1/2))+a^-1*b^-1*x^-1//2*(a+b*x)^-1*(A*b+-1*B*a))
@test integrate(x^-5//2*(a+b*x)^-2*(A+B*x), x) == :(a^-3*x^-1//2*(-3*B*a+5*A*b)+a^-7//2*b^(1/2)*(-3*B*a+5*A*b)*arctan(a^-1//2*b^(1/2)*x^(1/2))+-1//3*a^-2*b^-1*x^-3//2*(-3*B*a+5*A*b)+a^-1*b^-1*x^-3//2*(a+b*x)^-1*(A*b+-1*B*a))
@test integrate(x^-7//2*(a+b*x)^-2*(A+B*x), x) == :(1//3*a^-3*x^-3//2*(-5*B*a+7*A*b)+-1*b*a^-4*x^-1//2*(-5*B*a+7*A*b)+-1*a^-9//2*b^3//2*(-5*B*a+7*A*b)*arctan(a^-1//2*b^(1/2)*x^(1/2))+-1//5*a^-2*b^-1*x^-5//2*(-5*B*a+7*A*b)+a^-1*b^-1*x^-5//2*(a+b*x)^-1*(A*b+-1*B*a))
@test integrate(x^-9//2*(a+b*x)^-2*(A+B*x), x) == :(1//5*a^-3*x^-5//2*(-7*B*a+9*A*b)+a^-5*b^2*x^-1//2*(-7*B*a+9*A*b)+a^-11//2*b^5//2*(-7*B*a+9*A*b)*arctan(a^-1//2*b^(1/2)*x^(1/2))+-1//3*b*a^-4*x^-3//2*(-7*B*a+9*A*b)+-1//7*a^-2*b^-1*x^-7//2*(-7*B*a+9*A*b)+a^-1*b^-1*x^-7//2*(a+b*x)^-1*(A*b+-1*B*a))
@test integrate(x^7//2*(a+b*x)^-3*(A+B*x), x) == :(1//12*b^-4*x^3//2*(-63*B*a+35*A*b)+-7//4*a*b^-5*x^(1/2)*(-9*B*a+5*A*b)+-1//20*a^-1*b^-3*x^5//2*(-63*B*a+35*A*b)+7//4*a^3//2*b^-11//2*(-9*B*a+5*A*b)*arctan(a^-1//2*b^(1/2)*x^(1/2))+(1/2)*a^-1*b^-1*x^9//2*(a+b*x)^-2*(A*b+-1*B*a)+1//4*a^-1*b^-2*x^7//2*(a+b*x)^-1*(-9*B*a+5*A*b))
@test integrate(x^5//2*(a+b*x)^-3*(A+B*x), x) == :(1//4*b^-4*x^(1/2)*(-35*B*a+15*A*b)+-5//4*a^(1/2)*b^-9//2*(-7*B*a+3*A*b)*arctan(a^-1//2*b^(1/2)*x^(1/2))+-1//12*a^-1*b^-3*x^3//2*(-35*B*a+15*A*b)+(1/2)*a^-1*b^-1*x^7//2*(a+b*x)^-2*(A*b+-1*B*a)+1//4*a^-1*b^-2*x^5//2*(a+b*x)^-1*(-7*B*a+3*A*b))
@test integrate(x^3//2*(a+b*x)^-3*(A+B*x), x) == :(1//4*a^-1*b^-3*x^(1/2)*(-3*A*b+15*B*a)+1//4*a^-1//2*b^-7//2*(-15*B*a+3*A*b)*arctan(a^-1//2*b^(1/2)*x^(1/2))+(1/2)*a^-1*b^-1*x^5//2*(a+b*x)^-2*(A*b+-1*B*a)+1//4*a^-1*b^-2*x^3//2*(a+b*x)^-1*(A*b+-5*B*a))
@test integrate(x^(1/2)*(a+b*x)^-3*(A+B*x), x) == :(1//4*a^-3//2*b^-5//2*(A*b+3*B*a)*arctan(a^-1//2*b^(1/2)*x^(1/2))+(1/2)*a^-1*b^-1*x^3//2*(a+b*x)^-2*(A*b+-1*B*a)+-1//4*a^-1*b^-2*x^(1/2)*(a+b*x)^-1*(A*b+3*B*a))
@test integrate(x^-1//2*(a+b*x)^-3*(A+B*x), x) == :(1//4*a^-5//2*b^-3//2*(B*a+3*A*b)*arctan(a^-1//2*b^(1/2)*x^(1/2))+(1/2)*a^-1*b^-1*x^(1/2)*(a+b*x)^-2*(A*b+-1*B*a)+1//4*a^-2*b^-1*x^(1/2)*(a+b*x)^-1*(B*a+3*A*b))
@test integrate(x^-3//2*(a+b*x)^-3*(A+B*x), x) == :(-1//4*a^-3*b^-1*x^-1//2*(-3*B*a+15*A*b)+-1//4*a^-7//2*b^-1//2*(-3*B*a+15*A*b)*arctan(a^-1//2*b^(1/2)*x^(1/2))+(1/2)*a^-1*b^-1*x^-1//2*(a+b*x)^-2*(A*b+-1*B*a)+1//4*a^-2*b^-1*x^-1//2*(a+b*x)^-1*(-1*B*a+5*A*b))
@test integrate(x^-5//2*(a+b*x)^-3*(A+B*x), x) == :(1//4*a^-4*x^-1//2*(-15*B*a+35*A*b)+-1//12*a^-3*b^-1*x^-3//2*(-15*B*a+35*A*b)+5//4*a^-9//2*b^(1/2)*(-3*B*a+7*A*b)*arctan(a^-1//2*b^(1/2)*x^(1/2))+(1/2)*a^-1*b^-1*x^-3//2*(a+b*x)^-2*(A*b+-1*B*a)+1//4*a^-2*b^-1*x^-3//2*(a+b*x)^-1*(-3*B*a+7*A*b))
@test integrate(x^-7//2*(a+b*x)^-3*(A+B*x), x) == :(1//12*a^-4*x^-3//2*(-35*B*a+63*A*b)+-7//4*b*a^-5*x^-1//2*(-5*B*a+9*A*b)+-7//4*a^-11//2*b^3//2*(-5*B*a+9*A*b)*arctan(a^-1//2*b^(1/2)*x^(1/2))+-1//20*a^-3*b^-1*x^-5//2*(-35*B*a+63*A*b)+(1/2)*a^-1*b^-1*x^-5//2*(a+b*x)^-2*(A*b+-1*B*a)+1//4*a^-2*b^-1*x^-5//2*(a+b*x)^-1*(-5*B*a+9*A*b))
@test integrate(x^m*(a+b*x)^4*(A+B*x), x) == :(A*a^4*x^(1+m)*(1+m)^-1+B*b^4*x^(6+m)*(6+m)^-1+a^3*x^(2+m)*(2+m)^-1*(B*a+4*A*b)+b^3*x^(5+m)*(5+m)^-1*(A*b+4*B*a)+2*a*b^2*x^(4+m)*(4+m)^-1*(2*A*b+3*B*a)+2*b*a^2*x^(3+m)*(3+m)^-1*(2*B*a+3*A*b))
@test integrate(x^m*(a+b*x)^3*(A+B*x), x) == :(A*a^3*x^(1+m)*(1+m)^-1+B*b^3*x^(5+m)*(5+m)^-1+a^2*x^(2+m)*(2+m)^-1*(B*a+3*A*b)+b^2*x^(4+m)*(4+m)^-1*(A*b+3*B*a)+3*a*b*x^(3+m)*(3+m)^-1*(A*b+B*a))
@test integrate(x^m*(a+b*x)^2*(A+B*x), x) == :(A*a^2*x^(1+m)*(1+m)^-1+B*b^2*x^(4+m)*(4+m)^-1+a*x^(2+m)*(2+m)^-1*(B*a+2*A*b)+b*x^(3+m)*(3+m)^-1*(A*b+2*B*a))
@test integrate(x^m*(A+B*x)*(a+b*x), x) == :(x^(2+m)*(2+m)^-1*(A*b+B*a)+A*a*x^(1+m)*(1+m)^-1+B*b*x^(3+m)*(3+m)^-1)
@test integrate(x^m*(a+b*x)^2*(c+d*x)^5, x) == :(a^2*c^5*x^(1+m)*(1+m)^-1+b^2*d^5*x^(8+m)*(8+m)^-1+c^3*x^(3+m)*(3+m)^-1*(b^2*c^2+10*a^2*d^2+10*a*b*c*d)+d^3*x^(6+m)*(6+m)^-1*(a^2*d^2+10*b^2*c^2+10*a*b*c*d)+a*c^4*x^(2+m)*(2+m)^-1*(2*b*c+5*a*d)+b*d^4*x^(7+m)*(7+m)^-1*(2*a*d+5*b*c)+5*c*d^2*x^(5+m)*(5+m)^-1*(a^2*d^2+2*b^2*c^2+4*a*b*c*d)+5*d*c^2*x^(4+m)*(4+m)^-1*(b^2*c^2+2*a^2*d^2+4*a*b*c*d))
@test integrate((e*x)^m*(1+a*x)^4*(2+-2*a*x)^3, x) == :(8*e^-1*(e*x)^(1+m)*(1+m)^-1+-24*a^2*e^-3*(e*x)^(3+m)*(3+m)^-1+-24*a^3*e^-4*(e*x)^(4+m)*(4+m)^-1+-8*a^6*e^-7*(e*x)^(7+m)*(7+m)^-1+-8*a^7*e^-8*(e*x)^(8+m)*(8+m)^-1+8*a*e^-2*(e*x)^(2+m)*(2+m)^-1+24*a^4*e^-5*(e*x)^(5+m)*(5+m)^-1+24*a^5*e^-6*(e*x)^(6+m)*(6+m)^-1)
@test integrate((e*x)^m*(1+a*x)^3*(2+-2*a*x)^2, x) == :(4*e^-1*(e*x)^(1+m)*(1+m)^-1+-8*a^2*e^-3*(e*x)^(3+m)*(3+m)^-1+-8*a^3*e^-4*(e*x)^(4+m)*(4+m)^-1+4*a*e^-2*(e*x)^(2+m)*(2+m)^-1+4*a^4*e^-5*(e*x)^(5+m)*(5+m)^-1+4*a^5*e^-6*(e*x)^(6+m)*(6+m)^-1)
@test integrate((e*x)^m*(1+a*x)^2*(2+-2*a*x), x) == :(2*e^-1*(e*x)^(1+m)*(1+m)^-1+-2*a^2*e^-3*(e*x)^(3+m)*(3+m)^-1+-2*a^3*e^-4*(e*x)^(4+m)*(4+m)^-1+2*a*e^-2*(e*x)^(2+m)*(2+m)^-1)
@test integrate((e*x)^m*(a+b*x)^4*(a*d+-1*b*d*x)^3, x) == :(a^7*d^3*e^-1*(e*x)^(1+m)*(1+m)^-1+-1*b^7*d^3*e^-8*(e*x)^(8+m)*(8+m)^-1+b*a^6*d^3*e^-2*(e*x)^(2+m)*(2+m)^-1+-1*a*b^6*d^3*e^-7*(e*x)^(7+m)*(7+m)^-1+-3*a^4*b^3*d^3*e^-4*(e*x)^(4+m)*(4+m)^-1+-3*a^5*b^2*d^3*e^-3*(e*x)^(3+m)*(3+m)^-1+3*a^2*b^5*d^3*e^-6*(e*x)^(6+m)*(6+m)^-1+3*a^3*b^4*d^3*e^-5*(e*x)^(5+m)*(5+m)^-1)
@test integrate((e*x)^m*(a+b*x)^3*(a*d+-1*b*d*x)^2, x) == :(a^5*d^2*e^-1*(e*x)^(1+m)*(1+m)^-1+b^5*d^2*e^-6*(e*x)^(6+m)*(6+m)^-1+a*b^4*d^2*e^-5*(e*x)^(5+m)*(5+m)^-1+b*a^4*d^2*e^-2*(e*x)^(2+m)*(2+m)^-1+-2*a^2*b^3*d^2*e^-4*(e*x)^(4+m)*(4+m)^-1+-2*a^3*b^2*d^2*e^-3*(e*x)^(3+m)*(3+m)^-1)
@test integrate((e*x)^m*(a+b*x)^2*(a*d+-1*b*d*x), x) == :(d*a^3*e^-1*(e*x)^(1+m)*(1+m)^-1+-1*d*b^3*e^-4*(e*x)^(4+m)*(4+m)^-1+b*d*a^2*e^-2*(e*x)^(2+m)*(2+m)^-1+-1*a*d*b^2*e^-3*(e*x)^(3+m)*(3+m)^-1)
@test integrate((e*x)^m*(a*c+-1*b*c*x)^4*(a+b*x), x) == :(a^5*c^4*e^-1*(e*x)^(1+m)*(1+m)^-1+b^5*c^4*e^-6*(e*x)^(6+m)*(6+m)^-1+-3*a*b^4*c^4*e^-5*(e*x)^(5+m)*(5+m)^-1+-3*b*a^4*c^4*e^-2*(e*x)^(2+m)*(2+m)^-1+2*a^2*b^3*c^4*e^-4*(e*x)^(4+m)*(4+m)^-1+2*a^3*b^2*c^4*e^-3*(e*x)^(3+m)*(3+m)^-1)
@test integrate((e*x)^m*(a*c+-1*b*c*x)^3*(a+b*x), x) == :(a^4*c^3*e^-1*(e*x)^(1+m)*(1+m)^-1+-1*b^4*c^3*e^-5*(e*x)^(5+m)*(5+m)^-1+-2*b*a^3*c^3*e^-2*(e*x)^(2+m)*(2+m)^-1+2*a*b^3*c^3*e^-4*(e*x)^(4+m)*(4+m)^-1)
@test integrate((e*x)^m*(a*c+-1*b*c*x)^2*(a+b*x), x) == :(a^3*c^2*e^-1*(e*x)^(1+m)*(1+m)^-1+b^3*c^2*e^-4*(e*x)^(4+m)*(4+m)^-1+-1*a*b^2*c^2*e^-3*(e*x)^(3+m)*(3+m)^-1+-1*b*a^2*c^2*e^-2*(e*x)^(2+m)*(2+m)^-1)
@test integrate((e*x)^m*(a+b*x)*(a*c+-1*b*c*x), x) == :(c*a^2*e^-1*(e*x)^(1+m)*(1+m)^-1+-1*c*b^2*e^-3*(e*x)^(3+m)*(3+m)^-1)
@test integrate(x^4*(a+b*x)^(1/2)*(A+B*x), x) == :(1//11*b^-6*(a+b*x)^11//2*(-10*B*a+2*A*b)+2//13*B*b^-6*(a+b*x)^13//2+-4//9*a*b^-6*(a+b*x)^9//2*(-5*B*a+2*A*b)+-2//5*a^3*b^-6*(a+b*x)^5//2*(-5*B*a+4*A*b)+2//3*a^4*b^-6*(a+b*x)^3//2*(A*b+-1*B*a)+4//7*a^2*b^-6*(a+b*x)^7//2*(-5*B*a+3*A*b))
@test integrate(x^3*(a+b*x)^(1/2)*(A+B*x), x) == :(1//9*b^-5*(a+b*x)^9//2*(-8*B*a+2*A*b)+2//11*B*b^-5*(a+b*x)^11//2+-6//7*a*b^-5*(a+b*x)^7//2*(A*b+-2*B*a)+-2//3*a^3*b^-5*(a+b*x)^3//2*(A*b+-1*B*a)+2//5*a^2*b^-5*(a+b*x)^5//2*(-4*B*a+3*A*b))
@test integrate(x^2*(a+b*x)^(1/2)*(A+B*x), x) == :(1//7*b^-4*(a+b*x)^7//2*(-6*B*a+2*A*b)+2//9*B*b^-4*(a+b*x)^9//2+-2//5*a*b^-4*(a+b*x)^5//2*(-3*B*a+2*A*b)+2//3*a^2*b^-4*(a+b*x)^3//2*(A*b+-1*B*a))
@test integrate(x*(a+b*x)^(1/2)*(A+B*x), x) == :(1//5*b^-3*(a+b*x)^5//2*(-4*B*a+2*A*b)+2//7*B*b^-3*(a+b*x)^7//2+-2//3*a*b^-3*(a+b*x)^3//2*(A*b+-1*B*a))
@test integrate((a+b*x)^(1/2)*(A+B*x), x) == :(1//3*b^-2*(a+b*x)^3//2*(-2*B*a+2*A*b)+2//5*B*b^-2*(a+b*x)^5//2)
@test integrate(x^-1*(a+b*x)^(1/2)*(A+B*x), x) == :(2*A*(a+b*x)^(1/2)+-2*A*a^(1/2)*arctanh(a^-1//2*(a+b*x)^(1/2))+2//3*B*b^-1*(a+b*x)^3//2)
@test integrate(x^-2*(a+b*x)^(1/2)*(A+B*x), x) == :(a^-1*(a+b*x)^(1/2)*(A*b+2*B*a)+-1*a^-1//2*(A*b+2*B*a)*arctanh(a^-1//2*(a+b*x)^(1/2))+-1*A*a^-1*x^-1*(a+b*x)^3//2)
@test integrate(x^-3*(a+b*x)^(1/2)*(A+B*x), x) == :(-1//2*A*a^-1*x^-2*(a+b*x)^3//2+1//4*b*a^-3//2*(A*b+-4*B*a)*arctanh(a^-1//2*(a+b*x)^(1/2))+1//4*a^-1*x^-1*(a+b*x)^(1/2)*(A*b+-4*B*a))
@test integrate(x^-4*(a+b*x)^(1/2)*(A+B*x), x) == :(-1//3*A*a^-1*x^-3*(a+b*x)^3//2+-1//8*a^-5//2*b^2*(A*b+-2*B*a)*arctanh(a^-1//2*(a+b*x)^(1/2))+1//4*a^-1*x^-2*(a+b*x)^(1/2)*(A*b+-2*B*a)+1//8*b*a^-2*x^-1*(a+b*x)^(1/2)*(A*b+-2*B*a))
@test integrate(x^-5*(a+b*x)^(1/2)*(A+B*x), x) == :(-1//4*A*a^-1*x^-4*(a+b*x)^3//2+1//24*a^-1*x^-3*(a+b*x)^(1/2)*(-8*B*a+5*A*b)+1//64*a^-7//2*b^3*(-8*B*a+5*A*b)*arctanh(a^-1//2*(a+b*x)^(1/2))+-1//64*a^-3*b^2*x^-1*(a+b*x)^(1/2)*(-8*B*a+5*A*b)+1//96*b*a^-2*x^-2*(a+b*x)^(1/2)*(-8*B*a+5*A*b))
@test integrate(x^-6*(a+b*x)^(1/2)*(A+B*x), x) == :(-1//5*A*a^-1*x^-5*(a+b*x)^3//2+-1//128*a^-9//2*b^4*(-10*B*a+7*A*b)*arctanh(a^-1//2*(a+b*x)^(1/2))+1//40*a^-1*x^-4*(a+b*x)^(1/2)*(-10*B*a+7*A*b)+-1//192*a^-3*b^2*x^-2*(a+b*x)^(1/2)*(-10*B*a+7*A*b)+1//128*a^-4*b^3*x^-1*(a+b*x)^(1/2)*(-10*B*a+7*A*b)+1//240*b*a^-2*x^-3*(a+b*x)^(1/2)*(-10*B*a+7*A*b))
@test integrate(x^4*(a+b*x)^3//2*(A+B*x), x) == :(1//13*b^-6*(a+b*x)^13//2*(-10*B*a+2*A*b)+2//15*B*b^-6*(a+b*x)^15//2+-4//11*a*b^-6*(a+b*x)^11//2*(-5*B*a+2*A*b)+-2//7*a^3*b^-6*(a+b*x)^7//2*(-5*B*a+4*A*b)+2//5*a^4*b^-6*(a+b*x)^5//2*(A*b+-1*B*a)+4//9*a^2*b^-6*(a+b*x)^9//2*(-5*B*a+3*A*b))
@test integrate(x^3*(a+b*x)^3//2*(A+B*x), x) == :(1//11*b^-5*(a+b*x)^11//2*(-8*B*a+2*A*b)+2//13*B*b^-5*(a+b*x)^13//2+-2//3*a*b^-5*(a+b*x)^9//2*(A*b+-2*B*a)+-2//5*a^3*b^-5*(a+b*x)^5//2*(A*b+-1*B*a)+2//7*a^2*b^-5*(a+b*x)^7//2*(-4*B*a+3*A*b))
@test integrate(x^2*(a+b*x)^3//2*(A+B*x), x) == :(1//9*b^-4*(a+b*x)^9//2*(-6*B*a+2*A*b)+2//11*B*b^-4*(a+b*x)^11//2+-2//7*a*b^-4*(a+b*x)^7//2*(-3*B*a+2*A*b)+2//5*a^2*b^-4*(a+b*x)^5//2*(A*b+-1*B*a))
@test integrate(x*(a+b*x)^3//2*(A+B*x), x) == :(1//7*b^-3*(a+b*x)^7//2*(-4*B*a+2*A*b)+2//9*B*b^-3*(a+b*x)^9//2+-2//5*a*b^-3*(a+b*x)^5//2*(A*b+-1*B*a))
@test integrate((a+b*x)^3//2*(A+B*x), x) == :(1//5*b^-2*(a+b*x)^5//2*(-2*B*a+2*A*b)+2//7*B*b^-2*(a+b*x)^7//2)
@test integrate(x^-1*(a+b*x)^3//2*(A+B*x), x) == :(2//3*A*(a+b*x)^3//2+-2*A*a^3//2*arctanh(a^-1//2*(a+b*x)^(1/2))+2*A*a*(a+b*x)^(1/2)+2//5*B*b^-1*(a+b*x)^5//2)
@test integrate(x^-2*(a+b*x)^3//2*(A+B*x), x) == :((a+b*x)^(1/2)*(2*B*a+3*A*b)+-1*a^(1/2)*(2*B*a+3*A*b)*arctanh(a^-1//2*(a+b*x)^(1/2))+1//3*a^-1*(a+b*x)^3//2*(2*B*a+3*A*b)+-1*A*a^-1*x^-1*(a+b*x)^5//2)
@test integrate(x^-3*(a+b*x)^3//2*(A+B*x), x) == :(-3//4*b*a^-1//2*(A*b+4*B*a)*arctanh(a^-1//2*(a+b*x)^(1/2))+-1//2*A*a^-1*x^-2*(a+b*x)^5//2+-1//4*a^-1*x^-1*(a+b*x)^3//2*(A*b+4*B*a)+3//4*b*a^-1*(a+b*x)^(1/2)*(A*b+4*B*a))
@test integrate(x^-4*(a+b*x)^3//2*(A+B*x), x) == :(-1//3*A*a^-1*x^-3*(a+b*x)^5//2+1//8*a^-3//2*b^2*(A*b+-6*B*a)*arctanh(a^-1//2*(a+b*x)^(1/2))+1//12*a^-1*x^-2*(a+b*x)^3//2*(A*b+-6*B*a)+1//8*b*a^-1*x^-1*(a+b*x)^(1/2)*(A*b+-6*B*a))
@test integrate(x^-5*(a+b*x)^3//2*(A+B*x), x) == :(-1//4*A*a^-1*x^-4*(a+b*x)^5//2+-1//64*a^-5//2*b^3*(-8*B*a+3*A*b)*arctanh(a^-1//2*(a+b*x)^(1/2))+1//24*a^-1*x^-3*(a+b*x)^3//2*(-8*B*a+3*A*b)+1//32*b*a^-1*x^-2*(a+b*x)^(1/2)*(-8*B*a+3*A*b)+1//64*a^-2*b^2*x^-1*(a+b*x)^(1/2)*(-8*B*a+3*A*b))
@test integrate(x^-6*(a+b*x)^3//2*(A+B*x), x) == :(-1//5*A*a^-1*x^-5*(a+b*x)^5//2+1//8*a^-1*x^-4*(a+b*x)^3//2*(A*b+-2*B*a)+3//128*a^-7//2*b^4*(A*b+-2*B*a)*arctanh(a^-1//2*(a+b*x)^(1/2))+-3//128*a^-3*b^3*x^-1*(a+b*x)^(1/2)*(A*b+-2*B*a)+1//16*b*a^-1*x^-3*(a+b*x)^(1/2)*(A*b+-2*B*a)+1//64*a^-2*b^2*x^-2*(a+b*x)^(1/2)*(A*b+-2*B*a))
@test integrate(x^-7*(a+b*x)^3//2*(A+B*x), x) == :(-1//6*A*a^-1*x^-6*(a+b*x)^5//2+-1//512*a^-9//2*b^5*(-12*B*a+7*A*b)*arctanh(a^-1//2*(a+b*x)^(1/2))+1//60*a^-1*x^-5*(a+b*x)^3//2*(-12*B*a+7*A*b)+-1//768*a^-3*b^3*x^-2*(a+b*x)^(1/2)*(-12*B*a+7*A*b)+1//160*b*a^-1*x^-4*(a+b*x)^(1/2)*(-12*B*a+7*A*b)+1//512*a^-4*b^4*x^-1*(a+b*x)^(1/2)*(-12*B*a+7*A*b)+1//960*a^-2*b^2*x^-3*(a+b*x)^(1/2)*(-12*B*a+7*A*b))
@test integrate(x^4*(a+b*x)^5//2*(A+B*x), x) == :(1//15*b^-6*(a+b*x)^15//2*(-10*B*a+2*A*b)+2//17*B*b^-6*(a+b*x)^17//2+-4//13*a*b^-6*(a+b*x)^13//2*(-5*B*a+2*A*b)+-2//9*a^3*b^-6*(a+b*x)^9//2*(-5*B*a+4*A*b)+2//7*a^4*b^-6*(a+b*x)^7//2*(A*b+-1*B*a)+4//11*a^2*b^-6*(a+b*x)^11//2*(-5*B*a+3*A*b))
@test integrate(x^3*(a+b*x)^5//2*(A+B*x), x) == :(1//13*b^-5*(a+b*x)^13//2*(-8*B*a+2*A*b)+2//15*B*b^-5*(a+b*x)^15//2+-6//11*a*b^-5*(a+b*x)^11//2*(A*b+-2*B*a)+-2//7*a^3*b^-5*(a+b*x)^7//2*(A*b+-1*B*a)+2//9*a^2*b^-5*(a+b*x)^9//2*(-4*B*a+3*A*b))
@test integrate(x^2*(a+b*x)^5//2*(A+B*x), x) == :(1//11*b^-4*(a+b*x)^11//2*(-6*B*a+2*A*b)+2//13*B*b^-4*(a+b*x)^13//2+-2//9*a*b^-4*(a+b*x)^9//2*(-3*B*a+2*A*b)+2//7*a^2*b^-4*(a+b*x)^7//2*(A*b+-1*B*a))
@test integrate(x*(a+b*x)^5//2*(A+B*x), x) == :(1//9*b^-3*(a+b*x)^9//2*(-4*B*a+2*A*b)+2//11*B*b^-3*(a+b*x)^11//2+-2//7*a*b^-3*(a+b*x)^7//2*(A*b+-1*B*a))
@test integrate((a+b*x)^5//2*(A+B*x), x) == :(1//7*b^-2*(a+b*x)^7//2*(-2*B*a+2*A*b)+2//9*B*b^-2*(a+b*x)^9//2)
@test integrate(x^-1*(a+b*x)^5//2*(A+B*x), x) == :(2//5*A*(a+b*x)^5//2+-2*A*a^5//2*arctanh(a^-1//2*(a+b*x)^(1/2))+2*A*a^2*(a+b*x)^(1/2)+2//3*A*a*(a+b*x)^3//2+2//7*B*b^-1*(a+b*x)^7//2)
@test integrate(x^-2*(a+b*x)^5//2*(A+B*x), x) == :(1//3*(a+b*x)^3//2*(2*B*a+5*A*b)+a*(a+b*x)^(1/2)*(2*B*a+5*A*b)+-1*a^3//2*(2*B*a+5*A*b)*arctanh(a^-1//2*(a+b*x)^(1/2))+1//5*a^-1*(a+b*x)^5//2*(2*B*a+5*A*b)+-1*A*a^-1*x^-1*(a+b*x)^7//2)
@test integrate(x^-3*(a+b*x)^5//2*(A+B*x), x) == :(5//4*b*(a+b*x)^(1/2)*(3*A*b+4*B*a)+-5//4*b*a^(1/2)*(3*A*b+4*B*a)*arctanh(a^-1//2*(a+b*x)^(1/2))+-1//2*A*a^-1*x^-2*(a+b*x)^7//2+-1//4*a^-1*x^-1*(a+b*x)^5//2*(3*A*b+4*B*a)+5//12*b*a^-1*(a+b*x)^3//2*(3*A*b+4*B*a))
@test integrate(x^-4*(a+b*x)^5//2*(A+B*x), x) == :(-5//8*a^-1//2*b^2*(A*b+6*B*a)*arctanh(a^-1//2*(a+b*x)^(1/2))+-1//3*A*a^-1*x^-3*(a+b*x)^7//2+-1//12*a^-1*x^-2*(a+b*x)^5//2*(A*b+6*B*a)+5//8*a^-1*b^2*(a+b*x)^(1/2)*(A*b+6*B*a)+-5//24*b*a^-1*x^-1*(a+b*x)^3//2*(A*b+6*B*a))
@test integrate(x^-5*(a+b*x)^5//2*(A+B*x), x) == :(-1//4*A*a^-1*x^-4*(a+b*x)^7//2+1//24*a^-1*x^-3*(a+b*x)^5//2*(A*b+-8*B*a)+5//64*a^-3//2*b^3*(A*b+-8*B*a)*arctanh(a^-1//2*(a+b*x)^(1/2))+5//64*a^-1*b^2*x^-1*(a+b*x)^(1/2)*(A*b+-8*B*a)+5//96*b*a^-1*x^-2*(a+b*x)^3//2*(A*b+-8*B*a))
@test integrate(x^-6*(a+b*x)^5//2*(A+B*x), x) == :(-1//5*A*a^-1*x^-5*(a+b*x)^7//2+-1//128*a^-5//2*b^4*(-10*B*a+3*A*b)*arctanh(a^-1//2*(a+b*x)^(1/2))+1//40*a^-1*x^-4*(a+b*x)^5//2*(-10*B*a+3*A*b)+1//48*b*a^-1*x^-3*(a+b*x)^3//2*(-10*B*a+3*A*b)+1//64*a^-1*b^2*x^-2*(a+b*x)^(1/2)*(-10*B*a+3*A*b)+1//128*a^-2*b^3*x^-1*(a+b*x)^(1/2)*(-10*B*a+3*A*b))
@test integrate(x^-7*(a+b*x)^5//2*(A+B*x), x) == :(-1//6*A*a^-1*x^-6*(a+b*x)^7//2+1//60*a^-1*x^-5*(a+b*x)^5//2*(-12*B*a+5*A*b)+1//512*a^-7//2*b^5*(-12*B*a+5*A*b)*arctanh(a^-1//2*(a+b*x)^(1/2))+-1//512*a^-3*b^4*x^-1*(a+b*x)^(1/2)*(-12*B*a+5*A*b)+1//96*b*a^-1*x^-4*(a+b*x)^3//2*(-12*B*a+5*A*b)+1//192*a^-1*b^2*x^-3*(a+b*x)^(1/2)*(-12*B*a+5*A*b)+1//768*a^-2*b^3*x^-2*(a+b*x)^(1/2)*(-12*B*a+5*A*b))
@test integrate(x^-8*(a+b*x)^5//2*(A+B*x), x) == :(-5//1024*a^-9//2*b^6*(A*b+-2*B*a)*arctanh(a^-1//2*(a+b*x)^(1/2))+-1//7*A*a^-1*x^-7*(a+b*x)^7//2+1//12*a^-1*x^-6*(a+b*x)^5//2*(A*b+-2*B*a)+-5//1536*a^-3*b^4*x^-2*(a+b*x)^(1/2)*(A*b+-2*B*a)+1//24*b*a^-1*x^-5*(a+b*x)^3//2*(A*b+-2*B*a)+1//64*a^-1*b^2*x^-4*(a+b*x)^(1/2)*(A*b+-2*B*a)+1//384*a^-2*b^3*x^-3*(a+b*x)^(1/2)*(A*b+-2*B*a)+5//1024*a^-4*b^5*x^-1*(a+b*x)^(1/2)*(A*b+-2*B*a))
@test integrate(x^4*(a+b*x)^-1//2*(A+B*x), x) == :(1//9*b^-6*(a+b*x)^9//2*(-10*B*a+2*A*b)+2//11*B*b^-6*(a+b*x)^11//2+2*a^4*b^-6*(a+b*x)^(1/2)*(A*b+-1*B*a)+-4//7*a*b^-6*(a+b*x)^7//2*(-5*B*a+2*A*b)+-2//3*a^3*b^-6*(a+b*x)^3//2*(-5*B*a+4*A*b)+4//5*a^2*b^-6*(a+b*x)^5//2*(-5*B*a+3*A*b))
@test integrate(x^3*(a+b*x)^-1//2*(A+B*x), x) == :(1//7*b^-5*(a+b*x)^7//2*(-8*B*a+2*A*b)+2//9*B*b^-5*(a+b*x)^9//2+-2*a^3*b^-5*(a+b*x)^(1/2)*(A*b+-1*B*a)+-6//5*a*b^-5*(a+b*x)^5//2*(A*b+-2*B*a)+2//3*a^2*b^-5*(a+b*x)^3//2*(-4*B*a+3*A*b))
@test integrate(x^2*(a+b*x)^-1//2*(A+B*x), x) == :(1//5*b^-4*(a+b*x)^5//2*(-6*B*a+2*A*b)+2//7*B*b^-4*(a+b*x)^7//2+2*a^2*b^-4*(a+b*x)^(1/2)*(A*b+-1*B*a)+-2//3*a*b^-4*(a+b*x)^3//2*(-3*B*a+2*A*b))
@test integrate(x*(a+b*x)^-1//2*(A+B*x), x) == :(1//3*b^-3*(a+b*x)^3//2*(-4*B*a+2*A*b)+2//5*B*b^-3*(a+b*x)^5//2+-2*a*b^-3*(a+b*x)^(1/2)*(A*b+-1*B*a))
@test integrate((a+b*x)^-1//2*(A+B*x), x) == :(b^-2*(a+b*x)^(1/2)*(-2*B*a+2*A*b)+2//3*B*b^-2*(a+b*x)^3//2)
@test integrate(x^-1*(a+b*x)^-1//2*(A+B*x), x) == :(-2*A*a^-1//2*arctanh(a^-1//2*(a+b*x)^(1/2))+2*B*b^-1*(a+b*x)^(1/2))
@test integrate(x^-2*(a+b*x)^-1//2*(A+B*x), x) == :(a^-3//2*(A*b+-2*B*a)*arctanh(a^-1//2*(a+b*x)^(1/2))+-1*A*a^-1*x^-1*(a+b*x)^(1/2))
@test integrate(x^-3*(a+b*x)^-1//2*(A+B*x), x) == :(-1//2*A*a^-1*x^-2*(a+b*x)^(1/2)+-1//4*b*a^-5//2*(-4*B*a+3*A*b)*arctanh(a^-1//2*(a+b*x)^(1/2))+1//4*a^-2*x^-1*(a+b*x)^(1/2)*(-4*B*a+3*A*b))
@test integrate(x^-4*(a+b*x)^-1//2*(A+B*x), x) == :(-1//3*A*a^-1*x^-3*(a+b*x)^(1/2)+1//8*a^-7//2*b^2*(-6*B*a+5*A*b)*arctanh(a^-1//2*(a+b*x)^(1/2))+1//12*a^-2*x^-2*(a+b*x)^(1/2)*(-6*B*a+5*A*b)+-1//8*b*a^-3*x^-1*(a+b*x)^(1/2)*(-6*B*a+5*A*b))
@test integrate(x^-5*(a+b*x)^-1//2*(A+B*x), x) == :(-5//64*a^-9//2*b^3*(-8*B*a+7*A*b)*arctanh(a^-1//2*(a+b*x)^(1/2))+-1//4*A*a^-1*x^-4*(a+b*x)^(1/2)+1//24*a^-2*x^-3*(a+b*x)^(1/2)*(-8*B*a+7*A*b)+-5//96*b*a^-3*x^-2*(a+b*x)^(1/2)*(-8*B*a+7*A*b)+5//64*a^-4*b^2*x^-1*(a+b*x)^(1/2)*(-8*B*a+7*A*b))
@test integrate(x^-6*(a+b*x)^-1//2*(A+B*x), x) == :(-1//5*A*a^-1*x^-5*(a+b*x)^(1/2)+1//40*a^-2*x^-4*(a+b*x)^(1/2)*(-10*B*a+9*A*b)+7//128*a^-11//2*b^4*(-10*B*a+9*A*b)*arctanh(a^-1//2*(a+b*x)^(1/2))+-7//128*a^-5*b^3*x^-1*(a+b*x)^(1/2)*(-10*B*a+9*A*b)+-7//240*b*a^-3*x^-3*(a+b*x)^(1/2)*(-10*B*a+9*A*b)+7//192*a^-4*b^2*x^-2*(a+b*x)^(1/2)*(-10*B*a+9*A*b))
@test integrate(x^4*(a+b*x)^-3//2*(A+B*x), x) == :(1//7*b^-6*(a+b*x)^7//2*(-10*B*a+2*A*b)+2//9*B*b^-6*(a+b*x)^9//2+-2*a^3*b^-6*(a+b*x)^(1/2)*(-5*B*a+4*A*b)+-2*a^4*b^-6*(a+b*x)^-1//2*(A*b+-1*B*a)+-4//5*a*b^-6*(a+b*x)^5//2*(-5*B*a+2*A*b)+4//3*a^2*b^-6*(a+b*x)^3//2*(-5*B*a+3*A*b))
@test integrate(x^3*(a+b*x)^-3//2*(A+B*x), x) == :(1//5*b^-5*(a+b*x)^5//2*(-8*B*a+2*A*b)+2//7*B*b^-5*(a+b*x)^7//2+-2*a*b^-5*(a+b*x)^3//2*(A*b+-2*B*a)+2*a^2*b^-5*(a+b*x)^(1/2)*(-4*B*a+3*A*b)+2*a^3*b^-5*(a+b*x)^-1//2*(A*b+-1*B*a))
@test integrate(x^2*(a+b*x)^-3//2*(A+B*x), x) == :(1//3*b^-4*(a+b*x)^3//2*(-6*B*a+2*A*b)+2//5*B*b^-4*(a+b*x)^5//2+-2*a*b^-4*(a+b*x)^(1/2)*(-3*B*a+2*A*b)+-2*a^2*b^-4*(a+b*x)^-1//2*(A*b+-1*B*a))
@test integrate(x*(a+b*x)^-3//2*(A+B*x), x) == :(b^-3*(a+b*x)^(1/2)*(-4*B*a+2*A*b)+2//3*B*b^-3*(a+b*x)^3//2+2*a*b^-3*(a+b*x)^-1//2*(A*b+-1*B*a))
@test integrate((a+b*x)^-3//2*(A+B*x), x) == :(b^-2*(a+b*x)^-1//2*(-2*A*b+2*B*a)+2*B*b^-2*(a+b*x)^(1/2))
@test integrate(x^-1*(a+b*x)^-3//2*(A+B*x), x) == :(-2*A*a^-3//2*arctanh(a^-1//2*(a+b*x)^(1/2))+a^-1*b^-1*(a+b*x)^-1//2*(-2*B*a+2*A*b))
@test integrate(x^-2*(a+b*x)^-3//2*(A+B*x), x) == :(a^-5//2*(-2*B*a+3*A*b)*arctanh(a^-1//2*(a+b*x)^(1/2))+-1*a^-2*(a+b*x)^-1//2*(-2*B*a+3*A*b)+-1*A*a^-1*x^-1*(a+b*x)^-1//2)
@test integrate(x^-3*(a+b*x)^-3//2*(A+B*x), x) == :(-3//4*b*a^-7//2*(-4*B*a+5*A*b)*arctanh(a^-1//2*(a+b*x)^(1/2))+-1//2*A*a^-1*x^-2*(a+b*x)^-1//2+1//4*a^-2*x^-1*(a+b*x)^-1//2*(-4*B*a+5*A*b)+3//4*b*a^-3*(a+b*x)^-1//2*(-4*B*a+5*A*b))
@test integrate(x^-4*(a+b*x)^-3//2*(A+B*x), x) == :(-5//8*a^-4*b^2*(a+b*x)^-1//2*(-6*B*a+7*A*b)+-1//3*A*a^-1*x^-3*(a+b*x)^-1//2+1//12*a^-2*x^-2*(a+b*x)^-1//2*(-6*B*a+7*A*b)+5//8*a^-9//2*b^2*(-6*B*a+7*A*b)*arctanh(a^-1//2*(a+b*x)^(1/2))+-5//24*b*a^-3*x^-1*(a+b*x)^-1//2*(-6*B*a+7*A*b))
@test integrate(x^-5*(a+b*x)^-3//2*(A+B*x), x) == :(-35//64*a^-11//2*b^3*(-8*B*a+9*A*b)*arctanh(a^-1//2*(a+b*x)^(1/2))+-1//4*A*a^-1*x^-4*(a+b*x)^-1//2+1//24*a^-2*x^-3*(a+b*x)^-1//2*(-8*B*a+9*A*b)+35//64*a^-5*b^3*(a+b*x)^-1//2*(-8*B*a+9*A*b)+-7//96*b*a^-3*x^-2*(a+b*x)^-1//2*(-8*B*a+9*A*b)+35//192*a^-4*b^2*x^-1*(a+b*x)^-1//2*(-8*B*a+9*A*b))
@test integrate(x^4*(a+b*x)^-5//2*(A+B*x), x) == :(1//5*b^-6*(a+b*x)^5//2*(-10*B*a+2*A*b)+2//7*B*b^-6*(a+b*x)^7//2+2*a^3*b^-6*(a+b*x)^-1//2*(-5*B*a+4*A*b)+4*a^2*b^-6*(a+b*x)^(1/2)*(-5*B*a+3*A*b)+-4//3*a*b^-6*(a+b*x)^3//2*(-5*B*a+2*A*b)+-2//3*a^4*b^-6*(a+b*x)^-3//2*(A*b+-1*B*a))
@test integrate(x^3*(a+b*x)^-5//2*(A+B*x), x) == :(1//3*b^-5*(a+b*x)^3//2*(-8*B*a+2*A*b)+2//5*B*b^-5*(a+b*x)^5//2+-6*a*b^-5*(a+b*x)^(1/2)*(A*b+-2*B*a)+-2*a^2*b^-5*(a+b*x)^-1//2*(-4*B*a+3*A*b)+2//3*a^3*b^-5*(a+b*x)^-3//2*(A*b+-1*B*a))
@test integrate(x^2*(a+b*x)^-5//2*(A+B*x), x) == :(b^-4*(a+b*x)^(1/2)*(-6*B*a+2*A*b)+2//3*B*b^-4*(a+b*x)^3//2+2*a*b^-4*(a+b*x)^-1//2*(-3*B*a+2*A*b)+-2//3*a^2*b^-4*(a+b*x)^-3//2*(A*b+-1*B*a))
@test integrate(x*(a+b*x)^-5//2*(A+B*x), x) == :(-1*b^-3*(a+b*x)^-1//2*(-4*B*a+2*A*b)+2*B*b^-3*(a+b*x)^(1/2)+2//3*a*b^-3*(a+b*x)^-3//2*(A*b+-1*B*a))
@test integrate((a+b*x)^-5//2*(A+B*x), x) == :(-2*B*b^-2*(a+b*x)^-1//2+1//3*b^-2*(a+b*x)^-3//2*(-2*A*b+2*B*a))
@test integrate(x^-1*(a+b*x)^-5//2*(A+B*x), x) == :(-2*A*a^-5//2*arctanh(a^-1//2*(a+b*x)^(1/2))+2*A*a^-2*(a+b*x)^-1//2+1//3*a^-1*b^-1*(a+b*x)^-3//2*(-2*B*a+2*A*b))
@test integrate(x^-2*(a+b*x)^-5//2*(A+B*x), x) == :(a^-7//2*(-2*B*a+5*A*b)*arctanh(a^-1//2*(a+b*x)^(1/2))+-1*a^-3*(a+b*x)^-1//2*(-2*B*a+5*A*b)+1//3*a^-2*(a+b*x)^-3//2*(-5*A*b+2*B*a)+-1*A*a^-1*x^-1*(a+b*x)^-3//2)
@test integrate(x^-3*(a+b*x)^-5//2*(A+B*x), x) == :(-5//4*b*a^-9//2*(-4*B*a+7*A*b)*arctanh(a^-1//2*(a+b*x)^(1/2))+-1//2*A*a^-1*x^-2*(a+b*x)^-3//2+1//4*a^-2*x^-1*(a+b*x)^-3//2*(-4*B*a+7*A*b)+5//4*b*a^-4*(a+b*x)^-1//2*(-4*B*a+7*A*b)+5//12*b*a^-3*(a+b*x)^-3//2*(-4*B*a+7*A*b))
@test integrate(x^-4*(a+b*x)^-5//2*(A+B*x), x) == :(-35//8*a^-5*b^2*(a+b*x)^-1//2*(-2*B*a+3*A*b)+-35//24*a^-4*b^2*(a+b*x)^-3//2*(-2*B*a+3*A*b)+-1//3*A*a^-1*x^-3*(a+b*x)^-3//2+1//4*a^-2*x^-2*(a+b*x)^-3//2*(-2*B*a+3*A*b)+35//8*a^-11//2*b^2*(-2*B*a+3*A*b)*arctanh(a^-1//2*(a+b*x)^(1/2))+-7//8*b*a^-3*x^-1*(a+b*x)^-3//2*(-2*B*a+3*A*b))
@test integrate(x^-5*(a+b*x)^-5//2*(A+B*x), x) == :(-105//64*a^-13//2*b^3*(-8*B*a+11*A*b)*arctanh(a^-1//2*(a+b*x)^(1/2))+-1//4*A*a^-1*x^-4*(a+b*x)^-3//2+1//24*a^-2*x^-3*(a+b*x)^-3//2*(-8*B*a+11*A*b)+35//64*a^-5*b^3*(a+b*x)^-3//2*(-8*B*a+11*A*b)+105//64*a^-6*b^3*(a+b*x)^-1//2*(-8*B*a+11*A*b)+-3//32*b*a^-3*x^-2*(a+b*x)^-3//2*(-8*B*a+11*A*b)+21//64*a^-4*b^2*x^-1*(a+b*x)^-3//2*(-8*B*a+11*A*b))
@test integrate(x^-2*(a+b*x)^2*(c+d*x)^-1//2, x) == :(2*b^2*d^-1*(c+d*x)^(1/2)+-1*a*c^-3//2*(-1*a*d+4*b*c)*arctanh(c^-1//2*(c+d*x)^(1/2))+-1*a^2*c^-1*x^-1*(c+d*x)^(1/2))
@test integrate(x^3*(a+b*x)^-1*(c+d*x)^5//2, x) == :(-2//5*a^3*b^-4*(c+d*x)^5//2+2//11*b^-1*d^-3*(c+d*x)^11//2+-2*a^3*b^-6*(c+d*x)^(1/2)*(b*c+-1*a*d)^2+2*a^3*b^-13//2*(b*c+-1*a*d)^5//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+-2//3*a^3*b^-5*(c+d*x)^3//2*(b*c+-1*a*d)+-1//9*b^-2*d^-3*(c+d*x)^9//2*(2*a*d+4*b*c)+1//7*b^-3*d^-3*(c+d*x)^7//2*(2*a^2*d^2+2*b^2*c^2+2*a*b*c*d))
@test integrate(x^2*(a+b*x)^-1*(c+d*x)^5//2, x) == :(2//5*a^2*b^-3*(c+d*x)^5//2+2//9*b^-1*d^-2*(c+d*x)^9//2+-2*a^2*b^-11//2*(b*c+-1*a*d)^5//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+2*a^2*b^-5*(c+d*x)^(1/2)*(b*c+-1*a*d)^2+-1//7*b^-2*d^-2*(c+d*x)^7//2*(2*a*d+2*b*c)+2//3*a^2*b^-4*(c+d*x)^3//2*(b*c+-1*a*d))
@test integrate(x*(a+b*x)^-1*(c+d*x)^5//2, x) == :(-2//5*a*b^-2*(c+d*x)^5//2+2//7*b^-1*d^-1*(c+d*x)^7//2+-2*a*b^-4*(c+d*x)^(1/2)*(b*c+-1*a*d)^2+2*a*b^-9//2*(b*c+-1*a*d)^5//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+-2//3*a*b^-3*(c+d*x)^3//2*(b*c+-1*a*d))
@test integrate((a+b*x)^-1*(c+d*x)^5//2, x) == :(2//5*b^-1*(c+d*x)^5//2+-2*b^-7//2*(b*c+-1*a*d)^5//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+2*b^-3*(c+d*x)^(1/2)*(b*c+-1*a*d)^2+1//3*b^-2*(c+d*x)^3//2*(-2*a*d+2*b*c))
@test integrate(x^-1*(a+b*x)^-1*(c+d*x)^5//2, x) == :(-2*a^-1*c^5//2*arctanh(c^-1//2*(c+d*x)^(1/2))+2//3*d*b^-1*(c+d*x)^3//2+2*d*b^-2*(c+d*x)^(1/2)*(-1*a*d+2*b*c)+2*a^-1*b^-5//2*(b*c+-1*a*d)^5//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-2*(a+b*x)^-1*(c+d*x)^5//2, x) == :(a^-2*c^3//2*(-5*a*d+2*b*c)*arctanh(c^-1//2*(c+d*x)^(1/2))+-1*c*a^-1*x^-1*(c+d*x)^3//2+-2*a^-2*b^-3//2*(b*c+-1*a*d)^5//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+d*a^-1*b^-1*(c+d*x)^(1/2)*(b*c+2*a*d))
@test integrate(x^-3*(a+b*x)^-1*(c+d*x)^5//2, x) == :(2*a^-3*b^-1//2*(b*c+-1*a*d)^5//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//2*c*a^-1*x^-2*(c+d*x)^3//2+-1//4*a^-3*c^(1/2)*(8*b^2*c^2+15*a^2*d^2+-20*a*b*c*d)*arctanh(c^-1//2*(c+d*x)^(1/2))+1//4*c*a^-2*x^-1*(c+d*x)^(1/2)*(-7*a*d+4*b*c))
@test integrate(x^-4*(a+b*x)^-1*(c+d*x)^5//2, x) == :(-2*a^-4*b^(1/2)*(b*c+-1*a*d)^5//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//3*c*a^-1*x^-3*(c+d*x)^3//2+-1//8*a^-3*x^-1*(c+d*x)^(1/2)*(8*b^2*c^2+11*a^2*d^2+-18*a*b*c*d)+1//8*a^-4*c^-1//2*(-5*a^3*d^3+16*b^3*c^3+-40*a*d*b^2*c^2+30*b*c*a^2*d^2)*arctanh(c^-1//2*(c+d*x)^(1/2))+1//4*c*a^-2*x^-2*(c+d*x)^(1/2)*(-3*a*d+2*b*c))
@test integrate(x^-1//3*(c+d*x)^-1//2*(4c+d*x)^-1, x) == :(-1//2*2^1//3*c^-5//6*d^-2//3*arctanh(c^1//6*(c+d*x)^-1//2*(c^1//3+-1*2^1//3*d^1//3*x^1//3))+1//6*2^1//3*c^-5//6*d^-2//3*arctanh(c^-1//2*(c+d*x)^(1/2))+-1//6*2^1//3*3^(1/2)*c^-5//6*d^-2//3*arctan(3^(1/2)*c^1//6*(c+d*x)^-1//2*(c^1//3+2^1//3*d^1//3*x^1//3))+1//6*2^1//3*3^(1/2)*c^-5//6*d^-2//3*arctan(1//3*3^(1/2)*c^-1//2*(c+d*x)^(1/2)))
@test integrate(x^-1//3*(c+d*x)^-1//2*(8c+-1*d*x)^-1, x) == :(-1//6*c^-5//6*d^-2//3*arctanh(1//3*c^-1//2*(c+d*x)^(1/2))+1//6*c^-5//6*d^-2//3*arctanh(1//3*c^-1//6*(c+d*x)^-1//2*(c^1//3+d^1//3*x^1//3)^2)+-1//6*3^(1/2)*c^-5//6*d^-2//3*arctan(3^(1/2)*c^1//6*(c+d*x)^-1//2*(c^1//3+d^1//3*x^1//3)))
@test integrate(x^-2*(a+b*x)^-2*(c+d*x)^(1/2), x) == :(a^-3*c^-1//2*(-1*a*d+4*b*c)*arctanh(c^-1//2*(c+d*x)^(1/2))+-1*a^-1*x^-1*(a+b*x)^-1*(c+d*x)^(1/2)+-2*b*a^-2*(a+b*x)^-1*(c+d*x)^(1/2)+-1*a^-3*b^(1/2)*(b*c+-1*a*d)^-1//2*(-3*a*d+4*b*c)*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-1*(a+b*x)^-2*(c+d*x)^3//2, x) == :(-2*a^-2*c^3//2*arctanh(c^-1//2*(c+d*x)^(1/2))+a^-1*b^-1*(a+b*x)^-1*(c+d*x)^(1/2)*(b*c+-1*a*d)+a^-2*b^-3//2*(b*c+-1*a*d)^(1/2)*(a*d+2*b*c)*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-2*(a+b*x)^-2*(c+d*x)^3//2, x) == :(a^-3*c^(1/2)*(-3*a*d+4*b*c)*arctanh(c^-1//2*(c+d*x)^(1/2))+-1*a^-2*(a+b*x)^-1*(c+d*x)^(1/2)*(-1*a*d+2*b*c)+-1*c*a^-1*x^-1*(a+b*x)^-1*(c+d*x)^(1/2)+-1*a^-3*b^-1//2*(b*c+-1*a*d)^(1/2)*(-1*a*d+4*b*c)*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^3*(a+b*x)^-2*(c+d*x)^5//2, x) == :(11//9*b^-2*x^2*(c+d*x)^5//2+-1*b^-1*x^3*(a+b*x)^-1*(c+d*x)^5//2+-1//315*b^-4*d^-2*(c+d*x)^5//2*(-693*a^2*d^2+20*b^2*c^2+-5*b*d*x*(-99*a*d+10*b*c)+180*a*b*c*d)+1//3*a^2*b^-5*(c+d*x)^3//2*(-11*a*d+6*b*c)+a^2*b^-6*(c+d*x)^(1/2)*(b*c+-1*a*d)*(-11*a*d+6*b*c)+-1*a^2*b^-13//2*(b*c+-1*a*d)^3//2*(-11*a*d+6*b*c)*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^2*(a+b*x)^-2*(c+d*x)^5//2, x) == :(2//7*b^-2*d^-1*(c+d*x)^7//2+-1//3*a*b^-4*(c+d*x)^3//2*(-9*a*d+4*b*c)+a*b^-11//2*(b*c+-1*a*d)^3//2*(-9*a*d+4*b*c)*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+-1*a*b^-5*(c+d*x)^(1/2)*(b*c+-1*a*d)*(-9*a*d+4*b*c)+-1*a^2*b^-2*(a+b*x)^-1*(c+d*x)^7//2*(b*c+-1*a*d)^-1+-1//5*a*b^-3*(c+d*x)^5//2*(b*c+-1*a*d)^-1*(-9*a*d+4*b*c))
@test integrate(x*(a+b*x)^-2*(c+d*x)^5//2, x) == :(1//3*b^-3*(c+d*x)^3//2*(-7*a*d+2*b*c)+b^-4*(c+d*x)^(1/2)*(b*c+-1*a*d)*(-7*a*d+2*b*c)+-1*b^-9//2*(b*c+-1*a*d)^3//2*(-7*a*d+2*b*c)*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+1//5*b^-2*(c+d*x)^5//2*(b*c+-1*a*d)^-1*(-7*a*d+2*b*c)+a*b^-1*(a+b*x)^-1*(c+d*x)^7//2*(b*c+-1*a*d)^-1)
@test integrate((a+b*x)^-2*(c+d*x)^5//2, x) == :(-1*b^-1*(a+b*x)^-1*(c+d*x)^5//2+5//3*d*b^-2*(c+d*x)^3//2+-5*d*b^-7//2*(b*c+-1*a*d)^3//2*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+5*d*b^-3*(c+d*x)^(1/2)*(b*c+-1*a*d))
@test integrate(x^-1*(a+b*x)^-2*(c+d*x)^5//2, x) == :(-2*a^-2*c^5//2*arctanh(c^-1//2*(c+d*x)^(1/2))+a^-1*b^-1*(a+b*x)^-1*(c+d*x)^3//2*(b*c+-1*a*d)+a^-2*b^-5//2*(b*c+-1*a*d)^3//2*(2*b*c+3*a*d)*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+-1*d*a^-1*b^-2*(c+d*x)^(1/2)*(b*c+-3*a*d))
@test integrate(x^-3*(a+b*x)^-2*(c+d*x)^5//2, x) == :(-1//4*a^-4*c^(1/2)*(15*a^2*d^2+24*b^2*c^2+-40*a*b*c*d)*arctanh(c^-1//2*(c+d*x)^(1/2))+1//4*a^-3*(a+b*x)^-1*(c+d*x)^(1/2)*(4*a^2*d^2+12*b^2*c^2+-17*a*b*c*d)+a^-4*b^-1//2*(b*c+-1*a*d)^3//2*(-1*a*d+6*b*c)*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//2*c*a^-1*x^-2*(a+b*x)^-1*(c+d*x)^3//2+1//4*c*a^-2*x^-1*(a+b*x)^-1*(c+d*x)^(1/2)*(-7*a*d+6*b*c))
@test integrate(x^-4*(a+b*x)^-2*(c+d*x)^5//2, x) == :(1//8*a^-5*c^-1//2*(-5*a^3*d^3+64*b^3*c^3+-120*a*d*b^2*c^2+60*b*c*a^2*d^2)*arctanh(c^-1//2*(c+d*x)^(1/2))+-1*a^-5*b^(1/2)*(b*c+-1*a*d)^3//2*(-3*a*d+8*b*c)*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//3*c*a^-1*x^-3*(a+b*x)^-1*(c+d*x)^3//2+-1//8*b*a^-4*(a+b*x)^-1*(c+d*x)^(1/2)*(19*a^2*d^2+32*b^2*c^2+-52*a*b*c*d)+-1//24*a^-3*x^-1*(a+b*x)^-1*(c+d*x)^(1/2)*(33*a^2*d^2+48*b^2*c^2+-82*a*b*c*d)+1//12*c*a^-2*x^-2*(a+b*x)^-1*(c+d*x)^(1/2)*(-9*a*d+8*b*c))
@test integrate(x^-2*(a+b*x)^-2*(c+d*x)^-1//2, x) == :(a^-3*c^-3//2*(a*d+4*b*c)*arctanh(c^-1//2*(c+d*x)^(1/2))+-1*a^-1*c^-1*x^-1*(a+b*x)^-1*(c+d*x)^(1/2)+-1*a^-3*b^3//2*(b*c+-1*a*d)^-3//2*(-5*a*d+4*b*c)*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+-1*b*a^-2*c^-1*(a+b*x)^-1*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1*(-1*a*d+2*b*c))
@test integrate(x^-2*(a+b*x)^-2*(c+d*x)^-3//2, x) == :(a^-3*c^-5//2*(3*a*d+4*b*c)*arctanh(c^-1//2*(c+d*x)^(1/2))+-1*a^-1*c^-1*x^-1*(a+b*x)^-1*(c+d*x)^-1//2+-1*a^-3*b^5//2*(b*c+-1*a*d)^-5//2*(-7*a*d+4*b*c)*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+-1*d*a^-2*c^-2*(c+d*x)^-1//2*(b*c+-1*a*d)^-2*(2*b^2*c^2+3*a^2*d^2+-2*a*b*c*d)+-1*b*a^-2*c^-1*(a+b*x)^-1*(c+d*x)^-1//2*(b*c+-1*a*d)^-1*(-1*a*d+2*b*c))
@test integrate(x^-2*(a+b*x)^-2*(c+d*x)^-5//2, x) == :(a^-3*c^-7//2*(4*b*c+5*a*d)*arctanh(c^-1//2*(c+d*x)^(1/2))+-1*a^-1*c^-1*x^-1*(a+b*x)^-1*(c+d*x)^-3//2+-1*a^-3*b^7//2*(b*c+-1*a*d)^-7//2*(-9*a*d+4*b*c)*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//3*d*a^-2*c^-2*(c+d*x)^-3//2*(b*c+-1*a*d)^-2*(5*a^2*d^2+6*b^2*c^2+-6*a*b*c*d)+-1*b*a^-2*c^-1*(a+b*x)^-1*(c+d*x)^-3//2*(b*c+-1*a*d)^-1*(-1*a*d+2*b*c)+-1*d*a^-2*c^-3*(c+d*x)^-1//2*(b*c+-1*a*d)^-3*(-1*a*d+2*b*c)*(b^2*c^2+5*a^2*d^2+-1*a*b*c*d))
@test integrate(x^5//2*(a+b*x)^(1/2)*(A+B*x), x) == :(-1//128*a^4*b^-9//2*(-7*B*a+10*A*b)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+1//5*B*b^-1*x^7//2*(a+b*x)^3//2+1//40*b^-1*x^7//2*(a+b*x)^(1/2)*(-7*B*a+10*A*b)+-1//192*a^2*b^-3*x^3//2*(a+b*x)^(1/2)*(-7*B*a+10*A*b)+1//128*a^3*b^-4*x^(1/2)*(a+b*x)^(1/2)*(-7*B*a+10*A*b)+1//240*a*b^-2*x^5//2*(a+b*x)^(1/2)*(-7*B*a+10*A*b))
@test integrate(x^3//2*(a+b*x)^(1/2)*(A+B*x), x) == :(1//4*B*b^-1*x^5//2*(a+b*x)^3//2+1//24*b^-1*x^5//2*(a+b*x)^(1/2)*(-5*B*a+8*A*b)+1//64*a^3*b^-7//2*(-5*B*a+8*A*b)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+-1//64*a^2*b^-3*x^(1/2)*(a+b*x)^(1/2)*(-5*B*a+8*A*b)+1//96*a*b^-2*x^3//2*(a+b*x)^(1/2)*(-5*B*a+8*A*b))
@test integrate(x^(1/2)*(a+b*x)^(1/2)*(A+B*x), x) == :(-1//8*a^2*b^-5//2*(-1*B*a+2*A*b)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+1//3*B*b^-1*x^3//2*(a+b*x)^3//2+1//4*b^-1*x^3//2*(a+b*x)^(1/2)*(-1*B*a+2*A*b)+1//8*a*b^-2*x^(1/2)*(a+b*x)^(1/2)*(-1*B*a+2*A*b))
@test integrate(x^-1//2*(a+b*x)^(1/2)*(A+B*x), x) == :((1/2)*B*b^-1*x^(1/2)*(a+b*x)^3//2+1//4*a*b^-3//2*(-1*B*a+4*A*b)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+1//4*b^-1*x^(1/2)*(a+b*x)^(1/2)*(-1*B*a+4*A*b))
@test integrate(x^-3//2*(a+b*x)^(1/2)*(A+B*x), x) == :(b^-1//2*(B*a+2*A*b)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+a^-1*x^(1/2)*(a+b*x)^(1/2)*(B*a+2*A*b)+-2*A*a^-1*x^-1//2*(a+b*x)^3//2)
@test integrate(x^-5//2*(a+b*x)^(1/2)*(A+B*x), x) == :(-2*B*x^-1//2*(a+b*x)^(1/2)+2*B*b^(1/2)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+-2//3*A*a^-1*x^-3//2*(a+b*x)^3//2)
@test integrate(x^-7//2*(a+b*x)^(1/2)*(A+B*x), x) == :(-2//5*A*a^-1*x^-5//2*(a+b*x)^3//2+1//15*a^-2*x^-3//2*(a+b*x)^3//2*(-10*B*a+4*A*b))
@test integrate(x^-9//2*(a+b*x)^(1/2)*(A+B*x), x) == :(-2//7*A*a^-1*x^-7//2*(a+b*x)^3//2+1//35*a^-2*x^-5//2*(a+b*x)^3//2*(-14*B*a+8*A*b)+-4//105*b*a^-3*x^-3//2*(a+b*x)^3//2*(-7*B*a+4*A*b))
@test integrate(x^-11//2*(a+b*x)^(1/2)*(A+B*x), x) == :(-2//9*A*a^-1*x^-9//2*(a+b*x)^3//2+1//21*a^-2*x^-7//2*(a+b*x)^3//2*(-6*B*a+4*A*b)+-8//105*b*a^-3*x^-5//2*(a+b*x)^3//2*(-3*B*a+2*A*b)+16//315*a^-4*b^2*x^-3//2*(a+b*x)^3//2*(-3*B*a+2*A*b))
@test integrate(x^-13//2*(a+b*x)^(1/2)*(A+B*x), x) == :(-2//11*A*a^-1*x^-11//2*(a+b*x)^3//2+1//99*a^-2*x^-9//2*(a+b*x)^3//2*(-22*B*a+16*A*b)+-32//3465*a^-5*b^3*x^-3//2*(a+b*x)^3//2*(-11*B*a+8*A*b)+-4//231*b*a^-3*x^-7//2*(a+b*x)^3//2*(-11*B*a+8*A*b)+16//1155*a^-4*b^2*x^-5//2*(a+b*x)^3//2*(-11*B*a+8*A*b))
@test integrate(x^-15//2*(a+b*x)^(1/2)*(A+B*x), x) == :(-2//13*A*a^-1*x^-13//2*(a+b*x)^3//2+1//143*a^-2*x^-11//2*(a+b*x)^3//2*(-26*B*a+20*A*b)+-128//15015*a^-5*b^3*x^-5//2*(a+b*x)^3//2*(-13*B*a+10*A*b)+-16//1287*b*a^-3*x^-9//2*(a+b*x)^3//2*(-13*B*a+10*A*b)+32//3003*a^-4*b^2*x^-7//2*(a+b*x)^3//2*(-13*B*a+10*A*b)+256//45045*a^-6*b^4*x^-3//2*(a+b*x)^3//2*(-13*B*a+10*A*b))
@test integrate(x^5//2*(a+b*x)^3//2*(A+B*x), x) == :(-1//512*a^5*b^-9//2*(-7*B*a+12*A*b)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+1//6*B*b^-1*x^7//2*(a+b*x)^5//2+1//60*b^-1*x^7//2*(a+b*x)^3//2*(-7*B*a+12*A*b)+-1//768*a^3*b^-3*x^3//2*(a+b*x)^(1/2)*(-7*B*a+12*A*b)+1//160*a*b^-1*x^7//2*(a+b*x)^(1/2)*(-7*B*a+12*A*b)+1//512*a^4*b^-4*x^(1/2)*(a+b*x)^(1/2)*(-7*B*a+12*A*b)+1//960*a^2*b^-2*x^5//2*(a+b*x)^(1/2)*(-7*B*a+12*A*b))
@test integrate(x^3//2*(a+b*x)^3//2*(A+B*x), x) == :(1//5*B*b^-1*x^5//2*(a+b*x)^5//2+1//8*b^-1*x^5//2*(a+b*x)^3//2*(-1*B*a+2*A*b)+3//128*a^4*b^-7//2*(-1*B*a+2*A*b)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+-3//128*a^3*b^-3*x^(1/2)*(a+b*x)^(1/2)*(-1*B*a+2*A*b)+1//16*a*b^-1*x^5//2*(a+b*x)^(1/2)*(-1*B*a+2*A*b)+1//64*a^2*b^-2*x^3//2*(a+b*x)^(1/2)*(-1*B*a+2*A*b))
@test integrate(x^(1/2)*(a+b*x)^3//2*(A+B*x), x) == :(-1//64*a^3*b^-5//2*(-3*B*a+8*A*b)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+1//4*B*b^-1*x^3//2*(a+b*x)^5//2+1//24*b^-1*x^3//2*(a+b*x)^3//2*(-3*B*a+8*A*b)+1//32*a*b^-1*x^3//2*(a+b*x)^(1/2)*(-3*B*a+8*A*b)+1//64*a^2*b^-2*x^(1/2)*(a+b*x)^(1/2)*(-3*B*a+8*A*b))
@test integrate(x^-1//2*(a+b*x)^3//2*(A+B*x), x) == :(1//3*B*b^-1*x^(1/2)*(a+b*x)^5//2+1//8*a^2*b^-3//2*(-1*B*a+6*A*b)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+1//12*b^-1*x^(1/2)*(a+b*x)^3//2*(-1*B*a+6*A*b)+1//8*a*b^-1*x^(1/2)*(a+b*x)^(1/2)*(-1*B*a+6*A*b))
@test integrate(x^-3//2*(a+b*x)^3//2*(A+B*x), x) == :(1//4*x^(1/2)*(a+b*x)^(1/2)*(3*B*a+12*A*b)+(1/2)*a^-1*x^(1/2)*(a+b*x)^3//2*(B*a+4*A*b)+-2*A*a^-1*x^-1//2*(a+b*x)^5//2+3//4*a*b^-1//2*(B*a+4*A*b)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2))
@test integrate(x^-5//2*(a+b*x)^3//2*(A+B*x), x) == :(b^(1/2)*(2*A*b+3*B*a)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+-2//3*A*a^-1*x^-3//2*(a+b*x)^5//2+-1//3*a^-1*x^-1//2*(a+b*x)^3//2*(4*A*b+6*B*a)+b*a^-1*x^(1/2)*(a+b*x)^(1/2)*(2*A*b+3*B*a))
@test integrate(x^-7//2*(a+b*x)^3//2*(A+B*x), x) == :(2*B*b^3//2*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+-2//3*B*x^-3//2*(a+b*x)^3//2+-2*B*b*x^-1//2*(a+b*x)^(1/2)+-2//5*A*a^-1*x^-5//2*(a+b*x)^5//2)
@test integrate(x^-9//2*(a+b*x)^3//2*(A+B*x), x) == :(-2//7*A*a^-1*x^-7//2*(a+b*x)^5//2+1//35*a^-2*x^-5//2*(a+b*x)^5//2*(-14*B*a+4*A*b))
@test integrate(x^-11//2*(a+b*x)^3//2*(A+B*x), x) == :(-2//9*A*a^-1*x^-9//2*(a+b*x)^5//2+1//63*a^-2*x^-7//2*(a+b*x)^5//2*(-18*B*a+8*A*b)+-4//315*b*a^-3*x^-5//2*(a+b*x)^5//2*(-9*B*a+4*A*b))
@test integrate(x^-13//2*(a+b*x)^3//2*(A+B*x), x) == :(-2//11*A*a^-1*x^-11//2*(a+b*x)^5//2+1//99*a^-2*x^-9//2*(a+b*x)^5//2*(-22*B*a+12*A*b)+-8//693*b*a^-3*x^-7//2*(a+b*x)^5//2*(-11*B*a+6*A*b)+16//3465*a^-4*b^2*x^-5//2*(a+b*x)^5//2*(-11*B*a+6*A*b))
@test integrate(x^-15//2*(a+b*x)^3//2*(A+B*x), x) == :(-2//13*A*a^-1*x^-13//2*(a+b*x)^5//2+1//143*a^-2*x^-11//2*(a+b*x)^5//2*(-26*B*a+16*A*b)+-32//15015*a^-5*b^3*x^-5//2*(a+b*x)^5//2*(-13*B*a+8*A*b)+-4//429*b*a^-3*x^-9//2*(a+b*x)^5//2*(-13*B*a+8*A*b)+16//3003*a^-4*b^2*x^-7//2*(a+b*x)^5//2*(-13*B*a+8*A*b))
@test integrate(x^-17//2*(a+b*x)^3//2*(A+B*x), x) == :(-2//15*A*a^-1*x^-15//2*(a+b*x)^5//2+1//39*a^-2*x^-13//2*(a+b*x)^5//2*(-6*B*a+4*A*b)+-128//9009*a^-5*b^3*x^-7//2*(a+b*x)^5//2*(-3*B*a+2*A*b)+-16//429*b*a^-3*x^-11//2*(a+b*x)^5//2*(-3*B*a+2*A*b)+32//1287*a^-4*b^2*x^-9//2*(a+b*x)^5//2*(-3*B*a+2*A*b)+256//45045*a^-6*b^4*x^-5//2*(a+b*x)^5//2*(-3*B*a+2*A*b))
@test integrate(x^3//2*(a+b*x)^5//2*(A+B*x), x) == :(1//6*B*b^-1*x^5//2*(a+b*x)^7//2+1//60*b^-1*x^5//2*(a+b*x)^5//2*(-5*B*a+12*A*b)+1//512*a^5*b^-7//2*(-5*B*a+12*A*b)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+-1//512*a^4*b^-3*x^(1/2)*(a+b*x)^(1/2)*(-5*B*a+12*A*b)+1//96*a*b^-1*x^5//2*(a+b*x)^3//2*(-5*B*a+12*A*b)+1//192*a^2*b^-1*x^5//2*(a+b*x)^(1/2)*(-5*B*a+12*A*b)+1//768*a^3*b^-2*x^3//2*(a+b*x)^(1/2)*(-5*B*a+12*A*b))
@test integrate(x^(1/2)*(a+b*x)^5//2*(A+B*x), x) == :(-1//128*a^4*b^-5//2*(-3*B*a+10*A*b)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+1//5*B*b^-1*x^3//2*(a+b*x)^7//2+1//40*b^-1*x^3//2*(a+b*x)^5//2*(-3*B*a+10*A*b)+1//48*a*b^-1*x^3//2*(a+b*x)^3//2*(-3*B*a+10*A*b)+1//64*a^2*b^-1*x^3//2*(a+b*x)^(1/2)*(-3*B*a+10*A*b)+1//128*a^3*b^-2*x^(1/2)*(a+b*x)^(1/2)*(-3*B*a+10*A*b))
@test integrate(x^-1//2*(a+b*x)^5//2*(A+B*x), x) == :(1//4*B*b^-1*x^(1/2)*(a+b*x)^7//2+1//24*b^-1*x^(1/2)*(a+b*x)^5//2*(-1*B*a+8*A*b)+5//64*a^3*b^-3//2*(-1*B*a+8*A*b)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+5//64*a^2*b^-1*x^(1/2)*(a+b*x)^(1/2)*(-1*B*a+8*A*b)+5//96*a*b^-1*x^(1/2)*(a+b*x)^3//2*(-1*B*a+8*A*b))
@test integrate(x^-3//2*(a+b*x)^5//2*(A+B*x), x) == :(1//12*x^(1/2)*(a+b*x)^3//2*(5*B*a+30*A*b)+-2*A*a^-1*x^-1//2*(a+b*x)^7//2+1//3*a^-1*x^(1/2)*(a+b*x)^5//2*(B*a+6*A*b)+5//8*a*x^(1/2)*(a+b*x)^(1/2)*(B*a+6*A*b)+5//8*a^2*b^-1//2*(B*a+6*A*b)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2))
@test integrate(x^-5//2*(a+b*x)^5//2*(A+B*x), x) == :(-2//3*A*a^-1*x^-3//2*(a+b*x)^7//2+-1//3*a^-1*x^-1//2*(a+b*x)^5//2*(6*B*a+8*A*b)+5//4*a*b^(1/2)*(3*B*a+4*A*b)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+5//4*b*x^(1/2)*(a+b*x)^(1/2)*(3*B*a+4*A*b)+5//6*b*a^-1*x^(1/2)*(a+b*x)^3//2*(3*B*a+4*A*b))
@test integrate(x^-7//2*(a+b*x)^5//2*(A+B*x), x) == :(b^3//2*(2*A*b+5*B*a)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+-2//5*A*a^-1*x^-5//2*(a+b*x)^7//2+-1//15*a^-1*x^-3//2*(a+b*x)^5//2*(4*A*b+10*B*a)+a^-1*b^2*x^(1/2)*(a+b*x)^(1/2)*(2*A*b+5*B*a)+-2//3*b*a^-1*x^-1//2*(a+b*x)^3//2*(2*A*b+5*B*a))
@test integrate(x^-9//2*(a+b*x)^5//2*(A+B*x), x) == :(2*B*b^5//2*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+-2//5*B*x^-5//2*(a+b*x)^5//2+-2*B*b^2*x^-1//2*(a+b*x)^(1/2)+-2//3*B*b*x^-3//2*(a+b*x)^3//2+-2//7*A*a^-1*x^-7//2*(a+b*x)^7//2)
@test integrate(x^-11//2*(a+b*x)^5//2*(A+B*x), x) == :(-2//9*A*a^-1*x^-9//2*(a+b*x)^7//2+1//63*a^-2*x^-7//2*(a+b*x)^7//2*(-18*B*a+4*A*b))
@test integrate(x^-13//2*(a+b*x)^5//2*(A+B*x), x) == :(-2//11*A*a^-1*x^-11//2*(a+b*x)^7//2+1//99*a^-2*x^-9//2*(a+b*x)^7//2*(-22*B*a+8*A*b)+-4//693*b*a^-3*x^-7//2*(a+b*x)^7//2*(-11*B*a+4*A*b))
@test integrate(x^-15//2*(a+b*x)^5//2*(A+B*x), x) == :(-2//13*A*a^-1*x^-13//2*(a+b*x)^7//2+1//143*a^-2*x^-11//2*(a+b*x)^7//2*(-26*B*a+12*A*b)+-8//1287*b*a^-3*x^-9//2*(a+b*x)^7//2*(-13*B*a+6*A*b)+16//9009*a^-4*b^2*x^-7//2*(a+b*x)^7//2*(-13*B*a+6*A*b))
@test integrate(x^-17//2*(a+b*x)^5//2*(A+B*x), x) == :(-2//15*A*a^-1*x^-15//2*(a+b*x)^7//2+1//195*a^-2*x^-13//2*(a+b*x)^7//2*(-30*B*a+16*A*b)+-32//45045*a^-5*b^3*x^-7//2*(a+b*x)^7//2*(-15*B*a+8*A*b)+-4//715*b*a^-3*x^-11//2*(a+b*x)^7//2*(-15*B*a+8*A*b)+16//6435*a^-4*b^2*x^-9//2*(a+b*x)^7//2*(-15*B*a+8*A*b))
@test integrate(x^-19//2*(a+b*x)^5//2*(A+B*x), x) == :(-2//17*A*a^-1*x^-17//2*(a+b*x)^7//2+1//255*a^-2*x^-15//2*(a+b*x)^7//2*(-34*B*a+20*A*b)+-128//109395*a^-5*b^3*x^-9//2*(a+b*x)^7//2*(-17*B*a+10*A*b)+-16//3315*b*a^-3*x^-13//2*(a+b*x)^7//2*(-17*B*a+10*A*b)+32//12155*a^-4*b^2*x^-11//2*(a+b*x)^7//2*(-17*B*a+10*A*b)+256//765765*a^-6*b^4*x^-7//2*(a+b*x)^7//2*(-17*B*a+10*A*b))
@test integrate(x^7//2*(a+b*x)^-1//2*(A+B*x), x) == :(1//5*B*b^-1*x^9//2*(a+b*x)^(1/2)+1//40*b^-2*x^7//2*(a+b*x)^(1/2)*(-9*B*a+10*A*b)+7//128*a^4*b^-11//2*(-9*B*a+10*A*b)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+-7//128*a^3*b^-5*x^(1/2)*(a+b*x)^(1/2)*(-9*B*a+10*A*b)+-7//240*a*b^-3*x^5//2*(a+b*x)^(1/2)*(-9*B*a+10*A*b)+7//192*a^2*b^-4*x^3//2*(a+b*x)^(1/2)*(-9*B*a+10*A*b))
@test integrate(x^5//2*(a+b*x)^-1//2*(A+B*x), x) == :(-5//64*a^3*b^-9//2*(-7*B*a+8*A*b)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+1//4*B*b^-1*x^7//2*(a+b*x)^(1/2)+1//24*b^-2*x^5//2*(a+b*x)^(1/2)*(-7*B*a+8*A*b)+-5//96*a*b^-3*x^3//2*(a+b*x)^(1/2)*(-7*B*a+8*A*b)+5//64*a^2*b^-4*x^(1/2)*(a+b*x)^(1/2)*(-7*B*a+8*A*b))
@test integrate(x^3//2*(a+b*x)^-1//2*(A+B*x), x) == :(1//3*B*b^-1*x^5//2*(a+b*x)^(1/2)+1//8*a^2*b^-7//2*(-5*B*a+6*A*b)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+1//12*b^-2*x^3//2*(a+b*x)^(1/2)*(-5*B*a+6*A*b)+-1//8*a*b^-3*x^(1/2)*(a+b*x)^(1/2)*(-5*B*a+6*A*b))
@test integrate(x^(1/2)*(a+b*x)^-1//2*(A+B*x), x) == :((1/2)*B*b^-1*x^3//2*(a+b*x)^(1/2)+-1//4*a*b^-5//2*(-3*B*a+4*A*b)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+1//4*b^-2*x^(1/2)*(a+b*x)^(1/2)*(-3*B*a+4*A*b))
@test integrate(x^-1//2*(a+b*x)^-1//2*(A+B*x), x) == :(b^-3//2*(-1*B*a+2*A*b)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+B*b^-1*x^(1/2)*(a+b*x)^(1/2))
@test integrate(x^-3//2*(a+b*x)^-1//2*(A+B*x), x) == :(2*B*b^-1//2*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+-2*A*a^-1*x^-1//2*(a+b*x)^(1/2))
@test integrate(x^-5//2*(a+b*x)^-1//2*(A+B*x), x) == :(-2//3*A*a^-1*x^-3//2*(a+b*x)^(1/2)+1//3*a^-2*x^-1//2*(a+b*x)^(1/2)*(-6*B*a+4*A*b))
@test integrate(x^-7//2*(a+b*x)^-1//2*(A+B*x), x) == :(-2//5*A*a^-1*x^-5//2*(a+b*x)^(1/2)+1//15*a^-2*x^-3//2*(a+b*x)^(1/2)*(-10*B*a+8*A*b)+-4//15*b*a^-3*x^-1//2*(a+b*x)^(1/2)*(-5*B*a+4*A*b))
@test integrate(x^-9//2*(a+b*x)^-1//2*(A+B*x), x) == :(-2//7*A*a^-1*x^-7//2*(a+b*x)^(1/2)+1//35*a^-2*x^-5//2*(a+b*x)^(1/2)*(-14*B*a+12*A*b)+-8//105*b*a^-3*x^-3//2*(a+b*x)^(1/2)*(-7*B*a+6*A*b)+16//105*a^-4*b^2*x^-1//2*(a+b*x)^(1/2)*(-7*B*a+6*A*b))
@test integrate(x^-11//2*(a+b*x)^-1//2*(A+B*x), x) == :(-2//9*A*a^-1*x^-9//2*(a+b*x)^(1/2)+1//63*a^-2*x^-7//2*(a+b*x)^(1/2)*(-18*B*a+16*A*b)+-32//315*a^-5*b^3*x^-1//2*(a+b*x)^(1/2)*(-9*B*a+8*A*b)+-4//105*b*a^-3*x^-5//2*(a+b*x)^(1/2)*(-9*B*a+8*A*b)+16//315*a^-4*b^2*x^-3//2*(a+b*x)^(1/2)*(-9*B*a+8*A*b))
@test integrate(x^-13//2*(a+b*x)^-1//2*(A+B*x), x) == :(-2//11*A*a^-1*x^-11//2*(a+b*x)^(1/2)+1//99*a^-2*x^-9//2*(a+b*x)^(1/2)*(-22*B*a+20*A*b)+-128//3465*a^-5*b^3*x^-3//2*(a+b*x)^(1/2)*(-11*B*a+10*A*b)+-16//693*b*a^-3*x^-7//2*(a+b*x)^(1/2)*(-11*B*a+10*A*b)+32//1155*a^-4*b^2*x^-5//2*(a+b*x)^(1/2)*(-11*B*a+10*A*b)+256//3465*a^-6*b^4*x^-1//2*(a+b*x)^(1/2)*(-11*B*a+10*A*b))
@test integrate(x^-15//2*(a+b*x)^-1//2*(A+B*x), x) == :(-2//13*A*a^-1*x^-13//2*(a+b*x)^(1/2)+1//143*a^-2*x^-11//2*(a+b*x)^(1/2)*(-26*B*a+24*A*b)+-512//9009*a^-7*b^5*x^-1//2*(a+b*x)^(1/2)*(-13*B*a+12*A*b)+-64//3003*a^-5*b^3*x^-5//2*(a+b*x)^(1/2)*(-13*B*a+12*A*b)+-20//1287*b*a^-3*x^-9//2*(a+b*x)^(1/2)*(-13*B*a+12*A*b)+160//9009*a^-4*b^2*x^-7//2*(a+b*x)^(1/2)*(-13*B*a+12*A*b)+256//9009*a^-6*b^4*x^-3//2*(a+b*x)^(1/2)*(-13*B*a+12*A*b))
@test integrate(x^7//2*(a+b*x)^-3//2*(A+B*x), x) == :(-35//64*a^3*b^-11//2*(-9*B*a+8*A*b)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+1//24*b^-3*x^5//2*(a+b*x)^(1/2)*(-63*B*a+56*A*b)+a^-1*b^-1*x^9//2*(a+b*x)^-1//2*(-2*B*a+2*A*b)+-35//96*a*b^-4*x^3//2*(a+b*x)^(1/2)*(-9*B*a+8*A*b)+-1//4*a^-1*b^-2*x^7//2*(a+b*x)^(1/2)*(-9*B*a+8*A*b)+35//64*a^2*b^-5*x^(1/2)*(a+b*x)^(1/2)*(-9*B*a+8*A*b))
@test integrate(x^5//2*(a+b*x)^-3//2*(A+B*x), x) == :(1//12*b^-3*x^3//2*(a+b*x)^(1/2)*(-35*B*a+30*A*b)+5//8*a^2*b^-9//2*(-7*B*a+6*A*b)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+a^-1*b^-1*x^7//2*(a+b*x)^-1//2*(-2*B*a+2*A*b)+-5//8*a*b^-4*x^(1/2)*(a+b*x)^(1/2)*(-7*B*a+6*A*b)+-1//3*a^-1*b^-2*x^5//2*(a+b*x)^(1/2)*(-7*B*a+6*A*b))
@test integrate(x^3//2*(a+b*x)^-3//2*(A+B*x), x) == :(-3//4*a*b^-7//2*(-5*B*a+4*A*b)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+1//4*b^-3*x^(1/2)*(a+b*x)^(1/2)*(-15*B*a+12*A*b)+a^-1*b^-1*x^5//2*(a+b*x)^-1//2*(-2*B*a+2*A*b)+-1//2*a^-1*b^-2*x^3//2*(a+b*x)^(1/2)*(-5*B*a+4*A*b))
@test integrate(x^(1/2)*(a+b*x)^-3//2*(A+B*x), x) == :(b^-5//2*(-3*B*a+2*A*b)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+a^-1*b^-1*x^3//2*(a+b*x)^-1//2*(-2*B*a+2*A*b)+-1*a^-1*b^-2*x^(1/2)*(a+b*x)^(1/2)*(-3*B*a+2*A*b))
@test integrate(x^-1//2*(a+b*x)^-3//2*(A+B*x), x) == :(2*B*b^-3//2*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+a^-1*b^-1*x^(1/2)*(a+b*x)^-1//2*(-2*B*a+2*A*b))
@test integrate(x^-3//2*(a+b*x)^-3//2*(A+B*x), x) == :(-1*a^-2*x^(1/2)*(a+b*x)^-1//2*(-2*B*a+4*A*b)+-2*A*a^-1*x^-1//2*(a+b*x)^-1//2)
@test integrate(x^-5//2*(a+b*x)^-3//2*(A+B*x), x) == :(-2//3*A*a^-1*x^-3//2*(a+b*x)^-1//2+-1//3*a^-2*x^-1//2*(a+b*x)^-1//2*(-6*B*a+8*A*b)+1//3*a^-3*x^-1//2*(a+b*x)^(1/2)*(-12*B*a+16*A*b))
@test integrate(x^-7//2*(a+b*x)^-3//2*(A+B*x), x) == :(-2//5*A*a^-1*x^-5//2*(a+b*x)^-1//2+-1//5*a^-2*x^-3//2*(a+b*x)^-1//2*(-10*B*a+12*A*b)+1//15*a^-3*x^-3//2*(a+b*x)^(1/2)*(-40*B*a+48*A*b)+-16//15*b*a^-4*x^-1//2*(a+b*x)^(1/2)*(-5*B*a+6*A*b))
@test integrate(x^-9//2*(a+b*x)^-3//2*(A+B*x), x) == :(-2//7*A*a^-1*x^-7//2*(a+b*x)^-1//2+-1//7*a^-2*x^-5//2*(a+b*x)^-1//2*(-14*B*a+16*A*b)+1//35*a^-3*x^-5//2*(a+b*x)^(1/2)*(-84*B*a+96*A*b)+-16//35*b*a^-4*x^-3//2*(a+b*x)^(1/2)*(-7*B*a+8*A*b)+32//35*a^-5*b^2*x^-1//2*(a+b*x)^(1/2)*(-7*B*a+8*A*b))
@test integrate(x^-11//2*(a+b*x)^-3//2*(A+B*x), x) == :(-2//9*A*a^-1*x^-9//2*(a+b*x)^-1//2+-1//9*a^-2*x^-7//2*(a+b*x)^-1//2*(-18*B*a+20*A*b)+1//63*a^-3*x^-7//2*(a+b*x)^(1/2)*(-144*B*a+160*A*b)+-256//315*a^-6*b^3*x^-1//2*(a+b*x)^(1/2)*(-9*B*a+10*A*b)+-32//105*b*a^-4*x^-5//2*(a+b*x)^(1/2)*(-9*B*a+10*A*b)+128//315*a^-5*b^2*x^-3//2*(a+b*x)^(1/2)*(-9*B*a+10*A*b))
@test integrate(x^-13//2*(a+b*x)^-3//2*(A+B*x), x) == :(-2//11*A*a^-1*x^-11//2*(a+b*x)^-1//2+-1//11*a^-2*x^-9//2*(a+b*x)^-1//2*(-22*B*a+24*A*b)+1//99*a^-3*x^-9//2*(a+b*x)^(1/2)*(-220*B*a+240*A*b)+-256//693*a^-6*b^3*x^-3//2*(a+b*x)^(1/2)*(-11*B*a+12*A*b)+-160//693*b*a^-4*x^-7//2*(a+b*x)^(1/2)*(-11*B*a+12*A*b)+64//231*a^-5*b^2*x^-5//2*(a+b*x)^(1/2)*(-11*B*a+12*A*b)+512//693*a^-7*b^4*x^-1//2*(a+b*x)^(1/2)*(-11*B*a+12*A*b))
@test integrate(x^7//2*(a+b*x)^-5//2*(A+B*x), x) == :(1//12*b^-4*x^3//2*(a+b*x)^(1/2)*(-105*B*a+70*A*b)+35//8*a^2*b^-11//2*(-3*B*a+2*A*b)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+a^-1*b^-2*x^7//2*(a+b*x)^-1//2*(-6*B*a+4*A*b)+-35//8*a*b^-5*x^(1/2)*(a+b*x)^(1/2)*(-3*B*a+2*A*b)+-1//3*a^-1*b^-3*x^5//2*(a+b*x)^(1/2)*(-21*B*a+14*A*b)+1//3*a^-1*b^-1*x^9//2*(a+b*x)^-3//2*(-2*B*a+2*A*b))
@test integrate(x^5//2*(a+b*x)^-5//2*(A+B*x), x) == :(-5//4*a*b^-9//2*(-7*B*a+4*A*b)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+1//4*b^-4*x^(1/2)*(a+b*x)^(1/2)*(-35*B*a+20*A*b)+-1//6*a^-1*b^-3*x^3//2*(a+b*x)^(1/2)*(-35*B*a+20*A*b)+1//3*a^-1*b^-1*x^7//2*(a+b*x)^-3//2*(-2*B*a+2*A*b)+1//3*a^-1*b^-2*x^5//2*(a+b*x)^-1//2*(-14*B*a+8*A*b))
@test integrate(x^3//2*(a+b*x)^-5//2*(A+B*x), x) == :(b^-7//2*(-5*B*a+2*A*b)*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+-1*a^-1*b^-3*x^(1/2)*(a+b*x)^(1/2)*(-5*B*a+2*A*b)+1//3*a^-1*b^-1*x^5//2*(a+b*x)^-3//2*(-2*B*a+2*A*b)+1//3*a^-1*b^-2*x^3//2*(a+b*x)^-1//2*(-10*B*a+4*A*b))
@test integrate(x^(1/2)*(a+b*x)^-5//2*(A+B*x), x) == :(2*B*b^-5//2*arctanh(b^(1/2)*x^(1/2)*(a+b*x)^-1//2)+-2*B*b^-2*x^(1/2)*(a+b*x)^-1//2+1//3*a^-1*b^-1*x^3//2*(a+b*x)^-3//2*(-2*B*a+2*A*b))
@test integrate(x^-1//2*(a+b*x)^-5//2*(A+B*x), x) == :(1//3*a^-1*b^-1*x^(1/2)*(a+b*x)^-3//2*(-2*B*a+2*A*b)+1//3*a^-2*b^-1*x^(1/2)*(a+b*x)^-1//2*(2*B*a+4*A*b))
@test integrate(x^-3//2*(a+b*x)^-5//2*(A+B*x), x) == :(-2*A*a^-1*x^-1//2*(a+b*x)^-3//2+-1//3*a^-3*x^(1/2)*(a+b*x)^-1//2*(-4*B*a+16*A*b)+-1//3*a^-2*x^(1/2)*(a+b*x)^-3//2*(-2*B*a+8*A*b))
@test integrate(x^-5//2*(a+b*x)^-5//2*(A+B*x), x) == :(-2//3*A*a^-1*x^-3//2*(a+b*x)^-3//2+-1//3*a^-3*x^-1//2*(a+b*x)^-1//2*(-8*B*a+16*A*b)+-1//3*a^-2*x^-1//2*(a+b*x)^-3//2*(-2*B*a+4*A*b)+1//3*a^-4*x^-1//2*(a+b*x)^(1/2)*(-16*B*a+32*A*b))
@test integrate(x^-7//2*(a+b*x)^-5//2*(A+B*x), x) == :(-2//5*A*a^-1*x^-5//2*(a+b*x)^-3//2+-1//5*a^-3*x^-3//2*(a+b*x)^-1//2*(-20*B*a+32*A*b)+-1//15*a^-2*x^-3//2*(a+b*x)^-3//2*(-10*B*a+16*A*b)+1//15*a^-4*x^-3//2*(a+b*x)^(1/2)*(-80*B*a+128*A*b)+-32//15*b*a^-5*x^-1//2*(a+b*x)^(1/2)*(-5*B*a+8*A*b))
@test integrate(x^-9//2*(a+b*x)^-5//2*(A+B*x), x) == :(-2//7*A*a^-1*x^-7//2*(a+b*x)^-3//2+-1//21*a^-3*x^-5//2*(a+b*x)^-1//2*(-112*B*a+160*A*b)+-1//21*a^-2*x^-5//2*(a+b*x)^-3//2*(-14*B*a+20*A*b)+1//35*a^-4*x^-5//2*(a+b*x)^(1/2)*(-224*B*a+320*A*b)+-128//105*b*a^-5*x^-3//2*(a+b*x)^(1/2)*(-7*B*a+10*A*b)+256//105*a^-6*b^2*x^-1//2*(a+b*x)^(1/2)*(-7*B*a+10*A*b))
@test integrate(x^-11//2*(a+b*x)^-5//2*(A+B*x), x) == :(-2//9*A*a^-1*x^-9//2*(a+b*x)^-3//2+-1//9*a^-3*x^-7//2*(a+b*x)^-1//2*(-60*B*a+80*A*b)+-1//9*a^-2*x^-7//2*(a+b*x)^-3//2*(-6*B*a+8*A*b)+1//63*a^-4*x^-7//2*(a+b*x)^(1/2)*(-480*B*a+640*A*b)+-512//63*a^-7*b^3*x^-1//2*(a+b*x)^(1/2)*(-3*B*a+4*A*b)+-64//21*b*a^-5*x^-5//2*(a+b*x)^(1/2)*(-3*B*a+4*A*b)+256//63*a^-6*b^2*x^-3//2*(a+b*x)^(1/2)*(-3*B*a+4*A*b))
@test integrate(x^3*(a+b*x)^(1/2)*(c+d*x)^(1/2), x) == :(-1//128*b^-4*d^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-7*a^4*d^4+7*b^4*c^4+-2*b*c*a^3*d^3+2*a*d*b^3*c^3)+1//5*b^-1*d^-1*x^2*(a+b*x)^3//2*(c+d*x)^3//2+1//240*b^-3*d^-3*(a+b*x)^3//2*(c+d*x)^3//2*(35*a^2*d^2+35*b^2*c^2+-42*b*d*x*(a*d+b*c)+38*a*b*c*d)+-1//64*b^-4*d^-3*(a+b*x)^3//2*(c+d*x)^(1/2)*(a*d+b*c)*(7*a^2*d^2+7*b^2*c^2+2*a*b*c*d)+1//128*b^-9//2*d^-9//2*(b*c+-1*a*d)^2*(a*d+b*c)*(7*a^2*d^2+7*b^2*c^2+2*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate(x^2*(a+b*x)^(1/2)*(c+d*x)^(1/2), x) == :(-1//24*b^-2*d^-2*(a+b*x)^3//2*(c+d*x)^3//2*(5*a*d+5*b*c)+-1//32*b^-3*d^-2*(a+b*x)^3//2*(c+d*x)^(1/2)*(-5*(a*d+b*c)^2+4*a*b*c*d)+1//4*x*b^-1*d^-1*(a+b*x)^3//2*(c+d*x)^3//2+1//64*b^-7//2*d^-7//2*(b*c+-1*a*d)^2*(-5*(a*d+b*c)^2+4*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//64*b^-3*d^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-5*(a*d+b*c)^2+4*a*b*c*d)*(b*c+-1*a*d))
@test integrate(x*(a+b*x)^(1/2)*(c+d*x)^(1/2), x) == :((a+b*x)^(1/2)*(c+d*x)^(1/2)*(-1//8*c^2*d^-2+1//8*a^2*b^-2)+1//3*b^-1*d^-1*(a+b*x)^3//2*(c+d*x)^3//2+-1//4*b^-2*d^-1*(a+b*x)^3//2*(c+d*x)^(1/2)*(a*d+b*c)+1//8*b^-5//2*d^-5//2*(b*c+-1*a*d)^2*(a*d+b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate((a+b*x)^(1/2)*(c+d*x)^(1/2), x) == :((1/2)*b^-1*(a+b*x)^3//2*(c+d*x)^(1/2)+-1//4*b^-3//2*d^-3//2*(b*c+-1*a*d)^2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//4*b^-1*d^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d))
@test integrate(x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2), x) == :((a+b*x)^(1/2)*(c+d*x)^(1/2)+-2*a^(1/2)*c^(1/2)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+b^-1//2*d^-1//2*(a*d+b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate(x^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2), x) == :(-1*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)+2*b^(1/2)*d^(1/2)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1*a^-1//2*c^-1//2*(a*d+b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate(x^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2), x) == :(-1//2*c^-1*x^-2*(a+b*x)^(1/2)*(c+d*x)^3//2+1//4*a^-3//2*c^-3//2*(b*c+-1*a*d)^2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//4*a^-1*c^-1*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d))
@test integrate(x^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2), x) == :(1//8*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(a^-2*b^2+-1*c^-2*d^2)+-1//3*a^-1*c^-1*x^-3*(a+b*x)^3//2*(c+d*x)^3//2+-1//8*a^-5//2*c^-5//2*(b*c+-1*a*d)^2*(a*d+b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//4*a^-1*c^-2*x^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(a*d+b*c))
@test integrate(x^-5*(a+b*x)^(1/2)*(c+d*x)^(1/2), x) == :(-1//4*x^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)+1//64*a^-7//2*c^-7//2*(b*c+-1*a*d)^2*(5*a^2*d^2+5*b^2*c^2+6*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//24*a^-1*c^-1*x^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(a*d+b*c)+1//96*a^-2*c^-2*x^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(5*a^2*d^2+5*b^2*c^2+-2*a*b*c*d)+-1//192*a^-3*c^-3*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(a*d+b*c)*(15*a^2*d^2+15*b^2*c^2+-22*a*b*c*d))
@test integrate(x^-6*(a+b*x)^(1/2)*(c+d*x)^(1/2), x) == :(-1//5*x^-5*(a+b*x)^(1/2)*(c+d*x)^(1/2)+-1//40*a^-1*c^-1*x^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(a*d+b*c)+-1//128*a^-9//2*c^-9//2*(b*c+-1*a*d)^2*(a*d+b*c)*(7*a^2*d^2+7*b^2*c^2+2*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//240*a^-2*c^-2*x^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(7*a^2*d^2+7*b^2*c^2+-2*a*b*c*d)+1//1920*a^-4*c^-4*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(105*a^4*d^4+105*b^4*c^4+-40*a*d*b^3*c^3+-40*b*c*a^3*d^3+-34*a^2*b^2*c^2*d^2)+-1//960*a^-3*c^-3*x^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(a*d+b*c)*(35*a^2*d^2+35*b^2*c^2+-46*a*b*c*d))
@test integrate(x^2*(a+b*x)^(1/2)*(c+d*x)^3//2, x) == :(-1//40*b^-2*d^-2*(a+b*x)^3//2*(c+d*x)^5//2*(5*b*c+7*a*d)+-1//128*b^-9//2*d^-7//2*(b*c+-1*a*d)^3*(3*b^2*c^2+7*a^2*d^2+6*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//5*x*b^-1*d^-1*(a+b*x)^3//2*(c+d*x)^5//2+1//48*b^-3*d^-2*(a+b*x)^3//2*(c+d*x)^3//2*(3*b^2*c^2+7*a^2*d^2+6*a*b*c*d)+1//64*b^-4*d^-2*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)*(3*b^2*c^2+7*a^2*d^2+6*a*b*c*d)+1//128*b^-4*d^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^2*(3*b^2*c^2+7*a^2*d^2+6*a*b*c*d))
@test integrate(x*(a+b*x)^(1/2)*(c+d*x)^3//2, x) == :(1//4*b^-1*d^-1*(a+b*x)^3//2*(c+d*x)^5//2+-1//24*b^-2*d^-1*(a+b*x)^3//2*(c+d*x)^3//2*(3*b*c+5*a*d)+1//64*b^-7//2*d^-5//2*(b*c+-1*a*d)^3*(3*b*c+5*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//32*b^-3*d^-1*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)*(3*b*c+5*a*d)+-1//64*b^-3*d^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^2*(3*b*c+5*a*d))
@test integrate((a+b*x)^(1/2)*(c+d*x)^3//2, x) == :(1//3*b^-1*(a+b*x)^3//2*(c+d*x)^3//2+-1//8*b^-5//2*d^-3//2*(b*c+-1*a*d)^3*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//4*b^-2*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)+1//8*b^-2*d^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^2)
@test integrate(x^-1*(a+b*x)^(1/2)*(c+d*x)^3//2, x) == :((1/2)*(a+b*x)^(1/2)*(c+d*x)^3//2+-2*a^(1/2)*c^3//2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//4*b^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(a*d+3*b*c)+1//4*b^-3//2*d^-1//2*(-1*a^2*d^2+3*b^2*c^2+6*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate(x^-2*(a+b*x)^(1/2)*(c+d*x)^3//2, x) == :(-1*x^-1*(a+b*x)^(1/2)*(c+d*x)^3//2+2*d*(a+b*x)^(1/2)*(c+d*x)^(1/2)+b^-1//2*d^(1/2)*(a*d+3*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1*a^-1//2*c^(1/2)*(b*c+3*a*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate(x^-3*(a+b*x)^(1/2)*(c+d*x)^3//2, x) == :(2*b^(1/2)*d^3//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//2*x^-2*(a+b*x)^(1/2)*(c+d*x)^3//2+1//4*a^-3//2*c^-1//2*(b^2*c^2+-3*a^2*d^2+-6*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//4*a^-1*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+3*a*d))
@test integrate(x^-4*(a+b*x)^(1/2)*(c+d*x)^3//2, x) == :(-1//3*c^-1*x^-3*(a+b*x)^(1/2)*(c+d*x)^5//2+-1//8*a^-5//2*c^-3//2*(b*c+-1*a*d)^3*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//12*a^-1*c^-1*x^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(b*c+-1*a*d)+1//8*a^-2*c^-1*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^2)
@test integrate(x^-5*(a+b*x)^(1/2)*(c+d*x)^3//2, x) == :(-1//4*a^-1*c^-1*x^-4*(a+b*x)^3//2*(c+d*x)^5//2+1//64*a^-7//2*c^-5//2*(b*c+-1*a*d)^3*(3*a*d+5*b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//24*a^-1*c^-2*x^-3*(a+b*x)^(1/2)*(c+d*x)^5//2*(3*a*d+5*b*c)+-1//64*a^-3*c^-2*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^2*(3*a*d+5*b*c)+1//96*a^-2*c^-2*x^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(b*c+-1*a*d)*(3*a*d+5*b*c))
@test integrate(x^-6*(a+b*x)^(1/2)*(c+d*x)^3//2, x) == :(-1//5*x^-5*(a+b*x)^(1/2)*(c+d*x)^3//2+-1//40*a^-1*x^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+3*a*d)+-1//128*a^-9//2*c^-7//2*(b*c+-1*a*d)^3*(3*a^2*d^2+7*b^2*c^2+6*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//240*a^-1*x^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-12*b*d+-3*a*c^-1*d^2+7*c*a^-1*b^2)+-1//960*a^-3*c^-2*x^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-15*a^3*d^3+35*b^3*c^3+-61*a*d*b^2*c^2+9*b*c*a^2*d^2)+1//1920*a^-4*c^-3*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-45*a^4*d^4+105*b^4*c^4+-190*a*d*b^3*c^3+30*b*c*a^3*d^3+36*a^2*b^2*c^2*d^2))
@test integrate(x^2*(a+b*x)^(1/2)*(c+d*x)^5//2, x) == :(-1//60*b^-2*d^-2*(a+b*x)^3//2*(c+d*x)^7//2*(5*b*c+9*a*d)+-1//512*b^-11//2*d^-7//2*(b*c+-1*a*d)^4*(5*b^2*c^2+21*a^2*d^2+14*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//6*x*b^-1*d^-1*(a+b*x)^3//2*(c+d*x)^7//2+1//160*b^-3*d^-2*(a+b*x)^3//2*(c+d*x)^5//2*(5*b^2*c^2+21*a^2*d^2+14*a*b*c*d)+1//192*b^-4*d^-2*(a+b*x)^3//2*(c+d*x)^3//2*(b*c+-1*a*d)*(5*b^2*c^2+21*a^2*d^2+14*a*b*c*d)+1//256*b^-5*d^-2*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^2*(5*b^2*c^2+21*a^2*d^2+14*a*b*c*d)+1//512*b^-5*d^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^3*(5*b^2*c^2+21*a^2*d^2+14*a*b*c*d))
@test integrate(x*(a+b*x)^(1/2)*(c+d*x)^5//2, x) == :(1//5*b^-1*d^-1*(a+b*x)^3//2*(c+d*x)^7//2+-1//40*b^-2*d^-1*(a+b*x)^3//2*(c+d*x)^5//2*(3*b*c+7*a*d)+1//128*b^-9//2*d^-5//2*(b*c+-1*a*d)^4*(3*b*c+7*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//48*b^-3*d^-1*(a+b*x)^3//2*(c+d*x)^3//2*(b*c+-1*a*d)*(3*b*c+7*a*d)+-1//64*b^-4*d^-1*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^2*(3*b*c+7*a*d)+-1//128*b^-4*d^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^3*(3*b*c+7*a*d))
@test integrate((a+b*x)^(1/2)*(c+d*x)^5//2, x) == :(1//4*b^-1*(a+b*x)^3//2*(c+d*x)^5//2+-5//64*b^-7//2*d^-3//2*(b*c+-1*a*d)^4*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//24*b^-2*(a+b*x)^3//2*(c+d*x)^3//2*(-5*a*d+5*b*c)+5//32*b^-3*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^2+5//64*b^-3*d^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^3)
@test integrate(x^-1*(a+b*x)^(1/2)*(c+d*x)^5//2, x) == :(1//3*(a+b*x)^(1/2)*(c+d*x)^5//2+-2*a^(1/2)*c^5//2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//8*b^-5//2*d^-1//2*(a^3*d^3+5*b^3*c^3+-5*b*c*a^2*d^2+15*a*d*b^2*c^2)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//12*b^-1*(a+b*x)^(1/2)*(c+d*x)^3//2*(a*d+5*b*c)+1//8*b^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(a*d+b*c)*(-1*a*d+5*b*c))
@test integrate(x^-2*(a+b*x)^(1/2)*(c+d*x)^5//2, x) == :(-1*x^-1*(a+b*x)^(1/2)*(c+d*x)^5//2+3//2*d*(a+b*x)^(1/2)*(c+d*x)^3//2+-1*a^-1//2*c^3//2*(b*c+5*a*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//4*b^-3//2*d^(1/2)*(-1*a^2*d^2+15*b^2*c^2+10*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//4*d*b^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(a*d+11*b*c))
@test integrate(x^-3*(a+b*x)^(1/2)*(c+d*x)^5//2, x) == :(-1//2*x^-2*(a+b*x)^(1/2)*(c+d*x)^5//2+b^-1//2*d^3//2*(a*d+5*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//4*a^-3//2*c^(1/2)*(b^2*c^2+-15*a^2*d^2+-10*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//4*a^-1*x^-1*(a+b*x)^(1/2)*(c+d*x)^3//2*(b*c+5*a*d)+1//4*d*a^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+11*a*d))
@test integrate(x^-4*(a+b*x)^(1/2)*(c+d*x)^5//2, x) == :(2*b^(1/2)*d^5//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//3*x^-3*(a+b*x)^(1/2)*(c+d*x)^5//2+-1//8*a^-5//2*c^-1//2*(b^3*c^3+5*a^3*d^3+-5*a*d*b^2*c^2+15*b*c*a^2*d^2)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//12*a^-1*x^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(b*c+5*a*d)+1//8*a^-2*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(a*d+b*c)*(b*c+-5*a*d))
@test integrate(x^-5*(a+b*x)^(1/2)*(c+d*x)^5//2, x) == :(-1//4*c^-1*x^-4*(a+b*x)^(1/2)*(c+d*x)^7//2+5//64*a^-7//2*c^-3//2*(b*c+-1*a*d)^4*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-5//64*a^-3*c^-1*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^3+-1//24*a^-1*c^-1*x^-3*(a+b*x)^(1/2)*(c+d*x)^5//2*(b*c+-1*a*d)+5//96*a^-2*c^-1*x^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(b*c+-1*a*d)^2)
@test integrate(x^-6*(a+b*x)^(1/2)*(c+d*x)^5//2, x) == :(-1//5*a^-1*c^-1*x^-5*(a+b*x)^3//2*(c+d*x)^7//2+-1//128*a^-9//2*c^-5//2*(b*c+-1*a*d)^4*(3*a*d+7*b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//40*a^-1*c^-2*x^-4*(a+b*x)^(1/2)*(c+d*x)^7//2*(3*a*d+7*b*c)+-1//192*a^-3*c^-2*x^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(b*c+-1*a*d)^2*(3*a*d+7*b*c)+1//128*a^-4*c^-2*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^3*(3*a*d+7*b*c)+1//240*a^-2*c^-2*x^-3*(a+b*x)^(1/2)*(c+d*x)^5//2*(b*c+-1*a*d)*(3*a*d+7*b*c))
@test integrate(x^-7*(a+b*x)^(1/2)*(c+d*x)^5//2, x) == :(-1//6*x^-6*(a+b*x)^(1/2)*(c+d*x)^5//2+-1//60*a^-1*x^-5*(a+b*x)^(1/2)*(c+d*x)^3//2*(b*c+5*a*d)+1//160*a^-2*x^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-5*a^2*d^2+3*b^2*c^2+-6*a*b*c*d)+1//512*a^-11//2*c^-7//2*(b*c+-1*a*d)^4*(5*a^2*d^2+21*b^2*c^2+14*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//960*a^-3*c^-1*x^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(5*a^3*d^3+21*b^3*c^3+-61*a*d*b^2*c^2+51*b*c*a^2*d^2)+-1//7680*a^-5*c^-3*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(75*a^5*d^5+315*b^5*c^5+-945*a*d*b^4*c^4+-90*a^3*b^2*c^2*d^3+-65*b*c*a^4*d^4+838*a^2*b^3*c^3*d^2)+1//3840*a^-4*c^-2*x^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(25*a^4*d^4+105*b^4*c^4+-308*a*d*b^3*c^3+-20*b*c*a^3*d^3+262*a^2*b^2*c^2*d^2))
@test integrate(x^3*(a+b*x)^(1/2)*(c+d*x)^-1//2, x) == :(-1//64*b^-3*d^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(5*a^3*d^3+35*b^3*c^3+9*b*c*a^2*d^2+15*a*d*b^2*c^2)+1//4*b^-1*d^-1*x^2*(a+b*x)^3//2*(c+d*x)^(1/2)+1//64*b^-7//2*d^-9//2*(b*c+-1*a*d)*(5*a^3*d^3+35*b^3*c^3+9*b*c*a^2*d^2+15*a*d*b^2*c^2)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//96*b^-3*d^-3*(a+b*x)^3//2*(c+d*x)^(1/2)*(15*a^2*d^2+35*b^2*c^2+-4*b*d*x*(5*a*d+7*b*c)+22*a*b*c*d))
@test integrate(x^2*(a+b*x)^(1/2)*(c+d*x)^-1//2, x) == :(-1//8*b^-5//2*d^-7//2*(b*c+-1*a*d)*(a^2*d^2+5*b^2*c^2+2*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//12*b^-2*d^-2*(a+b*x)^3//2*(c+d*x)^(1/2)*(3*a*d+5*b*c)+1//3*x*b^-1*d^-1*(a+b*x)^3//2*(c+d*x)^(1/2)+1//8*b^-2*d^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(a^2*d^2+5*b^2*c^2+2*a*b*c*d))
@test integrate(x*(a+b*x)^(1/2)*(c+d*x)^-1//2, x) == :((1/2)*b^-1*d^-1*(a+b*x)^3//2*(c+d*x)^(1/2)+-1//4*b^-1*d^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(a*d+3*b*c)+1//4*b^-3//2*d^-5//2*(a*d+3*b*c)*(b*c+-1*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate((a+b*x)^(1/2)*(c+d*x)^-1//2, x) == :(d^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)+-1*b^-1//2*d^-3//2*(b*c+-1*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate(x^-1*(a+b*x)^(1/2)*(c+d*x)^-1//2, x) == :(-2*a^(1/2)*c^-1//2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+2*b^(1/2)*d^-1//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate(x^-2*(a+b*x)^(1/2)*(c+d*x)^-1//2, x) == :(-1*a^-1//2*c^-3//2*(b*c+-1*a*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1*c^-1*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2))
@test integrate(x^-3*(a+b*x)^(1/2)*(c+d*x)^-1//2, x) == :(-1//2*a^-1*c^-1*x^-2*(a+b*x)^3//2*(c+d*x)^(1/2)+1//4*a^-3//2*c^-5//2*(b*c+-1*a*d)*(b*c+3*a*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//4*a^-1*c^-2*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+3*a*d))
@test integrate(x^-4*(a+b*x)^(1/2)*(c+d*x)^-1//2, x) == :(-1//3*c^-1*x^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)+-1//8*a^-5//2*c^-7//2*(b*c+-1*a*d)*(b^2*c^2+5*a^2*d^2+2*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//12*a^-1*c^-2*x^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-5*a*d)+1//24*a^-2*c^-3*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+3*a*d)*(-5*a*d+3*b*c))
@test integrate(x^-5*(a+b*x)^(1/2)*(c+d*x)^-1//2, x) == :(-1//4*c^-1*x^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)+1//64*a^-7//2*c^-9//2*(b*c+-1*a*d)*(5*b^3*c^3+35*a^3*d^3+9*a*d*b^2*c^2+15*b*c*a^2*d^2)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//24*a^-1*c^-2*x^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-7*a*d)+-1//192*a^-3*c^-4*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-105*a^3*d^3+15*b^3*c^3+17*a*d*b^2*c^2+25*b*c*a^2*d^2)+1//96*a^-2*c^-3*x^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-35*a^2*d^2+5*b^2*c^2+6*a*b*c*d))
@test integrate(x^2*(a+b*x)^(1/2)*(c+d*x)^-3//2, x) == :((1/2)*b^-1*d^-2*(a+b*x)^3//2*(c+d*x)^(1/2)+1//4*b^-3//2*d^-7//2*(-1*a^2*d^2+15*b^2*c^2+-6*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+2*c^2*d^-2*(a+b*x)^3//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-1+1//4*d^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1*(6*a*c+d*a^2*b^-1+-15*b*c^2*d^-1))
@test integrate(x*(a+b*x)^(1/2)*(c+d*x)^-3//2, x) == :(-1*b^-1//2*d^-5//2*(-1*a*d+3*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+d^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1*(-1*a*d+3*b*c)+-2*c*d^-1*(a+b*x)^3//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-1)
@test integrate((a+b*x)^(1/2)*(c+d*x)^-3//2, x) == :(-2*d^-1*(a+b*x)^(1/2)*(c+d*x)^-1//2+2*b^(1/2)*d^-3//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate(x^-1*(a+b*x)^(1/2)*(c+d*x)^-3//2, x) == :(-2*a^(1/2)*c^-3//2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+2*c^-1*(a+b*x)^(1/2)*(c+d*x)^-1//2)
@test integrate(x^-2*(a+b*x)^(1/2)*(c+d*x)^-3//2, x) == :(-1*a^-1//2*c^-5//2*(b*c+-3*a*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+a^-1*c^-2*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-3*a*d)+-1*a^-1*c^-1*x^-1*(a+b*x)^3//2*(c+d*x)^-1//2)
@test integrate(x^-3*(a+b*x)^(1/2)*(c+d*x)^-3//2, x) == :(-1//2*c^-1*x^-2*(a+b*x)^(1/2)*(c+d*x)^-1//2+1//4*a^-3//2*c^-7//2*(b^2*c^2+-15*a^2*d^2+6*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//4*d*a^-1*c^-3*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-15*a*d)+-1//4*a^-1*c^-2*x^-1*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-5*a*d))
@test integrate(x^3*(a+b*x)^(1/2)*(c+d*x)^-5//2, x) == :(-2//3*d^-1*x^3*(a+b*x)^(1/2)*(c+d*x)^-3//2+1//4*b^-3//2*d^-9//2*(-1*a^2*d^2+35*b^2*c^2+-10*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//3*d^-2*x^2*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-1*(-12*a*d+14*b*c)+-1//12*b^-1*d^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1*(3*a^2*d^2+105*b^2*c^2+-100*a*b*c*d+-2*b*d*x*(-31*a*d+35*b*c)))
@test integrate(x^2*(a+b*x)^(1/2)*(c+d*x)^-5//2, x) == :(-1*b^-1//2*d^-7//2*(-1*a*d+5*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+d^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1*(-1*a*d+5*b*c)+-4*c*d^-2*(a+b*x)^3//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-1+2//3*c^2*d^-2*(a+b*x)^3//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-1)
@test integrate(x*(a+b*x)^(1/2)*(c+d*x)^-5//2, x) == :(-2*d^-2*(a+b*x)^(1/2)*(c+d*x)^-1//2+2*b^(1/2)*d^-5//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-2//3*c*d^-1*(a+b*x)^3//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-1)
@test integrate((a+b*x)^(1/2)*(c+d*x)^-5//2, x) == :(2*(a+b*x)^3//2*(c+d*x)^-3//2*(-3*a*d+3*b*c)^-1)
@test integrate(x^-1*(a+b*x)^(1/2)*(c+d*x)^-5//2, x) == :(-2*a^(1/2)*c^-5//2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+2*c^-2*(a+b*x)^(1/2)*(c+d*x)^-1//2+-2//3*d*c^-1*(a+b*x)^3//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-1)
@test integrate(x^-2*(a+b*x)^(1/2)*(c+d*x)^-5//2, x) == :(-1*a^-1//2*c^-7//2*(b*c+-5*a*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1*c^-1*x^-1*(a+b*x)^(1/2)*(c+d*x)^-3//2+-5//3*d*c^-2*(a+b*x)^(1/2)*(c+d*x)^-3//2+-1//3*d*c^-3*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-1*(-15*a*d+13*b*c))
@test integrate(x^-3*(a+b*x)^(1/2)*(c+d*x)^-5//2, x) == :(-1//2*c^-1*x^-2*(a+b*x)^(1/2)*(c+d*x)^-3//2+1//4*a^-3//2*c^-9//2*(b^2*c^2+-35*a^2*d^2+10*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//4*a^-1*c^-2*x^-1*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-7*a*d)+-1//12*d*a^-1*c^-3*(a+b*x)^(1/2)*(c+d*x)^-3//2*(-35*a*d+3*b*c)+-1//12*d*a^-1*c^-4*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-1*(3*b^2*c^2+105*a^2*d^2+-100*a*b*c*d))
@test integrate(x^2*(a+b*x)^3//2*(c+d*x)^(1/2), x) == :(-1//40*b^-2*d^-2*(a+b*x)^5//2*(c+d*x)^3//2*(5*a*d+7*b*c)+1//5*x*b^-1*d^-1*(a+b*x)^5//2*(c+d*x)^3//2+1//48*b^-3*d^-2*(a+b*x)^5//2*(c+d*x)^(1/2)*(3*a^2*d^2+7*b^2*c^2+6*a*b*c*d)+1//128*b^-7//2*d^-9//2*(b*c+-1*a*d)^3*(3*a^2*d^2+7*b^2*c^2+6*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//128*b^-3*d^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^2*(3*a^2*d^2+7*b^2*c^2+6*a*b*c*d)+1//192*b^-3*d^-3*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)*(3*a^2*d^2+7*b^2*c^2+6*a*b*c*d))
@test integrate(x*(a+b*x)^3//2*(c+d*x)^(1/2), x) == :(1//4*b^-1*d^-1*(a+b*x)^5//2*(c+d*x)^3//2+-1//24*b^-2*d^-1*(a+b*x)^5//2*(c+d*x)^(1/2)*(3*a*d+5*b*c)+-1//64*b^-5//2*d^-7//2*(b*c+-1*a*d)^3*(3*a*d+5*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//96*b^-2*d^-2*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)*(3*a*d+5*b*c)+1//64*b^-2*d^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^2*(3*a*d+5*b*c))
@test integrate((a+b*x)^3//2*(c+d*x)^(1/2), x) == :(1//3*b^-1*(a+b*x)^5//2*(c+d*x)^(1/2)+1//8*b^-3//2*d^-5//2*(b*c+-1*a*d)^3*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//8*b^-1*d^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^2+1//12*b^-1*d^-1*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d))
@test integrate(x^-1*(a+b*x)^3//2*(c+d*x)^(1/2), x) == :((1/2)*(a+b*x)^3//2*(c+d*x)^(1/2)+-2*a^3//2*c^(1/2)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//4*b^-1//2*d^-3//2*(b^2*c^2+-3*a^2*d^2+-6*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//4*d^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+3*a*d))
@test integrate(x^-2*(a+b*x)^3//2*(c+d*x)^(1/2), x) == :(-1*x^-1*(a+b*x)^3//2*(c+d*x)^(1/2)+2*b*(a+b*x)^(1/2)*(c+d*x)^(1/2)+b^(1/2)*d^-1//2*(b*c+3*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1*a^(1/2)*c^-1//2*(a*d+3*b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate(x^-3*(a+b*x)^3//2*(c+d*x)^(1/2), x) == :(2*b^3//2*d^(1/2)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//2*x^-2*(a+b*x)^3//2*(c+d*x)^(1/2)+-1//4*a^-1//2*c^-3//2*(-1*a^2*d^2+3*b^2*c^2+6*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//4*c^-1*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(a*d+3*b*c))
@test integrate(x^-4*(a+b*x)^3//2*(c+d*x)^(1/2), x) == :(-1//3*c^-1*x^-3*(a+b*x)^3//2*(c+d*x)^3//2+1//8*a^-3//2*c^-5//2*(b*c+-1*a*d)^3*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//4*c^-2*x^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(b*c+-1*a*d)+-1//8*a^-1*c^-2*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^2)
@test integrate(x^-5*(a+b*x)^3//2*(c+d*x)^(1/2), x) == :(-1//4*a^-1*c^-1*x^-4*(a+b*x)^5//2*(c+d*x)^3//2+-1//64*a^-5//2*c^-7//2*(b*c+-1*a*d)^3*(3*b*c+5*a*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//24*a^-1*c^-2*x^-3*(a+b*x)^3//2*(c+d*x)^3//2*(3*b*c+5*a*d)+1//32*a^-1*c^-3*x^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(b*c+-1*a*d)*(3*b*c+5*a*d)+1//64*a^-2*c^-3*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^2*(3*b*c+5*a*d))
@test integrate(x^-6*(a+b*x)^3//2*(c+d*x)^(1/2), x) == :(-1//5*x^-5*(a+b*x)^3//2*(c+d*x)^(1/2)+-1//40*c^-1*x^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(a*d+3*b*c)+-1//240*c^-1*x^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(12*b*d+-7*a*c^-1*d^2+3*c*a^-1*b^2)+1//128*a^-7//2*c^-9//2*(b*c+-1*a*d)^3*(3*b^2*c^2+7*a^2*d^2+6*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//1920*a^-3*c^-4*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-105*a^4*d^4+45*b^4*c^4+-36*a^2*b^2*c^2*d^2+-30*a*d*b^3*c^3+190*b*c*a^3*d^3)+1//960*a^-2*c^-3*x^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-35*a^3*d^3+15*b^3*c^3+-9*a*d*b^2*c^2+61*b*c*a^2*d^2))
@test integrate(x^2*(a+b*x)^3//2*(c+d*x)^3//2, x) == :(-1//60*b^-2*d^-2*(a+b*x)^5//2*(c+d*x)^5//2*(7*a*d+7*b*c)+-1//96*b^-3*d^-2*(a+b*x)^5//2*(c+d*x)^3//2*(-7*(a*d+b*c)^2+4*a*b*c*d)+-1//512*b^-9//2*d^-9//2*(b*c+-1*a*d)^4*(-7*(a*d+b*c)^2+4*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//6*x*b^-1*d^-1*(a+b*x)^5//2*(c+d*x)^5//2+-1//192*b^-4*d^-2*(a+b*x)^5//2*(c+d*x)^(1/2)*(-7*(a*d+b*c)^2+4*a*b*c*d)*(b*c+-1*a*d)+-1//768*b^-4*d^-3*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^2*(-7*(a*d+b*c)^2+4*a*b*c*d)+1//512*b^-4*d^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^3*(-7*(a*d+b*c)^2+4*a*b*c*d))
@test integrate(x*(a+b*x)^3//2*(c+d*x)^3//2, x) == :(1//5*b^-1*d^-1*(a+b*x)^5//2*(c+d*x)^5//2+-3//128*b^-7//2*d^-7//2*(b*c+-1*a*d)^4*(a*d+b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//8*b^-2*d^-1*(a+b*x)^5//2*(c+d*x)^3//2*(a*d+b*c)+-1//16*b^-3*d^-1*(a+b*x)^5//2*(c+d*x)^(1/2)*(a*d+b*c)*(b*c+-1*a*d)+-1//64*b^-3*d^-2*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^2*(a*d+b*c)+3//128*b^-3*d^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^3*(a*d+b*c))
@test integrate((a+b*x)^3//2*(c+d*x)^3//2, x) == :(1//4*b^-1*(a+b*x)^5//2*(c+d*x)^3//2+1//8*b^-2*(a+b*x)^5//2*(c+d*x)^(1/2)*(b*c+-1*a*d)+3//64*b^-5//2*d^-5//2*(b*c+-1*a*d)^4*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-3//64*b^-2*d^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^3+1//32*b^-2*d^-1*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^2)
@test integrate(x^-1*(a+b*x)^3//2*(c+d*x)^3//2, x) == :(1//3*(a+b*x)^3//2*(c+d*x)^3//2+(a+b*x)^(1/2)*(c+d*x)^(1/2)*(a*c+-1//8*b*c^2*d^-1+1//8*d*a^2*b^-1)+-2*a^3//2*c^3//2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//4*d^-1*(a+b*x)^(1/2)*(c+d*x)^3//2*(a*d+b*c)+-1//8*b^-3//2*d^-3//2*(a*d+b*c)*(a^2*d^2+b^2*c^2+-10*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate(x^-2*(a+b*x)^3//2*(c+d*x)^3//2, x) == :(-1*x^-1*(a+b*x)^3//2*(c+d*x)^3//2+1//4*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(3*b*c+9*a*d)+3//2*b*(a+b*x)^(1/2)*(c+d*x)^3//2+-3*a^(1/2)*c^(1/2)*(a*d+b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//4*b^-1//2*d^-1//2*(3*a^2*d^2+3*b^2*c^2+18*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate(x^-3*(a+b*x)^3//2*(c+d*x)^3//2, x) == :(-1//2*x^-2*(a+b*x)^3//2*(c+d*x)^3//2+3*b^(1/2)*d^(1/2)*(a*d+b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//4*a^-1//2*c^-1//2*(3*a^2*d^2+3*b^2*c^2+18*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//4*c^-1*x^-1*(a+b*x)^(1/2)*(c+d*x)^3//2*(3*a*d+3*b*c)+3//4*d*c^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(a*d+3*b*c))
@test integrate(x^-4*(a+b*x)^3//2*(c+d*x)^3//2, x) == :(2*b^3//2*d^3//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//3*x^-3*(a+b*x)^3//2*(c+d*x)^3//2+-1//8*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(8*b*d+c*a^-1*b^2+-1*a*c^-1*d^2)+-1//4*c^-1*x^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(a*d+b*c)+1//8*a^-3//2*c^-3//2*(a*d+b*c)*(a^2*d^2+b^2*c^2+-10*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate(x^-5*(a+b*x)^3//2*(c+d*x)^3//2, x) == :(-3//64*a^-5//2*c^-5//2*(b*c+-1*a*d)^4*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//4*c^-1*x^-4*(a+b*x)^3//2*(c+d*x)^5//2+-1//8*c^-2*x^-3*(a+b*x)^(1/2)*(c+d*x)^5//2*(b*c+-1*a*d)+-1//32*a^-1*c^-2*x^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(b*c+-1*a*d)^2+3//64*a^-2*c^-2*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^3)
@test integrate(x^-6*(a+b*x)^3//2*(c+d*x)^3//2, x) == :(-1//5*a^-1*c^-1*x^-5*(a+b*x)^5//2*(c+d*x)^5//2+3//128*a^-7//2*c^-7//2*(b*c+-1*a*d)^4*(a*d+b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//8*a^-1*c^-2*x^-4*(a+b*x)^3//2*(c+d*x)^5//2*(a*d+b*c)+-3//128*a^-3*c^-3*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^3*(a*d+b*c)+1//16*a^-1*c^-3*x^-3*(a+b*x)^(1/2)*(c+d*x)^5//2*(a*d+b*c)*(b*c+-1*a*d)+1//64*a^-2*c^-3*x^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(b*c+-1*a*d)^2*(a*d+b*c))
@test integrate(x^2*(a+b*x)^3//2*(c+d*x)^5//2, x) == :(-1//84*b^-2*d^-2*(a+b*x)^5//2*(c+d*x)^7//2*(7*b*c+9*a*d)+1//7*x*b^-1*d^-1*(a+b*x)^5//2*(c+d*x)^7//2+1//120*b^-3*d^-2*(a+b*x)^5//2*(c+d*x)^5//2*(5*b^2*c^2+9*a^2*d^2+10*a*b*c*d)+1//1024*b^-11//2*d^-9//2*(b*c+-1*a*d)^5*(5*b^2*c^2+9*a^2*d^2+10*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//1024*b^-5*d^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^4*(5*b^2*c^2+9*a^2*d^2+10*a*b*c*d)+1//192*b^-4*d^-2*(a+b*x)^5//2*(c+d*x)^3//2*(b*c+-1*a*d)*(5*b^2*c^2+9*a^2*d^2+10*a*b*c*d)+1//384*b^-5*d^-2*(a+b*x)^5//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^2*(5*b^2*c^2+9*a^2*d^2+10*a*b*c*d)+1//1536*b^-5*d^-3*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^3*(5*b^2*c^2+9*a^2*d^2+10*a*b*c*d))
@test integrate(x*(a+b*x)^3//2*(c+d*x)^5//2, x) == :(1//6*b^-1*d^-1*(a+b*x)^5//2*(c+d*x)^7//2+-1//60*b^-2*d^-1*(a+b*x)^5//2*(c+d*x)^5//2*(5*b*c+7*a*d)+-1//512*b^-9//2*d^-7//2*(b*c+-1*a*d)^5*(5*b*c+7*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//96*b^-3*d^-1*(a+b*x)^5//2*(c+d*x)^3//2*(b*c+-1*a*d)*(5*b*c+7*a*d)+-1//192*b^-4*d^-1*(a+b*x)^5//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^2*(5*b*c+7*a*d)+-1//768*b^-4*d^-2*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^3*(5*b*c+7*a*d)+1//512*b^-4*d^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^4*(5*b*c+7*a*d))
@test integrate((a+b*x)^3//2*(c+d*x)^5//2, x) == :(1//5*b^-1*(a+b*x)^5//2*(c+d*x)^5//2+1//8*b^-2*(a+b*x)^5//2*(c+d*x)^3//2*(b*c+-1*a*d)+1//16*b^-3*(a+b*x)^5//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^2+3//128*b^-7//2*d^-5//2*(b*c+-1*a*d)^5*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-3//128*b^-3*d^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^4+1//64*b^-3*d^-1*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^3)
@test integrate(x^-1*(a+b*x)^3//2*(c+d*x)^5//2, x) == :(1//4*(a+b*x)^3//2*(c+d*x)^5//2+(a+b*x)^(1/2)*(c+d*x)^3//2*(25//48*a*c+-5//96*b*c^2*d^-1+1//32*d*a^2*b^-1)+-2*a^3//2*c^5//2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//64*b^-5//2*d^-3//2*(-3*a^4*d^4+5*b^4*c^4+-90*a^2*b^2*c^2*d^2+-60*a*d*b^3*c^3+20*b*c*a^3*d^3)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//24*d^-1*(a+b*x)^(1/2)*(c+d*x)^5//2*(3*a*d+5*b*c)+-1//64*b^-2*d^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(3*a^3*d^3+5*b^3*c^3+-55*a*d*b^2*c^2+-17*b*c*a^2*d^2))
@test integrate(x^-2*(a+b*x)^3//2*(c+d*x)^5//2, x) == :(-1*x^-1*(a+b*x)^3//2*(c+d*x)^5//2+1//12*(a+b*x)^(1/2)*(c+d*x)^3//2*(5*b*c+19*a*d)+4//3*b*(a+b*x)^(1/2)*(c+d*x)^5//2+-1*a^(1/2)*c^3//2*(3*b*c+5*a*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//8*b^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(a^2*d^2+5*b^2*c^2+26*a*b*c*d)+1//8*b^-3//2*d^-1//2*(-1*a^3*d^3+5*b^3*c^3+15*b*c*a^2*d^2+45*a*d*b^2*c^2)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate(x^-3*(a+b*x)^3//2*(c+d*x)^5//2, x) == :(-1//2*x^-2*(a+b*x)^3//2*(c+d*x)^5//2+3*d*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(a*d+b*c)+-3//4*a^-1//2*c^(1/2)*(b^2*c^2+5*a^2*d^2+10*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+3//4*b^-1//2*d^(1/2)*(a^2*d^2+5*b^2*c^2+10*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//4*c^-1*x^-1*(a+b*x)^(1/2)*(c+d*x)^5//2*(3*b*c+5*a*d)+1//4*d*c^-1*(a+b*x)^(1/2)*(c+d*x)^3//2*(5*a*d+7*b*c))
@test integrate(x^-4*(a+b*x)^3//2*(c+d*x)^5//2, x) == :(-1//3*x^-3*(a+b*x)^3//2*(c+d*x)^5//2+b^(1/2)*d^3//2*(3*a*d+5*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//24*x^-1*(a+b*x)^(1/2)*(c+d*x)^3//2*(40*b*d+3*c*a^-1*b^2+5*a*c^-1*d^2)+1//8*a^-3//2*c^-1//2*(b^3*c^3+-5*a^3*d^3+-45*b*c*a^2*d^2+-15*a*d*b^2*c^2)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//12*c^-1*x^-2*(a+b*x)^(1/2)*(c+d*x)^5//2*(3*b*c+5*a*d)+1//8*d*a^-1*c^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b^2*c^2+5*a^2*d^2+26*a*b*c*d))
@test integrate(x^-5*(a+b*x)^3//2*(c+d*x)^5//2, x) == :(2*b^3//2*d^5//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//4*x^-4*(a+b*x)^3//2*(c+d*x)^5//2+-1//64*a^-5//2*c^-3//2*(-5*a^4*d^4+3*b^4*c^4+-20*a*d*b^3*c^3+60*b*c*a^3*d^3+90*a^2*b^2*c^2*d^2)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//96*x^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(50*b*d+-5*a*c^-1*d^2+3*c*a^-1*b^2)+-1//24*c^-1*x^-3*(a+b*x)^(1/2)*(c+d*x)^5//2*(3*b*c+5*a*d)+1//64*a^-2*c^-1*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(3*b^3*c^3+5*a^3*d^3+-55*b*c*a^2*d^2+-17*a*d*b^2*c^2))
@test integrate(x^-6*(a+b*x)^3//2*(c+d*x)^5//2, x) == :(-1//5*c^-1*x^-5*(a+b*x)^3//2*(c+d*x)^7//2+3//128*a^-7//2*c^-5//2*(b*c+-1*a*d)^5*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//40*c^-2*x^-4*(a+b*x)^(1/2)*(c+d*x)^7//2*(-3*a*d+3*b*c)+-3//128*a^-3*c^-2*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^4+-1//80*a^-1*c^-2*x^-3*(a+b*x)^(1/2)*(c+d*x)^5//2*(b*c+-1*a*d)^2+1//64*a^-2*c^-2*x^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(b*c+-1*a*d)^3)
@test integrate(x^-7*(a+b*x)^3//2*(c+d*x)^5//2, x) == :(-1//6*a^-1*c^-1*x^-6*(a+b*x)^5//2*(c+d*x)^7//2+-1//512*a^-9//2*c^-7//2*(b*c+-1*a*d)^5*(5*a*d+7*b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//60*a^-1*c^-2*x^-5*(a+b*x)^3//2*(c+d*x)^7//2*(5*a*d+7*b*c)+-1//768*a^-3*c^-3*x^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(b*c+-1*a*d)^3*(5*a*d+7*b*c)+1//160*a^-1*c^-3*x^-4*(a+b*x)^(1/2)*(c+d*x)^7//2*(b*c+-1*a*d)*(5*a*d+7*b*c)+1//512*a^-4*c^-3*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^4*(5*a*d+7*b*c)+1//960*a^-2*c^-3*x^-3*(a+b*x)^(1/2)*(c+d*x)^5//2*(b*c+-1*a*d)^2*(5*a*d+7*b*c))
@test integrate(x^2*(a+b*x)^3//2*(c+d*x)^-1//2, x) == :(-1//24*b^-2*d^-2*(a+b*x)^5//2*(c+d*x)^(1/2)*(3*a*d+7*b*c)+1//4*x*b^-1*d^-1*(a+b*x)^5//2*(c+d*x)^(1/2)+1//64*b^-5//2*d^-9//2*(b*c+-1*a*d)^2*(3*a^2*d^2+35*b^2*c^2+10*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//96*b^-2*d^-3*(a+b*x)^3//2*(c+d*x)^(1/2)*(3*a^2*d^2+35*b^2*c^2+10*a*b*c*d)+-1//64*b^-2*d^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)*(3*a^2*d^2+35*b^2*c^2+10*a*b*c*d))
@test integrate(x*(a+b*x)^3//2*(c+d*x)^-1//2, x) == :(1//3*b^-1*d^-1*(a+b*x)^5//2*(c+d*x)^(1/2)+-1//8*b^-3//2*d^-7//2*(b*c+-1*a*d)^2*(a*d+5*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//12*b^-1*d^-2*(a+b*x)^3//2*(c+d*x)^(1/2)*(a*d+5*b*c)+1//8*b^-1*d^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(a*d+5*b*c)*(b*c+-1*a*d))
@test integrate((a+b*x)^3//2*(c+d*x)^-1//2, x) == :((1/2)*d^-1*(a+b*x)^3//2*(c+d*x)^(1/2)+1//4*d^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-3*b*c+3*a*d)+3//4*b^-1//2*d^-5//2*(b*c+-1*a*d)^2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate(x^-1*(a+b*x)^3//2*(c+d*x)^-1//2, x) == :(-2*a^3//2*c^-1//2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+b*d^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)+-1*b^(1/2)*d^-3//2*(b*c+-3*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate(x^-2*(a+b*x)^3//2*(c+d*x)^-1//2, x) == :(2*b^3//2*d^-1//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1*a^(1/2)*c^-3//2*(-1*a*d+3*b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1*a*c^-1*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2))
@test integrate(x^-3*(a+b*x)^3//2*(c+d*x)^-1//2, x) == :(-3//4*a^-1//2*c^-5//2*(b*c+-1*a*d)^2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//2*c^-1*x^-2*(a+b*x)^3//2*(c+d*x)^(1/2)+1//4*c^-2*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-3*b*c+3*a*d))
@test integrate(x^-4*(a+b*x)^3//2*(c+d*x)^-1//2, x) == :(-1//3*a^-1*c^-1*x^-3*(a+b*x)^5//2*(c+d*x)^(1/2)+1//8*a^-3//2*c^-7//2*(b*c+-1*a*d)^2*(b*c+5*a*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//12*a^-1*c^-2*x^-2*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+5*a*d)+1//8*a^-1*c^-3*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)*(b*c+5*a*d))
@test integrate(x^-5*(a+b*x)^3//2*(c+d*x)^-1//2, x) == :(-1//4*a*c^-1*x^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)+-1//24*c^-2*x^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-7*a*d+9*b*c)+-1//64*a^-5//2*c^-9//2*(b*c+-1*a*d)^2*(3*b^2*c^2+35*a^2*d^2+10*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//96*a^-1*c^-3*x^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(3*b^2*c^2+35*a^2*d^2+-46*a*b*c*d)+1//192*a^-2*c^-4*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(9*b^3*c^3+105*a^3*d^3+-145*b*c*a^2*d^2+15*a*d*b^2*c^2))
@test integrate(x^2*(a+b*x)^3//2*(c+d*x)^-3//2, x) == :(1//3*b^-1*d^-2*(a+b*x)^5//2*(c+d*x)^(1/2)+2*c^2*d^-2*(a+b*x)^5//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-1+-1//8*b^-3//2*d^-9//2*(b*c+-1*a*d)*(-1*a^2*d^2+35*b^2*c^2+-10*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//8*b^-1*d^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-1*a^2*d^2+35*b^2*c^2+-10*a*b*c*d)+1//12*d^-2*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1*(10*a*c+d*a^2*b^-1+-35*b*c^2*d^-1))
@test integrate(x*(a+b*x)^3//2*(c+d*x)^-3//2, x) == :(-1//4*d^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-3*a*d+15*b*c)+(1/2)*d^-2*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1*(-1*a*d+5*b*c)+-2*c*d^-1*(a+b*x)^5//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-1+1//4*b^-1//2*d^-7//2*(-1*a*d+5*b*c)*(-3*a*d+3*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate((a+b*x)^3//2*(c+d*x)^-3//2, x) == :(-2*d^-1*(a+b*x)^3//2*(c+d*x)^-1//2+-3*b^(1/2)*d^-5//2*(b*c+-1*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+3*b*d^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2))
@test integrate(x^-1*(a+b*x)^3//2*(c+d*x)^-3//2, x) == :(-2*a^3//2*c^-3//2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+2*b^3//2*d^-3//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1*c^-1*d^-1*(a+b*x)^(1/2)*(c+d*x)^-1//2*(-2*a*d+2*b*c))
@test integrate(x^-2*(a+b*x)^3//2*(c+d*x)^-3//2, x) == :(c^-2*(a+b*x)^(1/2)*(c+d*x)^-1//2*(-3*a*d+3*b*c)+-1*c^-1*x^-1*(a+b*x)^3//2*(c+d*x)^-1//2+-3*a^(1/2)*c^-5//2*(b*c+-1*a*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate(x^-3*(a+b*x)^3//2*(c+d*x)^-3//2, x) == :(-1//2*a^-1*c^-1*x^-2*(a+b*x)^5//2*(c+d*x)^-1//2+-1//4*a^-1//2*c^-7//2*(b*c+-1*a*d)*(-15*a*d+3*b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//4*a^-1*c^-2*x^-1*(a+b*x)^3//2*(c+d*x)^-1//2*(b*c+-5*a*d)+1//4*a^-1*c^-3*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)*(-15*a*d+3*b*c))
@test integrate(x^-4*(a+b*x)^3//2*(c+d*x)^-3//2, x) == :(-1//3*a*c^-1*x^-3*(a+b*x)^(1/2)*(c+d*x)^-1//2+-1//12*c^-2*x^-2*(a+b*x)^(1/2)*(c+d*x)^-1//2*(-7*a*d+7*b*c)+1//8*a^-3//2*c^-9//2*(b*c+-1*a*d)*(b^2*c^2+-35*a^2*d^2+10*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//24*d*a^-1*c^-4*(a+b*x)^(1/2)*(c+d*x)^-1//2*(3*b^2*c^2+105*a^2*d^2+-100*a*b*c*d)+-1//24*a^-1*c^-3*x^-1*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)*(-35*a*d+3*b*c))
@test integrate(x^2*(a+b*x)^3//2*(c+d*x)^-5//2, x) == :(1//4*b^-1//2*d^-9//2*(3*a^2*d^2+35*b^2*c^2+-30*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//4*d^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1*(3*a^2*d^2+35*b^2*c^2+-30*a*b*c*d)+1//6*d^-3*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-2*(3*a^2*d^2+35*b^2*c^2+-30*a*b*c*d)+2//3*c^2*d^-2*(a+b*x)^5//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-1+-4//3*c*d^-2*(a+b*x)^5//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-2*(-3*a*d+4*b*c))
@test integrate(x*(a+b*x)^3//2*(c+d*x)^-5//2, x) == :(-1*b^(1/2)*d^-7//2*(-3*a*d+5*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-2//3*c*d^-1*(a+b*x)^5//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-1+-1//3*d^-2*(a+b*x)^3//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-1*(-6*a*d+10*b*c)+b*d^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1*(-3*a*d+5*b*c))
@test integrate((a+b*x)^3//2*(c+d*x)^-5//2, x) == :(2*b^3//2*d^-5//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-2//3*d^-1*(a+b*x)^3//2*(c+d*x)^-3//2+-2*b*d^-2*(a+b*x)^(1/2)*(c+d*x)^-1//2)
@test integrate(x^-1*(a+b*x)^3//2*(c+d*x)^-5//2, x) == :(-2*a^3//2*c^-5//2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+2//3*c^-1*(a+b*x)^3//2*(c+d*x)^-3//2+2*a*c^-2*(a+b*x)^(1/2)*(c+d*x)^-1//2)
@test integrate(x^-2*(a+b*x)^3//2*(c+d*x)^-5//2, x) == :(c^-3*(a+b*x)^(1/2)*(c+d*x)^-1//2*(-5*a*d+3*b*c)+-1*a^(1/2)*c^-7//2*(-5*a*d+3*b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1*a^-1*c^-1*x^-1*(a+b*x)^5//2*(c+d*x)^-3//2+1//3*a^-1*c^-2*(a+b*x)^3//2*(c+d*x)^-3//2*(-5*a*d+3*b*c))
@test integrate(x^-3*(a+b*x)^3//2*(c+d*x)^-5//2, x) == :(-1//4*a^-1//2*c^-9//2*(3*b^2*c^2+35*a^2*d^2+-30*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-5//12*d*c^-4*(a+b*x)^(1/2)*(c+d*x)^-1//2*(-21*a*d+11*b*c)+-1//2*a*c^-1*x^-2*(a+b*x)^(1/2)*(c+d*x)^-3//2+-1//4*c^-2*x^-1*(a+b*x)^(1/2)*(c+d*x)^-3//2*(-7*a*d+5*b*c)+-1//12*d*c^-3*(a+b*x)^(1/2)*(c+d*x)^-3//2*(-35*a*d+23*b*c))
@test integrate(x^2*(a+b*x)^5//2*(c+d*x)^(1/2), x) == :(-1//60*b^-2*d^-2*(a+b*x)^7//2*(c+d*x)^3//2*(5*a*d+9*b*c)+-1//512*b^-7//2*d^-11//2*(b*c+-1*a*d)^4*(5*a^2*d^2+21*b^2*c^2+14*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//6*x*b^-1*d^-1*(a+b*x)^7//2*(c+d*x)^3//2+1//160*b^-3*d^-2*(a+b*x)^7//2*(c+d*x)^(1/2)*(5*a^2*d^2+21*b^2*c^2+14*a*b*c*d)+-1//768*b^-3*d^-4*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^2*(5*a^2*d^2+21*b^2*c^2+14*a*b*c*d)+1//512*b^-3*d^-5*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^3*(5*a^2*d^2+21*b^2*c^2+14*a*b*c*d)+1//960*b^-3*d^-3*(a+b*x)^5//2*(c+d*x)^(1/2)*(b*c+-1*a*d)*(5*a^2*d^2+21*b^2*c^2+14*a*b*c*d))
@test integrate(x*(a+b*x)^5//2*(c+d*x)^(1/2), x) == :(1//5*b^-1*d^-1*(a+b*x)^7//2*(c+d*x)^3//2+-1//40*b^-2*d^-1*(a+b*x)^7//2*(c+d*x)^(1/2)*(3*a*d+7*b*c)+1//128*b^-5//2*d^-9//2*(b*c+-1*a*d)^4*(3*a*d+7*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//128*b^-2*d^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^3*(3*a*d+7*b*c)+-1//240*b^-2*d^-2*(a+b*x)^5//2*(c+d*x)^(1/2)*(b*c+-1*a*d)*(3*a*d+7*b*c)+1//192*b^-2*d^-3*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^2*(3*a*d+7*b*c))
@test integrate((a+b*x)^5//2*(c+d*x)^(1/2), x) == :(1//4*b^-1*(a+b*x)^7//2*(c+d*x)^(1/2)+-5//64*b^-3//2*d^-7//2*(b*c+-1*a*d)^4*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-5//96*b^-1*d^-2*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^2+1//24*b^-1*d^-1*(a+b*x)^5//2*(c+d*x)^(1/2)*(b*c+-1*a*d)+5//64*b^-1*d^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^3)
@test integrate(x^-1*(a+b*x)^5//2*(c+d*x)^(1/2), x) == :(1//3*(a+b*x)^5//2*(c+d*x)^(1/2)+-2*a^5//2*c^(1/2)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//8*b^-1//2*d^-5//2*(b^3*c^3+5*a^3*d^3+-5*a*d*b^2*c^2+15*b*c*a^2*d^2)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//12*d^-1*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+5*a*d)+-1//8*d^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(a*d+b*c)*(b*c+-5*a*d))
@test integrate(x^-2*(a+b*x)^5//2*(c+d*x)^(1/2), x) == :(-1*x^-1*(a+b*x)^5//2*(c+d*x)^(1/2)+3//2*b*(a+b*x)^3//2*(c+d*x)^(1/2)+-1*a^3//2*c^-1//2*(a*d+5*b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//4*b^(1/2)*d^-3//2*(b^2*c^2+-15*a^2*d^2+-10*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//4*b*d^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+11*a*d))
@test integrate(x^-3*(a+b*x)^5//2*(c+d*x)^(1/2), x) == :(-1//2*x^-2*(a+b*x)^5//2*(c+d*x)^(1/2)+b^3//2*d^-1//2*(b*c+5*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//4*a^(1/2)*c^-3//2*(-1*a^2*d^2+15*b^2*c^2+10*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//4*c^-1*x^-1*(a+b*x)^3//2*(c+d*x)^(1/2)*(a*d+5*b*c)+1//4*b*c^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(a*d+11*b*c))
@test integrate(x^-4*(a+b*x)^5//2*(c+d*x)^(1/2), x) == :(2*b^5//2*d^(1/2)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//3*x^-3*(a+b*x)^5//2*(c+d*x)^(1/2)+-1//8*a^-1//2*c^-5//2*(a^3*d^3+5*b^3*c^3+-5*b*c*a^2*d^2+15*a*d*b^2*c^2)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//12*c^-1*x^-2*(a+b*x)^3//2*(c+d*x)^(1/2)*(a*d+5*b*c)+-1//8*c^-2*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(a*d+b*c)*(-1*a*d+5*b*c))
@test integrate(x^-5*(a+b*x)^5//2*(c+d*x)^(1/2), x) == :(-1//4*c^-1*x^-4*(a+b*x)^5//2*(c+d*x)^3//2+5//64*a^-3//2*c^-7//2*(b*c+-1*a*d)^4*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-5//32*c^-3*x^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(b*c+-1*a*d)^2+-1//24*c^-2*x^-3*(a+b*x)^3//2*(c+d*x)^3//2*(-5*a*d+5*b*c)+-5//64*a^-1*c^-3*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^3)
@test integrate(x^-6*(a+b*x)^5//2*(c+d*x)^(1/2), x) == :(-1//5*a^-1*c^-1*x^-5*(a+b*x)^7//2*(c+d*x)^3//2+-1//128*a^-5//2*c^-9//2*(b*c+-1*a*d)^4*(3*b*c+7*a*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//40*a^-1*c^-2*x^-4*(a+b*x)^5//2*(c+d*x)^3//2*(3*b*c+7*a*d)+1//48*a^-1*c^-3*x^-3*(a+b*x)^3//2*(c+d*x)^3//2*(b*c+-1*a*d)*(3*b*c+7*a*d)+1//64*a^-1*c^-4*x^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(b*c+-1*a*d)^2*(3*b*c+7*a*d)+1//128*a^-2*c^-4*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^3*(3*b*c+7*a*d))
@test integrate(x^2*(a+b*x)^5//2*(c+d*x)^3//2, x) == :(-1//84*b^-2*d^-2*(a+b*x)^7//2*(c+d*x)^5//2*(7*a*d+9*b*c)+-1//1024*b^-9//2*d^-11//2*(b*c+-1*a*d)^5*(5*a^2*d^2+9*b^2*c^2+10*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//7*x*b^-1*d^-1*(a+b*x)^7//2*(c+d*x)^5//2+1//120*b^-3*d^-2*(a+b*x)^7//2*(c+d*x)^3//2*(5*a^2*d^2+9*b^2*c^2+10*a*b*c*d)+-1//1536*b^-4*d^-4*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^3*(5*a^2*d^2+9*b^2*c^2+10*a*b*c*d)+1//320*b^-4*d^-2*(a+b*x)^7//2*(c+d*x)^(1/2)*(b*c+-1*a*d)*(5*a^2*d^2+9*b^2*c^2+10*a*b*c*d)+1//1024*b^-4*d^-5*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^4*(5*a^2*d^2+9*b^2*c^2+10*a*b*c*d)+1//1920*b^-4*d^-3*(a+b*x)^5//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^2*(5*a^2*d^2+9*b^2*c^2+10*a*b*c*d))
@test integrate(x*(a+b*x)^5//2*(c+d*x)^3//2, x) == :(1//6*b^-1*d^-1*(a+b*x)^7//2*(c+d*x)^5//2+-1//60*b^-2*d^-1*(a+b*x)^7//2*(c+d*x)^3//2*(5*a*d+7*b*c)+1//512*b^-7//2*d^-9//2*(b*c+-1*a*d)^5*(5*a*d+7*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//160*b^-3*d^-1*(a+b*x)^7//2*(c+d*x)^(1/2)*(b*c+-1*a*d)*(5*a*d+7*b*c)+-1//512*b^-3*d^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^4*(5*a*d+7*b*c)+-1//960*b^-3*d^-2*(a+b*x)^5//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^2*(5*a*d+7*b*c)+1//768*b^-3*d^-3*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^3*(5*a*d+7*b*c))
@test integrate((a+b*x)^5//2*(c+d*x)^3//2, x) == :(1//5*b^-1*(a+b*x)^7//2*(c+d*x)^3//2+-3//128*b^-5//2*d^-7//2*(b*c+-1*a*d)^5*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//40*b^-2*(a+b*x)^7//2*(c+d*x)^(1/2)*(-3*a*d+3*b*c)+-1//64*b^-2*d^-2*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^3+1//80*b^-2*d^-1*(a+b*x)^5//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^2+3//128*b^-2*d^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^4)
@test integrate(x^-1*(a+b*x)^5//2*(c+d*x)^3//2, x) == :(1//4*(a+b*x)^5//2*(c+d*x)^3//2+-2*a^5//2*c^3//2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//24*d^-1*(a+b*x)^3//2*(c+d*x)^3//2*(3*b*c+5*a*d)+1//64*b^-3//2*d^-5//2*(-5*a^4*d^4+3*b^4*c^4+-20*a*d*b^3*c^3+60*b*c*a^3*d^3+90*a^2*b^2*c^2*d^2)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//32*d^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(a*d+3*b*c)*(b*c+-5*a*d)+1//64*b^-1*d^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*((a*d+3*b*c)*(b*c+-1*a*d)*(b*c+-5*a*d)+64*b*c*a^2*d^2))
@test integrate(x^-2*(a+b*x)^5//2*(c+d*x)^3//2, x) == :(-1*x^-1*(a+b*x)^5//2*(c+d*x)^3//2+4//3*b*(a+b*x)^3//2*(c+d*x)^3//2+-1*a^3//2*c^(1/2)*(3*a*d+5*b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//8*b^-1//2*d^-3//2*(b^3*c^3+-5*a^3*d^3+-45*b*c*a^2*d^2+-15*a*d*b^2*c^2)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//8*d^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b^2*c^2+-19*a^2*d^2+-14*a*b*c*d)+1//4*b*d^-1*(a+b*x)^(1/2)*(c+d*x)^3//2*(b*c+7*a*d))
@test integrate(x^-3*(a+b*x)^5//2*(c+d*x)^3//2, x) == :(-1//2*x^-2*(a+b*x)^5//2*(c+d*x)^3//2+-3//4*a^(1/2)*c^-1//2*(a^2*d^2+5*b^2*c^2+10*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//4*c^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(3*a^2*d^2+3*b^2*c^2+18*a*b*c*d)+3//4*b^(1/2)*d^-1//2*(b^2*c^2+5*a^2*d^2+10*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//4*c^-1*x^-1*(a+b*x)^3//2*(c+d*x)^3//2*(3*a*d+5*b*c)+3//4*b*c^-1*(a+b*x)^(1/2)*(c+d*x)^3//2*(a*d+3*b*c))
@test integrate(x^-4*(a+b*x)^5//2*(c+d*x)^3//2, x) == :(-1//3*x^-3*(a+b*x)^5//2*(c+d*x)^3//2+b^3//2*d^(1/2)*(3*b*c+5*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//8*a^-1//2*c^-3//2*(-1*a^3*d^3+5*b^3*c^3+15*b*c*a^2*d^2+45*a*d*b^2*c^2)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//8*c^-2*x^-1*(a+b*x)^(1/2)*(c+d*x)^3//2*(-1*a^2*d^2+5*b^2*c^2+12*a*b*c*d)+-1//12*c^-1*x^-2*(a+b*x)^3//2*(c+d*x)^3//2*(3*a*d+5*b*c)+1//8*d*c^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-1*a^2*d^2+19*b^2*c^2+14*a*b*c*d))
@test integrate(x^-5*(a+b*x)^5//2*(c+d*x)^3//2, x) == :(2*b^5//2*d^3//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//4*x^-4*(a+b*x)^5//2*(c+d*x)^3//2+1//64*a^-3//2*c^-5//2*(-3*a^4*d^4+5*b^4*c^4+-90*a^2*b^2*c^2*d^2+-60*a*d*b^3*c^3+20*b*c*a^3*d^3)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//24*c^-1*x^-3*(a+b*x)^3//2*(c+d*x)^3//2*(3*a*d+5*b*c)+-1//32*c^-2*x^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(b*c+3*a*d)*(-1*a*d+5*b*c)+-1//64*a^-1*c^-2*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(3*a^3*d^3+5*b^3*c^3+-17*b*c*a^2*d^2+73*a*d*b^2*c^2))
@test integrate(x^-6*(a+b*x)^5//2*(c+d*x)^3//2, x) == :(-3//128*a^-5//2*c^-7//2*(b*c+-1*a*d)^5*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//5*c^-1*x^-5*(a+b*x)^5//2*(c+d*x)^5//2+-1//8*c^-2*x^-4*(a+b*x)^3//2*(c+d*x)^5//2*(b*c+-1*a*d)+-1//16*c^-3*x^-3*(a+b*x)^(1/2)*(c+d*x)^5//2*(b*c+-1*a*d)^2+-1//64*a^-1*c^-3*x^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(b*c+-1*a*d)^3+3//128*a^-2*c^-3*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^4)
@test integrate(x*(a+b*x)^5//2*(c+d*x)^5//2, x) == :(1//7*b^-1*d^-1*(a+b*x)^7//2*(c+d*x)^7//2+-1//12*b^-2*d^-1*(a+b*x)^7//2*(c+d*x)^5//2*(a*d+b*c)+5//1024*b^-9//2*d^-9//2*(b*c+-1*a*d)^6*(a*d+b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-5//1024*b^-4*d^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^5*(a*d+b*c)+-1//24*b^-3*d^-1*(a+b*x)^7//2*(c+d*x)^3//2*(a*d+b*c)*(b*c+-1*a*d)+-1//64*b^-4*d^-1*(a+b*x)^7//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^2*(a*d+b*c)+-1//384*b^-4*d^-2*(a+b*x)^5//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^3*(a*d+b*c)+5//1536*b^-4*d^-3*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^4*(a*d+b*c))
@test integrate((a+b*x)^5//2*(c+d*x)^5//2, x) == :(1//6*b^-1*(a+b*x)^7//2*(c+d*x)^5//2+-5//512*b^-7//2*d^-7//2*(b*c+-1*a*d)^6*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//12*b^-2*(a+b*x)^7//2*(c+d*x)^3//2*(b*c+-1*a*d)+1//32*b^-3*(a+b*x)^7//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^2+-5//768*b^-3*d^-2*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^4+1//192*b^-3*d^-1*(a+b*x)^5//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^3+5//512*b^-3*d^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^5)
@test integrate(x^-1*(a+b*x)^5//2*(c+d*x)^5//2, x) == :(1//5*(a+b*x)^5//2*(c+d*x)^5//2+-2*a^5//2*c^5//2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//48*d^-2*(a+b*x)^(1/2)*(c+d*x)^5//2*(-3*a^2*d^2+3*b^2*c^2+-16*a*b*c*d)+1//8*d^-1*(a+b*x)^3//2*(c+d*x)^5//2*(a*d+b*c)+1//128*b^-2*d^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-3*a^4*d^4+3*b^4*c^4+-22*a*d*b^3*c^3+22*b*c*a^3*d^3+128*a^2*b^2*c^2*d^2)+1//128*b^-5//2*d^-5//2*(a*d+b*c)*(3*a^4*d^4+3*b^4*c^4+-28*a*d*b^3*c^3+-28*b*c*a^3*d^3+178*a^2*b^2*c^2*d^2)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//192*b^-1*d^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(3*a^3*d^3+3*b^3*c^3+-19*a*d*b^2*c^2+109*b*c*a^2*d^2))
@test integrate(x^-2*(a+b*x)^5//2*(c+d*x)^5//2, x) == :(-1*x^-1*(a+b*x)^5//2*(c+d*x)^5//2+5//4*b*(a+b*x)^3//2*(c+d*x)^5//2+-5*a^3//2*c^3//2*(a*d+b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//64*b^-3//2*d^-3//2*(5*a^4*d^4+5*b^4*c^4+-450*a^2*b^2*c^2*d^2+-100*a*d*b^3*c^3+-100*b*c*a^3*d^3)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//96*d^-1*(a+b*x)^(1/2)*(c+d*x)^3//2*(-155*a^2*d^2+5*b^2*c^2+-90*a*b*c*d)+1//64*b^-1*d^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-5*b^3*c^3+5*a^3*d^3+95*a*d*b^2*c^2+225*b*c*a^2*d^2)+5//24*b*d^-1*(a+b*x)^(1/2)*(c+d*x)^5//2*(b*c+7*a*d))
@test integrate(x^-3*(a+b*x)^5//2*(c+d*x)^5//2, x) == :((a+b*x)^(1/2)*(c+d*x)^(1/2)*(5//8*b^2*c^2+25//8*a^2*d^2+25//4*a*b*c*d)+-1//2*x^-2*(a+b*x)^5//2*(c+d*x)^5//2+1//12*c^-1*(a+b*x)^(1/2)*(c+d*x)^3//2*(5*b^2*c^2+15*a^2*d^2+40*a*b*c*d)+-5//4*a^(1/2)*c^(1/2)*(a*d+3*b*c)*(b*c+3*a*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//4*c^-1*x^-1*(a+b*x)^3//2*(c+d*x)^5//2*(5*a*d+5*b*c)+1//8*b^-1//2*d^-1//2*(5*a*d+5*b*c)*(a^2*d^2+b^2*c^2+14*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+5//12*b*c^-1*(a+b*x)^(1/2)*(c+d*x)^5//2*(3*a*d+5*b*c))
@test integrate(x^-4*(a+b*x)^5//2*(c+d*x)^5//2, x) == :(-1//3*x^-3*(a+b*x)^5//2*(c+d*x)^5//2+-1//8*a^-1//2*c^-1//2*(5*a*d+5*b*c)*(a^2*d^2+b^2*c^2+14*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//12*c^-1*x^-2*(a+b*x)^3//2*(c+d*x)^5//2*(5*a*d+5*b*c)+-1//24*c^-2*x^-1*(a+b*x)^(1/2)*(c+d*x)^5//2*(5*a^2*d^2+15*b^2*c^2+60*a*b*c*d)+5//4*b^(1/2)*d^(1/2)*(a*d+3*b*c)*(b*c+3*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+5//8*d*c^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(a^2*d^2+5*b^2*c^2+10*a*b*c*d)+5//24*d*c^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(a^2*d^2+9*b^2*c^2+14*a*b*c*d))
@test integrate(x^-5*(a+b*x)^5//2*(c+d*x)^5//2, x) == :(-1//4*x^-4*(a+b*x)^5//2*(c+d*x)^5//2+5*b^3//2*d^3//2*(a*d+b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//64*a^-3//2*c^-3//2*(5*a^4*d^4+5*b^4*c^4+-450*a^2*b^2*c^2*d^2+-100*a*d*b^3*c^3+-100*b*c*a^3*d^3)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//24*c^-1*x^-3*(a+b*x)^3//2*(c+d*x)^5//2*(5*a*d+5*b*c)+-1//96*c^-2*x^-2*(a+b*x)^(1/2)*(c+d*x)^5//2*(-5*a^2*d^2+15*b^2*c^2+70*a*b*c*d)+5//64*d*a^-1*c^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b^3*c^3+-1*a^3*d^3+19*b*c*a^2*d^2+45*a*d*b^2*c^2)+-1//192*a^-1*c^-2*x^-1*(a+b*x)^(1/2)*(c+d*x)^3//2*(5*a*d+15*b*c)*(b^2*c^2+-1*a^2*d^2+24*a*b*c*d))
@test integrate(x^-6*(a+b*x)^5//2*(c+d*x)^5//2, x) == :(2*b^5//2*d^5//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//5*x^-5*(a+b*x)^5//2*(c+d*x)^5//2+-1//8*c^-1*x^-4*(a+b*x)^3//2*(c+d*x)^5//2*(a*d+b*c)+-1//48*c^-2*x^-3*(a+b*x)^(1/2)*(c+d*x)^5//2*(-3*a^2*d^2+3*b^2*c^2+16*a*b*c*d)+-1//128*a^-5//2*c^-5//2*(a*d+b*c)*(3*a^4*d^4+3*b^4*c^4+-28*a*d*b^3*c^3+-28*b*c*a^3*d^3+178*a^2*b^2*c^2*d^2)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//192*a^-1*c^-2*x^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(3*a^3*d^3+3*b^3*c^3+-19*b*c*a^2*d^2+109*a*d*b^2*c^2)+1//128*a^-2*c^-2*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-3*a^4*d^4+3*b^4*c^4+-128*a^2*b^2*c^2*d^2+-22*a*d*b^3*c^3+22*b*c*a^3*d^3))
@test integrate(x^-7*(a+b*x)^5//2*(c+d*x)^5//2, x) == :(-1//6*c^-1*x^-6*(a+b*x)^5//2*(c+d*x)^7//2+5//512*a^-7//2*c^-7//2*(b*c+-1*a*d)^6*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//12*c^-2*x^-5*(a+b*x)^3//2*(c+d*x)^7//2*(b*c+-1*a*d)+-1//32*c^-3*x^-4*(a+b*x)^(1/2)*(c+d*x)^7//2*(b*c+-1*a*d)^2+-5//512*a^-3*c^-3*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^5+-1//192*a^-1*c^-3*x^-3*(a+b*x)^(1/2)*(c+d*x)^5//2*(b*c+-1*a*d)^3+5//768*a^-2*c^-3*x^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(b*c+-1*a*d)^4)
@test integrate(x^2*(a+b*x)^5//2*(c+d*x)^-1//2, x) == :(-1//40*b^-2*d^-2*(a+b*x)^7//2*(c+d*x)^(1/2)*(3*a*d+9*b*c)+-1//128*b^-5//2*d^-11//2*(b*c+-1*a*d)^3*(3*a^2*d^2+63*b^2*c^2+14*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//5*x*b^-1*d^-1*(a+b*x)^7//2*(c+d*x)^(1/2)+1//240*b^-2*d^-3*(a+b*x)^5//2*(c+d*x)^(1/2)*(3*a^2*d^2+63*b^2*c^2+14*a*b*c*d)+-1//192*b^-2*d^-4*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)*(3*a^2*d^2+63*b^2*c^2+14*a*b*c*d)+1//128*b^-2*d^-5*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^2*(3*a^2*d^2+63*b^2*c^2+14*a*b*c*d))
@test integrate(x*(a+b*x)^5//2*(c+d*x)^-1//2, x) == :(1//4*b^-1*d^-1*(a+b*x)^7//2*(c+d*x)^(1/2)+-1//24*b^-1*d^-2*(a+b*x)^5//2*(c+d*x)^(1/2)*(a*d+7*b*c)+5//64*b^-3//2*d^-9//2*(b*c+-1*a*d)^3*(a*d+7*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-5//64*b^-1*d^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^2*(a*d+7*b*c)+1//96*b^-1*d^-3*(a+b*x)^3//2*(c+d*x)^(1/2)*(a*d+7*b*c)*(-5*a*d+5*b*c))
@test integrate((a+b*x)^5//2*(c+d*x)^-1//2, x) == :(1//3*d^-1*(a+b*x)^5//2*(c+d*x)^(1/2)+-5//8*b^-1//2*d^-7//2*(b*c+-1*a*d)^3*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//12*d^-2*(a+b*x)^3//2*(c+d*x)^(1/2)*(-5*a*d+5*b*c)+5//8*d^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^2)
@test integrate(x^-1*(a+b*x)^5//2*(c+d*x)^-1//2, x) == :(-2*a^5//2*c^-1//2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+(1/2)*b*d^-1*(a+b*x)^3//2*(c+d*x)^(1/2)+1//4*b^(1/2)*d^-5//2*(3*b^2*c^2+15*a^2*d^2+-10*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//4*b*d^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-7*a*d+3*b*c))
@test integrate(x^-2*(a+b*x)^5//2*(c+d*x)^-1//2, x) == :(-1*a^3//2*c^-3//2*(-1*a*d+5*b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1*b^3//2*d^-3//2*(b*c+-5*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1*a*c^-1*x^-1*(a+b*x)^3//2*(c+d*x)^(1/2)+b*c^-1*d^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(a*d+b*c))
@test integrate(x^-3*(a+b*x)^5//2*(c+d*x)^-1//2, x) == :(2*b^5//2*d^-1//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//4*a^(1/2)*c^-5//2*(3*a^2*d^2+15*b^2*c^2+-10*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//2*a*c^-1*x^-2*(a+b*x)^3//2*(c+d*x)^(1/2)+-1//4*a*c^-2*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-3*a*d+7*b*c))
@test integrate(x^-4*(a+b*x)^5//2*(c+d*x)^-1//2, x) == :(-5//8*a^-1//2*c^-7//2*(b*c+-1*a*d)^3*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//3*c^-1*x^-3*(a+b*x)^5//2*(c+d*x)^(1/2)+-5//8*c^-3*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^2+-1//12*c^-2*x^-2*(a+b*x)^3//2*(c+d*x)^(1/2)*(-5*a*d+5*b*c))
@test integrate(x^-5*(a+b*x)^5//2*(c+d*x)^-1//2, x) == :(-1//4*a^-1*c^-1*x^-4*(a+b*x)^7//2*(c+d*x)^(1/2)+5//64*a^-3//2*c^-9//2*(b*c+-1*a*d)^3*(b*c+7*a*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//24*a^-1*c^-2*x^-3*(a+b*x)^5//2*(c+d*x)^(1/2)*(b*c+7*a*d)+1//96*a^-1*c^-3*x^-2*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+7*a*d)*(-5*a*d+5*b*c)+5//64*a^-1*c^-4*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^2*(b*c+7*a*d))
@test integrate(x^2*(a+b*x)^5//2*(c+d*x)^-3//2, x) == :(1//4*b^-1*d^-2*(a+b*x)^7//2*(c+d*x)^(1/2)+2*c^2*d^-2*(a+b*x)^7//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-1+1//24*d^-2*(a+b*x)^5//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1*(14*a*c+d*a^2*b^-1+-63*b*c^2*d^-1)+1//96*b^-1*d^-4*(a+b*x)^3//2*(c+d*x)^(1/2)*(-5*a^2*d^2+315*b^2*c^2+-70*a*b*c*d)+5//64*b^-3//2*d^-11//2*(b*c+-1*a*d)^2*(-1*a^2*d^2+63*b^2*c^2+-14*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//64*b^-1*d^-5*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-5*a*d+5*b*c)*(-1*a^2*d^2+63*b^2*c^2+-14*a*b*c*d))
@test integrate(x*(a+b*x)^5//2*(c+d*x)^-3//2, x) == :(-1//12*d^-3*(a+b*x)^3//2*(c+d*x)^(1/2)*(-5*a*d+35*b*c)+-2*c*d^-1*(a+b*x)^7//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-1+-5//8*b^-1//2*d^-9//2*(b*c+-1*a*d)^2*(-1*a*d+7*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//3*d^-2*(a+b*x)^5//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1*(-1*a*d+7*b*c)+1//8*d^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-1*a*d+7*b*c)*(-5*a*d+5*b*c))
@test integrate((a+b*x)^5//2*(c+d*x)^-3//2, x) == :(-2*d^-1*(a+b*x)^5//2*(c+d*x)^-1//2+5//2*b*d^-2*(a+b*x)^3//2*(c+d*x)^(1/2)+15//4*b^(1/2)*d^-7//2*(b*c+-1*a*d)^2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-15//4*b*d^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d))
@test integrate(x^-1*(a+b*x)^5//2*(c+d*x)^-3//2, x) == :(-2*a^5//2*c^-3//2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1*b^3//2*d^-5//2*(-5*a*d+3*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1*c^-1*d^-1*(a+b*x)^3//2*(c+d*x)^-1//2*(-2*a*d+2*b*c)+b*c^-1*d^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-2*a*d+3*b*c))
@test integrate(x^-2*(a+b*x)^5//2*(c+d*x)^-3//2, x) == :(2*b^5//2*d^-3//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1*a^3//2*c^-5//2*(-3*a*d+5*b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1*a*c^-1*x^-1*(a+b*x)^3//2*(c+d*x)^-1//2+-1*c^-2*d^-1*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)*(-3*a*d+2*b*c))
@test integrate(x^-3*(a+b*x)^5//2*(c+d*x)^-3//2, x) == :(-15//4*a^(1/2)*c^-7//2*(b*c+-1*a*d)^2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//2*c^-1*x^-2*(a+b*x)^5//2*(c+d*x)^-1//2+15//4*c^-3*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^2+-1//4*c^-2*x^-1*(a+b*x)^3//2*(c+d*x)^-1//2*(-5*a*d+5*b*c))
@test integrate(x^-4*(a+b*x)^5//2*(c+d*x)^-3//2, x) == :(-1//3*a^-1*c^-1*x^-3*(a+b*x)^7//2*(c+d*x)^-1//2+-1//8*a^-1//2*c^-9//2*(b*c+-1*a*d)^2*(-35*a*d+5*b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//12*a^-1*c^-2*x^-2*(a+b*x)^5//2*(c+d*x)^-1//2*(b*c+-7*a*d)+1//8*a^-1*c^-4*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^2*(-35*a*d+5*b*c)+-1//24*a^-1*c^-3*x^-1*(a+b*x)^3//2*(c+d*x)^-1//2*(b*c+-1*a*d)*(-35*a*d+5*b*c))
@test integrate(x^-5*(a+b*x)^5//2*(c+d*x)^-3//2, x) == :(-1//4*a*c^-1*x^-4*(a+b*x)^3//2*(c+d*x)^-1//2+5//64*a^-3//2*c^-11//2*(b*c+-1*a*d)^2*(b^2*c^2+-63*a^2*d^2+14*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//24*a*c^-2*x^-3*(a+b*x)^(1/2)*(c+d*x)^-1//2*(-9*a*d+11*b*c)+-1//96*c^-3*x^-2*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)*(-63*a*d+59*b*c)+-1//192*d*a^-1*c^-5*(a+b*x)^(1/2)*(c+d*x)^-1//2*(-945*a^3*d^3+15*b^3*c^3+-839*a*d*b^2*c^2+1785*b*c*a^2*d^2)+-1//192*a^-1*c^-4*x^-1*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)*(15*b^2*c^2+315*a^2*d^2+-322*a*b*c*d))
@test integrate(x^3*(a+b*x)^5//2*(c+d*x)^-5//2, x) == :(-2//3*d^-1*x^3*(a+b*x)^5//2*(c+d*x)^-3//2+-1//64*b^-1*d^-6*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(5*a^3*d^3+1155*b^3*c^3+-945*a*d*b^2*c^2+105*b*c*a^2*d^2)+1//64*b^-3//2*d^-13//2*(-5*a*d+5*b*c)*(a^3*d^3+231*b^3*c^3+-189*a*d*b^2*c^2+21*b*c*a^2*d^2)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//3*d^-2*x^2*(a+b*x)^5//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-1*(-12*a*d+22*b*c)+-1//24*b^-1*d^-4*(a+b*x)^5//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1*(5*a^2*d^2+231*b^2*c^2+-156*a*b*c*d+-2*b*d*x*(-59*a*d+99*b*c))+1//96*b^-1*d^-5*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1*(5*a^3*d^3+1155*b^3*c^3+-945*a*d*b^2*c^2+105*b*c*a^2*d^2))
@test integrate(x^2*(a+b*x)^5//2*(c+d*x)^-5//2, x) == :(1//8*d^-5*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(5*a^2*d^2+105*b^2*c^2+-70*a*b*c*d)+-1//8*b^-1//2*d^-11//2*(-5*a*d+5*b*c)*(a^2*d^2+21*b^2*c^2+-14*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//12*d^-4*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1*(5*a^2*d^2+105*b^2*c^2+-70*a*b*c*d)+1//3*d^-3*(a+b*x)^5//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-2*(a^2*d^2+21*b^2*c^2+-14*a*b*c*d)+2//3*c^2*d^-2*(a+b*x)^7//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-1+-4//3*c*d^-2*(a+b*x)^7//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-2*(-3*a*d+5*b*c))
@test integrate(x*(a+b*x)^5//2*(c+d*x)^-5//2, x) == :(-5//4*b*d^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-3*a*d+7*b*c)+-2//3*c*d^-1*(a+b*x)^7//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-1+-1//3*d^-2*(a+b*x)^5//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-1*(-6*a*d+14*b*c)+5//4*b^(1/2)*d^-9//2*(b*c+-1*a*d)*(-3*a*d+7*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+5//6*b*d^-3*(a+b*x)^3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1*(-3*a*d+7*b*c))
@test integrate((a+b*x)^5//2*(c+d*x)^-5//2, x) == :(-2//3*d^-1*(a+b*x)^5//2*(c+d*x)^-3//2+-5*b^3//2*d^-7//2*(b*c+-1*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+5*b^2*d^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)+-10//3*b*d^-2*(a+b*x)^3//2*(c+d*x)^-1//2)
@test integrate(x^-1*(a+b*x)^5//2*(c+d*x)^-5//2, x) == :((a+b*x)^(1/2)*(c+d*x)^-1//2*(-2*b^2*d^-2+2*a^2*c^-2)+-2*a^5//2*c^-5//2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+2*b^5//2*d^-5//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//3*c^-1*d^-1*(a+b*x)^3//2*(c+d*x)^-3//2*(-2*a*d+2*b*c))
@test integrate(x^-2*(a+b*x)^5//2*(c+d*x)^-5//2, x) == :(-1*c^-1*x^-1*(a+b*x)^5//2*(c+d*x)^-3//2+-5*a^3//2*c^-7//2*(b*c+-1*a*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//3*c^-2*(a+b*x)^3//2*(c+d*x)^-3//2*(-5*a*d+5*b*c)+5*a*c^-3*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d))
@test integrate(x^-3*(a+b*x)^5//2*(c+d*x)^-5//2, x) == :(-5//4*a^(1/2)*c^-9//2*(b*c+-1*a*d)*(-7*a*d+3*b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//2*a^-1*c^-1*x^-2*(a+b*x)^7//2*(c+d*x)^-3//2+1//4*c^-4*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)*(-35*a*d+15*b*c)+-1//4*a^-1*c^-2*x^-1*(a+b*x)^5//2*(c+d*x)^-3//2*(-7*a*d+3*b*c)+1//12*a^-1*c^-3*(a+b*x)^3//2*(c+d*x)^-3//2*(b*c+-1*a*d)*(-35*a*d+15*b*c))
@test integrate(x^-4*(a+b*x)^5//2*(c+d*x)^-5//2, x) == :(-1//3*a*c^-1*x^-3*(a+b*x)^3//2*(c+d*x)^-3//2+-1//8*a^-1//2*c^-11//2*(-5*a*d+5*b*c)*(b^2*c^2+21*a^2*d^2+-14*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//24*d*c^-5*(a+b*x)^(1/2)*(c+d*x)^-1//2*(113*b^2*c^2+315*a^2*d^2+-420*a*b*c*d)+-7//24*d*c^-4*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)*(-15*a*d+7*b*c)+-3//4*a*c^-2*x^-2*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)+-1//8*c^-3*x^-1*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)*(-21*a*d+11*b*c))
@test integrate(x^-5*(a+b*x)^5//2*(c+d*x)^-5//2, x) == :(-1//4*a*c^-1*x^-4*(a+b*x)^3//2*(c+d*x)^-3//2+1//64*a^-3//2*c^-13//2*(-5*a*d+5*b*c)*(b^3*c^3+231*a^3*d^3+-189*b*c*a^2*d^2+21*a*d*b^2*c^2)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-11//24*a*c^-2*x^-3*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)+-1//64*d*a^-1*c^-6*(a+b*x)^(1/2)*(c+d*x)^-1//2*(-1155*a^3*d^3+5*b^3*c^3+-581*a*d*b^2*c^2+1715*b*c*a^2*d^2)+-1//96*c^-3*x^-2*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)*(-99*a*d+59*b*c)+-1//64*d*a^-1*c^-5*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)*(5*b^2*c^2+385*a^2*d^2+-238*a*b*c*d)+-1//64*a^-1*c^-4*x^-1*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)*(5*b^2*c^2+231*a^2*d^2+-156*a*b*c*d))
@test integrate(x^2*(a+b*x)^-1//2*(c+d*x)^(1/2), x) == :(-1//12*b^-2*d^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(3*b*c+5*a*d)+1//3*x*b^-1*d^-1*(a+b*x)^(1/2)*(c+d*x)^3//2+1//8*b^-3*d^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b^2*c^2+5*a^2*d^2+2*a*b*c*d)+1//8*b^-7//2*d^-5//2*(b*c+-1*a*d)*(b^2*c^2+5*a^2*d^2+2*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate(x*(a+b*x)^-1//2*(c+d*x)^(1/2), x) == :((1/2)*b^-1*d^-1*(a+b*x)^(1/2)*(c+d*x)^3//2+-1//4*b^-2*d^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+3*a*d)+-1//4*b^-5//2*d^-3//2*(b*c+-1*a*d)*(b*c+3*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate((a+b*x)^-1//2*(c+d*x)^(1/2), x) == :(b^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)+b^-3//2*d^-1//2*(b*c+-1*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate(x^-1*(a+b*x)^-1//2*(c+d*x)^(1/2), x) == :(-2*a^-1//2*c^(1/2)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+2*b^-1//2*d^(1/2)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate(x^-2*(a+b*x)^-1//2*(c+d*x)^(1/2), x) == :(a^-3//2*c^-1//2*(b*c+-1*a*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1*a^-1*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2))
@test integrate(x^-3*(a+b*x)^-1//2*(c+d*x)^(1/2), x) == :(-1//2*a^-1*c^-1*x^-2*(a+b*x)^(1/2)*(c+d*x)^3//2+-1//4*a^-5//2*c^-3//2*(a*d+3*b*c)*(b*c+-1*a*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//4*a^-2*c^-1*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(a*d+3*b*c))
@test integrate(x^-4*(a+b*x)^-1//2*(c+d*x)^(1/2), x) == :(-1//3*a^-1*x^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)+1//8*a^-7//2*c^-5//2*(b*c+-1*a*d)*(a^2*d^2+5*b^2*c^2+2*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//12*a^-2*c^-1*x^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-1*a*d+5*b*c)+-1//24*a^-3*c^-2*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(a*d+3*b*c)*(-3*a*d+5*b*c))
@test integrate(x^2*(a+b*x)^-1//2*(c+d*x)^3//2, x) == :(-1//24*b^-2*d^-2*(a+b*x)^(1/2)*(c+d*x)^5//2*(3*b*c+7*a*d)+1//4*x*b^-1*d^-1*(a+b*x)^(1/2)*(c+d*x)^5//2+1//64*b^-9//2*d^-5//2*(b*c+-1*a*d)^2*(3*b^2*c^2+35*a^2*d^2+10*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//96*b^-3*d^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(3*b^2*c^2+35*a^2*d^2+10*a*b*c*d)+1//64*b^-4*d^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)*(3*b^2*c^2+35*a^2*d^2+10*a*b*c*d))
@test integrate(x*(a+b*x)^-1//2*(c+d*x)^3//2, x) == :(1//3*b^-1*d^-1*(a+b*x)^(1/2)*(c+d*x)^5//2+-1//8*b^-7//2*d^-3//2*(b*c+-1*a*d)^2*(b*c+5*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//12*b^-2*d^-1*(a+b*x)^(1/2)*(c+d*x)^3//2*(b*c+5*a*d)+-1//8*b^-3*d^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)*(b*c+5*a*d))
@test integrate((a+b*x)^-1//2*(c+d*x)^3//2, x) == :((1/2)*b^-1*(a+b*x)^(1/2)*(c+d*x)^3//2+1//4*b^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-3*a*d+3*b*c)+3//4*b^-5//2*d^-1//2*(b*c+-1*a*d)^2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate(x^-1*(a+b*x)^-1//2*(c+d*x)^3//2, x) == :(-2*a^-1//2*c^3//2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+d*b^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)+b^-3//2*d^(1/2)*(-1*a*d+3*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate(x^-2*(a+b*x)^-1//2*(c+d*x)^3//2, x) == :(2*b^-1//2*d^3//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+a^-3//2*c^(1/2)*(b*c+-3*a*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1*c*a^-1*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2))
@test integrate(x^-3*(a+b*x)^-1//2*(c+d*x)^3//2, x) == :(-3//4*a^-5//2*c^-1//2*(b*c+-1*a*d)^2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//2*a^-1*x^-2*(a+b*x)^(1/2)*(c+d*x)^3//2+1//4*a^-2*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-3*a*d+3*b*c))
@test integrate(x^-4*(a+b*x)^-1//2*(c+d*x)^3//2, x) == :(-1//3*a^-1*c^-1*x^-3*(a+b*x)^(1/2)*(c+d*x)^5//2+1//8*a^-7//2*c^-3//2*(b*c+-1*a*d)^2*(a*d+5*b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//12*a^-2*c^-1*x^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(a*d+5*b*c)+-1//8*a^-3*c^-1*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(a*d+5*b*c)*(b*c+-1*a*d))
@test integrate(x^-5*(a+b*x)^-1//2*(c+d*x)^3//2, x) == :(-1//4*c*a^-1*x^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)+-1//64*a^-9//2*c^-5//2*(b*c+-1*a*d)^2*(3*a^2*d^2+35*b^2*c^2+10*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//24*a^-2*x^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-9*a*d+7*b*c)+-1//96*a^-3*c^-1*x^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(3*a^2*d^2+35*b^2*c^2+-46*a*b*c*d)+1//192*a^-4*c^-2*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(9*a^3*d^3+105*b^3*c^3+-145*a*d*b^2*c^2+15*b*c*a^2*d^2))
@test integrate(x^2*(a+b*x)^-1//2*(c+d*x)^5//2, x) == :(-1//40*b^-2*d^-2*(a+b*x)^(1/2)*(c+d*x)^7//2*(3*b*c+9*a*d)+1//5*x*b^-1*d^-1*(a+b*x)^(1/2)*(c+d*x)^7//2+1//128*b^-11//2*d^-5//2*(b*c+-1*a*d)^3*(3*b^2*c^2+63*a^2*d^2+14*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//240*b^-3*d^-2*(a+b*x)^(1/2)*(c+d*x)^5//2*(3*b^2*c^2+63*a^2*d^2+14*a*b*c*d)+1//128*b^-5*d^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^2*(3*b^2*c^2+63*a^2*d^2+14*a*b*c*d)+1//192*b^-4*d^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(b*c+-1*a*d)*(3*b^2*c^2+63*a^2*d^2+14*a*b*c*d))
@test integrate(x*(a+b*x)^-1//2*(c+d*x)^5//2, x) == :(1//4*b^-1*d^-1*(a+b*x)^(1/2)*(c+d*x)^7//2+-5//64*b^-9//2*d^-3//2*(b*c+-1*a*d)^3*(b*c+7*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//24*b^-2*d^-1*(a+b*x)^(1/2)*(c+d*x)^5//2*(b*c+7*a*d)+-5//64*b^-4*d^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^2*(b*c+7*a*d)+-1//96*b^-3*d^-1*(a+b*x)^(1/2)*(c+d*x)^3//2*(b*c+7*a*d)*(-5*a*d+5*b*c))
@test integrate((a+b*x)^-1//2*(c+d*x)^5//2, x) == :(1//3*b^-1*(a+b*x)^(1/2)*(c+d*x)^5//2+1//12*b^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(-5*a*d+5*b*c)+5//8*b^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^2+5//8*b^-7//2*d^-1//2*(b*c+-1*a*d)^3*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate(x^-1*(a+b*x)^-1//2*(c+d*x)^5//2, x) == :(-2*a^-1//2*c^5//2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+(1/2)*d*b^-1*(a+b*x)^(1/2)*(c+d*x)^3//2+1//4*b^-5//2*d^(1/2)*(3*a^2*d^2+15*b^2*c^2+-10*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//4*d*b^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-3*a*d+7*b*c))
@test integrate(x^-2*(a+b*x)^-1//2*(c+d*x)^5//2, x) == :(a^-3//2*c^3//2*(b*c+-5*a*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+b^-3//2*d^3//2*(-1*a*d+5*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1*c*a^-1*x^-1*(a+b*x)^(1/2)*(c+d*x)^3//2+d*a^-1*b^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(a*d+b*c))
@test integrate(x^-3*(a+b*x)^-1//2*(c+d*x)^5//2, x) == :(2*b^-1//2*d^5//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//4*a^-5//2*c^(1/2)*(3*b^2*c^2+15*a^2*d^2+-10*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//2*c*a^-1*x^-2*(a+b*x)^(1/2)*(c+d*x)^3//2+1//4*c*a^-2*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-7*a*d+3*b*c))
@test integrate(x^-4*(a+b*x)^-1//2*(c+d*x)^5//2, x) == :(-1//3*a^-1*x^-3*(a+b*x)^(1/2)*(c+d*x)^5//2+5//8*a^-7//2*c^-1//2*(b*c+-1*a*d)^3*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-5//8*a^-3*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^2+1//12*a^-2*x^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(-5*a*d+5*b*c))
@test integrate(x^-5*(a+b*x)^-1//2*(c+d*x)^5//2, x) == :(-5//64*a^-9//2*c^-3//2*(b*c+-1*a*d)^3*(a*d+7*b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//4*a^-1*c^-1*x^-4*(a+b*x)^(1/2)*(c+d*x)^7//2+1//24*a^-2*c^-1*x^-3*(a+b*x)^(1/2)*(c+d*x)^5//2*(a*d+7*b*c)+-1//96*a^-3*c^-1*x^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(a*d+7*b*c)*(-5*a*d+5*b*c)+5//64*a^-4*c^-1*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^2*(a*d+7*b*c))
@test integrate(x^-6*(a+b*x)^-1//2*(c+d*x)^5//2, x) == :(-1//5*c*a^-1*x^-5*(a+b*x)^(1/2)*(c+d*x)^3//2+-1//240*a^-3*x^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(63*b^2*c^2+93*a^2*d^2+-148*a*b*c*d)+1//128*a^-11//2*c^-5//2*(b*c+-1*a*d)^3*(3*a^2*d^2+63*b^2*c^2+14*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//1920*a^-5*c^-2*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-45*a^4*d^4+945*b^4*c^4+-2310*a*d*b^3*c^3+-90*b*c*a^3*d^3+1564*a^2*b^2*c^2*d^2)+1//40*c*a^-2*x^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-13*a*d+9*b*c)+1//960*a^-4*c^-1*x^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-15*a^3*d^3+315*b^3*c^3+-749*a*d*b^2*c^2+481*b*c*a^2*d^2))
@test integrate(x^4*(1+x)^3//2*(1+-1x)^-1//2, x) == :(11//16*arcsin(x)+-11//16*(1+x)^(1/2)*(1+-1x)^(1/2)+-11//48*(1+x)^3//2*(1+-1x)^(1/2)+-1//6*x^3*(1+x)^5//2*(1+-1x)^(1/2)+-1//15*x^2*(1+x)^5//2*(1+-1x)^(1/2)+-1//120*(1+x)^5//2*(1+-1x)^(1/2)*(18+19x))
@test integrate(x^3*(1+x)^3//2*(1+-1x)^-1//2, x) == :(3//4*arcsin(x)+-3//4*(1+x)^(1/2)*(1+-1x)^(1/2)+-1//4*(1+x)^3//2*(1+-1x)^(1/2)+-1//10*(1+x)^5//2*(1+-1x)^(1/2)+-1//10*(1+x)^7//2*(1+-1x)^(1/2)+-1//5*x^2*(1+x)^5//2*(1+-1x)^(1/2))
@test integrate(x^2*(1+x)^3//2*(1+-1x)^-1//2, x) == :(7//8*arcsin(x)+-7//8*(1+x)^(1/2)*(1+-1x)^(1/2)+-7//24*(1+x)^3//2*(1+-1x)^(1/2)+-1//6*(1+x)^5//2*(1+-1x)^(1/2)+-1//4*x*(1+x)^5//2*(1+-1x)^(1/2))
@test integrate(x*(1+x)^3//2*(1+-1x)^-1//2, x) == :(-1*(1+x)^(1/2)*(1+-1x)^(1/2)+-1//3*(1+x)^3//2*(1+-1x)^(1/2)+-1//3*(1+x)^5//2*(1+-1x)^(1/2)+arcsin(x))
@test integrate((1+x)^3//2*(1+-1x)^-1//2, x) == :(3//2*arcsin(x)+-3//2*(1+x)^(1/2)*(1+-1x)^(1/2)+-1//2*(1+x)^3//2*(1+-1x)^(1/2))
@test integrate(x^-1*(1+x)^3//2*(1+-1x)^-1//2, x) == :(-1*arctanh((1+x)^(1/2)*(1+-1x)^(1/2))+2*arcsin(x)+-1*(1+x)^(1/2)*(1+-1x)^(1/2))
@test integrate(x^-2*(1+x)^3//2*(1+-1x)^-1//2, x) == :(-2*arctanh((1+x)^(1/2)*(1+-1x)^(1/2))+-1*x^-1*(1+x)^(1/2)*(1+-1x)^(1/2)+arcsin(x))
@test integrate(x^-3*(1+x)^3//2*(1+-1x)^-1//2, x) == :(-3//2*arctanh((1+x)^(1/2)*(1+-1x)^(1/2))+-3//2*x^-1*(1+x)^(1/2)*(1+-1x)^(1/2)+-1//2*x^-2*(1+x)^3//2*(1+-1x)^(1/2))
@test integrate(x^-4*(1+x)^3//2*(1+-1x)^-1//2, x) == :(-1*arctanh((1+x)^(1/2)*(1+-1x)^(1/2))+-1*x^-1*(1+x)^(1/2)*(1+-1x)^(1/2)+-1//3*x^-3*(1+x)^5//2*(1+-1x)^(1/2)+-1//3*x^-2*(1+x)^3//2*(1+-1x)^(1/2))
@test integrate(x^-5*(1+x)^3//2*(1+-1x)^-1//2, x) == :(-7//8*arctanh((1+x)^(1/2)*(1+-1x)^(1/2))+-7//8*x^-2*(1+x)^(1/2)*(1+-1x)^(1/2)+-4//3*x^-1*(1+x)^(1/2)*(1+-1x)^(1/2)+-2//3*x^-3*(1+x)^(1/2)*(1+-1x)^(1/2)+-1//4*x^-4*(1+x)^(1/2)*(1+-1x)^(1/2))
@test integrate(x^3*(a+b*x)^-1//2*(c+d*x)^-1//2, x) == :(-1//8*b^-7//2*d^-7//2*(a*d+b*c)*(5*a^2*d^2+5*b^2*c^2+-2*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//3*b^-1*d^-1*x^2*(a+b*x)^(1/2)*(c+d*x)^(1/2)+1//24*b^-3*d^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(15*a^2*d^2+15*b^2*c^2+-10*b*d*x*(a*d+b*c)+14*a*b*c*d))
@test integrate(x^2*(a+b*x)^-1//2*(c+d*x)^-1//2, x) == :(-1//4*b^-5//2*d^-5//2*(-3*(a*d+b*c)^2+4*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+(1/2)*x*b^-1*d^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)+-1//4*b^-2*d^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(3*a*d+3*b*c))
@test integrate(x*(a+b*x)^-1//2*(c+d*x)^-1//2, x) == :(b^-1*d^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)+-1*b^-3//2*d^-3//2*(a*d+b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate((a+b*x)^-1//2*(c+d*x)^-1//2, x) == :(2*b^-1//2*d^-1//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate(x^-1*(a+b*x)^-1//2*(c+d*x)^-1//2, x) == :(-2*a^-1//2*c^-1//2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate(x^-2*(a+b*x)^-1//2*(c+d*x)^-1//2, x) == :(a^-3//2*c^-3//2*(a*d+b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1*a^-1*c^-1*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2))
@test integrate(x^-3*(a+b*x)^-1//2*(c+d*x)^-1//2, x) == :(-1//4*a^-5//2*c^-5//2*(3*a^2*d^2+3*b^2*c^2+2*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//2*a^-1*c^-1*x^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)+1//4*a^-2*c^-2*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(3*a*d+3*b*c))
@test integrate(x^-4*(a+b*x)^-1//2*(c+d*x)^-1//2, x) == :(-1//3*a^-1*c^-1*x^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)+1//8*a^-7//2*c^-7//2*(a*d+b*c)*(5*a^2*d^2+5*b^2*c^2+-2*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//24*a^-3*c^-3*x^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(15*a^2*d^2+15*b^2*c^2+14*a*b*c*d)+1//12*a^-2*c^-2*x^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(5*a*d+5*b*c))
@test integrate(x^3*(a+b*x)^-1//2*(c+d*x)^-3//2, x) == :(1//4*b^-5//2*d^-7//2*(3*a^2*d^2+15*b^2*c^2+6*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-2*c*d^-1*x^2*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-1+-1//4*b^-2*d^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1*((a*d+3*b*c)*(-3*a*d+5*b*c)+-2*b*d*x*(-1*a*d+5*b*c)))
@test integrate(x^2*(a+b*x)^-1//2*(c+d*x)^-3//2, x) == :(b^-1*d^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)+-1*b^-3//2*d^-5//2*(a*d+3*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+2*c^2*d^-2*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-1)
@test integrate(x*(a+b*x)^-1//2*(c+d*x)^-3//2, x) == :(2*b^-1//2*d^-3//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-2*c*d^-1*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-1)
@test integrate((a+b*x)^-1//2*(c+d*x)^-3//2, x) == :(2*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-1)
@test integrate(x^-1*(a+b*x)^-1//2*(c+d*x)^-3//2, x) == :(-2*a^-1//2*c^-3//2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-2*d*c^-1*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-1)
@test integrate(x^-2*(a+b*x)^-1//2*(c+d*x)^-3//2, x) == :(a^-3//2*c^-5//2*(b*c+3*a*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1*a^-1*c^-1*x^-1*(a+b*x)^(1/2)*(c+d*x)^-1//2+-1*d*a^-1*c^-2*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-1*(b*c+-3*a*d))
@test integrate(x^-3*(a+b*x)^-1//2*(c+d*x)^-3//2, x) == :(-1//4*a^-5//2*c^-7//2*(3*b^2*c^2+15*a^2*d^2+6*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//2*a^-1*c^-1*x^-2*(a+b*x)^(1/2)*(c+d*x)^-1//2+1//4*a^-2*c^-2*x^-1*(a+b*x)^(1/2)*(c+d*x)^-1//2*(3*b*c+5*a*d)+1//4*d*a^-2*c^-3*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-1*(b*c+3*a*d)*(-5*a*d+3*b*c))
@test integrate(x^4*(a+b*x)^-1//2*(c+d*x)^-5//2, x) == :(1//4*b^-5//2*d^-9//2*(3*a^2*d^2+35*b^2*c^2+10*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-2//3*c*d^-1*x^3*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)^-1+-1//12*b^-2*d^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-2*(9*a^3*d^3+105*b^3*c^3+-145*a*d*b^2*c^2+-2*b*d*x*(3*a^2*d^2+35*b^2*c^2+-46*a*b*c*d)+15*b*c*a^2*d^2)+-2//3*c*d^-2*x^2*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-2*(-9*a*d+7*b*c))
@test integrate(x^3*(a+b*x)^-1//2*(c+d*x)^-5//2, x) == :(-1*b^-3//2*d^-7//2*(a*d+5*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-2//3*c*d^-1*x^2*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)^-1+1//3*b^-1*d^-3*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-2*(c*(3*a^2*d^2+15*b^2*c^2+-22*a*b*c*d)+d*x*(b*c+-1*a*d)*(-3*a*d+5*b*c)))
@test integrate(x^2*(a+b*x)^-1//2*(c+d*x)^-5//2, x) == :(2*b^-1//2*d^-5//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+2//3*c^2*d^-2*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)^-1+-4//3*c*d^-2*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-2*(-3*a*d+2*b*c))
@test integrate(x*(a+b*x)^-1//2*(c+d*x)^-5//2, x) == :(-2//3*c*d^-1*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)^-1+1//3*d^-1*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-2*(-6*a*d+2*b*c))
@test integrate((a+b*x)^-1//2*(c+d*x)^-5//2, x) == :(2*(a+b*x)^(1/2)*(c+d*x)^-3//2*(-3*a*d+3*b*c)^-1+4//3*b*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-2)
@test integrate(x^-1*(a+b*x)^-1//2*(c+d*x)^-5//2, x) == :(-2*a^-1//2*c^-5//2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-2//3*d*c^-1*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)^-1+-2//3*d*c^-2*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-2*(-3*a*d+5*b*c))
@test integrate(x^-2*(a+b*x)^-1//2*(c+d*x)^-5//2, x) == :(a^-3//2*c^-7//2*(b*c+5*a*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1*a^-1*c^-1*x^-1*(a+b*x)^(1/2)*(c+d*x)^-3//2+-1//3*d*a^-1*c^-3*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-2*(3*b^2*c^2+15*a^2*d^2+-22*a*b*c*d)+-1//3*d*a^-1*c^-2*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)^-1*(-5*a*d+3*b*c))
@test integrate(x^-3*(a+b*x)^-1//2*(c+d*x)^-5//2, x) == :(-1//4*a^-5//2*c^-9//2*(3*b^2*c^2+35*a^2*d^2+10*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//2*a^-1*c^-1*x^-2*(a+b*x)^(1/2)*(c+d*x)^-3//2+1//4*a^-2*c^-2*x^-1*(a+b*x)^(1/2)*(c+d*x)^-3//2*(3*b*c+7*a*d)+1//12*d*a^-2*c^-4*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-2*(9*b^3*c^3+105*a^3*d^3+-145*b*c*a^2*d^2+15*a*d*b^2*c^2)+1//12*d*a^-2*c^-3*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)^-1*(-35*a^2*d^2+9*b^2*c^2+18*a*b*c*d))
@test integrate(x^-1*(c*x)^-1//2*(a+b*x)^-1//2, x) == :(-2*a^-1*(c*x)^-1//2*(a+b*x)^(1/2))
@test integrate(x^-1*(a+b*x)^-1//2*(a*c+-1*b*c*x)^-1//2, x) == :(-1*a^-1*c^-1//2*arctanh(a^-1*c^-1//2*(a+b*x)^(1/2)*(a*c+-1*b*c*x)^(1/2)))
@test integrate(x^-1*(1+a+b*x)^-1//2*(1+-1a+-1*b*x)^-1//2, x) == :(-2*(1+-1*a^2)^-1//2*arctanh((1+a)^-1//2*(1+-1a)^(1/2)*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2))
@test integrate(x^3*(a+b*x)^-3//2*(c+d*x)^3//2, x) == :(-2*b^-1*x^3*(a+b*x)^-1//2*(c+d*x)^3//2+9//4*b^-2*x^2*(a+b*x)^(1/2)*(c+d*x)^3//2+-1//32*b^-4*d^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(-105*a^2*d^2+3*b^2*c^2+-4*b*d*x*(b*c+-21*a*d)+14*a*b*c*d)+1//64*b^-5*d^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-315*a^3*d^3+3*b^3*c^3+15*a*d*b^2*c^2+105*b*c*a^2*d^2)+1//64*b^-11//2*d^-5//2*(-3*a*d+3*b*c)*(b^3*c^3+-105*a^3*d^3+5*a*d*b^2*c^2+35*b*c*a^2*d^2)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate(x^2*(a+b*x)^-3//2*(c+d*x)^3//2, x) == :(1//3*b^-2*d^-1*(a+b*x)^(1/2)*(c+d*x)^5//2+-2*a^2*b^-2*(a+b*x)^-1//2*(c+d*x)^5//2*(b*c+-1*a*d)^-1+-1//8*b^-4*d^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b^2*c^2+-35*a^2*d^2+10*a*b*c*d)+-1//8*b^-9//2*d^-3//2*(b*c+-1*a*d)*(b^2*c^2+-35*a^2*d^2+10*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//12*b^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(b*c+-1*a*d)^-1*(10*a*c+b*c^2*d^-1+-35*d*a^2*b^-1))
@test integrate(x*(a+b*x)^-3//2*(c+d*x)^3//2, x) == :(1//4*b^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-15*a*d+3*b*c)+(1/2)*b^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(b*c+-1*a*d)^-1*(b*c+-5*a*d)+2*a*b^-1*(a+b*x)^-1//2*(c+d*x)^5//2*(b*c+-1*a*d)^-1+1//4*b^-7//2*d^-1//2*(b*c+-1*a*d)*(-15*a*d+3*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate((a+b*x)^-3//2*(c+d*x)^3//2, x) == :(-2*b^-1*(a+b*x)^-1//2*(c+d*x)^3//2+3*d*b^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)+3*b^-5//2*d^(1/2)*(b*c+-1*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate(x^-1*(a+b*x)^-3//2*(c+d*x)^3//2, x) == :(-2*a^-3//2*c^3//2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+2*b^-3//2*d^3//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+a^-1*b^-1*(a+b*x)^-1//2*(c+d*x)^(1/2)*(-2*a*d+2*b*c))
@test integrate(x^-2*(a+b*x)^-3//2*(c+d*x)^3//2, x) == :(a^-2*(a+b*x)^-1//2*(c+d*x)^(1/2)*(-3*b*c+3*a*d)+-1*a^-1*x^-1*(a+b*x)^-1//2*(c+d*x)^3//2+3*a^-5//2*c^(1/2)*(b*c+-1*a*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate(x^-3*(a+b*x)^-3//2*(c+d*x)^3//2, x) == :(-1//2*a^-1*c^-1*x^-2*(a+b*x)^-1//2*(c+d*x)^5//2+-1//4*a^-7//2*c^-1//2*(-1*a*d+5*b*c)*(-3*a*d+3*b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//4*a^-3*c^-1*(a+b*x)^-1//2*(c+d*x)^(1/2)*(-1*a*d+5*b*c)*(-3*a*d+3*b*c)+1//4*a^-2*c^-1*x^-1*(a+b*x)^-1//2*(c+d*x)^3//2*(-1*a*d+5*b*c))
@test integrate(x^-4*(a+b*x)^-3//2*(c+d*x)^3//2, x) == :(-1//3*c*a^-1*x^-3*(a+b*x)^-1//2*(c+d*x)^(1/2)+1//8*a^-9//2*c^-3//2*(b*c+-1*a*d)*(-1*a^2*d^2+35*b^2*c^2+-10*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//12*a^-2*x^-2*(a+b*x)^-1//2*(c+d*x)^(1/2)*(-7*a*d+7*b*c)+-1//24*b*a^-4*c^-1*(a+b*x)^-1//2*(c+d*x)^(1/2)*(3*a^2*d^2+105*b^2*c^2+-100*a*b*c*d)+-1//24*a^-3*c^-1*x^-1*(a+b*x)^-1//2*(c+d*x)^(1/2)*(b*c+-1*a*d)*(-3*a*d+35*b*c))
@test integrate(x^3*(a+b*x)^-3//2*(c+d*x)^5//2, x) == :(-2*b^-1*x^3*(a+b*x)^-1//2*(c+d*x)^5//2+11//5*b^-2*x^2*(a+b*x)^(1/2)*(c+d*x)^5//2+-1//80*b^-4*d^-2*(a+b*x)^(1/2)*(c+d*x)^5//2*(-231*a^2*d^2+5*b^2*c^2+-2*b*d*x*(-99*a*d+5*b*c)+30*a*b*c*d)+1//64*b^-5*d^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(b^3*c^3+-231*a^3*d^3+7*a*d*b^2*c^2+63*b*c*a^2*d^2)+3//128*b^-13//2*d^-5//2*(b*c+-1*a*d)^2*(b^3*c^3+-231*a^3*d^3+7*a*d*b^2*c^2+63*b*c*a^2*d^2)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//128*b^-6*d^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-3*a*d+3*b*c)*(b^3*c^3+-231*a^3*d^3+7*a*d*b^2*c^2+63*b*c*a^2*d^2))
@test integrate(x^2*(a+b*x)^-3//2*(c+d*x)^5//2, x) == :(1//4*b^-2*d^-1*(a+b*x)^(1/2)*(c+d*x)^7//2+-2*a^2*b^-2*(a+b*x)^-1//2*(c+d*x)^7//2*(b*c+-1*a*d)^-1+-5//64*b^-11//2*d^-3//2*(b*c+-1*a*d)^2*(b^2*c^2+-63*a^2*d^2+14*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//24*b^-2*(a+b*x)^(1/2)*(c+d*x)^5//2*(b*c+-1*a*d)^-1*(14*a*c+b*c^2*d^-1+-63*d*a^2*b^-1)+-1//96*b^-4*d^-1*(a+b*x)^(1/2)*(c+d*x)^3//2*(-315*a^2*d^2+5*b^2*c^2+70*a*b*c*d)+-1//64*b^-5*d^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-5*a*d+5*b*c)*(b^2*c^2+-63*a^2*d^2+14*a*b*c*d))
@test integrate(x*(a+b*x)^-3//2*(c+d*x)^5//2, x) == :(1//12*b^-3*(a+b*x)^(1/2)*(c+d*x)^3//2*(-35*a*d+5*b*c)+2*a*b^-1*(a+b*x)^-1//2*(c+d*x)^7//2*(b*c+-1*a*d)^-1+1//3*b^-2*(a+b*x)^(1/2)*(c+d*x)^5//2*(b*c+-1*a*d)^-1*(b*c+-7*a*d)+1//8*b^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)*(-35*a*d+5*b*c)+1//8*b^-9//2*d^-1//2*(b*c+-1*a*d)^2*(-35*a*d+5*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate((a+b*x)^-3//2*(c+d*x)^5//2, x) == :(-2*b^-1*(a+b*x)^-1//2*(c+d*x)^5//2+5//2*d*b^-2*(a+b*x)^(1/2)*(c+d*x)^3//2+15//4*b^-7//2*d^(1/2)*(b*c+-1*a*d)^2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+15//4*d*b^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d))
@test integrate(x^-1*(a+b*x)^-3//2*(c+d*x)^5//2, x) == :(-2*a^-3//2*c^5//2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+b^-5//2*d^3//2*(-3*a*d+5*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+a^-1*b^-1*(a+b*x)^-1//2*(c+d*x)^3//2*(-2*a*d+2*b*c)+-1*d*a^-1*b^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-3*a*d+2*b*c))
@test integrate(x^-2*(a+b*x)^-3//2*(c+d*x)^5//2, x) == :(2*b^-3//2*d^5//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+a^-5//2*c^3//2*(-5*a*d+3*b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1*c*a^-1*x^-1*(a+b*x)^-1//2*(c+d*x)^3//2+-1*a^-2*b^-1*(a+b*x)^-1//2*(c+d*x)^(1/2)*(b*c+-1*a*d)*(-2*a*d+3*b*c))
@test integrate(x^-3*(a+b*x)^-3//2*(c+d*x)^5//2, x) == :(-15//4*a^-7//2*c^(1/2)*(b*c+-1*a*d)^2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//2*a^-1*x^-2*(a+b*x)^-1//2*(c+d*x)^5//2+15//4*a^-3*(a+b*x)^-1//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^2+1//4*a^-2*x^-1*(a+b*x)^-1//2*(c+d*x)^3//2*(-5*a*d+5*b*c))
@test integrate(x^-4*(a+b*x)^-3//2*(c+d*x)^5//2, x) == :(-1//3*a^-1*c^-1*x^-3*(a+b*x)^-1//2*(c+d*x)^7//2+5//8*a^-9//2*c^-1//2*(b*c+-1*a*d)^2*(-1*a*d+7*b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-5//8*a^-4*c^-1*(a+b*x)^-1//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^2*(-1*a*d+7*b*c)+1//12*a^-2*c^-1*x^-2*(a+b*x)^-1//2*(c+d*x)^5//2*(-1*a*d+7*b*c)+-1//24*a^-3*c^-1*x^-1*(a+b*x)^-1//2*(c+d*x)^3//2*(-1*a*d+7*b*c)*(-5*a*d+5*b*c))
@test integrate(x^-5*(a+b*x)^-3//2*(c+d*x)^5//2, x) == :(-5//64*a^-11//2*c^-3//2*(b*c+-1*a*d)^2*(-1*a^2*d^2+63*b^2*c^2+-14*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//4*c*a^-1*x^-4*(a+b*x)^-1//2*(c+d*x)^3//2+-1//96*a^-3*x^-2*(a+b*x)^-1//2*(c+d*x)^(1/2)*(b*c+-1*a*d)*(-59*a*d+63*b*c)+1//24*c*a^-2*x^-3*(a+b*x)^-1//2*(c+d*x)^(1/2)*(-11*a*d+9*b*c)+1//192*b*a^-5*c^-1*(a+b*x)^-1//2*(c+d*x)^(1/2)*(-15*a^3*d^3+945*b^3*c^3+-1785*a*d*b^2*c^2+839*b*c*a^2*d^2)+1//192*a^-4*c^-1*x^-1*(a+b*x)^-1//2*(c+d*x)^(1/2)*(b*c+-1*a*d)*(15*a^2*d^2+315*b^2*c^2+-322*a*b*c*d))
@test integrate(x^4*(a+b*x)^-3//2*(c+d*x)^-3//2, x) == :(1//4*b^-7//2*d^-7//2*(15*a^2*d^2+15*b^2*c^2+18*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+2*a*b^-1*x^3*(a+b*x)^-1//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-1+-1//4*b^-3*d^-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-2*((a*d+b*c)*(15*a^2*d^2+15*b^2*c^2+-22*a*b*c*d)+-2*b*d*x*(5*a^2*d^2+5*b^2*c^2+-2*a*b*c*d))+-2*c*b^-1*d^-1*x^2*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-2*(a*d+b*c))
@test integrate(x^3*(a+b*x)^-3//2*(c+d*x)^-3//2, x) == :(-1*b^-5//2*d^-5//2*(3*a*d+3*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+b^-2*d^-2*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-2*(c*(3*a^2*d^2+3*b^2*c^2+-2*a*b*c*d)+d*x*(b*c+-1*a*d)*(b*c+-3*a*d))+2*a*b^-1*x^2*(a+b*x)^-1//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-1)
@test integrate(x^2*(a+b*x)^-3//2*(c+d*x)^-3//2, x) == :(2*b^-3//2*d^-3//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-2*a^2*b^-2*(a+b*x)^-1//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-1+-1*b^-2*d^-1*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-2*(2*a^2*d^2+2*b^2*c^2))
@test integrate(x*(a+b*x)^-3//2*(c+d*x)^-3//2, x) == :(d^-1*(a+b*x)^-1//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-2*(2*a*d+2*b*c)+-2*c*d^-1*(a+b*x)^-1//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-1)
@test integrate((a+b*x)^-3//2*(c+d*x)^-3//2, x) == :(-2*(a+b*x)^-1//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-1+-4*d*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-2)
@test integrate(x^-1*(a+b*x)^-3//2*(c+d*x)^-3//2, x) == :(-2*a^-3//2*c^-3//2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+2*b*a^-1*(a+b*x)^-1//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-1+2*d*a^-1*c^-1*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-2*(a*d+b*c))
@test integrate(x^-2*(a+b*x)^-3//2*(c+d*x)^-3//2, x) == :(a^-5//2*c^-5//2*(3*a*d+3*b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1*a^-1*c^-1*x^-1*(a+b*x)^-1//2*(c+d*x)^-1//2+-1*b*a^-2*c^-1*(a+b*x)^-1//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-1*(-1*a*d+3*b*c)+-1*d*a^-2*c^-2*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-2*(3*a^2*d^2+3*b^2*c^2+-2*a*b*c*d))
@test integrate(x^-3*(a+b*x)^-3//2*(c+d*x)^-3//2, x) == :(-1//4*a^-7//2*c^-7//2*(15*a^2*d^2+15*b^2*c^2+18*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//2*a^-1*c^-1*x^-2*(a+b*x)^-1//2*(c+d*x)^-1//2+1//4*a^-2*c^-2*x^-1*(a+b*x)^-1//2*(c+d*x)^-1//2*(5*a*d+5*b*c)+1//4*b*a^-3*c^-2*(a+b*x)^-1//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-1*(-5*a^2*d^2+15*b^2*c^2+-2*a*b*c*d)+1//4*d*a^-3*c^-3*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-2*(a*d+b*c)*(15*a^2*d^2+15*b^2*c^2+-22*a*b*c*d))
@test integrate(x^5*(a+b*x)^-3//2*(c+d*x)^-5//2, x) == :(1//4*b^-7//2*d^-9//2*(15*a^2*d^2+35*b^2*c^2+30*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+2*a*b^-1*x^4*(a+b*x)^-1//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-1+-1//12*b^-3*d^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-3*(-45*a^4*d^4+105*b^4*c^4+-190*a*d*b^3*c^3+-2*b*d*x*(-15*a^3*d^3+35*b^3*c^3+-61*a*d*b^2*c^2+9*b*c*a^2*d^2)+30*b*c*a^3*d^3+36*a^2*b^2*c^2*d^2)+-2//3*c*b^-1*d^-1*x^3*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)^-2*(b*c+3*a*d)+-2//3*c*b^-1*d^-2*x^2*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-3*(-3*a^2*d^2+7*b^2*c^2+-12*a*b*c*d))
@test integrate(x^4*(a+b*x)^-3//2*(c+d*x)^-5//2, x) == :(-1*b^-5//2*d^-7//2*(3*a*d+5*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+2*a*b^-1*x^3*(a+b*x)^-1//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-1+1//3*b^-2*d^-3*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-3*(c*(-9*a^3*d^3+15*b^3*c^3+-31*a*d*b^2*c^2+9*b*c*a^2*d^2)+d*x*(b*c+-1*a*d)*(5*b^2*c^2+9*a^2*d^2+-6*a*b*c*d))+-2//3*c*b^-1*d^-1*x^2*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)^-2*(b*c+3*a*d))
@test integrate(x^3*(a+b*x)^-3//2*(c+d*x)^-5//2, x) == :(2*b^-3//2*d^-5//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+2*a*b^-1*x^2*(a+b*x)^-1//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-1+-2//3*c*b^-1*d^-2*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)^-3*(c*(a*d+3*b*c)*(b*c+-3*a*d)+2*d*x*(-3*a^2*d^2+2*b^2*c^2+-3*a*b*c*d)))
@test integrate(x^2*(a+b*x)^-3//2*(c+d*x)^-5//2, x) == :(-2*a^2*b^-2*(a+b*x)^-1//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-1+-1//3*b^-2*d^-1*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)^-2*(2*b^2*c^2+6*a^2*d^2)+1//3*b^-1*d^-1*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-3*(-6*a^2*d^2+2*b^2*c^2+-12*a*b*c*d))
@test integrate(x*(a+b*x)^-3//2*(c+d*x)^-5//2, x) == :(1//3*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-3*(4*b*c+12*a*d)+2*a*b^-1*(a+b*x)^-1//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-1+1//3*b^-1*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)^-2*(2*b*c+6*a*d))
@test integrate((a+b*x)^-3//2*(c+d*x)^-5//2, x) == :(-2*(a+b*x)^-1//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-1+-8//3*d*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)^-2+-16//3*b*d*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-3)
@test integrate(x^-1*(a+b*x)^-3//2*(c+d*x)^-5//2, x) == :(-2*a^-3//2*c^-5//2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+2*b*a^-1*(a+b*x)^-1//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-1+2//3*d*a^-1*c^-1*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)^-2*(a*d+3*b*c)+2//3*d*a^-1*c^-2*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-3*(b*c+3*a*d)*(-1*a*d+3*b*c))
@test integrate(x^-2*(a+b*x)^-3//2*(c+d*x)^-5//2, x) == :(a^-5//2*c^-7//2*(3*b*c+5*a*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1*a^-1*c^-1*x^-1*(a+b*x)^-1//2*(c+d*x)^-3//2+-1*b*a^-2*c^-1*(a+b*x)^-1//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-1*(-1*a*d+3*b*c)+-1//3*d*a^-2*c^-3*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-3*(-15*a^3*d^3+9*b^3*c^3+-9*a*d*b^2*c^2+31*b*c*a^2*d^2)+-1//3*d*a^-2*c^-2*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)^-2*(5*a^2*d^2+9*b^2*c^2+-6*a*b*c*d))
@test integrate(x^-3*(a+b*x)^-3//2*(c+d*x)^-5//2, x) == :(-1//4*a^-7//2*c^-9//2*(15*b^2*c^2+35*a^2*d^2+30*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//2*a^-1*c^-1*x^-2*(a+b*x)^-1//2*(c+d*x)^-3//2+1//4*a^-2*c^-2*x^-1*(a+b*x)^-1//2*(c+d*x)^-3//2*(5*b*c+7*a*d)+1//4*b*a^-3*c^-2*(a+b*x)^-1//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-1*(-7*a^2*d^2+15*b^2*c^2)+1//12*d*a^-3*c^-4*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-3*(-105*a^4*d^4+45*b^4*c^4+-36*a^2*b^2*c^2*d^2+-30*a*d*b^3*c^3+190*b*c*a^3*d^3)+1//12*d*a^-3*c^-3*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)^-2*(35*a^3*d^3+45*b^3*c^3+-33*b*c*a^2*d^2+-15*a*d*b^2*c^2))
@test integrate(x^4*(a+b*x)^-5//2*(c+d*x)^5//2, x) == :(-2//3*b^-1*x^4*(a+b*x)^-3//2*(c+d*x)^5//2+1//128*b^-7*d^-2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(3*b^4*c^4+3003*a^4*d^4+-2772*b*c*a^3*d^3+28*a*d*b^3*c^3+378*a^2*b^2*c^2*d^2)+1//128*b^-15//2*d^-5//2*(b*c+-1*a*d)*(3*b^4*c^4+3003*a^4*d^4+-2772*b*c*a^3*d^3+28*a*d*b^3*c^3+378*a^2*b^2*c^2*d^2)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//3*b^-2*x^3*(a+b*x)^-1//2*(c+d*x)^5//2*(b*c+-1*a*d)^-1*(-26*a*d+16*b*c)+-1//240*b^-5*d^-2*(a+b*x)^(1/2)*(c+d*x)^5//2*(b*c+-1*a*d)^-1*(15*b^3*c^3+3003*a^3*d^3+-2343*b*c*a^2*d^2+-2*b*d*x*(15*b^2*c^2+1287*a^2*d^2+-902*a*b*c*d)+125*a*d*b^2*c^2)+1//15*b^-3*x^2*(a+b*x)^(1/2)*(c+d*x)^5//2*(b*c+-1*a*d)^-1*(-143*a*d+93*b*c)+1//192*b^-6*d^-2*(a+b*x)^(1/2)*(c+d*x)^3//2*(b*c+-1*a*d)^-1*(3*b^4*c^4+3003*a^4*d^4+-2772*b*c*a^3*d^3+28*a*d*b^3*c^3+378*a^2*b^2*c^2*d^2))
@test integrate(x^3*(a+b*x)^-5//2*(c+d*x)^5//2, x) == :(-2//3*b^-1*x^3*(a+b*x)^-3//2*(c+d*x)^5//2+-1//64*b^-6*d^-1*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(5*b^3*c^3+1155*a^3*d^3+-945*b*c*a^2*d^2+105*a*d*b^2*c^2)+-1//64*b^-13//2*d^-3//2*(-5*a*d+5*b*c)*(b^3*c^3+231*a^3*d^3+-189*b*c*a^2*d^2+21*a*d*b^2*c^2)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//3*b^-2*x^2*(a+b*x)^-1//2*(c+d*x)^5//2*(b*c+-1*a*d)^-1*(-22*a*d+12*b*c)+-1//96*b^-5*d^-1*(a+b*x)^(1/2)*(c+d*x)^3//2*(b*c+-1*a*d)^-1*(5*b^3*c^3+1155*a^3*d^3+-945*b*c*a^2*d^2+105*a*d*b^2*c^2)+1//24*b^-4*d^-1*(a+b*x)^(1/2)*(c+d*x)^5//2*(b*c+-1*a*d)^-1*(5*b^2*c^2+231*a^2*d^2+-156*a*b*c*d+2*b*d*x*(-99*a*d+59*b*c)))
@test integrate(x^2*(a+b*x)^-5//2*(c+d*x)^5//2, x) == :(1//8*b^-5*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(5*b^2*c^2+105*a^2*d^2+-70*a*b*c*d)+-2//3*a^2*b^-2*(a+b*x)^-3//2*(c+d*x)^7//2*(b*c+-1*a*d)^-1+1//3*b^-3*(a+b*x)^(1/2)*(c+d*x)^5//2*(b*c+-1*a*d)^-2*(b^2*c^2+21*a^2*d^2+-14*a*b*c*d)+1//8*b^-11//2*d^-1//2*(-5*a*d+5*b*c)*(b^2*c^2+21*a^2*d^2+-14*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//12*b^-4*(a+b*x)^(1/2)*(c+d*x)^3//2*(b*c+-1*a*d)^-1*(5*b^2*c^2+105*a^2*d^2+-70*a*b*c*d)+4//3*a*b^-2*(a+b*x)^-1//2*(c+d*x)^7//2*(b*c+-1*a*d)^-2*(-5*a*d+3*b*c))
@test integrate(x*(a+b*x)^-5//2*(c+d*x)^5//2, x) == :(-1//3*b^-2*(a+b*x)^-1//2*(c+d*x)^5//2*(b*c+-1*a*d)^-1*(-14*a*d+6*b*c)+2//3*a*b^-1*(a+b*x)^-3//2*(c+d*x)^7//2*(b*c+-1*a*d)^-1+5//4*d*b^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(-7*a*d+3*b*c)+5//4*b^-9//2*d^(1/2)*(b*c+-1*a*d)*(-7*a*d+3*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+5//6*d*b^-3*(a+b*x)^(1/2)*(c+d*x)^3//2*(b*c+-1*a*d)^-1*(-7*a*d+3*b*c))
@test integrate((a+b*x)^-5//2*(c+d*x)^5//2, x) == :(-2//3*b^-1*(a+b*x)^-3//2*(c+d*x)^5//2+5*b^-3*d^2*(a+b*x)^(1/2)*(c+d*x)^(1/2)+5*b^-7//2*d^3//2*(b*c+-1*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-10//3*d*b^-2*(a+b*x)^-1//2*(c+d*x)^3//2)
@test integrate(x^-1*(a+b*x)^-5//2*(c+d*x)^5//2, x) == :((a+b*x)^-1//2*(c+d*x)^(1/2)*(-2*b^-2*d^2+2*a^-2*c^2)+-2*a^-5//2*c^5//2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+2*b^-5//2*d^5//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//3*a^-1*b^-1*(a+b*x)^-3//2*(c+d*x)^3//2*(-2*a*d+2*b*c))
@test integrate(x^-2*(a+b*x)^-5//2*(c+d*x)^5//2, x) == :(-1*a^-1*x^-1*(a+b*x)^-3//2*(c+d*x)^5//2+5*a^-7//2*c^3//2*(b*c+-1*a*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//3*a^-2*(a+b*x)^-3//2*(c+d*x)^3//2*(-5*a*d+5*b*c)+-5*c*a^-3*(a+b*x)^-1//2*(c+d*x)^(1/2)*(b*c+-1*a*d))
@test integrate(x^-3*(a+b*x)^-5//2*(c+d*x)^5//2, x) == :(-5//4*a^-9//2*c^(1/2)*(b*c+-1*a*d)*(-3*a*d+7*b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//2*a^-1*c^-1*x^-2*(a+b*x)^-3//2*(c+d*x)^7//2+1//4*a^-4*(a+b*x)^-1//2*(c+d*x)^(1/2)*(b*c+-1*a*d)*(-15*a*d+35*b*c)+1//4*a^-2*c^-1*x^-1*(a+b*x)^-3//2*(c+d*x)^5//2*(-3*a*d+7*b*c)+1//12*a^-3*c^-1*(a+b*x)^-3//2*(c+d*x)^3//2*(b*c+-1*a*d)*(-15*a*d+35*b*c))
@test integrate(x^-4*(a+b*x)^-5//2*(c+d*x)^5//2, x) == :(-1//3*c*a^-1*x^-3*(a+b*x)^-3//2*(c+d*x)^3//2+-1//24*b*a^-5*(a+b*x)^-1//2*(c+d*x)^(1/2)*(113*a^2*d^2+315*b^2*c^2+-420*a*b*c*d)+1//8*a^-11//2*c^-1//2*(-5*a*d+5*b*c)*(a^2*d^2+21*b^2*c^2+-14*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-7//24*b*a^-4*(a+b*x)^-3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)*(-7*a*d+15*b*c)+-1//8*a^-3*x^-1*(a+b*x)^-3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)*(-11*a*d+21*b*c)+3//4*c*a^-2*x^-2*(a+b*x)^-3//2*(c+d*x)^(1/2)*(b*c+-1*a*d))
@test integrate(x^-5*(a+b*x)^-5//2*(c+d*x)^5//2, x) == :(-1//4*c*a^-1*x^-4*(a+b*x)^-3//2*(c+d*x)^3//2+-1//64*a^-13//2*c^-3//2*(-5*a*d+5*b*c)*(a^3*d^3+231*b^3*c^3+-189*a*d*b^2*c^2+21*b*c*a^2*d^2)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//96*a^-3*x^-2*(a+b*x)^-3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)*(-59*a*d+99*b*c)+1//64*b*a^-6*c^-1*(a+b*x)^-1//2*(c+d*x)^(1/2)*(-5*a^3*d^3+1155*b^3*c^3+-1715*a*d*b^2*c^2+581*b*c*a^2*d^2)+11//24*c*a^-2*x^-3*(a+b*x)^-3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)+1//64*b*a^-5*c^-1*(a+b*x)^-3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)*(5*a^2*d^2+385*b^2*c^2+-238*a*b*c*d)+1//64*a^-4*c^-1*x^-1*(a+b*x)^-3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)*(5*a^2*d^2+231*b^2*c^2+-156*a*b*c*d))
@test integrate(x^2*(a+b*x)^-5//2*(c+d*x)^-1//2, x) == :(2*b^-5//2*d^-1//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-2//3*a^2*b^-2*(a+b*x)^-3//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1+4//3*a*b^-2*(a+b*x)^-1//2*(c+d*x)^(1/2)*(b*c+-1*a*d)^-2*(-2*a*d+3*b*c))
@test integrate(x^6*(a+b*x)^-5//2*(c+d*x)^-5//2, x) == :(1//4*b^-9//2*d^-9//2*(35*a^2*d^2+35*b^2*c^2+50*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//12*b^-4*d^-4*(a+b*x)^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-4*((a*d+b*c)*(105*a^4*d^4+105*b^4*c^4+-340*a*d*b^3*c^3+-340*b*c*a^3*d^3+406*a^2*b^2*c^2*d^2)+-2*b*d*x*(35*a^4*d^4+35*b^4*c^4+-76*a*d*b^3*c^3+-76*b*c*a^3*d^3+18*a^2*b^2*c^2*d^2))+2//3*a*b^-1*x^5*(a+b*x)^-3//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-1+2//3*a*b^-2*x^4*(a+b*x)^-1//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-2*(-7*a*d+13*b*c)+-2//3*c*b^-2*d^-1*x^3*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)^-3*(b^2*c^2+-7*a^2*d^2+14*a*b*c*d)+-2//3*c*b^-2*d^-2*x^2*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-4*(a*d+b*c)*(7*a^2*d^2+7*b^2*c^2+-22*a*b*c*d))
@test integrate(x^5*(a+b*x)^-5//2*(c+d*x)^-5//2, x) == :(-1*b^-7//2*d^-7//2*(5*a*d+5*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+1//3*b^-3*d^-3*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-4*(c*(15*a^4*d^4+15*b^4*c^4+-40*a*d*b^3*c^3+-40*b*c*a^3*d^3+18*a^2*b^2*c^2*d^2)+d*x*(b*c+-1*a*d)*(-15*a^3*d^3+5*b^3*c^3+-9*a*d*b^2*c^2+35*b*c*a^2*d^2))+2//3*a*b^-1*x^4*(a+b*x)^-3//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-1+2//3*a*b^-2*x^3*(a+b*x)^-1//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-2*(-5*a*d+11*b*c)+-2//3*c*b^-2*d^-1*x^2*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)^-3*(b^2*c^2+-5*a^2*d^2+12*a*b*c*d))
@test integrate(x^4*(a+b*x)^-5//2*(c+d*x)^-5//2, x) == :(2*b^-5//2*d^-5//2*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+2//3*a*b^-1*x^3*(a+b*x)^-3//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-1+2*a*b^-2*x^2*(a+b*x)^-1//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-2*(-1*a*d+3*b*c)+-2//3*c*b^-2*d^-2*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)^-4*(c*(a*d+b*c)*(3*a^2*d^2+3*b^2*c^2+-14*a*b*c*d)+2*d*x*(2*b^3*c^3+3*a^3*d^3+-1*a*d*b^2*c^2+-12*b*c*a^2*d^2)))
@test integrate(x^3*(a+b*x)^-5//2*(c+d*x)^-5//2, x) == :(-2*x^3*(a+b*x)^-3//2*(c+d*x)^-3//2*(-3*a*d+3*b*c)^-1+-4*c*a^2*b^-2*(a+b*x)^-1//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-2+-4//3*c*b^-2*d^-1*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)^-3*(b^2*c^2+3*a^2*d^2)+4//3*c*b^-1*d^-1*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-4*(b^2*c^2+-3*a^2*d^2+-6*a*b*c*d))
@test integrate(x^2*(a+b*x)^-5//2*(c+d*x)^-5//2, x) == :(-2//3*a^2*b^-2*(a+b*x)^-3//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-1+1//3*b^-1*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-4*(4*a^2*d^2+4*b^2*c^2+24*a*b*c*d)+1//3*b^-2*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)^-3*(2*a^2*d^2+2*b^2*c^2+12*a*b*c*d)+4*a*c*b^-1*(a+b*x)^-1//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-2)
@test integrate(x*(a+b*x)^-5//2*(c+d*x)^-5//2, x) == :(-1//3*(a+b*x)^-1//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-3*(8*a*d+8*b*c)+-16//3*d*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-4*(a*d+b*c)+-2//3*c*d^-1*(a+b*x)^-3//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-1+1//3*d^-1*(a+b*x)^-3//2*(c+d*x)^-1//2*(b*c+-1*a*d)^-2*(2*a*d+2*b*c))
@test integrate((a+b*x)^-5//2*(c+d*x)^-5//2, x) == :(-2*(a+b*x)^-3//2*(c+d*x)^-3//2*(-3*a*d+3*b*c)^-1+4*d*(a+b*x)^-1//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-2+16//3*d^2*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)^-3+32//3*b*d^2*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-4)
@test integrate(x^-1*(a+b*x)^-5//2*(c+d*x)^-5//2, x) == :(-2*a^-5//2*c^-5//2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+2//3*b*a^-1*(a+b*x)^-3//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-1+2*b*a^-2*(a+b*x)^-1//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-2*(b*c+-3*a*d)+2//3*d*a^-2*c^-1*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)^-3*(-1*a^2*d^2+3*b^2*c^2+-10*a*b*c*d)+2//3*d*a^-2*c^-2*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-4*(a*d+b*c)*(3*a^2*d^2+3*b^2*c^2+-14*a*b*c*d))
@test integrate(x^-2*(a+b*x)^-5//2*(c+d*x)^-5//2, x) == :(a^-7//2*c^-7//2*(5*a*d+5*b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1*a^-1*c^-1*x^-1*(a+b*x)^-3//2*(c+d*x)^-3//2+-1*b*a^-3*c^-1*(a+b*x)^-1//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-2*(a^2*d^2+5*b^2*c^2+-10*a*b*c*d)+-1//3*b*a^-2*c^-1*(a+b*x)^-3//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-1*(-3*a*d+5*b*c)+-1//3*d*a^-3*c^-3*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-4*(15*a^4*d^4+15*b^4*c^4+-40*a*d*b^3*c^3+-40*b*c*a^3*d^3+18*a^2*b^2*c^2*d^2)+-1//3*d*a^-3*c^-2*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)^-3*(-5*a^3*d^3+15*b^3*c^3+-35*a*d*b^2*c^2+9*b*c*a^2*d^2))
@test integrate(x^-3*(a+b*x)^-5//2*(c+d*x)^-5//2, x) == :(-1//4*a^-9//2*c^-9//2*(35*a^2*d^2+35*b^2*c^2+50*a*b*c*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2)+-1//2*a^-1*c^-1*x^-2*(a+b*x)^-3//2*(c+d*x)^-3//2+1//4*a^-2*c^-2*x^-1*(a+b*x)^-3//2*(c+d*x)^-3//2*(7*a*d+7*b*c)+1//4*b*a^-4*c^-2*(a+b*x)^-1//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-2*(7*a^3*d^3+35*b^3*c^3+-55*a*d*b^2*c^2+-3*b*c*a^2*d^2)+1//12*b*a^-3*c^-2*(a+b*x)^-3//2*(c+d*x)^-3//2*(b*c+-1*a*d)^-1*(-21*a^2*d^2+35*b^2*c^2+-6*a*b*c*d)+1//12*d*a^-4*c^-3*(a+b*x)^(1/2)*(c+d*x)^-3//2*(b*c+-1*a*d)^-3*(-35*a^4*d^4+105*b^4*c^4+-200*a*d*b^3*c^3+18*a^2*b^2*c^2*d^2+48*b*c*a^3*d^3)+1//12*d*a^-4*c^-4*(a+b*x)^(1/2)*(c+d*x)^-1//2*(b*c+-1*a*d)^-4*(a*d+b*c)*(105*a^4*d^4+105*b^4*c^4+-340*a*d*b^3*c^3+-340*b*c*a^3*d^3+406*a^2*b^2*c^2*d^2))
@test integrate(x^2*(a+b*x)^(1/2)*(-1a+-1*b*x)^-1//2, x) == :(1//3*x^3*(a+b*x)^(1/2)*(-1a+-1*b*x)^-1//2)
@test integrate(x*(a+b*x)^(1/2)*(-1a+-1*b*x)^-1//2, x) == :((1/2)*x^2*(a+b*x)^(1/2)*(-1a+-1*b*x)^-1//2)
@test integrate((a+b*x)^(1/2)*(-1a+-1*b*x)^-1//2, x) == :(x*(a+b*x)^(1/2)*(-1a+-1*b*x)^-1//2)
@test integrate(x^-1*(a+b*x)^(1/2)*(-1a+-1*b*x)^-1//2, x) == :((a+b*x)^(1/2)*(-1a+-1*b*x)^-1//2*log(x))
@test integrate(x^-2*(a+b*x)^(1/2)*(-1a+-1*b*x)^-1//2, x) == :(-1*x^-1*(a+b*x)^(1/2)*(-1a+-1*b*x)^-1//2)
@test integrate(x^-3*(a+b*x)^(1/2)*(-1a+-1*b*x)^-1//2, x) == :(-1//2*x^-2*(a+b*x)^(1/2)*(-1a+-1*b*x)^-1//2)
@test integrate(x^(-1m)*(a+b*x)^(1/2)*(-1a+-1*b*x)^-1//2, x) == :(x^(1+-1m)*(1+-1m)^-1*(a+b*x)^(1/2)*(-1a+-1*b*x)^-1//2)
@test integrate(x^2*(a+b*x)^n*(-1a+-1*b*x)^(-1n), x) == :(1//3*x^3*(a+b*x)^n*(-1a+-1*b*x)^(-1n))
@test integrate(x*(a+b*x)^n*(-1a+-1*b*x)^(-1n), x) == :((1/2)*x^2*(a+b*x)^n*(-1a+-1*b*x)^(-1n))
@test integrate((a+b*x)^n*(-1a+-1*b*x)^(-1n), x) == :(x*(a+b*x)^n*(-1a+-1*b*x)^(-1n))
@test integrate(x^-1*(a+b*x)^n*(-1a+-1*b*x)^(-1n), x) == :((a+b*x)^n*(-1a+-1*b*x)^(-1n)*log(x))
@test integrate(x^-2*(a+b*x)^n*(-1a+-1*b*x)^(-1n), x) == :(-1*x^-1*(a+b*x)^n*(-1a+-1*b*x)^(-1n))
@test integrate(x^-3*(a+b*x)^n*(-1a+-1*b*x)^(-1n), x) == :(-1//2*x^-2*(a+b*x)^n*(-1a+-1*b*x)^(-1n))
@test integrate(x^(-1m)*(a+b*x)^n*(-1a+-1*b*x)^(-1n), x) == :(x^(1+-1m)*(1+-1m)^-1*(a+b*x)^n*(-1a+-1*b*x)^(-1n))
@test integrate(x^3*(1+x)^(1/2)*(1+-1x)^-5//2, x) == :(11//2*arcsin(x)+-13//3*x^2*(1+x)^(1/2)*(1+-1x)^-1//2+-1//6*(1+x)^(1/2)*(1+-1x)^(1/2)*(52+33x)+2//3*x^3*(1+x)^(1/2)*(1+-1x)^-3//2)
@test integrate(x*(1+x)^(1/2)*(1+-1x)^-5//2, x) == :(-2*(1+x)^(1/2)*(1+-1x)^-1//2+1//3*(1+x)^3//2*(1+-1x)^-3//2+arcsin(x))
@test integrate((1+x)^(1/2)*(1+-1x)^-5//2, x) == :(1//3*(1+x)^3//2*(1+-1x)^-3//2)
@test integrate((1+x)^(1/2)*(-1+x)^-5//2, x) == :(-1//3*(1+x)^3//2*(-1+x)^-3//2)
@test integrate(x^-1*(1+x)^(1/2)*(1+-1x)^-5//2, x) == :(-1*arctanh((1+x)^(1/2)*(1+-1x)^(1/2))+2*(1+x)^(1/2)*(1+-1x)^-1//2+1//3*(1+x)^3//2*(1+-1x)^-3//2)
@test integrate(x^-2*(1+x)^(1/2)*(1+-1x)^-5//2, x) == :(-3*arctanh((1+x)^(1/2)*(1+-1x)^(1/2))+14//3*(1+x)^(1/2)*(1+-1x)^-1//2+-5//3*x^-1*(1+x)^(1/2)*(1+-1x)^-1//2+2//3*x^-1*(1+x)^(1/2)*(1+-1x)^-3//2)
@test integrate(x^-3*(1+x)^(1/2)*(1+-1x)^-5//2, x) == :(-11//2*arctanh((1+x)^(1/2)*(1+-1x)^(1/2))+26//3*(1+x)^(1/2)*(1+-1x)^-1//2+-19//6*x^-1*(1+x)^(1/2)*(1+-1x)^-1//2+-7//6*x^-2*(1+x)^(1/2)*(1+-1x)^-1//2+2//3*x^-2*(1+x)^(1/2)*(1+-1x)^-3//2)
@test integrate(x^2*(1+x)^-1//2*(-1+x)^-1//2, x) == :((1/2)*arccosh(x)+(1/2)*x*(1+x)^(1/2)*(-1+x)^(1/2))
@test integrate(x*(1+x)^-1//2*(-1+x)^-1//2, x) == :((1+x)^(1/2)*(-1+x)^(1/2))
@test integrate((1+x)^-1//2*(-1+x)^-1//2, x) == :(arccosh(x))
@test integrate(x^-1*(1+x)^-1//2*(-1+x)^-1//2, x) == :(arctan((1+x)^(1/2)*(-1+x)^(1/2)))
@test integrate(x^-2*(1+x)^-1//2*(-1+x)^-1//2, x) == :(x^-1*(1+x)^(1/2)*(-1+x)^(1/2))
@test integrate(x^2*(1+x)^(1/2)*(-1+x)^(1/2), x) == :(-1//8*arccosh(x)+1//4*x*(1+x)^3//2*(-1+x)^3//2+1//8*x*(1+x)^(1/2)*(-1+x)^(1/2))
@test integrate(x*(1+x)^(1/2)*(-1+x)^(1/2), x) == :(1//3*(1+x)^3//2*(-1+x)^3//2)
@test integrate((1+x)^(1/2)*(-1+x)^(1/2), x) == :(-1//2*arccosh(x)+(1/2)*x*(1+x)^(1/2)*(-1+x)^(1/2))
@test integrate(x^-1*(1+x)^(1/2)*(-1+x)^(1/2), x) == :(-1*arctan((1+x)^(1/2)*(-1+x)^(1/2))+(1+x)^(1/2)*(-1+x)^(1/2))
@test integrate(x^-2*(1+x)^(1/2)*(-1+x)^(1/2), x) == :(-1*x^-1*(1+x)^(1/2)*(-1+x)^(1/2)+arccosh(x))
@test integrate((1+2x)^-1//2*(3+2x)^-1//2, x) == :(arcsinh((1/2)*2^(1/2)*(1+2x)^(1/2)))
@test integrate(x^-1*(-2+3x)^-1//2*(3+5x)^-1//2, x) == :(1//3*6^(1/2)*arctan((1/2)*6^(1/2)*(-2+3x)^(1/2)*(3+5x)^-1//2))
@test integrate(x^-1*(1+x)^-3//2*(-1+x)^-3//2, x) == :(-1*arctan((1+x)^(1/2)*(-1+x)^(1/2))+-1*(1+x)^-1//2*(-1+x)^-1//2)
@test integrate(x*(1+x)^(1/2)*(1+-1x)^(1/2), x) == :(-1//3*(1+x)^3//2*(1+-1x)^3//2)
@test integrate(x^3*(1+4x)^(1/2)*(2+3x)^3//2, x) == :(-8543//995328*(1+4x)^(1/2)*(2+3x)^5//2+42715//15925248*(1+4x)^(1/2)*(2+3x)^3//2+213575//42467328*(1+4x)^(1/2)*(2+3x)^(1/2)+1067875//254803968*3^(1/2)*arcsinh(1//5*15^(1/2)*(1+4x)^(1/2))+1//72*x^2*(1+4x)^3//2*(2+3x)^5//2+1//829440*(1+4x)^3//2*(2+3x)^5//2*(4103+-7968x))
@test integrate((1+a+b*x)^-1//2*(-1+a+b*x)^-1//2, x) == :(2*b^-1*arcsinh((1/2)*2^(1/2)*(-1+a+b*x)^(1/2)))
@test integrate(x^-1//2*(a+b*x)^-1//2*(a+-1*b*x)^-1//2, x) == :(2*a^(1/2)*b^-1//2*(1+b*x*a^-1)^(1/2)*(1+-1*b*x*a^-1)^(1/2)*(a+b*x)^-1//2*(a+-1*b*x)^-1//2*Elliptic.F(arcsin(a^-1//2*b^(1/2)*x^(1/2)),-1))
@test integrate((-1x)^-1//2*(a+b*x)^-1//2*(a+-1*b*x)^-1//2, x) == :(-2*a^(1/2)*b^-1//2*(1+b*x*a^-1)^(1/2)*(1+-1*b*x*a^-1)^(1/2)*(a+b*x)^-1//2*(a+-1*b*x)^-1//2*Elliptic.F(arcsin(a^-1//2*b^(1/2)*(-1x)^(1/2)),-1))
@test integrate((e*x)^-1//2*(a+b*x)^-1//2*(a+-1*b*x)^-1//2, x) == :(2*a^(1/2)*b^-1//2*e^-1//2*(1+b*x*a^-1)^(1/2)*(1+-1*b*x*a^-1)^(1/2)*(a+b*x)^-1//2*(a+-1*b*x)^-1//2*Elliptic.F(arcsin(a^-1//2*b^(1/2)*e^-1//2*(e*x)^(1/2)),-1))
@test integrate(x^-1//2*(2+b*x)^-1//2*(2+-1*b*x)^-1//2, x) == :(2^(1/2)*b^-1//2*Elliptic.F(arcsin((1/2)*2^(1/2)*b^(1/2)*x^(1/2)),-1))
@test integrate((-1x)^-1//2*(2+b*x)^-1//2*(2+-1*b*x)^-1//2, x) == :(-1*2^(1/2)*b^-1//2*Elliptic.F(arcsin((1/2)*2^(1/2)*b^(1/2)*(-1x)^(1/2)),-1))
@test integrate((e*x)^-1//2*(2+b*x)^-1//2*(2+-1*b*x)^-1//2, x) == :(2^(1/2)*b^-1//2*e^-1//2*Elliptic.F(arcsin((1/2)*2^(1/2)*b^(1/2)*e^-1//2*(e*x)^(1/2)),-1))
@test integrate(x^-1//2*(2+-3x)^-1//2*(2+3x)^-1//2, x) == :(1//3*6^(1/2)*Elliptic.F(arcsin((1/2)*6^(1/2)*x^(1/2)),-1))
@test integrate((-1x)^-1//2*(2+-3x)^-1//2*(2+3x)^-1//2, x) == :(-1//3*6^(1/2)*Elliptic.F(arcsin((1/2)*6^(1/2)*(-1x)^(1/2)),-1))
@test integrate((e*x)^-1//2*(2+-3x)^-1//2*(2+3x)^-1//2, x) == :(1//3*6^(1/2)*e^-1//2*Elliptic.F(arcsin((1/2)*6^(1/2)*e^-1//2*(e*x)^(1/2)),-1))
@test integrate(x^-1//2*(1+x)^-1//2*(1+-1x)^-1//2, x) == :(2*Elliptic.F(arcsin(x^(1/2)),-1))
@test integrate((1+x)^-1//2*(x+-1*x^2)^-1//2, x) == :(2*Elliptic.F(arcsin(x^(1/2)),-1))
@test integrate((b*x)^-1//2*(1+c*x)^-1//2*(1+-1*c*x)^-1//2, x) == :(2*b^-1//2*c^-1//2*Elliptic.F(arcsin(b^-1//2*c^(1/2)*(b*x)^(1/2)),-1))
@test integrate((b*x)^-1//2*(1+d*x)^-1//2*(1+-1*c*x)^-1//2, x) == :(2*b^-1//2*c^-1//2*Elliptic.F(arcsin(b^-1//2*c^(1/2)*(b*x)^(1/2)),-1*d*c^-1))
@test integrate(x^-1//2*(1+x)^(1/2)*(1+-1x)^-1//2, x) == :(2*Elliptic.E(arcsin(x^(1/2)),-1))
@test integrate((1+x)^(1/2)*(x+-1*x^2)^-1//2, x) == :(2*Elliptic.E(arcsin(x^(1/2)),-1))
@test integrate((b*x)^-1//2*(1+c*x)^(1/2)*(1+-1*c*x)^-1//2, x) == :(2*b^-1//2*c^-1//2*Elliptic.E(arcsin(b^-1//2*c^(1/2)*(b*x)^(1/2)),-1))
@test integrate((b*x)^-1//2*(1+c*x)^(1/2)*(1+-1*d*x)^-1//2, x) == :(2*b^-1//2*d^-1//2*Elliptic.E(arcsin(b^-1//2*d^(1/2)*(b*x)^(1/2)),-1*c*d^-1))
@test integrate(x^-1//2*(1+x)^-1//2*(1+-1x)^(1/2), x) == :(-2*x^-1//2*(-1x)^(1/2)*Elliptic.E(arcsin((-1x)^(1/2)),-1))
@test integrate((b*x)^-1//2*(1+c*x)^-1//2*(1+-1*c*x)^(1/2), x) == :(-2*c^-1//2*(-1b)^-1//2*Elliptic.E(arcsin(c^(1/2)*(-1b)^-1//2*(b*x)^(1/2)),-1))
@test integrate((b*x)^-1//2*(1+d*x)^-1//2*(1+-1*c*x)^(1/2), x) == :(-2*d^-1//2*(-1b)^-1//2*Elliptic.E(arcsin(d^(1/2)*(-1b)^-1//2*(b*x)^(1/2)),-1*c*d^-1))
@test integrate(x^-1//2*(2+-3x)^-1//2*(d+e*x)^-1//2, x) == :(2//3*3^(1/2)*(1+e*x*d^-1)^(1/2)*(d+e*x)^-1//2*Elliptic.F(arcsin((1/2)*6^(1/2)*x^(1/2)),-2//3*e*d^-1))
@test integrate(x^-1//2*(2+-3x)^-1//2*(d+e*x)^(1/2), x) == :(2//3*3^(1/2)*(1+e*x*d^-1)^-1//2*(d+e*x)^(1/2)*Elliptic.E(arcsin((1/2)*6^(1/2)*x^(1/2)),-2//3*e*d^-1))
@test integrate(x^4*(1+-1x)^-1//3*(2+-1x)^-1//3, x) == :(3//13*x^3*(1+-1x)^2//3*(2+-1x)^2//3+27//455*(1+-1x)^2//3*(2+-1x)^2//3*(89+34x)+99//130*x^2*(1+-1x)^2//3*(2+-1x)^2//3+-891*2^2//3*((-3+2x)^2)^(1/2)*((3+-2x)^2)^(1/2)*(1+-1x)^-1//3*(2+-1x)^-1//3*(273+-182x)^-1*(1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-1*(2+x^2+-3x)^1//3+-594*2^1//6*3^3//4*((-3+2x)^2)^(1/2)*((3+-2x)^2)^-1//2*((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-2*(1+2^2//3*(2+x^2+-3x)^1//3))^-1//2*((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-2*(1+-1*2^2//3*(2+x^2+-3x)^1//3+2*2^1//3*(2+x^2+-3x)^2//3))^(1/2)*(1+-1x)^-1//3*(2+-1x)^-1//3*(273+-182x)^-1*(2+x^2+-3x)^1//3*(1+2^2//3*(2+x^2+-3x)^1//3)*Elliptic.F(arcsin((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-1*(1+-1*3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)),-7+-4*3^(1/2))+891//182*2^2//3*3^1//4*((-3+2x)^2)^(1/2)*((3+-2x)^2)^-1//2*((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-2*(1+2^2//3*(2+x^2+-3x)^1//3))^-1//2*((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-2*(1+-1*2^2//3*(2+x^2+-3x)^1//3+2*2^1//3*(2+x^2+-3x)^2//3))^(1/2)*(1+-1x)^-1//3*(2+-1x)^-1//3*(2+-1*3^(1/2))^(1/2)*(3+-2x)^-1*(2+x^2+-3x)^1//3*(1+2^2//3*(2+x^2+-3x)^1//3)*Elliptic.E(arcsin((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-1*(1+-1*3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)),-7+-4*3^(1/2)))
@test integrate(x^3*(1+-1x)^-1//3*(2+-1x)^-1//3, x) == :(3//10*x^2*(1+-1x)^2//3*(2+-1x)^2//3+9//70*(1+-1x)^2//3*(2+-1x)^2//3*(23+8x)+-81//14*2^2//3*((-3+2x)^2)^(1/2)*((3+-2x)^2)^(1/2)*(1+-1x)^-1//3*(2+-1x)^-1//3*(3+-2x)^-1*(1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-1*(2+x^2+-3x)^1//3+-27*2^1//6*3^3//4*((-3+2x)^2)^(1/2)*((3+-2x)^2)^-1//2*((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-2*(1+2^2//3*(2+x^2+-3x)^1//3))^-1//2*((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-2*(1+-1*2^2//3*(2+x^2+-3x)^1//3+2*2^1//3*(2+x^2+-3x)^2//3))^(1/2)*(1+-1x)^-1//3*(2+-1x)^-1//3*(21+-14x)^-1*(2+x^2+-3x)^1//3*(1+2^2//3*(2+x^2+-3x)^1//3)*Elliptic.F(arcsin((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-1*(1+-1*3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)),-7+-4*3^(1/2))+81//28*2^2//3*3^1//4*((-3+2x)^2)^(1/2)*((3+-2x)^2)^-1//2*((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-2*(1+2^2//3*(2+x^2+-3x)^1//3))^-1//2*((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-2*(1+-1*2^2//3*(2+x^2+-3x)^1//3+2*2^1//3*(2+x^2+-3x)^2//3))^(1/2)*(1+-1x)^-1//3*(2+-1x)^-1//3*(2+-1*3^(1/2))^(1/2)*(3+-2x)^-1*(2+x^2+-3x)^1//3*(1+2^2//3*(2+x^2+-3x)^1//3)*Elliptic.E(arcsin((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-1*(1+-1*3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)),-7+-4*3^(1/2)))
@test integrate(x^2*(1+-1x)^-1//3*(2+-1x)^-1//3, x) == :(45//28*(1+-1x)^2//3*(2+-1x)^2//3+3//7*x*(1+-1x)^2//3*(2+-1x)^2//3+-99//28*2^2//3*((-3+2x)^2)^(1/2)*((3+-2x)^2)^(1/2)*(1+-1x)^-1//3*(2+-1x)^-1//3*(3+-2x)^-1*(1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-1*(2+x^2+-3x)^1//3+-33//14*2^1//6*3^3//4*((-3+2x)^2)^(1/2)*((3+-2x)^2)^-1//2*((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-2*(1+2^2//3*(2+x^2+-3x)^1//3))^-1//2*((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-2*(1+-1*2^2//3*(2+x^2+-3x)^1//3+2*2^1//3*(2+x^2+-3x)^2//3))^(1/2)*(1+-1x)^-1//3*(2+-1x)^-1//3*(3+-2x)^-1*(2+x^2+-3x)^1//3*(1+2^2//3*(2+x^2+-3x)^1//3)*Elliptic.F(arcsin((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-1*(1+-1*3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)),-7+-4*3^(1/2))+99//56*2^2//3*3^1//4*((-3+2x)^2)^(1/2)*((3+-2x)^2)^-1//2*((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-2*(1+2^2//3*(2+x^2+-3x)^1//3))^-1//2*((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-2*(1+-1*2^2//3*(2+x^2+-3x)^1//3+2*2^1//3*(2+x^2+-3x)^2//3))^(1/2)*(1+-1x)^-1//3*(2+-1x)^-1//3*(2+-1*3^(1/2))^(1/2)*(3+-2x)^-1*(2+x^2+-3x)^1//3*(1+2^2//3*(2+x^2+-3x)^1//3)*Elliptic.E(arcsin((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-1*(1+-1*3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)),-7+-4*3^(1/2)))
@test integrate(x*(1+-1x)^-1//3*(2+-1x)^-1//3, x) == :(3//4*(1+-1x)^2//3*(2+-1x)^2//3+-9//4*2^2//3*((-3+2x)^2)^(1/2)*((3+-2x)^2)^(1/2)*(1+-1x)^-1//3*(2+-1x)^-1//3*(3+-2x)^-1*(1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-1*(2+x^2+-3x)^1//3+-3//2*2^1//6*3^3//4*((-3+2x)^2)^(1/2)*((3+-2x)^2)^-1//2*((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-2*(1+2^2//3*(2+x^2+-3x)^1//3))^-1//2*((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-2*(1+-1*2^2//3*(2+x^2+-3x)^1//3+2*2^1//3*(2+x^2+-3x)^2//3))^(1/2)*(1+-1x)^-1//3*(2+-1x)^-1//3*(3+-2x)^-1*(2+x^2+-3x)^1//3*(1+2^2//3*(2+x^2+-3x)^1//3)*Elliptic.F(arcsin((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-1*(1+-1*3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)),-7+-4*3^(1/2))+9//8*2^2//3*3^1//4*((-3+2x)^2)^(1/2)*((3+-2x)^2)^-1//2*((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-2*(1+2^2//3*(2+x^2+-3x)^1//3))^-1//2*((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-2*(1+-1*2^2//3*(2+x^2+-3x)^1//3+2*2^1//3*(2+x^2+-3x)^2//3))^(1/2)*(1+-1x)^-1//3*(2+-1x)^-1//3*(2+-1*3^(1/2))^(1/2)*(3+-2x)^-1*(2+x^2+-3x)^1//3*(1+2^2//3*(2+x^2+-3x)^1//3)*Elliptic.E(arcsin((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-1*(1+-1*3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)),-7+-4*3^(1/2)))
@test integrate((1+-1x)^-1//3*(2+-1x)^-1//3, x) == :(-3//2*2^2//3*((-3+2x)^2)^(1/2)*((3+-2x)^2)^(1/2)*(1+-1x)^-1//3*(2+-1x)^-1//3*(3+-2x)^-1*(1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-1*(2+x^2+-3x)^1//3+-1*2^1//6*3^3//4*((-3+2x)^2)^(1/2)*((3+-2x)^2)^-1//2*((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-2*(1+2^2//3*(2+x^2+-3x)^1//3))^-1//2*((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-2*(1+-1*2^2//3*(2+x^2+-3x)^1//3+2*2^1//3*(2+x^2+-3x)^2//3))^(1/2)*(1+-1x)^-1//3*(2+-1x)^-1//3*(3+-2x)^-1*(2+x^2+-3x)^1//3*(1+2^2//3*(2+x^2+-3x)^1//3)*Elliptic.F(arcsin((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-1*(1+-1*3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)),-7+-4*3^(1/2))+3//4*2^2//3*3^1//4*((-3+2x)^2)^(1/2)*((3+-2x)^2)^-1//2*((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-2*(1+2^2//3*(2+x^2+-3x)^1//3))^-1//2*((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-2*(1+-1*2^2//3*(2+x^2+-3x)^1//3+2*2^1//3*(2+x^2+-3x)^2//3))^(1/2)*(1+-1x)^-1//3*(2+-1x)^-1//3*(2+-1*3^(1/2))^(1/2)*(3+-2x)^-1*(2+x^2+-3x)^1//3*(1+2^2//3*(2+x^2+-3x)^1//3)*Elliptic.E(arcsin((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-1*(1+-1*3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)),-7+-4*3^(1/2)))
@test integrate(x^-1*(1+-1x)^-1//3*(2+-1x)^-1//3, x) == :(-1//4*2^2//3*log(x)+3//8*2^2//3*log(-1*(1+-1x)^1//3+(1/2)*2^1//3*(2+-1x)^2//3)+-1//4*2^2//3*3^(1/2)*arctan(1//3*3^(1/2)+1//3*2^1//3*3^(1/2)*(1+-1x)^-1//3*(2+-1x)^2//3))
@test integrate(x^-2*(1+-1x)^-1//3*(2+-1x)^-1//3, x) == :(-1//8*2^2//3*log(x)+3//16*2^2//3*log(-1*(1+-1x)^1//3+(1/2)*2^1//3*(2+-1x)^2//3)+-1//2*x^-1*(1+-1x)^2//3*(2+-1x)^2//3+-1//8*2^2//3*3^(1/2)*arctan(1//3*3^(1/2)+1//3*2^1//3*3^(1/2)*(1+-1x)^-1//3*(2+-1x)^2//3)+-1//4*2^2//3*((-3+2x)^2)^(1/2)*((3+-2x)^2)^(1/2)*(1+-1x)^-1//3*(2+-1x)^-1//3*(3+-2x)^-1*(1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-1*(2+x^2+-3x)^1//3+-1//6*2^1//6*3^3//4*((-3+2x)^2)^(1/2)*((3+-2x)^2)^-1//2*((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-2*(1+2^2//3*(2+x^2+-3x)^1//3))^-1//2*((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-2*(1+-1*2^2//3*(2+x^2+-3x)^1//3+2*2^1//3*(2+x^2+-3x)^2//3))^(1/2)*(1+-1x)^-1//3*(2+-1x)^-1//3*(3+-2x)^-1*(2+x^2+-3x)^1//3*(1+2^2//3*(2+x^2+-3x)^1//3)*Elliptic.F(arcsin((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-1*(1+-1*3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)),-7+-4*3^(1/2))+1//8*2^2//3*3^1//4*((-3+2x)^2)^(1/2)*((3+-2x)^2)^-1//2*((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-2*(1+2^2//3*(2+x^2+-3x)^1//3))^-1//2*((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-2*(1+-1*2^2//3*(2+x^2+-3x)^1//3+2*2^1//3*(2+x^2+-3x)^2//3))^(1/2)*(1+-1x)^-1//3*(2+-1x)^-1//3*(2+-1*3^(1/2))^(1/2)*(3+-2x)^-1*(2+x^2+-3x)^1//3*(1+2^2//3*(2+x^2+-3x)^1//3)*Elliptic.E(arcsin((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-1*(1+-1*3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)),-7+-4*3^(1/2)))
@test integrate(x^-3*(1+-1x)^-1//3*(2+-1x)^-1//3, x) == :(-1//12*2^2//3*log(x)+1//8*2^2//3*log(-1*(1+-1x)^1//3+(1/2)*2^1//3*(2+-1x)^2//3)+-1//2*x^-1*(1+-1x)^2//3*(2+-1x)^2//3+-1//4*x^-2*(1+-1x)^2//3*(2+-1x)^2//3+-1//12*2^2//3*3^(1/2)*arctan(1//3*3^(1/2)+1//3*2^1//3*3^(1/2)*(1+-1x)^-1//3*(2+-1x)^2//3)+-1//4*2^2//3*((-3+2x)^2)^(1/2)*((3+-2x)^2)^(1/2)*(1+-1x)^-1//3*(2+-1x)^-1//3*(3+-2x)^-1*(1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-1*(2+x^2+-3x)^1//3+-1//6*2^1//6*3^3//4*((-3+2x)^2)^(1/2)*((3+-2x)^2)^-1//2*((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-2*(1+2^2//3*(2+x^2+-3x)^1//3))^-1//2*((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-2*(1+-1*2^2//3*(2+x^2+-3x)^1//3+2*2^1//3*(2+x^2+-3x)^2//3))^(1/2)*(1+-1x)^-1//3*(2+-1x)^-1//3*(3+-2x)^-1*(2+x^2+-3x)^1//3*(1+2^2//3*(2+x^2+-3x)^1//3)*Elliptic.F(arcsin((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-1*(1+-1*3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)),-7+-4*3^(1/2))+1//8*2^2//3*3^1//4*((-3+2x)^2)^(1/2)*((3+-2x)^2)^-1//2*((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-2*(1+2^2//3*(2+x^2+-3x)^1//3))^-1//2*((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-2*(1+-1*2^2//3*(2+x^2+-3x)^1//3+2*2^1//3*(2+x^2+-3x)^2//3))^(1/2)*(1+-1x)^-1//3*(2+-1x)^-1//3*(2+-1*3^(1/2))^(1/2)*(3+-2x)^-1*(2+x^2+-3x)^1//3*(1+2^2//3*(2+x^2+-3x)^1//3)*Elliptic.E(arcsin((1+3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)^-1*(1+-1*3^(1/2)+2^2//3*(2+x^2+-3x)^1//3)),-7+-4*3^(1/2)))
@test integrate(x^3*(a+b*x)^1//4*(c+d*x)^-1//4, x) == :(-1//512*b^-3*d^-4*(a+b*x)^1//4*(c+d*x)^3//4*(77*a^3*d^3+195*b^3*c^3+105*b*c*a^2*d^2+135*a*d*b^2*c^2)+1//4*b^-1*d^-1*x^2*(a+b*x)^5//4*(c+d*x)^3//4+1//384*b^-3*d^-3*(a+b*x)^5//4*(c+d*x)^3//4*(77*a^2*d^2+117*b^2*c^2+-8*b*d*x*(11*a*d+13*b*c)+94*a*b*c*d)+1//1024*b^-15//4*d^-17//4*(b*c+-1*a*d)*(77*a^3*d^3+195*b^3*c^3+105*b*c*a^2*d^2+135*a*d*b^2*c^2)*arctan(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+1//1024*b^-15//4*d^-17//4*(b*c+-1*a*d)*(77*a^3*d^3+195*b^3*c^3+105*b*c*a^2*d^2+135*a*d*b^2*c^2)*arctanh(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4))
@test integrate(x^2*(a+b*x)^1//4*(c+d*x)^-1//4, x) == :(-1//24*b^-2*d^-2*(a+b*x)^5//4*(c+d*x)^3//4*(7*a*d+9*b*c)+-1//64*b^-11//4*d^-13//4*(b*c+-1*a*d)*(7*a^2*d^2+15*b^2*c^2+10*a*b*c*d)*arctan(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+-1//64*b^-11//4*d^-13//4*(b*c+-1*a*d)*(7*a^2*d^2+15*b^2*c^2+10*a*b*c*d)*arctanh(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+1//3*x*b^-1*d^-1*(a+b*x)^5//4*(c+d*x)^3//4+1//32*b^-2*d^-3*(a+b*x)^1//4*(c+d*x)^3//4*(7*a^2*d^2+15*b^2*c^2+10*a*b*c*d))
@test integrate(x*(a+b*x)^1//4*(c+d*x)^-1//4, x) == :((1/2)*b^-1*d^-1*(a+b*x)^5//4*(c+d*x)^3//4+-1//8*b^-1*d^-2*(a+b*x)^1//4*(c+d*x)^3//4*(3*a*d+5*b*c)+1//16*b^-7//4*d^-9//4*(b*c+-1*a*d)*(3*a*d+5*b*c)*arctan(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+1//16*b^-7//4*d^-9//4*(b*c+-1*a*d)*(3*a*d+5*b*c)*arctanh(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4))
@test integrate((a+b*x)^1//4*(c+d*x)^-1//4, x) == :(d^-1*(a+b*x)^1//4*(c+d*x)^3//4+-1//2*b^-3//4*d^-5//4*(b*c+-1*a*d)*arctan(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+-1//2*b^-3//4*d^-5//4*(b*c+-1*a*d)*arctanh(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4))
@test integrate(x^-1*(a+b*x)^1//4*(c+d*x)^-1//4, x) == :(-2*a^1//4*c^-1//4*arctan(a^-1//4*c^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+-2*a^1//4*c^-1//4*arctanh(a^-1//4*c^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+2*b^1//4*d^-1//4*arctan(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+2*b^1//4*d^-1//4*arctanh(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4))
@test integrate(x^-2*(a+b*x)^1//4*(c+d*x)^-1//4, x) == :(-1*c^-1*x^-1*(a+b*x)^1//4*(c+d*x)^3//4+-1//2*a^-3//4*c^-5//4*(b*c+-1*a*d)*arctan(a^-1//4*c^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+-1//2*a^-3//4*c^-5//4*(b*c+-1*a*d)*arctanh(a^-1//4*c^1//4*(a+b*x)^1//4*(c+d*x)^-1//4))
@test integrate(x^-3*(a+b*x)^1//4*(c+d*x)^-1//4, x) == :(-1//2*a^-1*c^-1*x^-2*(a+b*x)^5//4*(c+d*x)^3//4+1//16*a^-7//4*c^-9//4*(b*c+-1*a*d)*(3*b*c+5*a*d)*arctan(a^-1//4*c^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+1//16*a^-7//4*c^-9//4*(b*c+-1*a*d)*(3*b*c+5*a*d)*arctanh(a^-1//4*c^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+1//8*a^-1*c^-2*x^-1*(a+b*x)^1//4*(c+d*x)^3//4*(3*b*c+5*a*d))
@test integrate(x^-4*(a+b*x)^1//4*(c+d*x)^-1//4, x) == :(-1//3*c^-1*x^-3*(a+b*x)^1//4*(c+d*x)^3//4+-1//64*a^-11//4*c^-13//4*(b*c+-1*a*d)*(7*b^2*c^2+15*a^2*d^2+10*a*b*c*d)*arctan(a^-1//4*c^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+-1//64*a^-11//4*c^-13//4*(b*c+-1*a*d)*(7*b^2*c^2+15*a^2*d^2+10*a*b*c*d)*arctanh(a^-1//4*c^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+-1//24*a^-1*c^-2*x^-2*(a+b*x)^1//4*(c+d*x)^3//4*(b*c+-9*a*d)+1//96*a^-2*c^-3*x^-1*(a+b*x)^1//4*(c+d*x)^3//4*(b*c+3*a*d)*(-15*a*d+7*b*c))
@test integrate(x^-5*(a+b*x)^1//4*(c+d*x)^-1//4, x) == :(-1//4*c^-1*x^-4*(a+b*x)^1//4*(c+d*x)^3//4+1//1024*a^-15//4*c^-17//4*(b*c+-1*a*d)*(77*b^3*c^3+195*a^3*d^3+105*a*d*b^2*c^2+135*b*c*a^2*d^2)*arctan(a^-1//4*c^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+1//1024*a^-15//4*c^-17//4*(b*c+-1*a*d)*(77*b^3*c^3+195*a^3*d^3+105*a*d*b^2*c^2+135*b*c*a^2*d^2)*arctanh(a^-1//4*c^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+-1//48*a^-1*c^-2*x^-3*(a+b*x)^1//4*(c+d*x)^3//4*(b*c+-13*a*d)+-1//1536*a^-3*c^-4*x^-1*(a+b*x)^1//4*(c+d*x)^3//4*(-585*a^3*d^3+77*b^3*c^3+61*a*d*b^2*c^2+63*b*c*a^2*d^2)+1//384*a^-2*c^-3*x^-2*(a+b*x)^1//4*(c+d*x)^3//4*(-117*a^2*d^2+11*b^2*c^2+10*a*b*c*d))
@test integrate(x^2*(1+x)^1//4*(1+-1x)^-1//4, x) == :(-3//8*(1+x)^1//4*(1+-1x)^3//4+-3//16*2^(1/2)*arctan(1+2^(1/2)*(1+x)^-1//4*(1+-1x)^1//4)+-3//32*2^(1/2)*log(1+(1+x)^-1//2*(1+-1x)^(1/2)+-1*2^(1/2)*(1+x)^-1//4*(1+-1x)^1//4)+-1//12*(1+x)^5//4*(1+-1x)^3//4+3//16*2^(1/2)*arctan(1+-1*2^(1/2)*(1+x)^-1//4*(1+-1x)^1//4)+3//32*2^(1/2)*log(1+(1+x)^-1//2*(1+-1x)^(1/2)+2^(1/2)*(1+x)^-1//4*(1+-1x)^1//4)+-1//3*x*(1+x)^5//4*(1+-1x)^3//4)
@test integrate(x*(1+x)^1//4*(1+-1x)^-1//4, x) == :(-1//2*(1+x)^5//4*(1+-1x)^3//4+-1//4*(1+x)^1//4*(1+-1x)^3//4+-1//8*2^(1/2)*arctan(1+2^(1/2)*(1+x)^-1//4*(1+-1x)^1//4)+-1//16*2^(1/2)*log(1+(1+x)^-1//2*(1+-1x)^(1/2)+-1*2^(1/2)*(1+x)^-1//4*(1+-1x)^1//4)+1//8*2^(1/2)*arctan(1+-1*2^(1/2)*(1+x)^-1//4*(1+-1x)^1//4)+1//16*2^(1/2)*log(1+(1+x)^-1//2*(1+-1x)^(1/2)+2^(1/2)*(1+x)^-1//4*(1+-1x)^1//4))
@test integrate((1+x)^1//4*(1+-1x)^-1//4, x) == :((1/2)*2^(1/2)*arctan(1+-1*2^(1/2)*(1+x)^-1//4*(1+-1x)^1//4)+-1*(1+x)^1//4*(1+-1x)^3//4+-1//2*2^(1/2)*arctan(1+2^(1/2)*(1+x)^-1//4*(1+-1x)^1//4)+-1//4*2^(1/2)*log(1+(1+x)^-1//2*(1+-1x)^(1/2)+-1*2^(1/2)*(1+x)^-1//4*(1+-1x)^1//4)+1//4*2^(1/2)*log(1+(1+x)^-1//2*(1+-1x)^(1/2)+2^(1/2)*(1+x)^-1//4*(1+-1x)^1//4))
@test integrate(x^-1*(1+x)^1//4*(1+-1x)^-1//4, x) == :(-2*arctan((1+x)^1//4*(1+-1x)^-1//4)+-2*arctanh((1+x)^1//4*(1+-1x)^-1//4)+2^(1/2)*arctan(1+-1*2^(1/2)*(1+x)^-1//4*(1+-1x)^1//4)+(1/2)*2^(1/2)*log(1+(1+x)^-1//2*(1+-1x)^(1/2)+2^(1/2)*(1+x)^-1//4*(1+-1x)^1//4)+-1*2^(1/2)*arctan(1+2^(1/2)*(1+x)^-1//4*(1+-1x)^1//4)+-1//2*2^(1/2)*log(1+(1+x)^-1//2*(1+-1x)^(1/2)+-1*2^(1/2)*(1+x)^-1//4*(1+-1x)^1//4))
@test integrate(x^-2*(1+x)^1//4*(1+-1x)^-1//4, x) == :(-1*arctan((1+x)^1//4*(1+-1x)^-1//4)+-1*arctanh((1+x)^1//4*(1+-1x)^-1//4)+-1*x^-1*(1+x)^1//4*(1+-1x)^3//4)
@test integrate(x^-3*(1+x)^1//4*(1+-1x)^-1//4, x) == :(-1//4*arctan((1+x)^1//4*(1+-1x)^-1//4)+-1//4*arctanh((1+x)^1//4*(1+-1x)^-1//4)+-1//2*x^-2*(1+x)^5//4*(1+-1x)^3//4+-1//4*x^-1*(1+x)^1//4*(1+-1x)^3//4)
@test integrate(x^-4*(1+x)^1//4*(1+-1x)^-1//4, x) == :(-3//8*arctan((1+x)^1//4*(1+-1x)^-1//4)+-3//8*arctanh((1+x)^1//4*(1+-1x)^-1//4)+-11//24*x^-1*(1+x)^1//4*(1+-1x)^3//4+-5//12*x^-2*(1+x)^1//4*(1+-1x)^3//4+-1//3*x^-3*(1+x)^1//4*(1+-1x)^3//4)
@test integrate(x^-5*(1+x)^1//4*(1+-1x)^-1//4, x) == :(-11//64*arctan((1+x)^1//4*(1+-1x)^-1//4)+-11//64*arctanh((1+x)^1//4*(1+-1x)^-1//4)+-83//192*x^-1*(1+x)^1//4*(1+-1x)^3//4+-29//96*x^-2*(1+x)^1//4*(1+-1x)^3//4+-7//24*x^-3*(1+x)^1//4*(1+-1x)^3//4+-1//4*x^-4*(1+x)^1//4*(1+-1x)^3//4)
@test integrate(x^3*(a+b*x)^-3//4*(c+d*x)^-1//4, x) == :(-1//64*b^-15//4*d^-13//4*(15*b^3*c^3+77*a^3*d^3+15*a*d*b^2*c^2+21*b*c*a^2*d^2)*arctan(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+-1//64*b^-15//4*d^-13//4*(15*b^3*c^3+77*a^3*d^3+15*a*d*b^2*c^2+21*b*c*a^2*d^2)*arctanh(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+1//3*b^-1*d^-1*x^2*(a+b*x)^1//4*(c+d*x)^3//4+1//96*b^-3*d^-3*(a+b*x)^1//4*(c+d*x)^3//4*(45*b^2*c^2+77*a^2*d^2+-4*b*d*x*(9*b*c+11*a*d)+54*a*b*c*d))
@test integrate(x^2*(a+b*x)^-3//4*(c+d*x)^-1//4, x) == :(1//16*b^-11//4*d^-9//4*(5*b^2*c^2+21*a^2*d^2+6*a*b*c*d)*arctan(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+1//16*b^-11//4*d^-9//4*(5*b^2*c^2+21*a^2*d^2+6*a*b*c*d)*arctanh(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+(1/2)*x*b^-1*d^-1*(a+b*x)^1//4*(c+d*x)^3//4+-1//8*b^-2*d^-2*(a+b*x)^1//4*(c+d*x)^3//4*(5*b*c+7*a*d))
@test integrate(x*(a+b*x)^-3//4*(c+d*x)^-1//4, x) == :(b^-1*d^-1*(a+b*x)^1//4*(c+d*x)^3//4+-1//2*b^-7//4*d^-5//4*(b*c+3*a*d)*arctan(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+-1//2*b^-7//4*d^-5//4*(b*c+3*a*d)*arctanh(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4))
@test integrate((a+b*x)^-3//4*(c+d*x)^-1//4, x) == :(2*b^-3//4*d^-1//4*arctan(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+2*b^-3//4*d^-1//4*arctanh(b^-1//4*d^1//4*(a+b*x)^1//4*(c+d*x)^-1//4))
@test integrate(x^-1*(a+b*x)^-3//4*(c+d*x)^-1//4, x) == :(-2*a^-3//4*c^-1//4*arctan(a^-1//4*c^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+-2*a^-3//4*c^-1//4*arctanh(a^-1//4*c^1//4*(a+b*x)^1//4*(c+d*x)^-1//4))
@test integrate(x^-2*(a+b*x)^-3//4*(c+d*x)^-1//4, x) == :((1/2)*a^-7//4*c^-5//4*(a*d+3*b*c)*arctan(a^-1//4*c^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+(1/2)*a^-7//4*c^-5//4*(a*d+3*b*c)*arctanh(a^-1//4*c^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+-1*a^-1*c^-1*x^-1*(a+b*x)^1//4*(c+d*x)^3//4)
@test integrate(x^-3*(a+b*x)^-3//4*(c+d*x)^-1//4, x) == :(-1//16*a^-11//4*c^-9//4*(5*a^2*d^2+21*b^2*c^2+6*a*b*c*d)*arctan(a^-1//4*c^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+-1//16*a^-11//4*c^-9//4*(5*a^2*d^2+21*b^2*c^2+6*a*b*c*d)*arctanh(a^-1//4*c^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+-1//2*a^-1*c^-1*x^-2*(a+b*x)^1//4*(c+d*x)^3//4+1//8*a^-2*c^-2*x^-1*(a+b*x)^1//4*(c+d*x)^3//4*(5*a*d+7*b*c))
@test integrate(x^-4*(a+b*x)^-3//4*(c+d*x)^-1//4, x) == :(1//64*a^-15//4*c^-13//4*(15*a^3*d^3+77*b^3*c^3+15*b*c*a^2*d^2+21*a*d*b^2*c^2)*arctan(a^-1//4*c^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+1//64*a^-15//4*c^-13//4*(15*a^3*d^3+77*b^3*c^3+15*b*c*a^2*d^2+21*a*d*b^2*c^2)*arctanh(a^-1//4*c^1//4*(a+b*x)^1//4*(c+d*x)^-1//4)+-1//3*a^-1*c^-1*x^-3*(a+b*x)^1//4*(c+d*x)^3//4+-1//96*a^-3*c^-3*x^-1*(a+b*x)^1//4*(c+d*x)^3//4*(45*a^2*d^2+77*b^2*c^2+54*a*b*c*d)+1//24*a^-2*c^-2*x^-2*(a+b*x)^1//4*(c+d*x)^3//4*(9*a*d+11*b*c))
@test integrate((e*x)^3//2*(1+x)^-1//4*(1+-1x)^-1//4, x) == :(-1//2*e*(e*x)^(1/2)*(1+-1*x^2)^3//4+-1//8*2^(1/2)*e^3//2*arctan(1+-1*2^(1/2)*e^-1//2*(e*x)^(1/2)*(1+-1*x^2)^-1//4)+-1//16*2^(1/2)*e^3//2*log(e^(1/2)+x*e^(1/2)*(1+-1*x^2)^-1//2+-1*2^(1/2)*(e*x)^(1/2)*(1+-1*x^2)^-1//4)+1//8*2^(1/2)*e^3//2*arctan(1+2^(1/2)*e^-1//2*(e*x)^(1/2)*(1+-1*x^2)^-1//4)+1//16*2^(1/2)*e^3//2*log(e^(1/2)+x*e^(1/2)*(1+-1*x^2)^-1//2+2^(1/2)*(e*x)^(1/2)*(1+-1*x^2)^-1//4))
@test integrate((e*x)^-1//2*(1+x)^-1//4*(1+-1x)^-1//4, x) == :((1/2)*2^(1/2)*e^-1//2*arctan(1+2^(1/2)*e^-1//2*(e*x)^(1/2)*(1+-1*x^2)^-1//4)+-1//2*2^(1/2)*e^-1//2*arctan(1+-1*2^(1/2)*e^-1//2*(e*x)^(1/2)*(1+-1*x^2)^-1//4)+-1//4*2^(1/2)*e^-1//2*log(e^(1/2)+x*e^(1/2)*(1+-1*x^2)^-1//2+-1*2^(1/2)*(e*x)^(1/2)*(1+-1*x^2)^-1//4)+1//4*2^(1/2)*e^-1//2*log(e^(1/2)+x*e^(1/2)*(1+-1*x^2)^-1//2+2^(1/2)*(e*x)^(1/2)*(1+-1*x^2)^-1//4))
@test integrate((e*x)^-5//2*(1+x)^-1//4*(1+-1x)^-1//4, x) == :(-2//3*e^-1*(e*x)^-3//2*(1+x)^3//4*(1+-1x)^3//4)
@test integrate((e*x)^-9//2*(1+x)^-1//4*(1+-1x)^-1//4, x) == :(-2//3*e^-1*(e*x)^-7//2*(1+-1*x^2)^3//4+8//21*e^-1*(e*x)^-7//2*(1+-1*x^2)^7//4)
@test integrate((e*x)^-13//2*(1+x)^-1//4*(1+-1x)^-1//4, x) == :(-64//231*e^-1*(e*x)^-11//2*(1+-1*x^2)^11//4+-2//3*e^-1*(e*x)^-11//2*(1+-1*x^2)^3//4+16//21*e^-1*(e*x)^-11//2*(1+-1*x^2)^7//4)
@test integrate((e*x)^5//2*(1+x)^-1//4*(1+-1x)^-1//4, x) == :(-1//2*e^3*(e*x)^-1//2*(1+-1*x^2)^3//4+-1//3*e*(e*x)^3//2*(1+-1*x^2)^3//4+(1/2)*e^2*(e*x)^(1/2)*(1+-1*x^-2)^1//4*(1+-1*x^2)^-1//4*Elliptic.E((1/2)*arccsc(x),2))
@test integrate((e*x)^(1/2)*(1+x)^-1//4*(1+-1x)^-1//4, x) == :(-1*e*(e*x)^-1//2*(1+-1*x^2)^3//4+(e*x)^(1/2)*(1+-1*x^-2)^1//4*(1+-1*x^2)^-1//4*Elliptic.E((1/2)*arccsc(x),2))
@test integrate((e*x)^-3//2*(1+x)^-1//4*(1+-1x)^-1//4, x) == :(-2*e^-2*(e*x)^(1/2)*(1+-1*x^-2)^1//4*(1+-1*x^2)^-1//4*Elliptic.E((1/2)*arccsc(x),2))
@test integrate((e*x)^-7//2*(1+x)^-1//4*(1+-1x)^-1//4, x) == :(-2//5*e^-1*(e*x)^-5//2*(1+-1*x^2)^3//4+-4//5*e^-4*(e*x)^(1/2)*(1+-1*x^-2)^1//4*(1+-1*x^2)^-1//4*Elliptic.E((1/2)*arccsc(x),2))
@test integrate((e*x)^-11//2*(1+x)^-1//4*(1+-1x)^-1//4, x) == :(-4//15*e^-3*(e*x)^-5//2*(1+-1*x^2)^3//4+-2//9*e^-1*(e*x)^-9//2*(1+-1*x^2)^3//4+-8//15*e^-6*(e*x)^(1/2)*(1+-1*x^-2)^1//4*(1+-1*x^2)^-1//4*Elliptic.E((1/2)*arccsc(x),2))
@test integrate(x^2*(a+b*x)^n*(c+d*x), x) == :(d*b^-4*(4+n)^-1*(a+b*x)^(4+n)+b^-4*(3+n)^-1*(a+b*x)^(3+n)*(b*c+-3*a*d)+a^2*b^-4*(1+n)^-1*(a+b*x)^(1+n)*(b*c+-1*a*d)+-1*a*b^-4*(2+n)^-1*(a+b*x)^(2+n)*(-3*a*d+2*b*c))
@test integrate(x*(a+b*x)^n*(c+d*x), x) == :(d*b^-3*(3+n)^-1*(a+b*x)^(3+n)+b^-3*(2+n)^-1*(a+b*x)^(2+n)*(b*c+-2*a*d)+-1*a*b^-3*(1+n)^-1*(a+b*x)^(1+n)*(b*c+-1*a*d))
@test integrate((a+b*x)^n*(c+d*x), x) == :(d*b^-2*(2+n)^-1*(a+b*x)^(2+n)+b^-2*(1+n)^-1*(a+b*x)^(1+n)*(b*c+-1*a*d))
@test integrate(x^2*(a+b*x)^n*(c+d*x)^2, x) == :(b^-5*d^2*(5+n)^-1*(a+b*x)^(5+n)+b^-5*(3+n)^-1*(a+b*x)^(3+n)*(b^2*c^2+6*a^2*d^2+-6*a*b*c*d)+a^2*b^-5*(1+n)^-1*(a+b*x)^(1+n)*(b*c+-1*a*d)^2+2*d*b^-5*(4+n)^-1*(a+b*x)^(4+n)*(b*c+-2*a*d)+-2*a*b^-5*(2+n)^-1*(a+b*x)^(2+n)*(b*c+-1*a*d)*(b*c+-2*a*d))
@test integrate(x*(a+b*x)^n*(c+d*x)^2, x) == :(b^-4*d^2*(4+n)^-1*(a+b*x)^(4+n)+d*b^-4*(3+n)^-1*(a+b*x)^(3+n)*(-3*a*d+2*b*c)+b^-4*(2+n)^-1*(a+b*x)^(2+n)*(b*c+-1*a*d)*(b*c+-3*a*d)+-1*a*b^-4*(1+n)^-1*(a+b*x)^(1+n)*(b*c+-1*a*d)^2)
@test integrate((a+b*x)^n*(c+d*x)^2, x) == :(b^-3*d^2*(3+n)^-1*(a+b*x)^(3+n)+b^-3*(1+n)^-1*(a+b*x)^(1+n)*(b*c+-1*a*d)^2+2*d*b^-3*(2+n)^-1*(a+b*x)^(2+n)*(b*c+-1*a*d))
@test integrate(x^2*(a+b*x)^n*(c+d*x)^3, x) == :(b^-6*d^3*(6+n)^-1*(a+b*x)^(6+n)+d*b^-6*(4+n)^-1*(a+b*x)^(4+n)*(3*b^2*c^2+10*a^2*d^2+-12*a*b*c*d)+a^2*b^-6*(1+n)^-1*(a+b*x)^(1+n)*(b*c+-1*a*d)^3+b^-6*d^2*(5+n)^-1*(a+b*x)^(5+n)*(-5*a*d+3*b*c)+b^-6*(3+n)^-1*(a+b*x)^(3+n)*(b*c+-1*a*d)*(b^2*c^2+10*a^2*d^2+-8*a*b*c*d)+-1*a*b^-6*(2+n)^-1*(a+b*x)^(2+n)*(b*c+-1*a*d)^2*(-5*a*d+2*b*c))
@test integrate(x*(a+b*x)^n*(c+d*x)^3, x) == :(b^-5*d^3*(5+n)^-1*(a+b*x)^(5+n)+b^-5*d^2*(4+n)^-1*(a+b*x)^(4+n)*(-4*a*d+3*b*c)+b^-5*(2+n)^-1*(a+b*x)^(2+n)*(b*c+-1*a*d)^2*(b*c+-4*a*d)+-1*a*b^-5*(1+n)^-1*(a+b*x)^(1+n)*(b*c+-1*a*d)^3+3*d*b^-5*(3+n)^-1*(a+b*x)^(3+n)*(b*c+-1*a*d)*(b*c+-2*a*d))
@test integrate((a+b*x)^n*(c+d*x)^3, x) == :(b^-4*d^3*(4+n)^-1*(a+b*x)^(4+n)+b^-4*(1+n)^-1*(a+b*x)^(1+n)*(b*c+-1*a*d)^3+3*d*b^-4*(2+n)^-1*(a+b*x)^(2+n)*(b*c+-1*a*d)^2+3*b^-4*d^2*(3+n)^-1*(a+b*x)^(3+n)*(b*c+-1*a*d))
@test integrate(x^(1+2n)*(a+b*x)^n*(2a+3*b*x), x) == :(x^(2+2n)*(1+n)^-1*(a+b*x)^(1+n))
@test integrate(x^2*(1+a*x)^-4*(1+-1*a*x)^-7, x) == :(-1//24*a^-3*(1+a*x)^-3*(1+-1*a*x)^-6*(1+-3*a*x))
@test integrate(x^2*(1+a*x)^-7*(1+-1*a*x)^-11, x) == :(-1//60*a^-3*(1+a*x)^-6*(1+-1*a*x)^-10*(1+-4*a*x))
@test integrate(x^2*(1+a*x)^-11*(1+-1*a*x)^-16, x) == :(-1//120*a^-3*(1+a*x)^-10*(1+-1*a*x)^-15*(1+-5*a*x))
@test integrate(x^2*(1+a*x)^(-1+-1//2*n*(-1+n))*(1+-1*a*x)^(-1+-1//2*n*(1+n)), x) == :(a^-3*n^-1*(1+-1*n^2)^-1*(1+a*x)^(n*(1/2+-1//2*n))*(1+-1*a*x)^(-1//2*n*(1+n))*(1+-1*a*n*x))
@test integrate((d+e*x)^4*(A+B*x)*(a+b*x), x) == :(-1//6*e^-3*(d+e*x)^6*(-1*A*b*e+-1*B*a*e+2*B*b*d)+1//5*e^-3*(d+e*x)^5*(B*d+-1*A*e)*(b*d+-1*a*e)+1//7*B*b*e^-3*(d+e*x)^7)
@test integrate((d+e*x)^3*(A+B*x)*(a+b*x), x) == :(-1//5*e^-3*(d+e*x)^5*(-1*A*b*e+-1*B*a*e+2*B*b*d)+1//4*e^-3*(d+e*x)^4*(B*d+-1*A*e)*(b*d+-1*a*e)+1//6*B*b*e^-3*(d+e*x)^6)
@test integrate((d+e*x)^2*(A+B*x)*(a+b*x), x) == :(-1//4*e^-3*(d+e*x)^4*(-1*A*b*e+-1*B*a*e+2*B*b*d)+1//3*e^-3*(d+e*x)^3*(B*d+-1*A*e)*(b*d+-1*a*e)+1//5*B*b*e^-3*(d+e*x)^5)
@test integrate((A+B*x)*(a+b*x)*(d+e*x), x) == :(x^2*((1/2)*A*a*e+(1/2)*A*b*d+(1/2)*B*a*d)+x^3*(1//3*A*b*e+1//3*B*a*e+1//3*B*b*d)+A*a*d*x+1//4*B*b*e*x^4)
@test integrate((A+B*x)*(a+b*x), x) == :((1/2)*x^2*(A*b+B*a)+A*a*x+1//3*B*b*x^3)
@test integrate((d+e*x)^-1*(A+B*x)*(a+b*x), x) == :(e^-3*(B*d+-1*A*e)*(b*d+-1*a*e)*log(d+e*x)+(1/2)*B*b^-1*e^-1*(a+b*x)^2+-1*b*x*e^-2*(B*d+-1*A*e))
@test integrate((d+e*x)^-2*(A+B*x)*(a+b*x), x) == :(-1*e^-3*(-1*A*b*e+-1*B*a*e+2*B*b*d)*log(d+e*x)+B*b*x*e^-2+-1*e^-3*(d+e*x)^-1*(B*d+-1*A*e)*(b*d+-1*a*e))
@test integrate((d+e*x)^-3*(A+B*x)*(a+b*x), x) == :(e^-3*(d+e*x)^-1*(-1*A*b*e+-1*B*a*e+2*B*b*d)+B*b*e^-3*log(d+e*x)+-1//2*e^-3*(d+e*x)^-2*(B*d+-1*A*e)*(b*d+-1*a*e))
@test integrate((d+e*x)^-4*(A+B*x)*(a+b*x), x) == :((1/2)*e^-3*(d+e*x)^-2*(-1*A*b*e+-1*B*a*e+2*B*b*d)+-1*B*b*e^-3*(d+e*x)^-1+-1//3*e^-3*(d+e*x)^-3*(B*d+-1*A*e)*(b*d+-1*a*e))
@test integrate((d+e*x)^-5*(A+B*x)*(a+b*x), x) == :(1//3*e^-3*(d+e*x)^-3*(-1*A*b*e+-1*B*a*e+2*B*b*d)+-1//2*B*b*e^-3*(d+e*x)^-2+-1//4*e^-3*(d+e*x)^-4*(B*d+-1*A*e)*(b*d+-1*a*e))
@test integrate((d+e*x)^-6*(A+B*x)*(a+b*x), x) == :(1//4*e^-3*(d+e*x)^-4*(-1*A*b*e+-1*B*a*e+2*B*b*d)+-1//3*B*b*e^-3*(d+e*x)^-3+-1//5*e^-3*(d+e*x)^-5*(B*d+-1*A*e)*(b*d+-1*a*e))
@test integrate((a+b*x)^2*(d+e*x)^4*(A+B*x), x) == :(-1//5*e^-4*(d+e*x)^5*(b*d+-1*a*e)^2*(B*d+-1*A*e)+-1//7*b*e^-4*(d+e*x)^7*(-1*A*b*e+-2*B*a*e+3*B*b*d)+1//6*e^-4*(d+e*x)^6*(b*d+-1*a*e)*(-1*B*a*e+-2*A*b*e+3*B*b*d)+1//8*B*b^2*e^-4*(d+e*x)^8)
@test integrate((a+b*x)^2*(d+e*x)^3*(A+B*x), x) == :(-1//4*e^-4*(d+e*x)^4*(b*d+-1*a*e)^2*(B*d+-1*A*e)+-1//6*b*e^-4*(d+e*x)^6*(-1*A*b*e+-2*B*a*e+3*B*b*d)+1//5*e^-4*(d+e*x)^5*(b*d+-1*a*e)*(-1*B*a*e+-2*A*b*e+3*B*b*d)+1//7*B*b^2*e^-4*(d+e*x)^7)
@test integrate((a+b*x)^2*(d+e*x)^2*(A+B*x), x) == :(1//3*b^-4*(a+b*x)^3*(b*d+-1*a*e)^2*(A*b+-1*B*a)+1//4*b^-4*(a+b*x)^4*(b*d+-1*a*e)*(B*b*d+-3*B*a*e+2*A*b*e)+1//5*e*b^-4*(a+b*x)^5*(A*b*e+-3*B*a*e+2*B*b*d)+1//6*B*b^-4*e^2*(a+b*x)^6)
@test integrate((a+b*x)^2*(A+B*x)*(d+e*x), x) == :(1//4*b^-3*(a+b*x)^4*(A*b*e+B*b*d+-2*B*a*e)+1//3*b^-3*(a+b*x)^3*(A*b+-1*B*a)*(b*d+-1*a*e)+1//5*B*e*b^-3*(a+b*x)^5)
@test integrate((a+b*x)^2*(A+B*x), x) == :(1//3*b^-2*(a+b*x)^3*(A*b+-1*B*a)+1//4*B*b^-2*(a+b*x)^4)
@test integrate((a+b*x)^2*(d+e*x)^-1*(A+B*x), x) == :(-1//2*e^-2*(a+b*x)^2*(B*d+-1*A*e)+-1*e^-4*(b*d+-1*a*e)^2*(B*d+-1*A*e)*log(d+e*x)+1//3*B*b^-1*e^-1*(a+b*x)^3+b*x*e^-3*(B*d+-1*A*e)*(b*d+-1*a*e))
@test integrate((a+b*x)^2*(d+e*x)^-2*(A+B*x), x) == :(e^-4*(d+e*x)^-1*(b*d+-1*a*e)^2*(B*d+-1*A*e)+e^-4*(b*d+-1*a*e)*(-1*B*a*e+-2*A*b*e+3*B*b*d)*log(d+e*x)+(1/2)*B*b^2*e^-2*x^2+-1*b*x*e^-3*(-1*A*b*e+-2*B*a*e+2*B*b*d))
@test integrate((a+b*x)^2*(d+e*x)^-3*(A+B*x), x) == :(B*x*b^2*e^-3+(1/2)*e^-4*(d+e*x)^-2*(b*d+-1*a*e)^2*(B*d+-1*A*e)+-1*b*e^-4*(-1*A*b*e+-2*B*a*e+3*B*b*d)*log(d+e*x)+-1*e^-4*(d+e*x)^-1*(b*d+-1*a*e)*(-1*B*a*e+-2*A*b*e+3*B*b*d))
@test integrate((a+b*x)^2*(d+e*x)^-4*(A+B*x), x) == :(B*b^2*e^-4*log(d+e*x)+-1//2*B*e^-4*(d+e*x)^-2*(b*d+-1*a*e)^2+2*B*b*e^-4*(d+e*x)^-1*(b*d+-1*a*e)+-1//3*e^-1*(a+b*x)^3*(d+e*x)^-3*(b*d+-1*a*e)^-1*(B*d+-1*A*e))
@test integrate((a+b*x)^2*(d+e*x)^-5*(A+B*x), x) == :(-1//4*e^-1*(a+b*x)^3*(d+e*x)^-4*(b*d+-1*a*e)^-1*(B*d+-1*A*e)+1//12*e^-1*(a+b*x)^3*(d+e*x)^-3*(b*d+-1*a*e)^-2*(A*b*e+-4*B*a*e+3*B*b*d))
@test integrate((a+b*x)^2*(d+e*x)^-6*(A+B*x), x) == :(-1//2*B*b^2*e^-4*(d+e*x)^-2+-1//4*e^-4*(d+e*x)^-4*(b*d+-1*a*e)*(-1*B*a*e+-2*A*b*e+3*B*b*d)+1//3*b*e^-4*(d+e*x)^-3*(-1*A*b*e+-2*B*a*e+3*B*b*d)+1//5*e^-4*(d+e*x)^-5*(b*d+-1*a*e)^2*(B*d+-1*A*e))
@test integrate((a+b*x)^2*(d+e*x)^-7*(A+B*x), x) == :(-1//3*B*b^2*e^-4*(d+e*x)^-3+-1//5*e^-4*(d+e*x)^-5*(b*d+-1*a*e)*(-1*B*a*e+-2*A*b*e+3*B*b*d)+1//4*b*e^-4*(d+e*x)^-4*(-1*A*b*e+-2*B*a*e+3*B*b*d)+1//6*e^-4*(d+e*x)^-6*(b*d+-1*a*e)^2*(B*d+-1*A*e))
@test integrate((a+b*x)^2*(d+e*x)^-8*(A+B*x), x) == :(-1//4*B*b^2*e^-4*(d+e*x)^-4+-1//6*e^-4*(d+e*x)^-6*(b*d+-1*a*e)*(-1*B*a*e+-2*A*b*e+3*B*b*d)+1//5*b*e^-4*(d+e*x)^-5*(-1*A*b*e+-2*B*a*e+3*B*b*d)+1//7*e^-4*(d+e*x)^-7*(b*d+-1*a*e)^2*(B*d+-1*A*e))
@test integrate((a+b*x)^3*(d+e*x)^5*(A+B*x), x) == :(-1//7*e^-5*(d+e*x)^7*(b*d+-1*a*e)^2*(-1*B*a*e+-3*A*b*e+4*B*b*d)+-1//9*b^2*e^-5*(d+e*x)^9*(-1*A*b*e+-3*B*a*e+4*B*b*d)+1//6*e^-5*(d+e*x)^6*(b*d+-1*a*e)^3*(B*d+-1*A*e)+1//10*B*b^3*e^-5*(d+e*x)^10+3//8*b*e^-5*(d+e*x)^8*(b*d+-1*a*e)*(-1*A*b*e+-1*B*a*e+2*B*b*d))
@test integrate((a+b*x)^3*(d+e*x)^4*(A+B*x), x) == :(-1//6*e^-5*(d+e*x)^6*(b*d+-1*a*e)^2*(-1*B*a*e+-3*A*b*e+4*B*b*d)+-1//8*b^2*e^-5*(d+e*x)^8*(-1*A*b*e+-3*B*a*e+4*B*b*d)+1//5*e^-5*(d+e*x)^5*(b*d+-1*a*e)^3*(B*d+-1*A*e)+1//9*B*b^3*e^-5*(d+e*x)^9+3//7*b*e^-5*(d+e*x)^7*(b*d+-1*a*e)*(-1*A*b*e+-1*B*a*e+2*B*b*d))
@test integrate((a+b*x)^3*(d+e*x)^3*(A+B*x), x) == :(1//4*b^-5*(a+b*x)^4*(b*d+-1*a*e)^3*(A*b+-1*B*a)+1//5*b^-5*(a+b*x)^5*(b*d+-1*a*e)^2*(B*b*d+-4*B*a*e+3*A*b*e)+1//7*b^-5*e^2*(a+b*x)^7*(A*b*e+-4*B*a*e+3*B*b*d)+1//8*B*b^-5*e^3*(a+b*x)^8+(1/2)*e*b^-5*(a+b*x)^6*(b*d+-1*a*e)*(A*b*e+B*b*d+-2*B*a*e))
@test integrate((a+b*x)^3*(d+e*x)^2*(A+B*x), x) == :(1//4*b^-4*(a+b*x)^4*(b*d+-1*a*e)^2*(A*b+-1*B*a)+1//5*b^-4*(a+b*x)^5*(b*d+-1*a*e)*(B*b*d+-3*B*a*e+2*A*b*e)+1//6*e*b^-4*(a+b*x)^6*(A*b*e+-3*B*a*e+2*B*b*d)+1//7*B*b^-4*e^2*(a+b*x)^7)
@test integrate((a+b*x)^3*(A+B*x)*(d+e*x), x) == :(1//5*b^-3*(a+b*x)^5*(A*b*e+B*b*d+-2*B*a*e)+1//4*b^-3*(a+b*x)^4*(A*b+-1*B*a)*(b*d+-1*a*e)+1//6*B*e*b^-3*(a+b*x)^6)
@test integrate((a+b*x)^3*(A+B*x), x) == :(1//4*b^-2*(a+b*x)^4*(A*b+-1*B*a)+1//5*B*b^-2*(a+b*x)^5)
@test integrate((a+b*x)^3*(d+e*x)^-1*(A+B*x), x) == :(-1//3*e^-2*(a+b*x)^3*(B*d+-1*A*e)+e^-5*(b*d+-1*a*e)^3*(B*d+-1*A*e)*log(d+e*x)+(1/2)*e^-3*(a+b*x)^2*(B*d+-1*A*e)*(b*d+-1*a*e)+1//4*B*b^-1*e^-1*(a+b*x)^4+-1*b*x*e^-4*(b*d+-1*a*e)^2*(B*d+-1*A*e))
@test integrate((a+b*x)^3*(d+e*x)^-2*(A+B*x), x) == :(-1*e^-5*(d+e*x)^-1*(b*d+-1*a*e)^3*(B*d+-1*A*e)+-1*e^-5*(b*d+-1*a*e)^2*(-1*B*a*e+-3*A*b*e+4*B*b*d)*log(d+e*x)+-1//2*b^2*e^-5*(d+e*x)^2*(-1*A*b*e+-3*B*a*e+4*B*b*d)+1//3*B*b^3*e^-5*(d+e*x)^3+3*b*x*e^-4*(b*d+-1*a*e)*(-1*A*b*e+-1*B*a*e+2*B*b*d))
@test integrate((a+b*x)^3*(d+e*x)^-3*(A+B*x), x) == :(e^-5*(d+e*x)^-1*(b*d+-1*a*e)^2*(-1*B*a*e+-3*A*b*e+4*B*b*d)+(1/2)*B*b^3*e^-3*x^2+-1*x*b^2*e^-4*(-1*A*b*e+-3*B*a*e+3*B*b*d)+-1//2*e^-5*(d+e*x)^-2*(b*d+-1*a*e)^3*(B*d+-1*A*e)+3*b*e^-5*(b*d+-1*a*e)*(-1*A*b*e+-1*B*a*e+2*B*b*d)*log(d+e*x))
@test integrate((a+b*x)^3*(d+e*x)^-4*(A+B*x), x) == :(B*x*b^3*e^-4+(1/2)*e^-5*(d+e*x)^-2*(b*d+-1*a*e)^2*(-1*B*a*e+-3*A*b*e+4*B*b*d)+-1*b^2*e^-5*(-1*A*b*e+-3*B*a*e+4*B*b*d)*log(d+e*x)+-1//3*e^-5*(d+e*x)^-3*(b*d+-1*a*e)^3*(B*d+-1*A*e)+-3*b*e^-5*(d+e*x)^-1*(b*d+-1*a*e)*(-1*A*b*e+-1*B*a*e+2*B*b*d))
@test integrate((a+b*x)^3*(d+e*x)^-5*(A+B*x), x) == :(B*b^3*e^-5*log(d+e*x)+1//3*B*e^-5*(d+e*x)^-3*(b*d+-1*a*e)^3+3*B*b^2*e^-5*(d+e*x)^-1*(b*d+-1*a*e)+-3//2*B*b*e^-5*(d+e*x)^-2*(b*d+-1*a*e)^2+-1//4*e^-1*(a+b*x)^4*(d+e*x)^-4*(b*d+-1*a*e)^-1*(B*d+-1*A*e))
@test integrate((a+b*x)^3*(d+e*x)^-6*(A+B*x), x) == :(-1//5*e^-1*(a+b*x)^4*(d+e*x)^-5*(b*d+-1*a*e)^-1*(B*d+-1*A*e)+1//20*e^-1*(a+b*x)^4*(d+e*x)^-4*(b*d+-1*a*e)^-2*(A*b*e+-5*B*a*e+4*B*b*d))
@test integrate((a+b*x)^3*(d+e*x)^-7*(A+B*x), x) == :(-1//6*e^-1*(a+b*x)^4*(d+e*x)^-6*(b*d+-1*a*e)^-1*(B*d+-1*A*e)+1//15*e^-1*(a+b*x)^4*(d+e*x)^-5*(b*d+-1*a*e)^-2*(A*b*e+-3*B*a*e+2*B*b*d)+1//60*b*e^-1*(a+b*x)^4*(d+e*x)^-4*(b*d+-1*a*e)^-3*(A*b*e+-3*B*a*e+2*B*b*d))
@test integrate((a+b*x)^3*(d+e*x)^-8*(A+B*x), x) == :(-1//3*B*b^3*e^-5*(d+e*x)^-3+-1//7*e^-5*(d+e*x)^-7*(b*d+-1*a*e)^3*(B*d+-1*A*e)+1//4*b^2*e^-5*(d+e*x)^-4*(-1*A*b*e+-3*B*a*e+4*B*b*d)+1//6*e^-5*(d+e*x)^-6*(b*d+-1*a*e)^2*(-1*B*a*e+-3*A*b*e+4*B*b*d)+-3//5*b*e^-5*(d+e*x)^-5*(b*d+-1*a*e)*(-1*A*b*e+-1*B*a*e+2*B*b*d))
@test integrate((a+b*x)^3*(d+e*x)^-9*(A+B*x), x) == :(-1//4*B*b^3*e^-5*(d+e*x)^-4+-1//8*e^-5*(d+e*x)^-8*(b*d+-1*a*e)^3*(B*d+-1*A*e)+1//5*b^2*e^-5*(d+e*x)^-5*(-1*A*b*e+-3*B*a*e+4*B*b*d)+1//7*e^-5*(d+e*x)^-7*(b*d+-1*a*e)^2*(-1*B*a*e+-3*A*b*e+4*B*b*d)+-1//2*b*e^-5*(d+e*x)^-6*(b*d+-1*a*e)*(-1*A*b*e+-1*B*a*e+2*B*b*d))
@test integrate((a+b*x)^3*(d+e*x)^-10*(A+B*x), x) == :(-1//5*B*b^3*e^-5*(d+e*x)^-5+-1//9*e^-5*(d+e*x)^-9*(b*d+-1*a*e)^3*(B*d+-1*A*e)+1//6*b^2*e^-5*(d+e*x)^-6*(-1*A*b*e+-3*B*a*e+4*B*b*d)+1//8*e^-5*(d+e*x)^-8*(b*d+-1*a*e)^2*(-1*B*a*e+-3*A*b*e+4*B*b*d)+-3//7*b*e^-5*(d+e*x)^-7*(b*d+-1*a*e)*(-1*A*b*e+-1*B*a*e+2*B*b*d))
@test integrate((a+b*x)^6*(d+e*x)^8*(A+B*x), x) == :(-1//9*e^-8*(d+e*x)^9*(b*d+-1*a*e)^6*(B*d+-1*A*e)+-1//15*b^5*e^-8*(d+e*x)^15*(-1*A*b*e+-6*B*a*e+7*B*b*d)+1//10*e^-8*(d+e*x)^10*(b*d+-1*a*e)^5*(-1*B*a*e+-6*A*b*e+7*B*b*d)+1//16*B*b^6*e^-8*(d+e*x)^16+-5//13*b^3*e^-8*(d+e*x)^13*(b*d+-1*a*e)^2*(-4*B*a*e+-3*A*b*e+7*B*b*d)+-3//11*b*e^-8*(d+e*x)^11*(b*d+-1*a*e)^4*(-5*A*b*e+-2*B*a*e+7*B*b*d)+3//14*b^4*e^-8*(d+e*x)^14*(b*d+-1*a*e)*(-5*B*a*e+-2*A*b*e+7*B*b*d)+5//12*b^2*e^-8*(d+e*x)^12*(b*d+-1*a*e)^3*(-4*A*b*e+-3*B*a*e+7*B*b*d))
@test integrate((a+b*x)^6*(d+e*x)^7*(A+B*x), x) == :(-1//8*e^-8*(d+e*x)^8*(b*d+-1*a*e)^6*(B*d+-1*A*e)+-1//14*b^5*e^-8*(d+e*x)^14*(-1*A*b*e+-6*B*a*e+7*B*b*d)+1//9*e^-8*(d+e*x)^9*(b*d+-1*a*e)^5*(-1*B*a*e+-6*A*b*e+7*B*b*d)+1//15*B*b^6*e^-8*(d+e*x)^15+-5//12*b^3*e^-8*(d+e*x)^12*(b*d+-1*a*e)^2*(-4*B*a*e+-3*A*b*e+7*B*b*d)+-3//10*b*e^-8*(d+e*x)^10*(b*d+-1*a*e)^4*(-5*A*b*e+-2*B*a*e+7*B*b*d)+3//13*b^4*e^-8*(d+e*x)^13*(b*d+-1*a*e)*(-5*B*a*e+-2*A*b*e+7*B*b*d)+5//11*b^2*e^-8*(d+e*x)^11*(b*d+-1*a*e)^3*(-4*A*b*e+-3*B*a*e+7*B*b*d))
@test integrate((a+b*x)^6*(d+e*x)^6*(A+B*x), x) == :(1//7*b^-8*(a+b*x)^7*(b*d+-1*a*e)^6*(A*b+-1*B*a)+1//8*b^-8*(a+b*x)^8*(b*d+-1*a*e)^5*(B*b*d+-7*B*a*e+6*A*b*e)+1//13*b^-8*e^5*(a+b*x)^13*(A*b*e+-7*B*a*e+6*B*b*d)+1//14*B*b^-8*e^6*(a+b*x)^14+(1/2)*b^-8*e^2*(a+b*x)^10*(b*d+-1*a*e)^3*(-7*B*a*e+3*B*b*d+4*A*b*e)+1//3*e*b^-8*(a+b*x)^9*(b*d+-1*a*e)^4*(-7*B*a*e+2*B*b*d+5*A*b*e)+1//4*b^-8*e^4*(a+b*x)^12*(b*d+-1*a*e)*(-7*B*a*e+2*A*b*e+5*B*b*d)+5//11*b^-8*e^3*(a+b*x)^11*(b*d+-1*a*e)^2*(-7*B*a*e+3*A*b*e+4*B*b*d))
@test integrate((a+b*x)^6*(d+e*x)^5*(A+B*x), x) == :(1//7*b^-7*(a+b*x)^7*(b*d+-1*a*e)^5*(A*b+-1*B*a)+1//8*b^-7*(a+b*x)^8*(b*d+-1*a*e)^4*(B*b*d+-6*B*a*e+5*A*b*e)+1//12*b^-7*e^4*(a+b*x)^12*(A*b*e+-6*B*a*e+5*B*b*d)+1//13*B*b^-7*e^5*(a+b*x)^13+b^-7*e^2*(a+b*x)^10*(b*d+-1*a*e)^2*(A*b*e+B*b*d+-2*B*a*e)+5//9*e*b^-7*(a+b*x)^9*(b*d+-1*a*e)^3*(B*b*d+-3*B*a*e+2*A*b*e)+5//11*b^-7*e^3*(a+b*x)^11*(b*d+-1*a*e)*(A*b*e+-3*B*a*e+2*B*b*d))
@test integrate((a+b*x)^6*(d+e*x)^4*(A+B*x), x) == :(1//7*b^-6*(a+b*x)^7*(b*d+-1*a*e)^4*(A*b+-1*B*a)+1//8*b^-6*(a+b*x)^8*(b*d+-1*a*e)^3*(B*b*d+-5*B*a*e+4*A*b*e)+1//11*b^-6*e^3*(a+b*x)^11*(A*b*e+-5*B*a*e+4*B*b*d)+1//12*B*b^-6*e^4*(a+b*x)^12+1//5*b^-6*e^2*(a+b*x)^10*(b*d+-1*a*e)*(-5*B*a*e+2*A*b*e+3*B*b*d)+2//9*e*b^-6*(a+b*x)^9*(b*d+-1*a*e)^2*(-5*B*a*e+2*B*b*d+3*A*b*e))
@test integrate((a+b*x)^6*(d+e*x)^3*(A+B*x), x) == :(1//7*b^-5*(a+b*x)^7*(b*d+-1*a*e)^3*(A*b+-1*B*a)+1//8*b^-5*(a+b*x)^8*(b*d+-1*a*e)^2*(B*b*d+-4*B*a*e+3*A*b*e)+1//10*b^-5*e^2*(a+b*x)^10*(A*b*e+-4*B*a*e+3*B*b*d)+1//11*B*b^-5*e^3*(a+b*x)^11+1//3*e*b^-5*(a+b*x)^9*(b*d+-1*a*e)*(A*b*e+B*b*d+-2*B*a*e))
@test integrate((a+b*x)^6*(d+e*x)^2*(A+B*x), x) == :(1//7*b^-4*(a+b*x)^7*(b*d+-1*a*e)^2*(A*b+-1*B*a)+1//8*b^-4*(a+b*x)^8*(b*d+-1*a*e)*(B*b*d+-3*B*a*e+2*A*b*e)+1//9*e*b^-4*(a+b*x)^9*(A*b*e+-3*B*a*e+2*B*b*d)+1//10*B*b^-4*e^2*(a+b*x)^10)
@test integrate((a+b*x)^6*(A+B*x)*(d+e*x), x) == :(1//8*b^-3*(a+b*x)^8*(A*b*e+B*b*d+-2*B*a*e)+1//7*b^-3*(a+b*x)^7*(A*b+-1*B*a)*(b*d+-1*a*e)+1//9*B*e*b^-3*(a+b*x)^9)
@test integrate((a+b*x)^6*(A+B*x), x) == :(1//7*b^-2*(a+b*x)^7*(A*b+-1*B*a)+1//8*B*b^-2*(a+b*x)^8)
@test integrate((a+b*x)^6*(d+e*x)^-1*(A+B*x), x) == :(-1//6*e^-2*(a+b*x)^6*(B*d+-1*A*e)+-1*e^-8*(b*d+-1*a*e)^6*(B*d+-1*A*e)*log(d+e*x)+-1//2*e^-6*(a+b*x)^2*(b*d+-1*a*e)^4*(B*d+-1*A*e)+-1//4*e^-4*(a+b*x)^4*(b*d+-1*a*e)^2*(B*d+-1*A*e)+1//3*e^-5*(a+b*x)^3*(b*d+-1*a*e)^3*(B*d+-1*A*e)+1//5*e^-3*(a+b*x)^5*(B*d+-1*A*e)*(b*d+-1*a*e)+1//7*B*b^-1*e^-1*(a+b*x)^7+b*x*e^-7*(b*d+-1*a*e)^5*(B*d+-1*A*e))
@test integrate((a+b*x)^6*(d+e*x)^-2*(A+B*x), x) == :(e^-8*(d+e*x)^-1*(b*d+-1*a*e)^6*(B*d+-1*A*e)+e^-8*(b*d+-1*a*e)^5*(-1*B*a*e+-6*A*b*e+7*B*b*d)*log(d+e*x)+-1//5*b^5*e^-8*(d+e*x)^5*(-1*A*b*e+-6*B*a*e+7*B*b*d)+1//6*B*b^6*e^-8*(d+e*x)^6+-3*b*x*e^-7*(b*d+-1*a*e)^4*(-5*A*b*e+-2*B*a*e+7*B*b*d)+-5//3*b^3*e^-8*(d+e*x)^3*(b*d+-1*a*e)^2*(-4*B*a*e+-3*A*b*e+7*B*b*d)+3//4*b^4*e^-8*(d+e*x)^4*(b*d+-1*a*e)*(-5*B*a*e+-2*A*b*e+7*B*b*d)+5//2*b^2*e^-8*(d+e*x)^2*(b*d+-1*a*e)^3*(-4*A*b*e+-3*B*a*e+7*B*b*d))
@test integrate((a+b*x)^6*(d+e*x)^-3*(A+B*x), x) == :((1/2)*e^-8*(d+e*x)^-2*(b*d+-1*a*e)^6*(B*d+-1*A*e)+-1*e^-8*(d+e*x)^-1*(b*d+-1*a*e)^5*(-1*B*a*e+-6*A*b*e+7*B*b*d)+-1//4*b^5*e^-8*(d+e*x)^4*(-1*A*b*e+-6*B*a*e+7*B*b*d)+1//5*B*b^6*e^-8*(d+e*x)^5+b^4*e^-8*(d+e*x)^3*(b*d+-1*a*e)*(-5*B*a*e+-2*A*b*e+7*B*b*d)+-3*b*e^-8*(b*d+-1*a*e)^4*(-5*A*b*e+-2*B*a*e+7*B*b*d)*log(d+e*x)+5*x*b^2*e^-7*(b*d+-1*a*e)^3*(-4*A*b*e+-3*B*a*e+7*B*b*d)+-5//2*b^3*e^-8*(d+e*x)^2*(b*d+-1*a*e)^2*(-4*B*a*e+-3*A*b*e+7*B*b*d))
@test integrate((a+b*x)^6*(d+e*x)^-4*(A+B*x), x) == :(-1//2*e^-8*(d+e*x)^-2*(b*d+-1*a*e)^5*(-1*B*a*e+-6*A*b*e+7*B*b*d)+-1//3*b^5*e^-8*(d+e*x)^3*(-1*A*b*e+-6*B*a*e+7*B*b*d)+1//3*e^-8*(d+e*x)^-3*(b*d+-1*a*e)^6*(B*d+-1*A*e)+1//4*B*b^6*e^-8*(d+e*x)^4+-5*x*b^3*e^-7*(b*d+-1*a*e)^2*(-4*B*a*e+-3*A*b*e+7*B*b*d)+3*b*e^-8*(d+e*x)^-1*(b*d+-1*a*e)^4*(-5*A*b*e+-2*B*a*e+7*B*b*d)+5*b^2*e^-8*(b*d+-1*a*e)^3*(-4*A*b*e+-3*B*a*e+7*B*b*d)*log(d+e*x)+3//2*b^4*e^-8*(d+e*x)^2*(b*d+-1*a*e)*(-5*B*a*e+-2*A*b*e+7*B*b*d))
@test integrate((a+b*x)^6*(d+e*x)^-5*(A+B*x), x) == :(-1//2*b^5*e^-8*(d+e*x)^2*(-1*A*b*e+-6*B*a*e+7*B*b*d)+-1//3*e^-8*(d+e*x)^-3*(b*d+-1*a*e)^5*(-1*B*a*e+-6*A*b*e+7*B*b*d)+1//3*B*b^6*e^-8*(d+e*x)^3+1//4*e^-8*(d+e*x)^-4*(b*d+-1*a*e)^6*(B*d+-1*A*e)+-5*b^2*e^-8*(d+e*x)^-1*(b*d+-1*a*e)^3*(-4*A*b*e+-3*B*a*e+7*B*b*d)+-5*b^3*e^-8*(b*d+-1*a*e)^2*(-4*B*a*e+-3*A*b*e+7*B*b*d)*log(d+e*x)+3*x*b^4*e^-7*(b*d+-1*a*e)*(-5*B*a*e+-2*A*b*e+7*B*b*d)+3//2*b*e^-8*(d+e*x)^-2*(b*d+-1*a*e)^4*(-5*A*b*e+-2*B*a*e+7*B*b*d))
@test integrate((a+b*x)^6*(d+e*x)^-6*(A+B*x), x) == :((1/2)*B*b^6*e^-6*x^2+-1*x*b^5*e^-7*(-1*A*b*e+-6*B*a*e+6*B*b*d)+-1//4*e^-8*(d+e*x)^-4*(b*d+-1*a*e)^5*(-1*B*a*e+-6*A*b*e+7*B*b*d)+1//5*e^-8*(d+e*x)^-5*(b*d+-1*a*e)^6*(B*d+-1*A*e)+b*e^-8*(d+e*x)^-3*(b*d+-1*a*e)^4*(-5*A*b*e+-2*B*a*e+7*B*b*d)+3*b^4*e^-8*(b*d+-1*a*e)*(-5*B*a*e+-2*A*b*e+7*B*b*d)*log(d+e*x)+5*b^3*e^-8*(d+e*x)^-1*(b*d+-1*a*e)^2*(-4*B*a*e+-3*A*b*e+7*B*b*d)+-5//2*b^2*e^-8*(d+e*x)^-2*(b*d+-1*a*e)^3*(-4*A*b*e+-3*B*a*e+7*B*b*d))
@test integrate((a+b*x)^6*(d+e*x)^-7*(A+B*x), x) == :(B*x*b^6*e^-7+-1*b^5*e^-8*(-1*A*b*e+-6*B*a*e+7*B*b*d)*log(d+e*x)+-1//5*e^-8*(d+e*x)^-5*(b*d+-1*a*e)^5*(-1*B*a*e+-6*A*b*e+7*B*b*d)+1//6*e^-8*(d+e*x)^-6*(b*d+-1*a*e)^6*(B*d+-1*A*e)+-3*b^4*e^-8*(d+e*x)^-1*(b*d+-1*a*e)*(-5*B*a*e+-2*A*b*e+7*B*b*d)+-5//3*b^2*e^-8*(d+e*x)^-3*(b*d+-1*a*e)^3*(-4*A*b*e+-3*B*a*e+7*B*b*d)+3//4*b*e^-8*(d+e*x)^-4*(b*d+-1*a*e)^4*(-5*A*b*e+-2*B*a*e+7*B*b*d)+5//2*b^3*e^-8*(d+e*x)^-2*(b*d+-1*a*e)^2*(-4*B*a*e+-3*A*b*e+7*B*b*d))
@test integrate((a+b*x)^6*(d+e*x)^-8*(A+B*x), x) == :(B*b^6*e^-8*log(d+e*x)+-1//6*B*e^-8*(d+e*x)^-6*(b*d+-1*a*e)^6+6*B*b^5*e^-8*(d+e*x)^-1*(b*d+-1*a*e)+-15//2*B*b^4*e^-8*(d+e*x)^-2*(b*d+-1*a*e)^2+-15//4*B*b^2*e^-8*(d+e*x)^-4*(b*d+-1*a*e)^4+-1//7*e^-1*(a+b*x)^7*(d+e*x)^-7*(b*d+-1*a*e)^-1*(B*d+-1*A*e)+6//5*B*b*e^-8*(d+e*x)^-5*(b*d+-1*a*e)^5+20//3*B*b^3*e^-8*(d+e*x)^-3*(b*d+-1*a*e)^3)
@test integrate((a+b*x)^6*(d+e*x)^-9*(A+B*x), x) == :(-1//8*e^-1*(a+b*x)^7*(d+e*x)^-8*(b*d+-1*a*e)^-1*(B*d+-1*A*e)+1//56*e^-1*(a+b*x)^7*(d+e*x)^-7*(b*d+-1*a*e)^-2*(A*b*e+-8*B*a*e+7*B*b*d))
@test integrate((a+b*x)^6*(d+e*x)^-10*(A+B*x), x) == :(-1//9*e^-1*(a+b*x)^7*(d+e*x)^-9*(b*d+-1*a*e)^-1*(B*d+-1*A*e)+1//72*e^-1*(a+b*x)^7*(d+e*x)^-8*(b*d+-1*a*e)^-2*(-9*B*a*e+2*A*b*e+7*B*b*d)+1//504*b*e^-1*(a+b*x)^7*(d+e*x)^-7*(b*d+-1*a*e)^-3*(-9*B*a*e+2*A*b*e+7*B*b*d))
@test integrate((a+b*x)^6*(d+e*x)^-11*(A+B*x), x) == :(-1//10*e^-1*(a+b*x)^7*(d+e*x)^-10*(b*d+-1*a*e)^-1*(B*d+-1*A*e)+1//90*e^-1*(a+b*x)^7*(d+e*x)^-9*(b*d+-1*a*e)^-2*(-10*B*a*e+3*A*b*e+7*B*b*d)+1//360*b*e^-1*(a+b*x)^7*(d+e*x)^-8*(b*d+-1*a*e)^-3*(-10*B*a*e+3*A*b*e+7*B*b*d)+1//2520*b^2*e^-1*(a+b*x)^7*(d+e*x)^-7*(b*d+-1*a*e)^-4*(-10*B*a*e+3*A*b*e+7*B*b*d))
@test integrate((a+b*x)^6*(d+e*x)^-12*(A+B*x), x) == :(-1//11*e^-1*(a+b*x)^7*(d+e*x)^-11*(b*d+-1*a*e)^-1*(B*d+-1*A*e)+1//110*e^-1*(a+b*x)^7*(d+e*x)^-10*(b*d+-1*a*e)^-2*(-11*B*a*e+4*A*b*e+7*B*b*d)+1//330*b*e^-1*(a+b*x)^7*(d+e*x)^-9*(b*d+-1*a*e)^-3*(-11*B*a*e+4*A*b*e+7*B*b*d)+1//1320*b^2*e^-1*(a+b*x)^7*(d+e*x)^-8*(b*d+-1*a*e)^-4*(-11*B*a*e+4*A*b*e+7*B*b*d)+1//9240*b^3*e^-1*(a+b*x)^7*(d+e*x)^-7*(b*d+-1*a*e)^-5*(-11*B*a*e+4*A*b*e+7*B*b*d))
@test integrate((a+b*x)^6*(d+e*x)^-13*(A+B*x), x) == :(-1//5*B*b^6*e^-8*(d+e*x)^-5+-1//11*e^-8*(d+e*x)^-11*(b*d+-1*a*e)^5*(-1*B*a*e+-6*A*b*e+7*B*b*d)+1//6*b^5*e^-8*(d+e*x)^-6*(-1*A*b*e+-6*B*a*e+7*B*b*d)+1//12*e^-8*(d+e*x)^-12*(b*d+-1*a*e)^6*(B*d+-1*A*e)+-5//9*b^2*e^-8*(d+e*x)^-9*(b*d+-1*a*e)^3*(-4*A*b*e+-3*B*a*e+7*B*b*d)+-3//7*b^4*e^-8*(d+e*x)^-7*(b*d+-1*a*e)*(-5*B*a*e+-2*A*b*e+7*B*b*d)+3//10*b*e^-8*(d+e*x)^-10*(b*d+-1*a*e)^4*(-5*A*b*e+-2*B*a*e+7*B*b*d)+5//8*b^3*e^-8*(d+e*x)^-8*(b*d+-1*a*e)^2*(-4*B*a*e+-3*A*b*e+7*B*b*d))
@test integrate((a+b*x)^6*(d+e*x)^-14*(A+B*x), x) == :(-1//6*B*b^6*e^-8*(d+e*x)^-6+-1//12*e^-8*(d+e*x)^-12*(b*d+-1*a*e)^5*(-1*B*a*e+-6*A*b*e+7*B*b*d)+1//7*b^5*e^-8*(d+e*x)^-7*(-1*A*b*e+-6*B*a*e+7*B*b*d)+1//13*e^-8*(d+e*x)^-13*(b*d+-1*a*e)^6*(B*d+-1*A*e)+-3//8*b^4*e^-8*(d+e*x)^-8*(b*d+-1*a*e)*(-5*B*a*e+-2*A*b*e+7*B*b*d)+-1//2*b^2*e^-8*(d+e*x)^-10*(b*d+-1*a*e)^3*(-4*A*b*e+-3*B*a*e+7*B*b*d)+3//11*b*e^-8*(d+e*x)^-11*(b*d+-1*a*e)^4*(-5*A*b*e+-2*B*a*e+7*B*b*d)+5//9*b^3*e^-8*(d+e*x)^-9*(b*d+-1*a*e)^2*(-4*B*a*e+-3*A*b*e+7*B*b*d))
@test integrate((a+b*x)^6*(d+e*x)^-15*(A+B*x), x) == :(-1//7*B*b^6*e^-8*(d+e*x)^-7+-1//13*e^-8*(d+e*x)^-13*(b*d+-1*a*e)^5*(-1*B*a*e+-6*A*b*e+7*B*b*d)+1//8*b^5*e^-8*(d+e*x)^-8*(-1*A*b*e+-6*B*a*e+7*B*b*d)+1//14*e^-8*(d+e*x)^-14*(b*d+-1*a*e)^6*(B*d+-1*A*e)+(1/2)*b^3*e^-8*(d+e*x)^-10*(b*d+-1*a*e)^2*(-4*B*a*e+-3*A*b*e+7*B*b*d)+-5//11*b^2*e^-8*(d+e*x)^-11*(b*d+-1*a*e)^3*(-4*A*b*e+-3*B*a*e+7*B*b*d)+-1//3*b^4*e^-8*(d+e*x)^-9*(b*d+-1*a*e)*(-5*B*a*e+-2*A*b*e+7*B*b*d)+1//4*b*e^-8*(d+e*x)^-12*(b*d+-1*a*e)^4*(-5*A*b*e+-2*B*a*e+7*B*b*d))
@test integrate((a+b*x)^10*(d+e*x)^13*(A+B*x), x) == :(-1//14*e^-12*(d+e*x)^14*(b*d+-1*a*e)^10*(B*d+-1*A*e)+-1//24*b^9*e^-12*(d+e*x)^24*(-1*A*b*e+-10*B*a*e+11*B*b*d)+1//15*e^-12*(d+e*x)^15*(b*d+-1*a*e)^9*(-1*B*a*e+-10*A*b*e+11*B*b*d)+1//25*B*b^10*e^-12*(d+e*x)^25+-21//10*b^5*e^-12*(d+e*x)^20*(b*d+-1*a*e)^4*(-6*B*a*e+-5*A*b*e+11*B*b*d)+-15//22*b^7*e^-12*(d+e*x)^22*(b*d+-1*a*e)^2*(-8*B*a*e+-3*A*b*e+11*B*b*d)+-5//3*b^3*e^-12*(d+e*x)^18*(b*d+-1*a*e)^6*(-7*A*b*e+-4*B*a*e+11*B*b*d)+-5//16*b*e^-12*(d+e*x)^16*(b*d+-1*a*e)^8*(-9*A*b*e+-2*B*a*e+11*B*b*d)+5//23*b^8*e^-12*(d+e*x)^23*(b*d+-1*a*e)*(-9*B*a*e+-2*A*b*e+11*B*b*d)+10//7*b^6*e^-12*(d+e*x)^21*(b*d+-1*a*e)^3*(-7*B*a*e+-4*A*b*e+11*B*b*d)+15//17*b^2*e^-12*(d+e*x)^17*(b*d+-1*a*e)^7*(-8*A*b*e+-3*B*a*e+11*B*b*d)+42//19*b^4*e^-12*(d+e*x)^19*(b*d+-1*a*e)^5*(-6*A*b*e+-5*B*a*e+11*B*b*d))
@test integrate((a+b*x)^10*(d+e*x)^12*(A+B*x), x) == :(-1//13*e^-12*(d+e*x)^13*(b*d+-1*a*e)^10*(B*d+-1*A*e)+-1//23*b^9*e^-12*(d+e*x)^23*(-1*A*b*e+-10*B*a*e+11*B*b*d)+1//14*e^-12*(d+e*x)^14*(b*d+-1*a*e)^9*(-1*B*a*e+-10*A*b*e+11*B*b*d)+1//24*B*b^10*e^-12*(d+e*x)^24+-42//19*b^5*e^-12*(d+e*x)^19*(b*d+-1*a*e)^4*(-6*B*a*e+-5*A*b*e+11*B*b*d)+-30//17*b^3*e^-12*(d+e*x)^17*(b*d+-1*a*e)^6*(-7*A*b*e+-4*B*a*e+11*B*b*d)+-5//7*b^7*e^-12*(d+e*x)^21*(b*d+-1*a*e)^2*(-8*B*a*e+-3*A*b*e+11*B*b*d)+-1//3*b*e^-12*(d+e*x)^15*(b*d+-1*a*e)^8*(-9*A*b*e+-2*B*a*e+11*B*b*d)+3//2*b^6*e^-12*(d+e*x)^20*(b*d+-1*a*e)^3*(-7*B*a*e+-4*A*b*e+11*B*b*d)+5//22*b^8*e^-12*(d+e*x)^22*(b*d+-1*a*e)*(-9*B*a*e+-2*A*b*e+11*B*b*d)+7//3*b^4*e^-12*(d+e*x)^18*(b*d+-1*a*e)^5*(-6*A*b*e+-5*B*a*e+11*B*b*d)+15//16*b^2*e^-12*(d+e*x)^16*(b*d+-1*a*e)^7*(-8*A*b*e+-3*B*a*e+11*B*b*d))
@test integrate((a+b*x)^10*(d+e*x)^11*(A+B*x), x) == :(-1//12*e^-12*(d+e*x)^12*(b*d+-1*a*e)^10*(B*d+-1*A*e)+-1//22*b^9*e^-12*(d+e*x)^22*(-1*A*b*e+-10*B*a*e+11*B*b*d)+1//13*e^-12*(d+e*x)^13*(b*d+-1*a*e)^9*(-1*B*a*e+-10*A*b*e+11*B*b*d)+1//23*B*b^10*e^-12*(d+e*x)^23+b^2*e^-12*(d+e*x)^15*(b*d+-1*a*e)^7*(-8*A*b*e+-3*B*a*e+11*B*b*d)+-15//8*b^3*e^-12*(d+e*x)^16*(b*d+-1*a*e)^6*(-7*A*b*e+-4*B*a*e+11*B*b*d)+-7//3*b^5*e^-12*(d+e*x)^18*(b*d+-1*a*e)^4*(-6*B*a*e+-5*A*b*e+11*B*b*d)+-5//14*b*e^-12*(d+e*x)^14*(b*d+-1*a*e)^8*(-9*A*b*e+-2*B*a*e+11*B*b*d)+-3//4*b^7*e^-12*(d+e*x)^20*(b*d+-1*a*e)^2*(-8*B*a*e+-3*A*b*e+11*B*b*d)+5//21*b^8*e^-12*(d+e*x)^21*(b*d+-1*a*e)*(-9*B*a*e+-2*A*b*e+11*B*b*d)+30//19*b^6*e^-12*(d+e*x)^19*(b*d+-1*a*e)^3*(-7*B*a*e+-4*A*b*e+11*B*b*d)+42//17*b^4*e^-12*(d+e*x)^17*(b*d+-1*a*e)^5*(-6*A*b*e+-5*B*a*e+11*B*b*d))
@test integrate((a+b*x)^10*(d+e*x)^10*(A+B*x), x) == :(1//11*b^-12*(a+b*x)^11*(b*d+-1*a*e)^10*(A*b+-1*B*a)+1//12*b^-12*(a+b*x)^12*(b*d+-1*a*e)^9*(B*b*d+-11*B*a*e+10*A*b*e)+1//21*b^-12*e^9*(a+b*x)^21*(A*b*e+-11*B*a*e+10*B*b*d)+1//22*B*b^-12*e^10*(a+b*x)^22+2*b^-12*e^3*(a+b*x)^15*(b*d+-1*a*e)^6*(-11*B*a*e+4*B*b*d+7*A*b*e)+1//4*b^-12*e^8*(a+b*x)^20*(b*d+-1*a*e)*(-11*B*a*e+2*A*b*e+9*B*b*d)+5//3*b^-12*e^6*(a+b*x)^18*(b*d+-1*a*e)^3*(-11*B*a*e+4*A*b*e+7*B*b*d)+5//13*e*b^-12*(a+b*x)^13*(b*d+-1*a*e)^8*(-11*B*a*e+2*B*b*d+9*A*b*e)+15//14*b^-12*e^2*(a+b*x)^14*(b*d+-1*a*e)^7*(-11*B*a*e+3*B*b*d+8*A*b*e)+15//19*b^-12*e^7*(a+b*x)^19*(b*d+-1*a*e)^2*(-11*B*a*e+3*A*b*e+8*B*b*d)+21//8*b^-12*e^4*(a+b*x)^16*(b*d+-1*a*e)^5*(-11*B*a*e+5*B*b*d+6*A*b*e)+42//17*b^-12*e^5*(a+b*x)^17*(b*d+-1*a*e)^4*(-11*B*a*e+5*A*b*e+6*B*b*d))
@test integrate((a+b*x)^10*(d+e*x)^9*(A+B*x), x) == :(1//11*b^-11*(a+b*x)^11*(b*d+-1*a*e)^9*(A*b+-1*B*a)+1//12*b^-11*(a+b*x)^12*(b*d+-1*a*e)^8*(B*b*d+-10*B*a*e+9*A*b*e)+1//20*b^-11*e^8*(a+b*x)^20*(A*b*e+-10*B*a*e+9*B*b*d)+1//21*B*b^-11*e^9*(a+b*x)^21+2//3*b^-11*e^6*(a+b*x)^18*(b*d+-1*a*e)^2*(-10*B*a*e+3*A*b*e+7*B*b*d)+6//7*b^-11*e^2*(a+b*x)^14*(b*d+-1*a*e)^6*(-10*B*a*e+3*B*b*d+7*A*b*e)+9//13*e*b^-11*(a+b*x)^13*(b*d+-1*a*e)^7*(B*b*d+-5*B*a*e+4*A*b*e)+9//19*b^-11*e^7*(a+b*x)^19*(b*d+-1*a*e)*(A*b*e+-5*B*a*e+4*B*b*d)+14//5*b^-11*e^3*(a+b*x)^15*(b*d+-1*a*e)^5*(-5*B*a*e+2*B*b*d+3*A*b*e)+42//17*b^-11*e^5*(a+b*x)^17*(b*d+-1*a*e)^3*(-5*B*a*e+2*A*b*e+3*B*b*d)+63//8*b^-11*e^4*(a+b*x)^16*(b*d+-1*a*e)^4*(A*b*e+B*b*d+-2*B*a*e))
@test integrate((a+b*x)^10*(d+e*x)^8*(A+B*x), x) == :(1//11*b^-10*(a+b*x)^11*(b*d+-1*a*e)^8*(A*b+-1*B*a)+1//12*b^-10*(a+b*x)^12*(b*d+-1*a*e)^7*(B*b*d+-9*B*a*e+8*A*b*e)+1//19*b^-10*e^7*(a+b*x)^19*(A*b*e+-9*B*a*e+8*B*b*d)+1//20*B*b^-10*e^8*(a+b*x)^20+2*b^-10*e^2*(a+b*x)^14*(b*d+-1*a*e)^5*(B*b*d+-3*B*a*e+2*A*b*e)+2//9*b^-10*e^6*(a+b*x)^18*(b*d+-1*a*e)*(-9*B*a*e+2*A*b*e+7*B*b*d)+4//13*e*b^-10*(a+b*x)^13*(b*d+-1*a*e)^6*(-9*B*a*e+2*B*b*d+7*A*b*e)+7//8*b^-10*e^4*(a+b*x)^16*(b*d+-1*a*e)^3*(-9*B*a*e+4*A*b*e+5*B*b*d)+14//15*b^-10*e^3*(a+b*x)^15*(b*d+-1*a*e)^4*(-9*B*a*e+4*B*b*d+5*A*b*e)+28//17*b^-10*e^5*(a+b*x)^17*(b*d+-1*a*e)^2*(A*b*e+-3*B*a*e+2*B*b*d))
@test integrate((a+b*x)^10*(d+e*x)^7*(A+B*x), x) == :(1//11*b^-9*(a+b*x)^11*(b*d+-1*a*e)^7*(A*b+-1*B*a)+1//12*b^-9*(a+b*x)^12*(b*d+-1*a*e)^6*(B*b*d+-8*B*a*e+7*A*b*e)+1//18*b^-9*e^6*(a+b*x)^18*(A*b*e+-8*B*a*e+7*B*b*d)+1//19*B*b^-9*e^7*(a+b*x)^19+(1/2)*b^-9*e^2*(a+b*x)^14*(b*d+-1*a*e)^4*(-8*B*a*e+3*B*b*d+5*A*b*e)+7//3*b^-9*e^3*(a+b*x)^15*(b*d+-1*a*e)^3*(A*b*e+B*b*d+-2*B*a*e)+7//13*e*b^-9*(a+b*x)^13*(b*d+-1*a*e)^5*(B*b*d+-4*B*a*e+3*A*b*e)+7//16*b^-9*e^4*(a+b*x)^16*(b*d+-1*a*e)^2*(-8*B*a*e+3*A*b*e+5*B*b*d)+7//17*b^-9*e^5*(a+b*x)^17*(b*d+-1*a*e)*(A*b*e+-4*B*a*e+3*B*b*d))
@test integrate((a+b*x)^10*(d+e*x)^6*(A+B*x), x) == :(1//11*b^-8*(a+b*x)^11*(b*d+-1*a*e)^6*(A*b+-1*B*a)+1//12*b^-8*(a+b*x)^12*(b*d+-1*a*e)^5*(B*b*d+-7*B*a*e+6*A*b*e)+1//17*b^-8*e^5*(a+b*x)^17*(A*b*e+-7*B*a*e+6*B*b*d)+1//18*B*b^-8*e^6*(a+b*x)^18+1//3*b^-8*e^3*(a+b*x)^15*(b*d+-1*a*e)^2*(-7*B*a*e+3*A*b*e+4*B*b*d)+3//13*e*b^-8*(a+b*x)^13*(b*d+-1*a*e)^4*(-7*B*a*e+2*B*b*d+5*A*b*e)+3//16*b^-8*e^4*(a+b*x)^16*(b*d+-1*a*e)*(-7*B*a*e+2*A*b*e+5*B*b*d)+5//14*b^-8*e^2*(a+b*x)^14*(b*d+-1*a*e)^3*(-7*B*a*e+3*B*b*d+4*A*b*e))
@test integrate((a+b*x)^10*(d+e*x)^5*(A+B*x), x) == :(1//11*b^-7*(a+b*x)^11*(b*d+-1*a*e)^5*(A*b+-1*B*a)+1//12*b^-7*(a+b*x)^12*(b*d+-1*a*e)^4*(B*b*d+-6*B*a*e+5*A*b*e)+1//16*b^-7*e^4*(a+b*x)^16*(A*b*e+-6*B*a*e+5*B*b*d)+1//17*B*b^-7*e^5*(a+b*x)^17+1//3*b^-7*e^3*(a+b*x)^15*(b*d+-1*a*e)*(A*b*e+-3*B*a*e+2*B*b*d)+5//7*b^-7*e^2*(a+b*x)^14*(b*d+-1*a*e)^2*(A*b*e+B*b*d+-2*B*a*e)+5//13*e*b^-7*(a+b*x)^13*(b*d+-1*a*e)^3*(B*b*d+-3*B*a*e+2*A*b*e))
@test integrate((a+b*x)^10*(d+e*x)^4*(A+B*x), x) == :(1//11*b^-6*(a+b*x)^11*(b*d+-1*a*e)^4*(A*b+-1*B*a)+1//12*b^-6*(a+b*x)^12*(b*d+-1*a*e)^3*(B*b*d+-5*B*a*e+4*A*b*e)+1//15*b^-6*e^3*(a+b*x)^15*(A*b*e+-5*B*a*e+4*B*b*d)+1//16*B*b^-6*e^4*(a+b*x)^16+1//7*b^-6*e^2*(a+b*x)^14*(b*d+-1*a*e)*(-5*B*a*e+2*A*b*e+3*B*b*d)+2//13*e*b^-6*(a+b*x)^13*(b*d+-1*a*e)^2*(-5*B*a*e+2*B*b*d+3*A*b*e))
@test integrate((a+b*x)^10*(d+e*x)^3*(A+B*x), x) == :(1//11*b^-5*(a+b*x)^11*(b*d+-1*a*e)^3*(A*b+-1*B*a)+1//12*b^-5*(a+b*x)^12*(b*d+-1*a*e)^2*(B*b*d+-4*B*a*e+3*A*b*e)+1//14*b^-5*e^2*(a+b*x)^14*(A*b*e+-4*B*a*e+3*B*b*d)+1//15*B*b^-5*e^3*(a+b*x)^15+3//13*e*b^-5*(a+b*x)^13*(b*d+-1*a*e)*(A*b*e+B*b*d+-2*B*a*e))
@test integrate((a+b*x)^10*(d+e*x)^2*(A+B*x), x) == :(1//11*b^-4*(a+b*x)^11*(b*d+-1*a*e)^2*(A*b+-1*B*a)+1//12*b^-4*(a+b*x)^12*(b*d+-1*a*e)*(B*b*d+-3*B*a*e+2*A*b*e)+1//13*e*b^-4*(a+b*x)^13*(A*b*e+-3*B*a*e+2*B*b*d)+1//14*B*b^-4*e^2*(a+b*x)^14)
@test integrate((a+b*x)^10*(A+B*x)*(d+e*x), x) == :(1//12*b^-3*(a+b*x)^12*(A*b*e+B*b*d+-2*B*a*e)+1//11*b^-3*(a+b*x)^11*(A*b+-1*B*a)*(b*d+-1*a*e)+1//13*B*e*b^-3*(a+b*x)^13)
@test integrate((a+b*x)^10*(A+B*x), x) == :(1//11*b^-2*(a+b*x)^11*(A*b+-1*B*a)+1//12*B*b^-2*(a+b*x)^12)
@test integrate((a+b*x)^10*(d+e*x)^-1*(A+B*x), x) == :(-1//10*e^-2*(a+b*x)^10*(B*d+-1*A*e)+-1*e^-12*(b*d+-1*a*e)^10*(B*d+-1*A*e)*log(d+e*x)+-1//2*e^-10*(a+b*x)^2*(b*d+-1*a*e)^8*(B*d+-1*A*e)+-1//4*e^-8*(a+b*x)^4*(b*d+-1*a*e)^6*(B*d+-1*A*e)+-1//6*e^-6*(a+b*x)^6*(b*d+-1*a*e)^4*(B*d+-1*A*e)+-1//8*e^-4*(a+b*x)^8*(b*d+-1*a*e)^2*(B*d+-1*A*e)+1//3*e^-9*(a+b*x)^3*(b*d+-1*a*e)^7*(B*d+-1*A*e)+1//5*e^-7*(a+b*x)^5*(b*d+-1*a*e)^5*(B*d+-1*A*e)+1//7*e^-5*(a+b*x)^7*(b*d+-1*a*e)^3*(B*d+-1*A*e)+1//9*e^-3*(a+b*x)^9*(B*d+-1*A*e)*(b*d+-1*a*e)+1//11*B*b^-1*e^-1*(a+b*x)^11+b*x*e^-11*(b*d+-1*a*e)^9*(B*d+-1*A*e))
@test integrate((a+b*x)^10*(d+e*x)^-2*(A+B*x), x) == :(e^-12*(d+e*x)^-1*(b*d+-1*a*e)^10*(B*d+-1*A*e)+e^-12*(b*d+-1*a*e)^9*(-1*B*a*e+-10*A*b*e+11*B*b*d)*log(d+e*x)+-1//9*b^9*e^-12*(d+e*x)^9*(-1*A*b*e+-10*B*a*e+11*B*b*d)+1//10*B*b^10*e^-12*(d+e*x)^10+-10*b^3*e^-12*(d+e*x)^3*(b*d+-1*a*e)^6*(-7*A*b*e+-4*B*a*e+11*B*b*d)+-5*b*x*e^-11*(b*d+-1*a*e)^8*(-9*A*b*e+-2*B*a*e+11*B*b*d)+5*b^6*e^-12*(d+e*x)^6*(b*d+-1*a*e)^3*(-7*B*a*e+-4*A*b*e+11*B*b*d)+-42//5*b^5*e^-12*(d+e*x)^5*(b*d+-1*a*e)^4*(-6*B*a*e+-5*A*b*e+11*B*b*d)+-15//7*b^7*e^-12*(d+e*x)^7*(b*d+-1*a*e)^2*(-8*B*a*e+-3*A*b*e+11*B*b*d)+5//8*b^8*e^-12*(d+e*x)^8*(b*d+-1*a*e)*(-9*B*a*e+-2*A*b*e+11*B*b*d)+15//2*b^2*e^-12*(d+e*x)^2*(b*d+-1*a*e)^7*(-8*A*b*e+-3*B*a*e+11*B*b*d)+21//2*b^4*e^-12*(d+e*x)^4*(b*d+-1*a*e)^5*(-6*A*b*e+-5*B*a*e+11*B*b*d))
@test integrate((a+b*x)^10*(d+e*x)^-3*(A+B*x), x) == :((1/2)*e^-12*(d+e*x)^-2*(b*d+-1*a*e)^10*(B*d+-1*A*e)+-1*e^-12*(d+e*x)^-1*(b*d+-1*a*e)^9*(-1*B*a*e+-10*A*b*e+11*B*b*d)+-1//8*b^9*e^-12*(d+e*x)^8*(-1*A*b*e+-10*B*a*e+11*B*b*d)+1//9*B*b^10*e^-12*(d+e*x)^9+-15*b^3*e^-12*(d+e*x)^2*(b*d+-1*a*e)^6*(-7*A*b*e+-4*B*a*e+11*B*b*d)+-5*b*e^-12*(b*d+-1*a*e)^8*(-9*A*b*e+-2*B*a*e+11*B*b*d)*log(d+e*x)+6*b^6*e^-12*(d+e*x)^5*(b*d+-1*a*e)^3*(-7*B*a*e+-4*A*b*e+11*B*b*d)+14*b^4*e^-12*(d+e*x)^3*(b*d+-1*a*e)^5*(-6*A*b*e+-5*B*a*e+11*B*b*d)+15*x*b^2*e^-11*(b*d+-1*a*e)^7*(-8*A*b*e+-3*B*a*e+11*B*b*d)+-21//2*b^5*e^-12*(d+e*x)^4*(b*d+-1*a*e)^4*(-6*B*a*e+-5*A*b*e+11*B*b*d)+-5//2*b^7*e^-12*(d+e*x)^6*(b*d+-1*a*e)^2*(-8*B*a*e+-3*A*b*e+11*B*b*d)+5//7*b^8*e^-12*(d+e*x)^7*(b*d+-1*a*e)*(-9*B*a*e+-2*A*b*e+11*B*b*d))
@test integrate((a+b*x)^10*(d+e*x)^-4*(A+B*x), x) == :(-1//2*e^-12*(d+e*x)^-2*(b*d+-1*a*e)^9*(-1*B*a*e+-10*A*b*e+11*B*b*d)+-1//7*b^9*e^-12*(d+e*x)^7*(-1*A*b*e+-10*B*a*e+11*B*b*d)+1//3*e^-12*(d+e*x)^-3*(b*d+-1*a*e)^10*(B*d+-1*A*e)+1//8*B*b^10*e^-12*(d+e*x)^8+-30*x*b^3*e^-11*(b*d+-1*a*e)^6*(-7*A*b*e+-4*B*a*e+11*B*b*d)+-14*b^5*e^-12*(d+e*x)^3*(b*d+-1*a*e)^4*(-6*B*a*e+-5*A*b*e+11*B*b*d)+-3*b^7*e^-12*(d+e*x)^5*(b*d+-1*a*e)^2*(-8*B*a*e+-3*A*b*e+11*B*b*d)+5*b*e^-12*(d+e*x)^-1*(b*d+-1*a*e)^8*(-9*A*b*e+-2*B*a*e+11*B*b*d)+15*b^2*e^-12*(b*d+-1*a*e)^7*(-8*A*b*e+-3*B*a*e+11*B*b*d)*log(d+e*x)+21*b^4*e^-12*(d+e*x)^2*(b*d+-1*a*e)^5*(-6*A*b*e+-5*B*a*e+11*B*b*d)+5//6*b^8*e^-12*(d+e*x)^6*(b*d+-1*a*e)*(-9*B*a*e+-2*A*b*e+11*B*b*d)+15//2*b^6*e^-12*(d+e*x)^4*(b*d+-1*a*e)^3*(-7*B*a*e+-4*A*b*e+11*B*b*d))
@test integrate((a+b*x)^10*(d+e*x)^-5*(A+B*x), x) == :(-1//3*e^-12*(d+e*x)^-3*(b*d+-1*a*e)^9*(-1*B*a*e+-10*A*b*e+11*B*b*d)+-1//6*b^9*e^-12*(d+e*x)^6*(-1*A*b*e+-10*B*a*e+11*B*b*d)+1//4*e^-12*(d+e*x)^-4*(b*d+-1*a*e)^10*(B*d+-1*A*e)+1//7*B*b^10*e^-12*(d+e*x)^7+b^8*e^-12*(d+e*x)^5*(b*d+-1*a*e)*(-9*B*a*e+-2*A*b*e+11*B*b*d)+-30*b^3*e^-12*(b*d+-1*a*e)^6*(-7*A*b*e+-4*B*a*e+11*B*b*d)*log(d+e*x)+-21*b^5*e^-12*(d+e*x)^2*(b*d+-1*a*e)^4*(-6*B*a*e+-5*A*b*e+11*B*b*d)+-15*b^2*e^-12*(d+e*x)^-1*(b*d+-1*a*e)^7*(-8*A*b*e+-3*B*a*e+11*B*b*d)+10*b^6*e^-12*(d+e*x)^3*(b*d+-1*a*e)^3*(-7*B*a*e+-4*A*b*e+11*B*b*d)+42*x*b^4*e^-11*(b*d+-1*a*e)^5*(-6*A*b*e+-5*B*a*e+11*B*b*d)+-15//4*b^7*e^-12*(d+e*x)^4*(b*d+-1*a*e)^2*(-8*B*a*e+-3*A*b*e+11*B*b*d)+5//2*b*e^-12*(d+e*x)^-2*(b*d+-1*a*e)^8*(-9*A*b*e+-2*B*a*e+11*B*b*d))
@test integrate((a+b*x)^10*(d+e*x)^-6*(A+B*x), x) == :(-1//4*e^-12*(d+e*x)^-4*(b*d+-1*a*e)^9*(-1*B*a*e+-10*A*b*e+11*B*b*d)+-1//5*b^9*e^-12*(d+e*x)^5*(-1*A*b*e+-10*B*a*e+11*B*b*d)+1//5*e^-12*(d+e*x)^-5*(b*d+-1*a*e)^10*(B*d+-1*A*e)+1//6*B*b^10*e^-12*(d+e*x)^6+-42*x*b^5*e^-11*(b*d+-1*a*e)^4*(-6*B*a*e+-5*A*b*e+11*B*b*d)+-5*b^7*e^-12*(d+e*x)^3*(b*d+-1*a*e)^2*(-8*B*a*e+-3*A*b*e+11*B*b*d)+15*b^6*e^-12*(d+e*x)^2*(b*d+-1*a*e)^3*(-7*B*a*e+-4*A*b*e+11*B*b*d)+30*b^3*e^-12*(d+e*x)^-1*(b*d+-1*a*e)^6*(-7*A*b*e+-4*B*a*e+11*B*b*d)+42*b^4*e^-12*(b*d+-1*a*e)^5*(-6*A*b*e+-5*B*a*e+11*B*b*d)*log(d+e*x)+-15//2*b^2*e^-12*(d+e*x)^-2*(b*d+-1*a*e)^7*(-8*A*b*e+-3*B*a*e+11*B*b*d)+5//3*b*e^-12*(d+e*x)^-3*(b*d+-1*a*e)^8*(-9*A*b*e+-2*B*a*e+11*B*b*d)+5//4*b^8*e^-12*(d+e*x)^4*(b*d+-1*a*e)*(-9*B*a*e+-2*A*b*e+11*B*b*d))
@test integrate((a+b*x)^10*(d+e*x)^-7*(A+B*x), x) == :(-1//4*b^9*e^-12*(d+e*x)^4*(-1*A*b*e+-10*B*a*e+11*B*b*d)+-1//5*e^-12*(d+e*x)^-5*(b*d+-1*a*e)^9*(-1*B*a*e+-10*A*b*e+11*B*b*d)+1//5*B*b^10*e^-12*(d+e*x)^5+1//6*e^-12*(d+e*x)^-6*(b*d+-1*a*e)^10*(B*d+-1*A*e)+-42*b^4*e^-12*(d+e*x)^-1*(b*d+-1*a*e)^5*(-6*A*b*e+-5*B*a*e+11*B*b*d)+-42*b^5*e^-12*(b*d+-1*a*e)^4*(-6*B*a*e+-5*A*b*e+11*B*b*d)*log(d+e*x)+-5*b^2*e^-12*(d+e*x)^-3*(b*d+-1*a*e)^7*(-8*A*b*e+-3*B*a*e+11*B*b*d)+15*b^3*e^-12*(d+e*x)^-2*(b*d+-1*a*e)^6*(-7*A*b*e+-4*B*a*e+11*B*b*d)+30*x*b^6*e^-11*(b*d+-1*a*e)^3*(-7*B*a*e+-4*A*b*e+11*B*b*d)+-15//2*b^7*e^-12*(d+e*x)^2*(b*d+-1*a*e)^2*(-8*B*a*e+-3*A*b*e+11*B*b*d)+5//3*b^8*e^-12*(d+e*x)^3*(b*d+-1*a*e)*(-9*B*a*e+-2*A*b*e+11*B*b*d)+5//4*b*e^-12*(d+e*x)^-4*(b*d+-1*a*e)^8*(-9*A*b*e+-2*B*a*e+11*B*b*d))
@test integrate((a+b*x)^10*(d+e*x)^-8*(A+B*x), x) == :(-1//3*b^9*e^-12*(d+e*x)^3*(-1*A*b*e+-10*B*a*e+11*B*b*d)+-1//6*e^-12*(d+e*x)^-6*(b*d+-1*a*e)^9*(-1*B*a*e+-10*A*b*e+11*B*b*d)+1//4*B*b^10*e^-12*(d+e*x)^4+1//7*e^-12*(d+e*x)^-7*(b*d+-1*a*e)^10*(B*d+-1*A*e)+b*e^-12*(d+e*x)^-5*(b*d+-1*a*e)^8*(-9*A*b*e+-2*B*a*e+11*B*b*d)+-21*b^4*e^-12*(d+e*x)^-2*(b*d+-1*a*e)^5*(-6*A*b*e+-5*B*a*e+11*B*b*d)+-15*x*b^7*e^-11*(b*d+-1*a*e)^2*(-8*B*a*e+-3*A*b*e+11*B*b*d)+10*b^3*e^-12*(d+e*x)^-3*(b*d+-1*a*e)^6*(-7*A*b*e+-4*B*a*e+11*B*b*d)+30*b^6*e^-12*(b*d+-1*a*e)^3*(-7*B*a*e+-4*A*b*e+11*B*b*d)*log(d+e*x)+42*b^5*e^-12*(d+e*x)^-1*(b*d+-1*a*e)^4*(-6*B*a*e+-5*A*b*e+11*B*b*d)+-15//4*b^2*e^-12*(d+e*x)^-4*(b*d+-1*a*e)^7*(-8*A*b*e+-3*B*a*e+11*B*b*d)+5//2*b^8*e^-12*(d+e*x)^2*(b*d+-1*a*e)*(-9*B*a*e+-2*A*b*e+11*B*b*d))
@test integrate((a+b*x)^10*(d+e*x)^-9*(A+B*x), x) == :(-1//2*b^9*e^-12*(d+e*x)^2*(-1*A*b*e+-10*B*a*e+11*B*b*d)+-1//7*e^-12*(d+e*x)^-7*(b*d+-1*a*e)^9*(-1*B*a*e+-10*A*b*e+11*B*b*d)+1//3*B*b^10*e^-12*(d+e*x)^3+1//8*e^-12*(d+e*x)^-8*(b*d+-1*a*e)^10*(B*d+-1*A*e)+-30*b^6*e^-12*(d+e*x)^-1*(b*d+-1*a*e)^3*(-7*B*a*e+-4*A*b*e+11*B*b*d)+-15*b^7*e^-12*(b*d+-1*a*e)^2*(-8*B*a*e+-3*A*b*e+11*B*b*d)*log(d+e*x)+-14*b^4*e^-12*(d+e*x)^-3*(b*d+-1*a*e)^5*(-6*A*b*e+-5*B*a*e+11*B*b*d)+-3*b^2*e^-12*(d+e*x)^-5*(b*d+-1*a*e)^7*(-8*A*b*e+-3*B*a*e+11*B*b*d)+5*x*b^8*e^-11*(b*d+-1*a*e)*(-9*B*a*e+-2*A*b*e+11*B*b*d)+21*b^5*e^-12*(d+e*x)^-2*(b*d+-1*a*e)^4*(-6*B*a*e+-5*A*b*e+11*B*b*d)+5//6*b*e^-12*(d+e*x)^-6*(b*d+-1*a*e)^8*(-9*A*b*e+-2*B*a*e+11*B*b*d)+15//2*b^3*e^-12*(d+e*x)^-4*(b*d+-1*a*e)^6*(-7*A*b*e+-4*B*a*e+11*B*b*d))
@test integrate((a+b*x)^10*(d+e*x)^-10*(A+B*x), x) == :((1/2)*B*b^10*e^-10*x^2+-1*x*b^9*e^-11*(-1*A*b*e+-10*B*a*e+10*B*b*d)+-1//8*e^-12*(d+e*x)^-8*(b*d+-1*a*e)^9*(-1*B*a*e+-10*A*b*e+11*B*b*d)+1//9*e^-12*(d+e*x)^-9*(b*d+-1*a*e)^10*(B*d+-1*A*e)+-15*b^6*e^-12*(d+e*x)^-2*(b*d+-1*a*e)^3*(-7*B*a*e+-4*A*b*e+11*B*b*d)+5*b^8*e^-12*(b*d+-1*a*e)*(-9*B*a*e+-2*A*b*e+11*B*b*d)*log(d+e*x)+6*b^3*e^-12*(d+e*x)^-5*(b*d+-1*a*e)^6*(-7*A*b*e+-4*B*a*e+11*B*b*d)+14*b^5*e^-12*(d+e*x)^-3*(b*d+-1*a*e)^4*(-6*B*a*e+-5*A*b*e+11*B*b*d)+15*b^7*e^-12*(d+e*x)^-1*(b*d+-1*a*e)^2*(-8*B*a*e+-3*A*b*e+11*B*b*d)+-21//2*b^4*e^-12*(d+e*x)^-4*(b*d+-1*a*e)^5*(-6*A*b*e+-5*B*a*e+11*B*b*d)+-5//2*b^2*e^-12*(d+e*x)^-6*(b*d+-1*a*e)^7*(-8*A*b*e+-3*B*a*e+11*B*b*d)+5//7*b*e^-12*(d+e*x)^-7*(b*d+-1*a*e)^8*(-9*A*b*e+-2*B*a*e+11*B*b*d))
@test integrate((a+b*x)^10*(d+e*x)^-11*(A+B*x), x) == :(B*x*b^10*e^-11+-1*b^9*e^-12*(-1*A*b*e+-10*B*a*e+11*B*b*d)*log(d+e*x)+-1//9*e^-12*(d+e*x)^-9*(b*d+-1*a*e)^9*(-1*B*a*e+-10*A*b*e+11*B*b*d)+1//10*e^-12*(d+e*x)^-10*(b*d+-1*a*e)^10*(B*d+-1*A*e)+-10*b^6*e^-12*(d+e*x)^-3*(b*d+-1*a*e)^3*(-7*B*a*e+-4*A*b*e+11*B*b*d)+-5*b^8*e^-12*(d+e*x)^-1*(b*d+-1*a*e)*(-9*B*a*e+-2*A*b*e+11*B*b*d)+5*b^3*e^-12*(d+e*x)^-6*(b*d+-1*a*e)^6*(-7*A*b*e+-4*B*a*e+11*B*b*d)+-42//5*b^4*e^-12*(d+e*x)^-5*(b*d+-1*a*e)^5*(-6*A*b*e+-5*B*a*e+11*B*b*d)+-15//7*b^2*e^-12*(d+e*x)^-7*(b*d+-1*a*e)^7*(-8*A*b*e+-3*B*a*e+11*B*b*d)+5//8*b*e^-12*(d+e*x)^-8*(b*d+-1*a*e)^8*(-9*A*b*e+-2*B*a*e+11*B*b*d)+15//2*b^7*e^-12*(d+e*x)^-2*(b*d+-1*a*e)^2*(-8*B*a*e+-3*A*b*e+11*B*b*d)+21//2*b^5*e^-12*(d+e*x)^-4*(b*d+-1*a*e)^4*(-6*B*a*e+-5*A*b*e+11*B*b*d))
@test integrate((a+b*x)^10*(d+e*x)^-12*(A+B*x), x) == :(B*b^10*e^-12*log(d+e*x)+-1//10*B*e^-12*(d+e*x)^-10*(b*d+-1*a*e)^10+-35*B*b^4*e^-12*(d+e*x)^-6*(b*d+-1*a*e)^6+10*B*b^9*e^-12*(d+e*x)^-1*(b*d+-1*a*e)+40*B*b^7*e^-12*(d+e*x)^-3*(b*d+-1*a*e)^3+-105//2*B*b^6*e^-12*(d+e*x)^-4*(b*d+-1*a*e)^4+-45//2*B*b^8*e^-12*(d+e*x)^-2*(b*d+-1*a*e)^2+-45//8*B*b^2*e^-12*(d+e*x)^-8*(b*d+-1*a*e)^8+-1//11*e^-1*(a+b*x)^11*(d+e*x)^-11*(b*d+-1*a*e)^-1*(B*d+-1*A*e)+10//9*B*b*e^-12*(d+e*x)^-9*(b*d+-1*a*e)^9+120//7*B*b^3*e^-12*(d+e*x)^-7*(b*d+-1*a*e)^7+252//5*B*b^5*e^-12*(d+e*x)^-5*(b*d+-1*a*e)^5)
@test integrate((a+b*x)^10*(d+e*x)^-13*(A+B*x), x) == :(-1//12*e^-1*(a+b*x)^11*(d+e*x)^-12*(b*d+-1*a*e)^-1*(B*d+-1*A*e)+1//132*e^-1*(a+b*x)^11*(d+e*x)^-11*(b*d+-1*a*e)^-2*(A*b*e+-12*B*a*e+11*B*b*d))
@test integrate((a+b*x)^10*(d+e*x)^-14*(A+B*x), x) == :(-1//13*e^-1*(a+b*x)^11*(d+e*x)^-13*(b*d+-1*a*e)^-1*(B*d+-1*A*e)+1//156*e^-1*(a+b*x)^11*(d+e*x)^-12*(b*d+-1*a*e)^-2*(-13*B*a*e+2*A*b*e+11*B*b*d)+1//1716*b*e^-1*(a+b*x)^11*(d+e*x)^-11*(b*d+-1*a*e)^-3*(-13*B*a*e+2*A*b*e+11*B*b*d))
@test integrate((a+b*x)^10*(d+e*x)^-15*(A+B*x), x) == :(-1//14*e^-1*(a+b*x)^11*(d+e*x)^-14*(b*d+-1*a*e)^-1*(B*d+-1*A*e)+1//182*e^-1*(a+b*x)^11*(d+e*x)^-13*(b*d+-1*a*e)^-2*(-14*B*a*e+3*A*b*e+11*B*b*d)+1//1092*b*e^-1*(a+b*x)^11*(d+e*x)^-12*(b*d+-1*a*e)^-3*(-14*B*a*e+3*A*b*e+11*B*b*d)+1//12012*b^2*e^-1*(a+b*x)^11*(d+e*x)^-11*(b*d+-1*a*e)^-4*(-14*B*a*e+3*A*b*e+11*B*b*d))
@test integrate((a+b*x)^10*(d+e*x)^-16*(A+B*x), x) == :(-1//15*e^-1*(a+b*x)^11*(d+e*x)^-15*(b*d+-1*a*e)^-1*(B*d+-1*A*e)+1//210*e^-1*(a+b*x)^11*(d+e*x)^-14*(b*d+-1*a*e)^-2*(-15*B*a*e+4*A*b*e+11*B*b*d)+1//910*b*e^-1*(a+b*x)^11*(d+e*x)^-13*(b*d+-1*a*e)^-3*(-15*B*a*e+4*A*b*e+11*B*b*d)+1//5460*b^2*e^-1*(a+b*x)^11*(d+e*x)^-12*(b*d+-1*a*e)^-4*(-15*B*a*e+4*A*b*e+11*B*b*d)+1//60060*b^3*e^-1*(a+b*x)^11*(d+e*x)^-11*(b*d+-1*a*e)^-5*(-15*B*a*e+4*A*b*e+11*B*b*d))
@test integrate((a+b*x)^10*(d+e*x)^-17*(A+B*x), x) == :(-1//16*e^-1*(a+b*x)^11*(d+e*x)^-16*(b*d+-1*a*e)^-1*(B*d+-1*A*e)+1//240*e^-1*(a+b*x)^11*(d+e*x)^-15*(b*d+-1*a*e)^-2*(-16*B*a*e+5*A*b*e+11*B*b*d)+1//840*b*e^-1*(a+b*x)^11*(d+e*x)^-14*(b*d+-1*a*e)^-3*(-16*B*a*e+5*A*b*e+11*B*b*d)+1//3640*b^2*e^-1*(a+b*x)^11*(d+e*x)^-13*(b*d+-1*a*e)^-4*(-16*B*a*e+5*A*b*e+11*B*b*d)+1//21840*b^3*e^-1*(a+b*x)^11*(d+e*x)^-12*(b*d+-1*a*e)^-5*(-16*B*a*e+5*A*b*e+11*B*b*d)+1//240240*b^4*e^-1*(a+b*x)^11*(d+e*x)^-11*(b*d+-1*a*e)^-6*(-16*B*a*e+5*A*b*e+11*B*b*d))
@test integrate((a+b*x)^10*(d+e*x)^-18*(A+B*x), x) == :(-1//17*e^-1*(a+b*x)^11*(d+e*x)^-17*(b*d+-1*a*e)^-1*(B*d+-1*A*e)+1//272*e^-1*(a+b*x)^11*(d+e*x)^-16*(b*d+-1*a*e)^-2*(-17*B*a*e+6*A*b*e+11*B*b*d)+1//816*b*e^-1*(a+b*x)^11*(d+e*x)^-15*(b*d+-1*a*e)^-3*(-17*B*a*e+6*A*b*e+11*B*b*d)+1//2856*b^2*e^-1*(a+b*x)^11*(d+e*x)^-14*(b*d+-1*a*e)^-4*(-17*B*a*e+6*A*b*e+11*B*b*d)+1//12376*b^3*e^-1*(a+b*x)^11*(d+e*x)^-13*(b*d+-1*a*e)^-5*(-17*B*a*e+6*A*b*e+11*B*b*d)+1//74256*b^4*e^-1*(a+b*x)^11*(d+e*x)^-12*(b*d+-1*a*e)^-6*(-17*B*a*e+6*A*b*e+11*B*b*d)+1//816816*b^5*e^-1*(a+b*x)^11*(d+e*x)^-11*(b*d+-1*a*e)^-7*(-17*B*a*e+6*A*b*e+11*B*b*d))
@test integrate((a+b*x)^10*(d+e*x)^-19*(A+B*x), x) == :(-1//18*e^-1*(a+b*x)^11*(d+e*x)^-18*(b*d+-1*a*e)^-1*(B*d+-1*A*e)+1//306*e^-1*(a+b*x)^11*(d+e*x)^-17*(b*d+-1*a*e)^-2*(-18*B*a*e+7*A*b*e+11*B*b*d)+1//816*b*e^-1*(a+b*x)^11*(d+e*x)^-16*(b*d+-1*a*e)^-3*(-18*B*a*e+7*A*b*e+11*B*b*d)+1//2448*b^2*e^-1*(a+b*x)^11*(d+e*x)^-15*(b*d+-1*a*e)^-4*(-18*B*a*e+7*A*b*e+11*B*b*d)+1//8568*b^3*e^-1*(a+b*x)^11*(d+e*x)^-14*(b*d+-1*a*e)^-5*(-18*B*a*e+7*A*b*e+11*B*b*d)+1//37128*b^4*e^-1*(a+b*x)^11*(d+e*x)^-13*(b*d+-1*a*e)^-6*(-18*B*a*e+7*A*b*e+11*B*b*d)+1//222768*b^5*e^-1*(a+b*x)^11*(d+e*x)^-12*(b*d+-1*a*e)^-7*(-18*B*a*e+7*A*b*e+11*B*b*d)+1//2450448*b^6*e^-1*(a+b*x)^11*(d+e*x)^-11*(b*d+-1*a*e)^-8*(-18*B*a*e+7*A*b*e+11*B*b*d))
@test integrate((a+b*x)^10*(d+e*x)^-20*(A+B*x), x) == :(-1//8*B*b^10*e^-12*(d+e*x)^-8+-1//18*e^-12*(d+e*x)^-18*(b*d+-1*a*e)^9*(-1*B*a*e+-10*A*b*e+11*B*b*d)+1//9*b^9*e^-12*(d+e*x)^-9*(-1*A*b*e+-10*B*a*e+11*B*b*d)+1//19*e^-12*(d+e*x)^-19*(b*d+-1*a*e)^10*(B*d+-1*A*e)+-3*b^4*e^-12*(d+e*x)^-14*(b*d+-1*a*e)^5*(-6*A*b*e+-5*B*a*e+11*B*b*d)+2*b^3*e^-12*(d+e*x)^-15*(b*d+-1*a*e)^6*(-7*A*b*e+-4*B*a*e+11*B*b*d)+-15//16*b^2*e^-12*(d+e*x)^-16*(b*d+-1*a*e)^7*(-8*A*b*e+-3*B*a*e+11*B*b*d)+-5//2*b^6*e^-12*(d+e*x)^-12*(b*d+-1*a*e)^3*(-7*B*a*e+-4*A*b*e+11*B*b*d)+-1//2*b^8*e^-12*(d+e*x)^-10*(b*d+-1*a*e)*(-9*B*a*e+-2*A*b*e+11*B*b*d)+5//17*b*e^-12*(d+e*x)^-17*(b*d+-1*a*e)^8*(-9*A*b*e+-2*B*a*e+11*B*b*d)+15//11*b^7*e^-12*(d+e*x)^-11*(b*d+-1*a*e)^2*(-8*B*a*e+-3*A*b*e+11*B*b*d)+42//13*b^5*e^-12*(d+e*x)^-13*(b*d+-1*a*e)^4*(-6*B*a*e+-5*A*b*e+11*B*b*d))
@test integrate((a+b*x)^10*(d+e*x)^-21*(A+B*x), x) == :(-1//9*B*b^10*e^-12*(d+e*x)^-9+-1//19*e^-12*(d+e*x)^-19*(b*d+-1*a*e)^9*(-1*B*a*e+-10*A*b*e+11*B*b*d)+1//10*b^9*e^-12*(d+e*x)^-10*(-1*A*b*e+-10*B*a*e+11*B*b*d)+1//20*e^-12*(d+e*x)^-20*(b*d+-1*a*e)^10*(B*d+-1*A*e)+3*b^5*e^-12*(d+e*x)^-14*(b*d+-1*a*e)^4*(-6*B*a*e+-5*A*b*e+11*B*b*d)+-30//13*b^6*e^-12*(d+e*x)^-13*(b*d+-1*a*e)^3*(-7*B*a*e+-4*A*b*e+11*B*b*d)+-15//17*b^2*e^-12*(d+e*x)^-17*(b*d+-1*a*e)^7*(-8*A*b*e+-3*B*a*e+11*B*b*d)+-14//5*b^4*e^-12*(d+e*x)^-15*(b*d+-1*a*e)^5*(-6*A*b*e+-5*B*a*e+11*B*b*d)+-5//11*b^8*e^-12*(d+e*x)^-11*(b*d+-1*a*e)*(-9*B*a*e+-2*A*b*e+11*B*b*d)+5//4*b^7*e^-12*(d+e*x)^-12*(b*d+-1*a*e)^2*(-8*B*a*e+-3*A*b*e+11*B*b*d)+5//18*b*e^-12*(d+e*x)^-18*(b*d+-1*a*e)^8*(-9*A*b*e+-2*B*a*e+11*B*b*d)+15//8*b^3*e^-12*(d+e*x)^-16*(b*d+-1*a*e)^6*(-7*A*b*e+-4*B*a*e+11*B*b*d))
@test integrate((a+b*x)^10*(d+e*x)^-22*(A+B*x), x) == :(-1//10*B*b^10*e^-12*(d+e*x)^-10+-1//20*e^-12*(d+e*x)^-20*(b*d+-1*a*e)^9*(-1*B*a*e+-10*A*b*e+11*B*b*d)+1//11*b^9*e^-12*(d+e*x)^-11*(-1*A*b*e+-10*B*a*e+11*B*b*d)+1//21*e^-12*(d+e*x)^-21*(b*d+-1*a*e)^10*(B*d+-1*A*e)+-21//8*b^4*e^-12*(d+e*x)^-16*(b*d+-1*a*e)^5*(-6*A*b*e+-5*B*a*e+11*B*b*d)+-15//7*b^6*e^-12*(d+e*x)^-14*(b*d+-1*a*e)^3*(-7*B*a*e+-4*A*b*e+11*B*b*d)+-5//6*b^2*e^-12*(d+e*x)^-18*(b*d+-1*a*e)^7*(-8*A*b*e+-3*B*a*e+11*B*b*d)+-5//12*b^8*e^-12*(d+e*x)^-12*(b*d+-1*a*e)*(-9*B*a*e+-2*A*b*e+11*B*b*d)+5//19*b*e^-12*(d+e*x)^-19*(b*d+-1*a*e)^8*(-9*A*b*e+-2*B*a*e+11*B*b*d)+14//5*b^5*e^-12*(d+e*x)^-15*(b*d+-1*a*e)^4*(-6*B*a*e+-5*A*b*e+11*B*b*d)+15//13*b^7*e^-12*(d+e*x)^-13*(b*d+-1*a*e)^2*(-8*B*a*e+-3*A*b*e+11*B*b*d)+30//17*b^3*e^-12*(d+e*x)^-17*(b*d+-1*a*e)^6*(-7*A*b*e+-4*B*a*e+11*B*b*d))
@test integrate((a+b*x)^-1*(d+e*x)^5*(A+B*x), x) == :(1//5*b^-2*(d+e*x)^5*(A*b+-1*B*a)+b^-7*(b*d+-1*a*e)^5*(A*b+-1*B*a)*log(a+b*x)+(1/2)*b^-5*(d+e*x)^2*(b*d+-1*a*e)^3*(A*b+-1*B*a)+1//3*b^-4*(d+e*x)^3*(b*d+-1*a*e)^2*(A*b+-1*B*a)+1//4*b^-3*(d+e*x)^4*(A*b+-1*B*a)*(b*d+-1*a*e)+1//6*B*b^-1*e^-1*(d+e*x)^6+e*x*b^-6*(b*d+-1*a*e)^4*(A*b+-1*B*a))
@test integrate((a+b*x)^-1*(d+e*x)^4*(A+B*x), x) == :(1//4*b^-2*(d+e*x)^4*(A*b+-1*B*a)+b^-6*(b*d+-1*a*e)^4*(A*b+-1*B*a)*log(a+b*x)+(1/2)*b^-4*(d+e*x)^2*(b*d+-1*a*e)^2*(A*b+-1*B*a)+1//3*b^-3*(d+e*x)^3*(A*b+-1*B*a)*(b*d+-1*a*e)+1//5*B*b^-1*e^-1*(d+e*x)^5+e*x*b^-5*(b*d+-1*a*e)^3*(A*b+-1*B*a))
@test integrate((a+b*x)^-1*(d+e*x)^3*(A+B*x), x) == :(1//3*b^-2*(d+e*x)^3*(A*b+-1*B*a)+b^-5*(b*d+-1*a*e)^3*(A*b+-1*B*a)*log(a+b*x)+(1/2)*b^-3*(d+e*x)^2*(A*b+-1*B*a)*(b*d+-1*a*e)+1//4*B*b^-1*e^-1*(d+e*x)^4+e*x*b^-4*(b*d+-1*a*e)^2*(A*b+-1*B*a))
@test integrate((a+b*x)^-1*(d+e*x)^2*(A+B*x), x) == :((1/2)*b^-2*(d+e*x)^2*(A*b+-1*B*a)+b^-4*(b*d+-1*a*e)^2*(A*b+-1*B*a)*log(a+b*x)+1//3*B*b^-1*e^-1*(d+e*x)^3+e*x*b^-3*(A*b+-1*B*a)*(b*d+-1*a*e))
@test integrate((a+b*x)^-1*(A+B*x)*(d+e*x), x) == :(B*x*b^-2*(b*d+-1*a*e)+b^-3*(A*b+-1*B*a)*(b*d+-1*a*e)*log(a+b*x)+(1/2)*e*B^-1*b^-1*(A+B*x)^2)
@test integrate((a+b*x)^-1*(A+B*x), x) == :(B*x*b^-1+b^-2*(A*b+-1*B*a)*log(a+b*x))
@test integrate((a+b*x)^-1*(d+e*x)^-1*(A+B*x), x) == :(b^-1*(b*d+-1*a*e)^-1*(A*b+-1*B*a)*log(a+b*x)+e^-1*(b*d+-1*a*e)^-1*(B*d+-1*A*e)*log(d+e*x))
@test integrate((a+b*x)^-1*(d+e*x)^-2*(A+B*x), x) == :((b*d+-1*a*e)^-2*(A*b+-1*B*a)*log(a+b*x)+-1*(b*d+-1*a*e)^-2*(A*b+-1*B*a)*log(d+e*x)+-1*e^-1*(d+e*x)^-1*(b*d+-1*a*e)^-1*(B*d+-1*A*e))
@test integrate((a+b*x)^-1*(d+e*x)^-3*(A+B*x), x) == :((d+e*x)^-1*(b*d+-1*a*e)^-2*(A*b+-1*B*a)+b*(b*d+-1*a*e)^-3*(A*b+-1*B*a)*log(a+b*x)+(1/2)*e^-1*(d+e*x)^-2*(b*d+-1*a*e)^-1*(A*e+-1*B*d)+-1*b*(b*d+-1*a*e)^-3*(A*b+-1*B*a)*log(d+e*x))
@test integrate((a+b*x)^-1*(d+e*x)^-4*(A+B*x), x) == :((1/2)*(d+e*x)^-2*(b*d+-1*a*e)^-2*(A*b+-1*B*a)+b*(d+e*x)^-1*(b*d+-1*a*e)^-3*(A*b+-1*B*a)+b^2*(b*d+-1*a*e)^-4*(A*b+-1*B*a)*log(a+b*x)+-1*b^2*(b*d+-1*a*e)^-4*(A*b+-1*B*a)*log(d+e*x)+1//3*e^-1*(d+e*x)^-3*(b*d+-1*a*e)^-1*(A*e+-1*B*d))
@test integrate((a+b*x)^-1*(d+e*x)^-5*(A+B*x), x) == :(1//3*(d+e*x)^-3*(b*d+-1*a*e)^-2*(A*b+-1*B*a)+b^2*(d+e*x)^-1*(b*d+-1*a*e)^-4*(A*b+-1*B*a)+b^3*(b*d+-1*a*e)^-5*(A*b+-1*B*a)*log(a+b*x)+(1/2)*b*(d+e*x)^-2*(b*d+-1*a*e)^-3*(A*b+-1*B*a)+-1*b^3*(b*d+-1*a*e)^-5*(A*b+-1*B*a)*log(d+e*x)+1//4*e^-1*(d+e*x)^-4*(b*d+-1*a*e)^-1*(A*e+-1*B*d))
@test integrate((a+b*x)^-2*(d+e*x)^5*(A+B*x), x) == :(b^-7*(b*d+-1*a*e)^4*(B*b*d+-6*B*a*e+5*A*b*e)*log(a+b*x)+-1*b^-7*(a+b*x)^-1*(b*d+-1*a*e)^5*(A*b+-1*B*a)+1//4*b^-7*e^4*(a+b*x)^4*(A*b*e+-6*B*a*e+5*B*b*d)+1//5*B*b^-7*e^5*(a+b*x)^5+5*e*x*b^-6*(b*d+-1*a*e)^3*(B*b*d+-3*B*a*e+2*A*b*e)+5*b^-7*e^2*(a+b*x)^2*(b*d+-1*a*e)^2*(A*b*e+B*b*d+-2*B*a*e)+5//3*b^-7*e^3*(a+b*x)^3*(b*d+-1*a*e)*(A*b*e+-3*B*a*e+2*B*b*d))
@test integrate((a+b*x)^-2*(d+e*x)^4*(A+B*x), x) == :(b^-6*(b*d+-1*a*e)^3*(B*b*d+-5*B*a*e+4*A*b*e)*log(a+b*x)+-1*b^-6*(a+b*x)^-1*(b*d+-1*a*e)^4*(A*b+-1*B*a)+1//3*b^-6*e^3*(a+b*x)^3*(A*b*e+-5*B*a*e+4*B*b*d)+1//4*B*b^-6*e^4*(a+b*x)^4+b^-6*e^2*(a+b*x)^2*(b*d+-1*a*e)*(-5*B*a*e+2*A*b*e+3*B*b*d)+2*e*x*b^-5*(b*d+-1*a*e)^2*(-5*B*a*e+2*B*b*d+3*A*b*e))
@test integrate((a+b*x)^-2*(d+e*x)^3*(A+B*x), x) == :(b^-5*(b*d+-1*a*e)^2*(B*b*d+-4*B*a*e+3*A*b*e)*log(a+b*x)+(1/2)*b^-5*e^2*(a+b*x)^2*(A*b*e+-4*B*a*e+3*B*b*d)+-1*b^-5*(a+b*x)^-1*(b*d+-1*a*e)^3*(A*b+-1*B*a)+1//3*B*b^-5*e^3*(a+b*x)^3+3*e*x*b^-4*(b*d+-1*a*e)*(A*b*e+B*b*d+-2*B*a*e))
@test integrate((a+b*x)^-2*(d+e*x)^2*(A+B*x), x) == :(e*x*b^-3*(A*b*e+-2*B*a*e+2*B*b*d)+b^-4*(b*d+-1*a*e)*(B*b*d+-3*B*a*e+2*A*b*e)*log(a+b*x)+(1/2)*B*b^-2*e^2*x^2+-1*b^-4*(a+b*x)^-1*(b*d+-1*a*e)^2*(A*b+-1*B*a))
@test integrate((a+b*x)^-2*(A+B*x)*(d+e*x), x) == :(b^-3*(A*b*e+B*b*d+-2*B*a*e)*log(a+b*x)+B*e*x*b^-2+-1*b^-3*(a+b*x)^-1*(A*b+-1*B*a)*(b*d+-1*a*e))
@test integrate((a+b*x)^-2*(A+B*x), x) == :(B*b^-2*log(a+b*x)+-1*b^-2*(a+b*x)^-1*(A*b+-1*B*a))
@test integrate((a+b*x)^-2*(d+e*x)^-1*(A+B*x), x) == :((b*d+-1*a*e)^-2*(B*d+-1*A*e)*log(a+b*x)+-1*(b*d+-1*a*e)^-2*(B*d+-1*A*e)*log(d+e*x)+-1*b^-1*(a+b*x)^-1*(b*d+-1*a*e)^-1*(A*b+-1*B*a))
@test integrate((a+b*x)^-2*(d+e*x)^-2*(A+B*x), x) == :((d+e*x)^-1*(b*d+-1*a*e)^-2*(B*d+-1*A*e)+(b*d+-1*a*e)^-3*(B*a*e+B*b*d+-2*A*b*e)*log(a+b*x)+-1*(a+b*x)^-1*(b*d+-1*a*e)^-2*(A*b+-1*B*a)+-1*(b*d+-1*a*e)^-3*(B*a*e+B*b*d+-2*A*b*e)*log(d+e*x))
@test integrate((a+b*x)^-2*(d+e*x)^-3*(A+B*x), x) == :((d+e*x)^-1*(b*d+-1*a*e)^-3*(B*a*e+B*b*d+-2*A*b*e)+(1/2)*(d+e*x)^-2*(b*d+-1*a*e)^-2*(B*d+-1*A*e)+b*(b*d+-1*a*e)^-4*(B*b*d+-3*A*b*e+2*B*a*e)*log(a+b*x)+-1*b*(a+b*x)^-1*(b*d+-1*a*e)^-3*(A*b+-1*B*a)+-1*b*(b*d+-1*a*e)^-4*(B*b*d+-3*A*b*e+2*B*a*e)*log(d+e*x))
@test integrate((a+b*x)^-2*(d+e*x)^-4*(A+B*x), x) == :((1/2)*(d+e*x)^-2*(b*d+-1*a*e)^-3*(B*a*e+B*b*d+-2*A*b*e)+1//3*(d+e*x)^-3*(b*d+-1*a*e)^-2*(B*d+-1*A*e)+b*(d+e*x)^-1*(b*d+-1*a*e)^-4*(B*b*d+-3*A*b*e+2*B*a*e)+b^2*(b*d+-1*a*e)^-5*(B*b*d+-4*A*b*e+3*B*a*e)*log(a+b*x)+-1*b^2*(a+b*x)^-1*(b*d+-1*a*e)^-4*(A*b+-1*B*a)+-1*b^2*(b*d+-1*a*e)^-5*(B*b*d+-4*A*b*e+3*B*a*e)*log(d+e*x))
@test integrate((a+b*x)^-2*(d+e*x)^-5*(A+B*x), x) == :(1//3*(d+e*x)^-3*(b*d+-1*a*e)^-3*(B*a*e+B*b*d+-2*A*b*e)+1//4*(d+e*x)^-4*(b*d+-1*a*e)^-2*(B*d+-1*A*e)+b^2*(d+e*x)^-1*(b*d+-1*a*e)^-5*(B*b*d+-4*A*b*e+3*B*a*e)+b^3*(b*d+-1*a*e)^-6*(B*b*d+-5*A*b*e+4*B*a*e)*log(a+b*x)+(1/2)*b*(d+e*x)^-2*(b*d+-1*a*e)^-4*(B*b*d+-3*A*b*e+2*B*a*e)+-1*b^3*(a+b*x)^-1*(b*d+-1*a*e)^-5*(A*b+-1*B*a)+-1*b^3*(b*d+-1*a*e)^-6*(B*b*d+-5*A*b*e+4*B*a*e)*log(d+e*x))
@test integrate((a+b*x)^-3*(d+e*x)^5*(A+B*x), x) == :(-1*b^-7*(a+b*x)^-1*(b*d+-1*a*e)^4*(B*b*d+-6*B*a*e+5*A*b*e)+-1//2*b^-7*(a+b*x)^-2*(b*d+-1*a*e)^5*(A*b+-1*B*a)+1//3*b^-7*e^4*(a+b*x)^3*(A*b*e+-6*B*a*e+5*B*b*d)+1//4*B*b^-7*e^5*(a+b*x)^4+5*e*b^-7*(b*d+-1*a*e)^3*(B*b*d+-3*B*a*e+2*A*b*e)*log(a+b*x)+10*x*b^-6*e^2*(b*d+-1*a*e)^2*(A*b*e+B*b*d+-2*B*a*e)+5//2*b^-7*e^3*(a+b*x)^2*(b*d+-1*a*e)*(A*b*e+-3*B*a*e+2*B*b*d))
@test integrate((a+b*x)^-3*(d+e*x)^4*(A+B*x), x) == :((1/2)*b^-6*e^3*(a+b*x)^2*(A*b*e+-5*B*a*e+4*B*b*d)+-1*b^-6*(a+b*x)^-1*(b*d+-1*a*e)^3*(B*b*d+-5*B*a*e+4*A*b*e)+-1//2*b^-6*(a+b*x)^-2*(b*d+-1*a*e)^4*(A*b+-1*B*a)+1//3*B*b^-6*e^4*(a+b*x)^3+2*e*b^-6*(b*d+-1*a*e)^2*(-5*B*a*e+2*B*b*d+3*A*b*e)*log(a+b*x)+2*x*b^-5*e^2*(b*d+-1*a*e)*(-5*B*a*e+2*A*b*e+3*B*b*d))
@test integrate((a+b*x)^-3*(d+e*x)^3*(A+B*x), x) == :(x*b^-4*e^2*(A*b*e+-3*B*a*e+3*B*b*d)+(1/2)*B*b^-3*e^3*x^2+-1*b^-5*(a+b*x)^-1*(b*d+-1*a*e)^2*(B*b*d+-4*B*a*e+3*A*b*e)+-1//2*b^-5*(a+b*x)^-2*(b*d+-1*a*e)^3*(A*b+-1*B*a)+3*e*b^-5*(b*d+-1*a*e)*(A*b*e+B*b*d+-2*B*a*e)*log(a+b*x))
@test integrate((a+b*x)^-3*(d+e*x)^2*(A+B*x), x) == :(B*x*b^-3*e^2+e*b^-4*(A*b*e+-3*B*a*e+2*B*b*d)*log(a+b*x)+-1*b^-4*(a+b*x)^-1*(b*d+-1*a*e)*(B*b*d+-3*B*a*e+2*A*b*e)+-1//2*b^-4*(a+b*x)^-2*(b*d+-1*a*e)^2*(A*b+-1*B*a))
@test integrate((a+b*x)^-3*(A+B*x)*(d+e*x), x) == :(-1*b^-3*(a+b*x)^-1*(A*b*e+B*b*d+-2*B*a*e)+B*e*b^-3*log(a+b*x)+-1//2*b^-3*(a+b*x)^-2*(A*b+-1*B*a)*(b*d+-1*a*e))
@test integrate((a+b*x)^-3*(A+B*x), x) == :(-1*(A+B*x)^2*(a+b*x)^-2*(-2*B*a+2*A*b)^-1)
@test integrate((a+b*x)^-3*(d+e*x)^-1*(A+B*x), x) == :(-1*(a+b*x)^-1*(b*d+-1*a*e)^-2*(B*d+-1*A*e)+e*(b*d+-1*a*e)^-3*(B*d+-1*A*e)*log(d+e*x)+(1/2)*b^-1*(a+b*x)^-2*(b*d+-1*a*e)^-1*(B*a+-1*A*b)+-1*e*(b*d+-1*a*e)^-3*(B*d+-1*A*e)*log(a+b*x))
@test integrate((a+b*x)^-3*(d+e*x)^-2*(A+B*x), x) == :(-1*(a+b*x)^-1*(b*d+-1*a*e)^-3*(B*a*e+B*b*d+-2*A*b*e)+-1//2*(a+b*x)^-2*(b*d+-1*a*e)^-2*(A*b+-1*B*a)+e*(b*d+-1*a*e)^-4*(B*a*e+-3*A*b*e+2*B*b*d)*log(d+e*x)+-1*e*(d+e*x)^-1*(b*d+-1*a*e)^-3*(B*d+-1*A*e)+-1*e*(b*d+-1*a*e)^-4*(B*a*e+-3*A*b*e+2*B*b*d)*log(a+b*x))
@test integrate((a+b*x)^-3*(d+e*x)^-3*(A+B*x), x) == :(-1*b*(a+b*x)^-1*(b*d+-1*a*e)^-4*(B*b*d+-3*A*b*e+2*B*a*e)+-1*e*(d+e*x)^-1*(b*d+-1*a*e)^-4*(B*a*e+-3*A*b*e+2*B*b*d)+-1//2*b*(a+b*x)^-2*(b*d+-1*a*e)^-3*(A*b+-1*B*a)+-1//2*e*(d+e*x)^-2*(b*d+-1*a*e)^-3*(B*d+-1*A*e)+-3*b*e*(b*d+-1*a*e)^-5*(B*a*e+B*b*d+-2*A*b*e)*log(a+b*x)+3*b*e*(b*d+-1*a*e)^-5*(B*a*e+B*b*d+-2*A*b*e)*log(d+e*x))
@test integrate((a+b*x)^-3*(d+e*x)^-4*(A+B*x), x) == :(-1*b^2*(a+b*x)^-1*(b*d+-1*a*e)^-5*(B*b*d+-4*A*b*e+3*B*a*e)+-1//2*e*(d+e*x)^-2*(b*d+-1*a*e)^-4*(B*a*e+-3*A*b*e+2*B*b*d)+-1//2*b^2*(a+b*x)^-2*(b*d+-1*a*e)^-4*(A*b+-1*B*a)+-1//3*e*(d+e*x)^-3*(b*d+-1*a*e)^-3*(B*d+-1*A*e)+-3*b*e*(d+e*x)^-1*(b*d+-1*a*e)^-5*(B*a*e+B*b*d+-2*A*b*e)+-2*e*b^2*(b*d+-1*a*e)^-6*(-5*A*b*e+2*B*b*d+3*B*a*e)*log(a+b*x)+2*e*b^2*(b*d+-1*a*e)^-6*(-5*A*b*e+2*B*b*d+3*B*a*e)*log(d+e*x))
@test integrate((2+3x)^8*(1+-2x)*(3+5x), x) == :(-10//297*(2+3x)^11+-7//243*(2+3x)^9+37//270*(2+3x)^10)
@test integrate((2+3x)^7*(1+-2x)*(3+5x), x) == :(-7//216*(2+3x)^8+-1//27*(2+3x)^10+37//243*(2+3x)^9)
@test integrate((2+3x)^6*(1+-2x)*(3+5x), x) == :(-10//243*(2+3x)^9+-1//27*(2+3x)^7+37//216*(2+3x)^8)
@test integrate((2+3x)^5*(1+-2x)*(3+5x), x) == :(-7//162*(2+3x)^6+-5//108*(2+3x)^8+37//189*(2+3x)^7)
@test integrate((2+3x)^4*(1+-2x)*(3+5x), x) == :(-10//189*(2+3x)^7+-7//135*(2+3x)^5+37//162*(2+3x)^6)
@test integrate((2+3x)^3*(1+-2x)*(3+5x), x) == :(-7//108*(2+3x)^4+-5//81*(2+3x)^6+37//135*(2+3x)^5)
@test integrate((2+3x)^2*(1+-2x)*(3+5x), x) == :(-18*x^5+12x+16*x^2+-129//4*x^4+-25//3*x^3)
@test integrate((1+-2x)*(2+3x)*(3+5x), x) == :(6x+-23//3*x^3+-15//2*x^4+7//2*x^2)
@test integrate((1+-2x)*(3+5x), x) == :(3x+-10//3*x^3+-1//2*x^2)
@test integrate((2+3x)^-1*(1+-2x)*(3+5x), x) == :(-7//27*log(2+3x)+-5//3*x^2+17//9*x)
@test integrate((2+3x)^-2*(1+-2x)*(3+5x), x) == :(7*(54+81x)^-1+-10//9*x+37//27*log(2+3x))
@test integrate((2+3x)^-3*(1+-2x)*(3+5x), x) == :(-37*(54+81x)^-1+-10//27*log(2+3x)+7//54*(2+3x)^-2)
@test integrate((2+3x)^-4*(1+-2x)*(3+5x), x) == :(10*(54+81x)^-1+-37//54*(2+3x)^-2+7//81*(2+3x)^-3)
@test integrate((2+3x)^-5*(1+-2x)*(3+5x), x) == :(-37//81*(2+3x)^-3+5//27*(2+3x)^-2+7//108*(2+3x)^-4)
@test integrate((2+3x)^-6*(1+-2x)*(3+5x), x) == :(-37//108*(2+3x)^-4+7//135*(2+3x)^-5+10//81*(2+3x)^-3)
@test integrate((2+3x)^8*(3+5x)^2*(1+-2x), x) == :(-25//486*(2+3x)^12+-4//45*(2+3x)^10+7//729*(2+3x)^9+65//297*(2+3x)^11)
@test integrate((2+3x)^7*(3+5x)^2*(1+-2x), x) == :(-50//891*(2+3x)^11+-8//81*(2+3x)^9+7//648*(2+3x)^8+13//54*(2+3x)^10)
@test integrate((2+3x)^6*(3+5x)^2*(1+-2x), x) == :(-5//81*(2+3x)^10+-1//9*(2+3x)^8+1//81*(2+3x)^7+65//243*(2+3x)^9)
@test integrate((2+3x)^5*(3+5x)^2*(1+-2x), x) == :(-50//729*(2+3x)^9+-8//63*(2+3x)^7+7//486*(2+3x)^6+65//216*(2+3x)^8)
@test integrate((2+3x)^4*(3+5x)^2*(1+-2x), x) == :(-25//324*(2+3x)^8+-4//27*(2+3x)^6+7//405*(2+3x)^5+65//189*(2+3x)^7)
@test integrate((2+3x)^3*(3+5x)^2*(1+-2x), x) == :(72x+210*x^2+-3366//5*x^5+-1350//7*x^7+-1215//2*x^6+-769//4*x^4+638//3*x^3)
@test integrate((2+3x)^2*(3+5x)^2*(1+-2x), x) == :(-183*x^5+-128*x^4+-75*x^6+36x+78*x^2+85//3*x^3)
@test integrate((3+5x)^2*(1+-2x)*(2+3x), x) == :(-30*x^5+18x+-205//4*x^4+-34//3*x^3+51//2*x^2)
@test integrate((3+5x)^2*(1+-2x), x) == :(6*x^2+9x+-35//3*x^3+-25//2*x^4)
@test integrate((2+3x)^-1*(3+5x)^2*(1+-2x), x) == :(-50//9*x^3+-5//18*x^2+7//81*log(2+3x)+118//27*x)
@test integrate((2+3x)^-2*(3+5x)^2*(1+-2x), x) == :(-7*(162+243x)^-1+-25//9*x^2+-8//9*log(2+3x)+95//27*x)
@test integrate((2+3x)^-3*(3+5x)^2*(1+-2x), x) == :(8*(18+27x)^-1+-50//27*x+-7//162*(2+3x)^-2+65//27*log(2+3x))
@test integrate((2+3x)^-4*(3+5x)^2*(1+-2x), x) == :(-65*(54+81x)^-1+-50//81*log(2+3x)+-7//243*(2+3x)^-3+4//9*(2+3x)^-2)
@test integrate((2+3x)^-5*(3+5x)^2*(1+-2x), x) == :(3//4*(2+3x)^-3*(3+5x)^3+7//12*(2+3x)^-4*(3+5x)^3)
@test integrate((2+3x)^-6*(3+5x)^2*(1+-2x), x) == :(-65//81*(2+3x)^-3+-7//405*(2+3x)^-5+2//9*(2+3x)^-4+25//81*(2+3x)^-2)
@test integrate((2+3x)^-7*(3+5x)^2*(1+-2x), x) == :(-65//108*(2+3x)^-4+-7//486*(2+3x)^-6+8//45*(2+3x)^-5+50//243*(2+3x)^-3)
@test integrate((2+3x)^-8*(3+5x)^2*(1+-2x), x) == :(-13//27*(2+3x)^-5+-1//81*(2+3x)^-7+4//27*(2+3x)^-6+25//162*(2+3x)^-4)
@test integrate((2+3x)^8*(3+5x)^3*(1+-2x), x) == :(-250//3159*(2+3x)^13+-185//891*(2+3x)^11+-7//2187*(2+3x)^9+107//2430*(2+3x)^10+1025//2916*(2+3x)^12)
@test integrate((2+3x)^7*(3+5x)^3*(1+-2x), x) == :(-125//1458*(2+3x)^12+-37//162*(2+3x)^10+-7//1944*(2+3x)^8+107//2187*(2+3x)^9+1025//2673*(2+3x)^11)
@test integrate((2+3x)^6*(3+5x)^3*(1+-2x), x) == :(-250//2673*(2+3x)^11+-185//729*(2+3x)^9+-1//243*(2+3x)^7+107//1944*(2+3x)^8+205//486*(2+3x)^10)
@test integrate((2+3x)^5*(3+5x)^3*(1+-2x), x) == :(-185//648*(2+3x)^8+-25//243*(2+3x)^10+-7//1458*(2+3x)^6+107//1701*(2+3x)^7+1025//2187*(2+3x)^9)
@test integrate((2+3x)^4*(3+5x)^3*(1+-2x), x) == :(-250//2187*(2+3x)^9+-185//567*(2+3x)^7+-7//1215*(2+3x)^5+107//1458*(2+3x)^6+1025//1944*(2+3x)^8)
@test integrate((2+3x)^3*(3+5x)^3*(1+-2x), x) == :(216x+810*x^2+1338*x^3+-22275//7*x^7+-13943//5*x^5+-9255//2*x^6+-3375//4*x^8+883//4*x^4)
@test integrate((2+3x)^2*(3+5x)^3*(1+-2x), x) == :(-1061*x^5+108x+324*x^2+345*x^3+-2250//7*x^7+-1975//2*x^6+-1111//4*x^4)
@test integrate((3+5x)^3*(1+-2x)*(2+3x), x) == :(-1//125*(3+5x)^6+11//500*(3+5x)^4+31//625*(3+5x)^5)
@test integrate((3+5x)^3*(1+-2x), x) == :(-2//125*(3+5x)^5+11//100*(3+5x)^4)
@test integrate((2+3x)^-1*(3+5x)^3*(1+-2x), x) == :(-475//27*x^3+-125//6*x^4+-7//243*log(2+3x)+545//54*x^2+1097//81*x)
@test integrate((2+3x)^-2*(3+5x)^3*(1+-2x), x) == :(7*(486+729x)^-1+-250//27*x^3+25//54*x^2+55//9*x+107//243*log(2+3x))
@test integrate((2+3x)^-3*(3+5x)^3*(1+-2x), x) == :(-107*(486+729x)^-1+-185//81*log(2+3x)+-125//27*x^2+7//486*(2+3x)^-2+175//27*x)
@test integrate((2+3x)^-4*(3+5x)^3*(1+-2x), x) == :(185*(162+243x)^-1+-250//81*x+-107//486*(2+3x)^-2+7//729*(2+3x)^-3+1025//243*log(2+3x))
@test integrate((2+3x)^-5*(3+5x)^3*(1+-2x), x) == :(-1025*(486+729x)^-1+-250//243*log(2+3x)+-107//729*(2+3x)^-3+7//972*(2+3x)^-4+185//162*(2+3x)^-2)
@test integrate((2+3x)^-6*(3+5x)^3*(1+-2x), x) == :(5//12*(2+3x)^-4*(3+5x)^4+7//15*(2+3x)^-5*(3+5x)^4)
@test integrate((2+3x)^-7*(3+5x)^3*(1+-2x), x) == :(7//18*(2+3x)^-6*(3+5x)^4+29//36*(2+3x)^-4*(3+5x)^4+29//45*(2+3x)^-5*(3+5x)^4)
@test integrate((2+3x)^-8*(3+5x)^3*(1+-2x), x) == :(-1025//972*(2+3x)^-4+-107//1458*(2+3x)^-6+1//243*(2+3x)^-7+37//81*(2+3x)^-5+250//729*(2+3x)^-3)
@test integrate((2+3x)^3*(5+-2x)^6*(-16+33x), x) == :(-1//2*(2+3x)^4*(5+-2x)^7)
@test integrate((2+3x)^6*(3+5x)^-1*(1+-2x), x) == :(-152469//2500*x^4+-106677//625*x^5+-7047//50*x^6+-1458//35*x^7+11//390625*log(3+5x)+152469//3125*x^3+1666663//78125*x+1777779//31250*x^2)
@test integrate((2+3x)^5*(3+5x)^-1*(1+-2x), x) == :(-17469//500*x^4+-5427//125*x^5+-81//5*x^6+11//78125*log(3+5x)+2469//625*x^3+127779//6250*x^2+166663//15625*x)
@test integrate((2+3x)^4*(3+5x)^-1*(1+-2x), x) == :(-1269//100*x^4+-531//125*x^3+-162//25*x^5+11//15625*log(3+5x)+7779//1250*x^2+16663//3125*x)
@test integrate((2+3x)^3*(3+5x)^-1*(1+-2x), x) == :(-81//25*x^3+-27//10*x^4+11//3125*log(3+5x)+279//250*x^2+1663//625*x)
@test integrate((2+3x)^2*(3+5x)^-1*(1+-2x), x) == :(-21//50*x^2+-6//5*x^3+11//625*log(3+5x)+163//125*x)
@test integrate((3+5x)^-1*(1+-2x)*(2+3x), x) == :(-3//5*x^2+11//125*log(3+5x)+13//25*x)
@test integrate((3+5x)^-1*(1+-2x), x) == :(-2//5*x+11//25*log(3+5x))
@test integrate((2+3x)^-1*(3+5x)^-1*(1+-2x), x) == :(-7//3*log(2+3x)+11//5*log(3+5x))
@test integrate((2+3x)^-2*(3+5x)^-1*(1+-2x), x) == :(-11*log(2+3x)+7*(6+9x)^-1+11*log(3+5x))
@test integrate((2+3x)^-3*(3+5x)^-1*(1+-2x), x) == :(-55*log(2+3x)+11*(2+3x)^-1+55*log(3+5x)+7//6*(2+3x)^-2)
@test integrate((2+3x)^-4*(3+5x)^-1*(1+-2x), x) == :(-275*log(2+3x)+55*(2+3x)^-1+275*log(3+5x)+7//9*(2+3x)^-3+11//2*(2+3x)^-2)
@test integrate((2+3x)^-5*(3+5x)^-1*(1+-2x), x) == :(-1375*log(2+3x)+275*(2+3x)^-1+1375*log(3+5x)+7//12*(2+3x)^-4+11//3*(2+3x)^-3+55//2*(2+3x)^-2)
@test integrate((2+3x)^-6*(3+5x)^-1*(1+-2x), x) == :(-6875*log(2+3x)+1375*(2+3x)^-1+6875*log(3+5x)+7//15*(2+3x)^-5+11//4*(2+3x)^-4+55//3*(2+3x)^-3+275//2*(2+3x)^-2)
@test integrate((2+3x)^-7*(3+5x)^-1*(1+-2x), x) == :(-34375*log(2+3x)+6875*(2+3x)^-1+34375*log(3+5x)+7//18*(2+3x)^-6+11//5*(2+3x)^-5+55//4*(2+3x)^-4+275//3*(2+3x)^-3+1375//2*(2+3x)^-2)
@test integrate((2+3x)^7*(3+5x)^-2*(1+-2x), x) == :(-11*(5859375+9765625x)^-1+-513783//12500*x^4+-336798//3125*x^5+-21627//250*x^6+-4374//175*x^7+229//1953125*log(3+5x)+92592//3125*x^3+5555478//390625*x+5740767//156250*x^2)
@test integrate((2+3x)^6*(3+5x)^-2*(1+-2x), x) == :(-11*(1171875+1953125x)^-1+-16767//625*x^5+-14094//625*x^4+-243//25*x^6+196//390625*log(3+5x)+5553//3125*x^3+40743//3125*x^2+555489//78125*x)
@test integrate((2+3x)^5*(3+5x)^-2*(1+-2x), x) == :(-11*(234375+390625x)^-1+-3969//500*x^4+-1854//625*x^3+-486//125*x^5+163//78125*log(3+5x)+444//125*x+24093//6250*x^2)
@test integrate((2+3x)^4*(3+5x)^-2*(1+-2x), x) == :(-11*(46875+78125x)^-1+-261//125*x^3+-81//50*x^4+26//3125*log(3+5x)+378//625*x^2+5511//3125*x)
@test integrate((2+3x)^3*(3+5x)^-2*(1+-2x), x) == :(-11*(9375+15625x)^-1+-81//250*x^2+-18//25*x^3+97//3125*log(3+5x)+522//625*x)
@test integrate((2+3x)^2*(3+5x)^-2*(1+-2x), x) == :(-11*(1875+3125x)^-1+-9//25*x^2+33//125*x+64//625*log(3+5x))
@test integrate((3+5x)^-2*(1+-2x)*(2+3x), x) == :(-11*(375+625x)^-1+-6//25*x+31//125*log(3+5x))
@test integrate((3+5x)^-2*(1+-2x), x) == :(-11*(75+125x)^-1+-2//25*log(3+5x))
@test integrate((2+3x)^-1*(3+5x)^-2*(1+-2x), x) == :(-11*(15+25x)^-1+-7*log(3+5x)+7*log(2+3x))
@test integrate((2+3x)^-2*(3+5x)^-2*(1+-2x), x) == :(-68*log(3+5x)+-11*(3+5x)^-1+-7*(2+3x)^-1+68*log(2+3x))
@test integrate((2+3x)^-3*(3+5x)^-2*(1+-2x), x) == :(-505*log(3+5x)+-68*(2+3x)^-1+-55*(3+5x)^-1+505*log(2+3x)+-7//2*(2+3x)^-2)
@test integrate((2+3x)^-4*(3+5x)^-2*(1+-2x), x) == :(-3350*log(3+5x)+-505*(2+3x)^-1+-275*(3+5x)^-1+-34*(2+3x)^-2+3350*log(2+3x)+-7//3*(2+3x)^-3)
@test integrate((2+3x)^-5*(3+5x)^-2*(1+-2x), x) == :(-20875*log(3+5x)+-3350*(2+3x)^-1+-1375*(3+5x)^-1+20875*log(2+3x)+-505//2*(2+3x)^-2+-68//3*(2+3x)^-3+-7//4*(2+3x)^-4)
@test integrate((2+3x)^-6*(3+5x)^-2*(1+-2x), x) == :(-125000*log(3+5x)+-20875*(2+3x)^-1+-6875*(3+5x)^-1+-1675*(2+3x)^-2+-17*(2+3x)^-4+125000*log(2+3x)+-505//3*(2+3x)^-3+-7//5*(2+3x)^-5)
@test integrate((2+3x)^-7*(3+5x)^-2*(1+-2x), x) == :(-728125*log(3+5x)+-125000*(2+3x)^-1+-34375*(3+5x)^-1+728125*log(2+3x)+-20875//2*(2+3x)^-2+-3350//3*(2+3x)^-3+-505//4*(2+3x)^-4+-68//5*(2+3x)^-5+-7//6*(2+3x)^-6)
@test integrate((2+3x)^7*(3+5x)^-3*(1+-2x), x) == :(-229*(5859375+9765625x)^-1+-181521//12500*x^4+-51759//3125*x^5+-729//125*x^6+-11//3906250*(3+5x)^-2+2037//1953125*log(3+5x)+2052//3125*x^3+129654//15625*x^2+1851147//390625*x)
@test integrate((2+3x)^6*(3+5x)^-3*(1+-2x), x) == :(-196*(1171875+1953125x)^-1+-12393//2500*x^4+-6399//3125*x^3+-1458//625*x^5+-11//781250*(3+5x)^-2+297//125*x^2+1449//390625*log(3+5x)+36936//15625*x)
@test integrate((2+3x)^5*(3+5x)^-3*(1+-2x), x) == :(-163*(234375+390625x)^-1+-837//625*x^3+-243//250*x^4+-11//156250*(3+5x)^-2+192//15625*log(3+5x)+1971//6250*x^2+3636//3125*x)
@test integrate((2+3x)^4*(3+5x)^-3*(1+-2x), x) == :(-26*(9375+15625x)^-1+-297//1250*x^2+-54//125*x^3+-11//31250*(3+5x)^-2+114//3125*log(3+5x)+1647//3125*x)
@test integrate((2+3x)^3*(3+5x)^-3*(1+-2x), x) == :(-97*(9375+15625x)^-1+-27//125*x^2+-11//6250*(3+5x)^-2+81//625*x+279//3125*log(3+5x))
@test integrate((2+3x)^2*(3+5x)^-3*(1+-2x), x) == :(-64*(1875+3125x)^-1+-18//125*x+-11//1250*(3+5x)^-2+87//625*log(3+5x))
@test integrate((3+5x)^-3*(1+-2x)*(2+3x), x) == :(-31*(375+625x)^-1+-11//250*(3+5x)^-2+-6//125*log(3+5x))
@test integrate((3+5x)^-3*(1+-2x), x) == :(-1//22*(1+-2x)^2*(3+5x)^-2)
@test integrate((2+3x)^-1*(3+5x)^-3*(1+-2x), x) == :(-21*log(2+3x)+7*(3+5x)^-1+21*log(3+5x)+-11//10*(3+5x)^-2)
@test integrate((2+3x)^-2*(3+5x)^-3*(1+-2x), x) == :(-309*log(2+3x)+21*(2+3x)^-1+68*(3+5x)^-1+309*log(3+5x)+-11//2*(3+5x)^-2)
@test integrate((2+3x)^-3*(3+5x)^-3*(1+-2x), x) == :(-3060*log(2+3x)+309*(2+3x)^-1+505*(3+5x)^-1+3060*log(3+5x)+-55//2*(3+5x)^-2+21//2*(2+3x)^-2)
@test integrate((2+3x)^-4*(3+5x)^-3*(1+-2x), x) == :(-25350*log(2+3x)+7*(2+3x)^-3+3060*(2+3x)^-1+3350*(3+5x)^-1+25350*log(3+5x)+-275//2*(3+5x)^-2+309//2*(2+3x)^-2)
@test integrate((2+3x)^-5*(3+5x)^-3*(1+-2x), x) == :(-189375*log(2+3x)+103*(2+3x)^-3+1530*(2+3x)^-2+20875*(3+5x)^-1+25350*(2+3x)^-1+189375*log(3+5x)+-1375//2*(3+5x)^-2+21//4*(2+3x)^-4)
@test integrate((2+3x)^-6*(3+5x)^-3*(1+-2x), x) == :(-1321875*log(2+3x)+1020*(2+3x)^-3+12675*(2+3x)^-2+125000*(3+5x)^-1+189375*(2+3x)^-1+1321875*log(3+5x)+-6875//2*(3+5x)^-2+21//5*(2+3x)^-5+309//4*(2+3x)^-4)
@test integrate((1+-2x)^2*(2+3x)^8*(3+5x), x) == :(-49//729*(2+3x)^9+-16//99*(2+3x)^11+5//243*(2+3x)^12+91//270*(2+3x)^10)
@test integrate((1+-2x)^2*(2+3x)^7*(3+5x), x) == :(-49//648*(2+3x)^8+-8//45*(2+3x)^10+20//891*(2+3x)^11+91//243*(2+3x)^9)
@test integrate((1+-2x)^2*(2+3x)^6*(3+5x), x) == :(-16//81*(2+3x)^9+-7//81*(2+3x)^7+2//81*(2+3x)^10+91//216*(2+3x)^8)
@test integrate((1+-2x)^2*(2+3x)^5*(3+5x), x) == :(-49//486*(2+3x)^6+-2//9*(2+3x)^8+13//27*(2+3x)^7+20//729*(2+3x)^9)
@test integrate((1+-2x)^2*(2+3x)^4*(3+5x), x) == :(-49//405*(2+3x)^5+-16//63*(2+3x)^7+5//162*(2+3x)^8+91//162*(2+3x)^6)
@test integrate((1+-2x)^2*(2+3x)^3*(3+5x), x) == :(24x+26*x^2+144*x^6+-425//4*x^4+-154//3*x^3+99//5*x^5+540//7*x^7)
@test integrate((1+-2x)^2*(2+3x)^2*(3+5x), x) == :(4*x^2+12x+30*x^6+-89//3*x^3+-79//4*x^4+168//5*x^5)
@test integrate((1+-2x)^2*(2+3x)*(3+5x), x) == :(4*x^4+6x+12*x^5+-37//3*x^3+-5//2*x^2)
@test integrate((1+-2x)^2*(3+5x), x) == :(3x+5*x^4+-8//3*x^3+-7//2*x^2)
@test integrate((1+-2x)^2*(2+3x)^-1*(3+5x), x) == :(-49//81*log(2+3x)+-32//9*x^2+20//9*x^3+65//27*x)
@test integrate((1+-2x)^2*(2+3x)^-2*(3+5x), x) == :(49*(162+243x)^-1+-104//27*x+10//9*x^2+91//27*log(2+3x))
@test integrate((1+-2x)^2*(2+3x)^-3*(3+5x), x) == :(-91*(54+81x)^-1+-16//9*log(2+3x)+20//27*x+49//162*(2+3x)^-2)
@test integrate((1+-2x)^2*(2+3x)^-4*(3+5x), x) == :(16*(18+27x)^-1+-91//54*(2+3x)^-2+20//81*log(2+3x)+49//243*(2+3x)^-3)
@test integrate((1+-2x)^2*(2+3x)^-5*(3+5x), x) == :(-23//294*(1+-2x)^3*(2+3x)^-3+1//84*(1+-2x)^3*(2+3x)^-4)
@test integrate((1+-2x)^2*(2+3x)^-6*(3+5x), x) == :(-91//108*(2+3x)^-4+-10//81*(2+3x)^-2+16//27*(2+3x)^-3+49//405*(2+3x)^-5)
@test integrate((1+-2x)^2*(2+3x)^-7*(3+5x), x) == :(-91//135*(2+3x)^-5+-20//243*(2+3x)^-3+4//9*(2+3x)^-4+49//486*(2+3x)^-6)
@test integrate((1+-2x)^2*(2+3x)^-8*(3+5x), x) == :(-91//162*(2+3x)^-6+-5//81*(2+3x)^-4+7//81*(2+3x)^-7+16//45*(2+3x)^-5)
@test integrate((1+-2x)^2*(2+3x)^8*(3+5x)^2, x) == :(-259//1215*(2+3x)^10+-185//729*(2+3x)^12+49//2187*(2+3x)^9+100//3159*(2+3x)^13+503//891*(2+3x)^11)
@test integrate((1+-2x)^2*(2+3x)^7*(3+5x)^2, x) == :(-740//2673*(2+3x)^11+-518//2187*(2+3x)^9+25//729*(2+3x)^12+49//1944*(2+3x)^8+503//810*(2+3x)^10)
@test integrate((1+-2x)^2*(2+3x)^6*(3+5x)^2, x) == :(-259//972*(2+3x)^8+-74//243*(2+3x)^10+7//243*(2+3x)^7+100//2673*(2+3x)^11+503//729*(2+3x)^9)
@test integrate((1+-2x)^2*(2+3x)^5*(3+5x)^2, x) == :(-740//2187*(2+3x)^9+-74//243*(2+3x)^7+10//243*(2+3x)^10+49//1458*(2+3x)^6+503//648*(2+3x)^8)
@test integrate((1+-2x)^2*(2+3x)^4*(3+5x)^2, x) == :(-259//729*(2+3x)^6+-185//486*(2+3x)^8+49//1215*(2+3x)^5+100//2187*(2+3x)^9+503//567*(2+3x)^7)
@test integrate((1+-2x)^2*(2+3x)^3*(3+5x)^2, x) == :(72x+138*x^2+-2045//4*x^4+-1828//5*x^5+-202//3*x^3+675//2*x^8+1029//2*x^6+5940//7*x^7)
@test integrate((1+-2x)^2*(2+3x)^2*(3+5x)^2, x) == :(36x+42*x^2+230*x^6+-341//2*x^4+-227//3*x^3+109//5*x^5+900//7*x^7)
@test integrate((1+-2x)^2*(3+5x)^2*(2+3x), x) == :(18x+50*x^6+52*x^5+-137//4*x^4+-136//3*x^3+15//2*x^2)
@test integrate((1+-2x)^2*(3+5x)^2, x) == :(-3*x^2+5*x^4+9x+20*x^5+-59//3*x^3)
@test integrate((1+-2x)^2*(2+3x)^-1*(3+5x)^2, x) == :(-251//54*x^2+-140//27*x^3+25//3*x^4+49//243*log(2+3x)+340//81*x)
@test integrate((1+-2x)^2*(2+3x)^-2*(3+5x)^2, x) == :(-49*(486+729x)^-1+-518//243*log(2+3x)+-170//27*x^2+100//27*x^3+143//27*x)
@test integrate((1+-2x)^2*(2+3x)^-3*(3+5x)^2, x) == :(518*(486+729x)^-1+-49//486*(2+3x)^-2+-20//3*x+50//27*x^2+503//81*log(2+3x))
@test integrate((1+-2x)^2*(2+3x)^-4*(3+5x)^2, x) == :(-503*(162+243x)^-1+-740//243*log(2+3x)+-49//729*(2+3x)^-3+100//81*x+259//243*(2+3x)^-2)
@test integrate((1+-2x)^2*(2+3x)^-5*(3+5x)^2, x) == :(740*(486+729x)^-1+-503//162*(2+3x)^-2+-49//972*(2+3x)^-4+100//243*log(2+3x)+518//729*(2+3x)^-3)
@test integrate((1+-2x)^2*(2+3x)^-6*(3+5x)^2, x) == :(-100*(486+729x)^-1+-503//243*(2+3x)^-3+-49//1215*(2+3x)^-5+259//486*(2+3x)^-4+370//243*(2+3x)^-2)
@test integrate((1+-2x)^2*(2+3x)^-7*(3+5x)^2, x) == :(-503//324*(2+3x)^-4+-50//243*(2+3x)^-2+-49//1458*(2+3x)^-6+518//1215*(2+3x)^-5+740//729*(2+3x)^-3)
@test integrate((1+-2x)^2*(2+3x)^-8*(3+5x)^2, x) == :(-503//405*(2+3x)^-5+-100//729*(2+3x)^-3+-7//243*(2+3x)^-7+185//243*(2+3x)^-4+259//729*(2+3x)^-6)
@test integrate((1+-2x)^2*(2+3x)^10*(3+5x)^3, x) == :(-4099//9477*(2+3x)^13+-760//2187*(2+3x)^15+-49//8019*(2+3x)^11+125//2916*(2+3x)^16+763//8748*(2+3x)^12+8285//10206*(2+3x)^14)
@test integrate((1+-2x)^2*(2+3x)^9*(3+5x)^3, x) == :(-4099//8748*(2+3x)^12+-1900//5103*(2+3x)^14+-49//7290*(2+3x)^10+100//2187*(2+3x)^15+763//8019*(2+3x)^11+8285//9477*(2+3x)^13)
@test integrate((1+-2x)^2*(2+3x)^8*(3+5x)^3, x) == :(-4099//8019*(2+3x)^11+-3800//9477*(2+3x)^13+-49//6561*(2+3x)^9+250//5103*(2+3x)^14+763//7290*(2+3x)^10+8285//8748*(2+3x)^12)
@test integrate((1+-2x)^2*(2+3x)^7*(3+5x)^3, x) == :(-4099//7290*(2+3x)^10+-950//2187*(2+3x)^12+-49//5832*(2+3x)^8+500//9477*(2+3x)^13+763//6561*(2+3x)^9+8285//8019*(2+3x)^11)
@test integrate((1+-2x)^2*(2+3x)^6*(3+5x)^3, x) == :(-4099//6561*(2+3x)^9+-3800//8019*(2+3x)^11+-7//729*(2+3x)^7+125//2187*(2+3x)^12+763//5832*(2+3x)^8+1657//1458*(2+3x)^10)
@test integrate((1+-2x)^2*(2+3x)^5*(3+5x)^3, x) == :(-4099//5832*(2+3x)^8+-380//729*(2+3x)^10+-49//4374*(2+3x)^6+109//729*(2+3x)^7+500//8019*(2+3x)^11+8285//6561*(2+3x)^9)
@test integrate((1+-2x)^2*(2+3x)^4*(3+5x)^3, x) == :(-4099//5103*(2+3x)^7+-3800//6561*(2+3x)^9+-49//3645*(2+3x)^5+50//729*(2+3x)^10+763//4374*(2+3x)^6+8285//5832*(2+3x)^8)
@test integrate((1+-2x)^2*(2+3x)^3*(3+5x)^3, x) == :(216x+258*x^3+594*x^2+1500*x^9+4725*x^8+-15709//5*x^5+-7145//4*x^4+121//6*x^6+33255//7*x^7)
@test integrate((1+-2x)^2*(2+3x)^2*(3+5x)^3, x) == :(-87*x^3+108x+216*x^2+-3181//4*x^4+-3083//5*x^5+1125//2*x^8+4685//6*x^6+9600//7*x^7)
@test integrate((1+-2x)^2*(3+5x)^3*(2+3x), x) == :(-111*x^3+19*x^5+54x+-1091//4*x^4+135//2*x^2+1100//3*x^6+1500//7*x^7)
@test integrate((1+-2x)^2*(3+5x)^3, x) == :(-44//625*(3+5x)^5+2//375*(3+5x)^6+121//500*(3+5x)^4)
@test integrate((1+-2x)^2*(2+3x)^-1*(3+5x)^3, x) == :(-2515//81*x^3+-559//162*x^2+-49//729*log(2+3x)+50//9*x^4+100//3*x^5+3305//243*x)
@test integrate((1+-2x)^2*(2+3x)^-2*(3+5x)^3, x) == :(49*(1458+2187x)^-1+-800//81*x^3+-305//54*x^2+125//9*x^4+763//729*log(2+3x)+1271//243*x)
@test integrate((1+-2x)^2*(2+3x)^-3*(3+5x)^3, x) == :(-763*(1458+2187x)^-1+-4099//729*log(2+3x)+-100//9*x^2+49//1458*(2+3x)^-2+500//81*x^3+895//81*x)
@test integrate((1+-2x)^2*(2+3x)^-4*(3+5x)^3, x) == :(4099*(1458+2187x)^-1+-2800//243*x+-763//1458*(2+3x)^-2+49//2187*(2+3x)^-3+250//81*x^2+8285//729*log(2+3x))
@test integrate((1+-2x)^2*(2+3x)^-5*(3+5x)^3, x) == :(-8285*(1458+2187x)^-1+-3800//729*log(2+3x)+-763//2187*(2+3x)^-3+49//2916*(2+3x)^-4+500//243*x+4099//1458*(2+3x)^-2)
@test integrate((1+-2x)^2*(2+3x)^-6*(3+5x)^3, x) == :(3800*(1458+2187x)^-1+-8285//1458*(2+3x)^-2+-763//2916*(2+3x)^-4+49//3645*(2+3x)^-5+500//729*log(2+3x)+4099//2187*(2+3x)^-3)
@test integrate((1+-2x)^2*(2+3x)^-7*(3+5x)^3, x) == :(-500*(1458+2187x)^-1+-8285//2187*(2+3x)^-3+-763//3645*(2+3x)^-5+49//4374*(2+3x)^-6+1900//729*(2+3x)^-2+4099//2916*(2+3x)^-4)
@test integrate((1+-2x)^2*(2+3x)^-8*(3+5x)^3, x) == :(-8285//2916*(2+3x)^-4+-763//4374*(2+3x)^-6+-250//729*(2+3x)^-2+7//729*(2+3x)^-7+3800//2187*(2+3x)^-3+4099//3645*(2+3x)^-5)
@test integrate((1+-2x)^2*(2+3x)^7*(3+5x)^-1, x) == :(-20577159//62500*x^4+-7315947//15625*x^5+121//9765625*log(3+5x)+972//5*x^9+16767//25*x^8+130383//1250*x^6+672867//875*x^7+1327159//78125*x^3+80555569//781250*x^2+83333293//1953125*x)
@test integrate((1+-2x)^2*(2+3x)^6*(3+5x)^-1, x) == :(-1677159//12500*x^4+-422841//15625*x^3+-228447//3125*x^5+121//1953125*log(3+5x)+729//10*x^8+34992//175*x^7+35883//250*x^6+5555569//156250*x^2+8333293//390625*x)
@test integrate((1+-2x)^2*(2+3x)^5*(3+5x)^-1, x) == :(-102159//2500*x^4+-72841//3125*x^3+121//390625*log(3+5x)+972//35*x^7+1404//25*x^6+7803//625*x^5+305569//31250*x^2+833293//78125*x)
@test integrate((1+-2x)^2*(2+3x)^4*(3+5x)^-1, x) == :(-7841//625*x^3+-3159//500*x^4+54//5*x^6+121//78125*log(3+5x)+1728//125*x^5+5569//6250*x^2+83293//15625*x)
@test integrate((1+-2x)^2*(2+3x)^3*(3+5x)^-1, x) == :(-1931//1250*x^2+-591//125*x^3+54//25*x^4+108//25*x^5+121//15625*log(3+5x)+8293//3125*x)
@test integrate((1+-2x)^2*(2+3x)^2*(3+5x)^-1, x) == :(-431//250*x^2+-16//25*x^3+9//5*x^4+121//3125*log(3+5x)+793//625*x)
@test integrate((1+-2x)^2*(3+5x)^-1*(2+3x), x) == :(-28//25*x^2+4//5*x^3+43//125*x+121//625*log(3+5x))
@test integrate((1+-2x)^2*(3+5x)^-1, x) == :(-32//25*x+2//5*x^2+121//125*log(3+5x))
@test integrate((1+-2x)^2*(2+3x)^-1*(3+5x)^-1, x) == :(-49//9*log(2+3x)+4//15*x+121//25*log(3+5x))
@test integrate((1+-2x)^2*(2+3x)^-2*(3+5x)^-1, x) == :(49*(18+27x)^-1+-217//9*log(2+3x)+121//5*log(3+5x))
@test integrate((1+-2x)^2*(2+3x)^-3*(3+5x)^-1, x) == :(-121*log(2+3x)+121*log(3+5x)+217*(18+27x)^-1+49//18*(2+3x)^-2)
@test integrate((1+-2x)^2*(2+3x)^-4*(3+5x)^-1, x) == :(-605*log(2+3x)+121*(2+3x)^-1+605*log(3+5x)+49//27*(2+3x)^-3+217//18*(2+3x)^-2)
@test integrate((1+-2x)^2*(2+3x)^-5*(3+5x)^-1, x) == :(-3025*log(2+3x)+605*(2+3x)^-1+3025*log(3+5x)+49//36*(2+3x)^-4+121//2*(2+3x)^-2+217//27*(2+3x)^-3)
@test integrate((1+-2x)^2*(2+3x)^-6*(3+5x)^-1, x) == :(-15125*log(2+3x)+3025*(2+3x)^-1+15125*log(3+5x)+49//45*(2+3x)^-5+121//3*(2+3x)^-3+217//36*(2+3x)^-4+605//2*(2+3x)^-2)
@test integrate((1+-2x)^2*(2+3x)^-7*(3+5x)^-1, x) == :(-75625*log(2+3x)+15125*(2+3x)^-1+75625*log(3+5x)+49//54*(2+3x)^-6+121//4*(2+3x)^-4+217//45*(2+3x)^-5+605//3*(2+3x)^-3+3025//2*(2+3x)^-2)
@test integrate((1+-2x)^2*(2+3x)^-8*(3+5x)^-1, x) == :(-378125*log(2+3x)+75625*(2+3x)^-1+378125*log(3+5x)+7//9*(2+3x)^-7+121//5*(2+3x)^-5+217//54*(2+3x)^-6+605//4*(2+3x)^-4+3025//3*(2+3x)^-3+15125//2*(2+3x)^-2)
@test integrate((1+-2x)^2*(2+3x)^7*(3+5x)^-2, x) == :(-121*(29296875+48828125x)^-1+-1512378//78125*x^3+-656424//15625*x^5+-213867//2500*x^4+2187//50*x^8+2497//9765625*log(3+5x)+107892//875*x^7+116397//1250*x^6+17592879//781250*x^2+27776932//1953125*x)
@test integrate((1+-2x)^2*(2+3x)^6*(3+5x)^-2, x) == :(-121*(5859375+9765625x)^-1+-157599//6250*x^4+-48771//3125*x^3+2134//1953125*log(3+5x)+2916//175*x^7+4374//125*x^6+28917//3125*x^5+463086//78125*x^2+2777053//390625*x)
@test integrate((1+-2x)^2*(2+3x)^5*(3+5x)^-2, x) == :(-121*(1171875+1953125x)^-1+-25332//3125*x^3+-8721//2500*x^4+162//25*x^6+1771//390625*log(3+5x)+1893//6250*x^2+5508//625*x^5+277174//78125*x)
@test integrate((1+-2x)^2*(2+3x)^4*(3+5x)^-2, x) == :(-121*(234375+390625x)^-1+-3621//3125*x^2+-1809//625*x^3+189//125*x^4+324//125*x^5+1408//78125*log(3+5x)+5459//3125*x)
@test integrate((1+-2x)^2*(2+3x)^3*(3+5x)^-2, x) == :(-121*(46875+78125x)^-1+-1449//1250*x^2+-36//125*x^3+27//25*x^4+209//3125*log(3+5x)+2416//3125*x)
@test integrate((1+-2x)^2*(2+3x)^2*(3+5x)^-2, x) == :(-121*(9375+15625x)^-1+-78//125*x^2+12//25*x^3+37//625*x+682//3125*log(3+5x))
@test integrate((1+-2x)^2*(3+5x)^-2*(2+3x), x) == :(-121*(1875+3125x)^-1+-92//125*x+6//25*x^2+319//625*log(3+5x))
@test integrate((1+-2x)^2*(3+5x)^-2, x) == :(-121*(375+625x)^-1+-44//125*log(3+5x)+4//25*x)
@test integrate((1+-2x)^2*(2+3x)^-1*(3+5x)^-2, x) == :(-121*(75+125x)^-1+-407//25*log(3+5x)+49//3*log(2+3x))
@test integrate((1+-2x)^2*(2+3x)^-2*(3+5x)^-2, x) == :(-154*log(3+5x)+-121*(15+25x)^-1+-49*(6+9x)^-1+154*log(2+3x))
@test integrate((1+-2x)^2*(2+3x)^-3*(3+5x)^-2, x) == :(-1133*log(3+5x)+-154*(2+3x)^-1+-121*(3+5x)^-1+1133*log(2+3x)+-49//6*(2+3x)^-2)
@test integrate((1+-2x)^2*(2+3x)^-4*(3+5x)^-2, x) == :(-7480*log(3+5x)+-1133*(2+3x)^-1+-605*(3+5x)^-1+-77*(2+3x)^-2+7480*log(2+3x)+-49//9*(2+3x)^-3)
@test integrate((1+-2x)^2*(2+3x)^-5*(3+5x)^-2, x) == :(-46475*log(3+5x)+-7480*(2+3x)^-1+-3025*(3+5x)^-1+46475*log(2+3x)+-1133//2*(2+3x)^-2+-154//3*(2+3x)^-3+-49//12*(2+3x)^-4)
@test integrate((1+-2x)^2*(2+3x)^-6*(3+5x)^-2, x) == :(-277750*log(3+5x)+-46475*(2+3x)^-1+-15125*(3+5x)^-1+-3740*(2+3x)^-2+277750*log(2+3x)+-1133//3*(2+3x)^-3+-77//2*(2+3x)^-4+-49//15*(2+3x)^-5)
@test integrate((1+-2x)^2*(2+3x)^-7*(3+5x)^-2, x) == :(-1615625*log(3+5x)+-277750*(2+3x)^-1+-75625*(3+5x)^-1+1615625*log(2+3x)+-46475//2*(2+3x)^-2+-7480//3*(2+3x)^-3+-1133//4*(2+3x)^-4+-154//5*(2+3x)^-5+-49//18*(2+3x)^-6)
@test integrate((1+-2x)^2*(2+3x)^-8*(3+5x)^-2, x) == :(-9212500*log(3+5x)+-1615625*(2+3x)^-1+-378125*(3+5x)^-1+-138875*(2+3x)^-2+-1870*(2+3x)^-4+9212500*log(2+3x)+-46475//3*(2+3x)^-3+-1133//5*(2+3x)^-5+-77//3*(2+3x)^-6+-7//3*(2+3x)^-7)
@test integrate((1+-2x)^2*(2+3x)^8*(3+5x)^-3, x) == :(-572*(29296875+48828125x)^-1+-5350194//390625*x^3+-1700919//31250*x^4+-74601//3125*x^5+-121//97656250*(3+5x)^-2+5888//9765625*log(3+5x)+6561//250*x^8+332424//4375*x^7+376407//6250*x^6+55559043//3906250*x^2+92582457//9765625*x)
@test integrate((1+-2x)^2*(2+3x)^7*(3+5x)^-3, x) == :(-2497*(29296875+48828125x)^-1+-193833//12500*x^4+-162612//15625*x^3+-121//19531250*(3+5x)^-2+8748//875*x^7+13608//625*x^6+21949//9765625*log(3+5x)+104247//15625*x^5+1390203//390625*x^2+9251661//1953125*x)
@test integrate((1+-2x)^2*(2+3x)^6*(3+5x)^-3, x) == :(-2134*(5859375+9765625x)^-1+-23571//12500*x^4+-16299//3125*x^3+-121//3906250*(3+5x)^-2+189//15625*x^2+486//125*x^6+15547//1953125*log(3+5x)+17496//3125*x^5+920502//390625*x)
@test integrate((1+-2x)^2*(2+3x)^5*(3+5x)^-3, x) == :(-1771*(1171875+1953125x)^-1+-5499//3125*x^3+-5301//6250*x^2+-121//781250*(3+5x)^-2+648//625*x^4+972//625*x^5+10234//390625*log(3+5x)+17796//15625*x)
@test integrate((1+-2x)^2*(2+3x)^4*(3+5x)^-3, x) == :(-1408*(234375+390625x)^-1+-4779//6250*x^2+-121//156250*(3+5x)^-2+-72//625*x^3+81//125*x^4+1202//15625*log(3+5x)+1419//3125*x)
@test integrate((1+-2x)^2*(2+3x)^3*(3+5x)^-3, x) == :(-209*(9375+15625x)^-1+-216//625*x^2+-153//3125*x+-121//31250*(3+5x)^-2+23//125*log(3+5x)+36//125*x^3)
@test integrate((1+-2x)^2*(2+3x)^2*(3+5x)^-3, x) == :(-682*(9375+15625x)^-1+-264//625*x+-121//6250*(3+5x)^-2+18//125*x^2+829//3125*log(3+5x))
@test integrate((1+-2x)^2*(3+5x)^-3*(2+3x), x) == :(-319*(1875+3125x)^-1+-128//625*log(3+5x)+-121//1250*(3+5x)^-2+12//125*x)
@test integrate((1+-2x)^2*(3+5x)^-3, x) == :(44*(375+625x)^-1+-121//250*(3+5x)^-2+4//125*log(3+5x))
@test integrate((1+-2x)^2*(2+3x)^-1*(3+5x)^-3, x) == :(-49*log(2+3x)+49*log(3+5x)+407*(75+125x)^-1+-121//50*(3+5x)^-2)
@test integrate((1+-2x)^2*(2+3x)^-2*(3+5x)^-3, x) == :(-707*log(2+3x)+49*(2+3x)^-1+154*(3+5x)^-1+707*log(3+5x)+-121//10*(3+5x)^-2)
@test integrate((1+-2x)^2*(2+3x)^-3*(3+5x)^-3, x) == :(-6934*log(2+3x)+707*(2+3x)^-1+1133*(3+5x)^-1+6934*log(3+5x)+-121//2*(3+5x)^-2+49//2*(2+3x)^-2)
@test integrate((1+-2x)^2*(2+3x)^-4*(3+5x)^-3, x) == :(-57110*log(2+3x)+6934*(2+3x)^-1+7480*(3+5x)^-1+57110*log(3+5x)+-605//2*(3+5x)^-2+49//3*(2+3x)^-3+707//2*(2+3x)^-2)
@test integrate((1+-2x)^2*(2+3x)^-5*(3+5x)^-3, x) == :(-424975*log(2+3x)+3467*(2+3x)^-2+46475*(3+5x)^-1+57110*(2+3x)^-1+424975*log(3+5x)+-3025//2*(3+5x)^-2+49//4*(2+3x)^-4+707//3*(2+3x)^-3)
@test integrate((1+-2x)^2*(2+3x)^-6*(3+5x)^-3, x) == :(-2958125*log(2+3x)+28555*(2+3x)^-2+277750*(3+5x)^-1+424975*(2+3x)^-1+2958125*log(3+5x)+-15125//2*(3+5x)^-2+49//5*(2+3x)^-5+707//4*(2+3x)^-4+6934//3*(2+3x)^-3)
@test integrate((1+-2x)^2*(2+3x)^-7*(3+5x)^-3, x) == :(-19637500*log(2+3x)+1615625*(3+5x)^-1+2958125*(2+3x)^-1+19637500*log(3+5x)+-75625//2*(3+5x)^-2+49//6*(2+3x)^-6+707//5*(2+3x)^-5+3467//2*(2+3x)^-4+57110//3*(2+3x)^-3+424975//2*(2+3x)^-2)
@test integrate((1+-2x)^2*(2+3x)^-8*(3+5x)^-3, x) == :(-125825000*log(2+3x)+7*(2+3x)^-7+9212500*(3+5x)^-1+19637500*(2+3x)^-1+125825000*log(3+5x)+-378125//2*(3+5x)^-2+707//6*(2+3x)^-6+6934//5*(2+3x)^-5+28555//2*(2+3x)^-4+424975//3*(2+3x)^-3+2958125//2*(2+3x)^-2)
@test integrate((1+-2x)^3*(2+3x)^8*(3+5x), x) == :(-518//891*(2+3x)^11+-343//2187*(2+3x)^9+-40//3159*(2+3x)^13+107//729*(2+3x)^12+2009//2430*(2+3x)^10)
@test integrate((1+-2x)^3*(2+3x)^7*(3+5x), x) == :(-343//1944*(2+3x)^8+-259//405*(2+3x)^10+-10//729*(2+3x)^12+428//2673*(2+3x)^11+2009//2187*(2+3x)^9)
@test integrate((1+-2x)^3*(2+3x)^6*(3+5x), x) == :(-518//729*(2+3x)^9+-49//243*(2+3x)^7+-40//2673*(2+3x)^11+214//1215*(2+3x)^10+2009//1944*(2+3x)^8)
@test integrate((1+-2x)^3*(2+3x)^5*(3+5x), x) == :(-343//1458*(2+3x)^6+-259//324*(2+3x)^8+-4//243*(2+3x)^10+287//243*(2+3x)^7+428//2187*(2+3x)^9)
@test integrate((1+-2x)^3*(2+3x)^4*(3+5x), x) == :(-343//1215*(2+3x)^5+-74//81*(2+3x)^7+-40//2187*(2+3x)^9+107//486*(2+3x)^8+2009//1458*(2+3x)^6)
@test integrate((1+-2x)^3*(2+3x)^3*(3+5x), x) == :(-135*x^8+-86*x^3+2*x^2+24x+111*x^6+-1188//7*x^7+-117//4*x^4+949//5*x^5)
@test integrate((1+-2x)^3*(2+3x)^2*(3+5x), x) == :(-35*x^3+-26*x^6+-8*x^2+12x+-360//7*x^7+99//4*x^4+326//5*x^5)
@test integrate((1+-2x)^3*(2+3x)*(3+5x), x) == :(-77//32*(1+-2x)^4+-5//16*(1+-2x)^6+17//10*(1+-2x)^5)
@test integrate((1+-2x)^3*(3+5x), x) == :(-11//16*(1+-2x)^4+1//4*(1+-2x)^5)
@test integrate((1+-2x)^3*(2+3x)^-1*(3+5x), x) == :(-343//243*log(2+3x)+-161//27*x^2+-10//3*x^4+188//27*x^3+293//81*x)
@test integrate((1+-2x)^3*(2+3x)^-2*(3+5x), x) == :(343*(486+729x)^-1+-286//27*x+-40//27*x^3+134//27*x^2+2009//243*log(2+3x))
@test integrate((1+-2x)^3*(2+3x)^-3*(3+5x), x) == :(-2009*(486+729x)^-1+-518//81*log(2+3x)+-20//27*x^2+116//27*x+343//486*(2+3x)^-2)
@test integrate((1+-2x)^3*(2+3x)^-4*(3+5x), x) == :(518*(162+243x)^-1+-2009//486*(2+3x)^-2+-40//81*x+343//729*(2+3x)^-3+428//243*log(2+3x))
@test integrate((1+-2x)^3*(2+3x)^-5*(3+5x), x) == :(-428*(486+729x)^-1+-2009//729*(2+3x)^-3+-40//243*log(2+3x)+259//81*(2+3x)^-2+343//972*(2+3x)^-4)
@test integrate((1+-2x)^3*(2+3x)^-6*(3+5x), x) == :(-173//2940*(1+-2x)^4*(2+3x)^-4+1//105*(1+-2x)^4*(2+3x)^-5)
@test integrate((1+-2x)^3*(2+3x)^-7*(3+5x), x) == :(-103//2205*(1+-2x)^4*(2+3x)^-5+-103//30870*(1+-2x)^4*(2+3x)^-4+1//126*(1+-2x)^4*(2+3x)^-6)
@test integrate((1+-2x)^3*(2+3x)^-8*(3+5x), x) == :(-2009//1458*(2+3x)^-6+-107//243*(2+3x)^-4+40//729*(2+3x)^-3+49//243*(2+3x)^-7+518//405*(2+3x)^-5)
@test integrate((1+-2x)^3*(2+3x)^8*(3+5x)^2, x) == :(-4099//4374*(2+3x)^12+-1862//3645*(2+3x)^10+-100//5103*(2+3x)^14+343//6561*(2+3x)^9+2180//9477*(2+3x)^13+11599//8019*(2+3x)^11)
@test integrate((1+-2x)^3*(2+3x)^7*(3+5x)^2, x) == :(-8198//8019*(2+3x)^11+-3724//6561*(2+3x)^9+-200//9477*(2+3x)^13+343//5832*(2+3x)^8+545//2187*(2+3x)^12+11599//7290*(2+3x)^10)
@test integrate((1+-2x)^3*(2+3x)^6*(3+5x)^2, x) == :(-4099//3645*(2+3x)^10+-931//1458*(2+3x)^8+-50//2187*(2+3x)^12+49//729*(2+3x)^7+2180//8019*(2+3x)^11+11599//6561*(2+3x)^9)
@test integrate((1+-2x)^3*(2+3x)^5*(3+5x)^2, x) == :(-8198//6561*(2+3x)^9+-532//729*(2+3x)^7+-200//8019*(2+3x)^11+218//729*(2+3x)^10+343//4374*(2+3x)^6+11599//5832*(2+3x)^8)
@test integrate((1+-2x)^3*(2+3x)^4*(3+5x)^2, x) == :(-4099//2916*(2+3x)^8+-1862//2187*(2+3x)^6+-20//729*(2+3x)^10+343//3645*(2+3x)^5+1657//729*(2+3x)^7+2180//6561*(2+3x)^9)
@test integrate((1+-2x)^3*(2+3x)^3*(3+5x)^2, x) == :(-600*x^9+66*x^2+72x+-2295//2*x^8+-1641//4*x^4+-754//3*x^3+-234//7*x^7+2262//5*x^5+6743//6*x^6)
@test integrate((1+-2x)^3*(2+3x)^2*(3+5x)^2, x) == :(-225*x^8+-57*x^4+6*x^2+36x+-1860//7*x^7+-395//3*x^3+581//3*x^6+1473//5*x^5)
@test integrate((1+-2x)^3*(3+5x)^2*(2+3x), x) == :(18x+-600//7*x^7+-166//3*x^3+-110//3*x^6+-21//2*x^2+135//4*x^4+534//5*x^5)
@test integrate((1+-2x)^3*(3+5x)^2, x) == :(-121//32*(1+-2x)^4+-25//48*(1+-2x)^6+11//4*(1+-2x)^5)
@test integrate((1+-2x)^3*(2+3x)^-1*(3+5x)^2, x) == :(-1433//162*x^2+-40//3*x^5+82//81*x^3+145//9*x^4+343//729*log(2+3x)+922//243*x)
@test integrate((1+-2x)^3*(2+3x)^-2*(3+5x)^2, x) == :(-343*(1458+2187x)^-1+-3724//729*log(2+3x)+-313//27*x^2+-50//9*x^4+980//81*x^3+2323//243*x)
@test integrate((1+-2x)^3*(2+3x)^-3*(3+5x)^2, x) == :(3724*(1458+2187x)^-1+-1546//81*x+-343//1458*(2+3x)^-2+-200//81*x^3+230//27*x^2+11599//729*log(2+3x))
@test integrate((1+-2x)^3*(2+3x)^-4*(3+5x)^2, x) == :(-11599*(1458+2187x)^-1+-8198//729*log(2+3x)+-343//2187*(2+3x)^-3+-100//81*x^2+1780//243*x+1862//729*(2+3x)^-2)
@test integrate((1+-2x)^3*(2+3x)^-5*(3+5x)^2, x) == :(8198*(1458+2187x)^-1+-11599//1458*(2+3x)^-2+-343//2916*(2+3x)^-4+-200//243*x+2180//729*log(2+3x)+3724//2187*(2+3x)^-3)
@test integrate((1+-2x)^3*(2+3x)^-6*(3+5x)^2, x) == :(-2180*(1458+2187x)^-1+-11599//2187*(2+3x)^-3+-343//3645*(2+3x)^-5+-200//729*log(2+3x)+931//729*(2+3x)^-4+4099//729*(2+3x)^-2)
@test integrate((1+-2x)^3*(2+3x)^-7*(3+5x)^2, x) == :(200*(1458+2187x)^-1+-11599//2916*(2+3x)^-4+-1090//729*(2+3x)^-2+-343//4374*(2+3x)^-6+3724//3645*(2+3x)^-5+8198//2187*(2+3x)^-3)
@test integrate((1+-2x)^3*(2+3x)^-8*(3+5x)^2, x) == :(-11599//3645*(2+3x)^-5+-2180//2187*(2+3x)^-3+-49//729*(2+3x)^-7+100//729*(2+3x)^-2+1862//2187*(2+3x)^-6+4099//1458*(2+3x)^-4)
@test integrate((1+-2x)^3*(2+3x)^7*(3+5x)^3, x) == :(-10073//7290*(2+3x)^10+-7195//4374*(2+3x)^12+-500//15309*(2+3x)^14+-343//17496*(2+3x)^8+1813//6561*(2+3x)^9+3700//9477*(2+3x)^13+66193//24057*(2+3x)^11)
@test integrate((1+-2x)^3*(2+3x)^6*(3+5x)^3, x) == :(-14390//8019*(2+3x)^11+-10073//6561*(2+3x)^9+-1000//28431*(2+3x)^13+-49//2187*(2+3x)^7+925//2187*(2+3x)^12+1813//5832*(2+3x)^8+66193//21870*(2+3x)^10)
@test integrate((1+-2x)^3*(2+3x)^5*(3+5x)^3, x) == :(-10073//5832*(2+3x)^8+-1439//729*(2+3x)^10+-343//13122*(2+3x)^6+-250//6561*(2+3x)^12+259//729*(2+3x)^7+3700//8019*(2+3x)^11+66193//19683*(2+3x)^9)
@test integrate((1+-2x)^3*(2+3x)^4*(3+5x)^3, x) == :(-24030*x^10+-23370*x^9+-5548*x^4+-312*x^3+432x+1080*x^2+22949*x^7+-81000//11*x^11+-28917//5*x^5+19607//2*x^6+41619//8*x^8)
@test integrate((1+-2x)^3*(2+3x)^3*(3+5x)^3, x) == :(-6900*x^9+-2700*x^10+-534*x^3+216x+378*x^2+-14355//4*x^8+-8693//4*x^4+-1419//5*x^5+10513//2*x^6+33013//7*x^7)
@test integrate((1+-2x)^3*(2+3x)^2*(3+5x)^3, x) == :(-1000*x^9+-375*x^3+108x+108*x^2+-3675//2*x^8+-2659//4*x^4+230//7*x^7+3279//5*x^5+3617//2*x^6)
@test integrate((1+-2x)^3*(3+5x)^3*(2+3x), x) == :(-375*x^8+-201*x^3+54x+335*x^6+-2900//7*x^7+-425//4*x^4+27//2*x^2+2277//5*x^5)
@test integrate((1+-2x)^3*(3+5x)^3, x) == :(-87*x^3+-50*x^6+27x+174*x^5+-1000//7*x^7+-27//2*x^2+179//4*x^4)
@test integrate((1+-2x)^3*(2+3x)^-1*(3+5x)^3, x) == :(-8287//486*x^2+-6427//243*x^3+-500//9*x^6+-343//2187*log(2+3x)+220//9*x^5+2815//54*x^4+10013//729*x)
@test integrate((1+-2x)^3*(2+3x)^-2*(3+5x)^3, x) == :(343*(4374+6561x)^-1+-5287//486*x^2+-200//9*x^5+-190//81*x^3+775//27*x^4+1813//729*log(2+3x)+2287//729*x)
@test integrate((1+-2x)^3*(2+3x)^-3*(3+5x)^3, x) == :(-1813*(1458+2187x)^-1+-10073//729*log(2+3x)+-1795//81*x^2+-250//27*x^4+343//4374*(2+3x)^-2+1700//81*x^3+16253//729*x)
@test integrate((1+-2x)^3*(2+3x)^-4*(3+5x)^3, x) == :(10073*(1458+2187x)^-1+-24970//729*x+-1813//1458*(2+3x)^-2+-1000//243*x^3+343//6561*(2+3x)^-3+3550//243*x^2+66193//2187*log(2+3x))
@test integrate((1+-2x)^3*(2+3x)^-5*(3+5x)^3, x) == :(-66193*(4374+6561x)^-1+-14390//729*log(2+3x)+-1813//2187*(2+3x)^-3+-500//243*x^2+343//8748*(2+3x)^-4+9100//729*x+10073//1458*(2+3x)^-2)
@test integrate((1+-2x)^3*(2+3x)^-6*(3+5x)^3, x) == :(14390*(1458+2187x)^-1+-66193//4374*(2+3x)^-2+-1813//2916*(2+3x)^-4+-1000//729*x+343//10935*(2+3x)^-5+3700//729*log(2+3x)+10073//2187*(2+3x)^-3)
@test integrate((1+-2x)^3*(2+3x)^-7*(3+5x)^3, x) == :(-3700*(1458+2187x)^-1+-66193//6561*(2+3x)^-3+-1813//3645*(2+3x)^-5+-1000//2187*log(2+3x)+343//13122*(2+3x)^-6+7195//729*(2+3x)^-2+10073//2916*(2+3x)^-4)
@test integrate((1+-2x)^3*(2+3x)^-8*(3+5x)^3, x) == :(1000*(4374+6561x)^-1+-66193//8748*(2+3x)^-4+-1850//729*(2+3x)^-2+-1813//4374*(2+3x)^-6+49//2187*(2+3x)^-7+10073//3645*(2+3x)^-5+14390//2187*(2+3x)^-3)
@test integrate((1+-2x)^3*(2+3x)^6*(3+5x)^-1, x) == :(-17453753//234375*x^3+-5848749//62500*x^4+-40338//875*x^7+-13851//50*x^8+-648//5*x^9+1331//9765625*log(3+5x)+331713//1250*x^6+2212083//15625*x^5+11111259//781250*x^2+41666223//1953125*x)
@test integrate((1+-2x)^3*(2+3x)^5*(3+5x)^-1, x) == :(-1703753//46875*x^3+-138741//156250*x^2+-73749//12500*x^4+-11988//175*x^7+-243//5*x^8+1331//1953125*log(3+5x)+4419//125*x^6+243333//3125*x^5+4166223//390625*x)
@test integrate((1+-2x)^3*(2+3x)^4*(3+5x)^-1, x) == :(-138741//31250*x^2+-128753//9375*x^3+-648//35*x^7+-306//25*x^6+1331//390625*log(3+5x)+14958//625*x^5+31251//2500*x^4+416223//78125*x)
@test integrate((1+-2x)^3*(2+3x)^3*(3+5x)^-1, x) == :(-26241//6250*x^2+-5003//1875*x^3+-36//5*x^6+108//125*x^5+1331//78125*log(3+5x)+2313//250*x^4+41223//15625*x)
@test integrate((1+-2x)^3*(2+3x)^2*(3+5x)^-1, x) == :(-3741//1250*x^2+-72//25*x^5+69//25*x^4+622//375*x^3+1331//15625*log(3+5x)+3723//3125*x)
@test integrate((1+-2x)^3*(3+5x)^-1*(2+3x), x) == :(-183//125*x^2+-27//625*x+-6//5*x^4+172//75*x^3+1331//3125*log(3+5x))
@test integrate((1+-2x)^3*(3+5x)^-1, x) == :(-402//125*x+-8//15*x^3+42//25*x^2+1331//625*log(3+5x))
@test integrate((1+-2x)^3*(2+3x)^-1*(3+5x)^-1, x) == :(-343//27*log(2+3x)+-4//15*x^2+332//225*x+1331//125*log(3+5x))
@test integrate((1+-2x)^3*(2+3x)^-2*(3+5x)^-1, x) == :(343*(54+81x)^-1+-1421//27*log(2+3x)+-8//45*x+1331//25*log(3+5x))
@test integrate((1+-2x)^3*(2+3x)^-3*(3+5x)^-1, x) == :(1421*(54+81x)^-1+-7189//27*log(2+3x)+343//54*(2+3x)^-2+1331//5*log(3+5x))
@test integrate((1+-2x)^3*(2+3x)^-4*(3+5x)^-1, x) == :(-1331*log(2+3x)+1331*log(3+5x)+7189*(54+81x)^-1+343//81*(2+3x)^-3+1421//54*(2+3x)^-2)
@test integrate((1+-2x)^3*(2+3x)^-5*(3+5x)^-1, x) == :(-6655*log(2+3x)+1331*(2+3x)^-1+6655*log(3+5x)+343//108*(2+3x)^-4+1421//81*(2+3x)^-3+7189//54*(2+3x)^-2)
@test integrate((1+-2x)^3*(2+3x)^-6*(3+5x)^-1, x) == :(-33275*log(2+3x)+6655*(2+3x)^-1+33275*log(3+5x)+343//135*(2+3x)^-5+1331//2*(2+3x)^-2+1421//108*(2+3x)^-4+7189//81*(2+3x)^-3)
@test integrate((1+-2x)^3*(2+3x)^-7*(3+5x)^-1, x) == :(-166375*log(2+3x)+33275*(2+3x)^-1+166375*log(3+5x)+343//162*(2+3x)^-6+1331//3*(2+3x)^-3+1421//135*(2+3x)^-5+6655//2*(2+3x)^-2+7189//108*(2+3x)^-4)
@test integrate((1+-2x)^3*(2+3x)^-8*(3+5x)^-1, x) == :(-831875*log(2+3x)+166375*(2+3x)^-1+831875*log(3+5x)+49//27*(2+3x)^-7+1331//4*(2+3x)^-4+1421//162*(2+3x)^-6+6655//3*(2+3x)^-3+7189//135*(2+3x)^-5+33275//2*(2+3x)^-2)
@test integrate((1+-2x)^3*(2+3x)^6*(3+5x)^-2, x) == :(-1331*(29296875+48828125x)^-1+-1836723//78125*x^3+-461623//390625*x^2+-37908//875*x^7+-5643//3125*x^4+-729//25*x^8+12231//625*x^6+23232//9765625*log(3+5x)+774981//15625*x^5+13880997//1953125*x)
@test integrate((1+-2x)^3*(2+3x)^5*(3+5x)^-2, x) == :(-1331*(5859375+9765625x)^-1+-507023//156250*x^2+-26594//3125*x^3+-1944//175*x^7+-1026//125*x^6+19239//1953125*log(3+5x)+44982//3125*x^5+108387//12500*x^4+1382328//390625*x)
@test integrate((1+-2x)^3*(2+3x)^4*(3+5x)^-2, x) == :(-1331*(1171875+1953125x)^-1+-4217//3125*x^3+-1816//625*x^2+-108//25*x^6+108//625*x^5+7317//1250*x^4+15246//390625*log(3+5x)+133659//78125*x)
@test integrate((1+-2x)^3*(2+3x)^3*(3+5x)^-2, x) == :(-1331*(234375+390625x)^-1+-12077//6250*x^2+-216//125*x^5+189//125*x^4+786//625*x^3+1998//3125*x+11253//78125*log(3+5x))
@test integrate((1+-2x)^3*(2+3x)^2*(3+5x)^-2, x) == :(-1331*(46875+78125x)^-1+-1179//3125*x+-427//625*x^2+-18//25*x^4+164//125*x^3+1452//3125*log(3+5x))
@test integrate((1+-2x)^3*(3+5x)^-2*(2+3x), x) == :(-1331*(9375+15625x)^-1+-1098//625*x+-8//25*x^3+122//125*x^2+3267//3125*log(3+5x))
@test integrate((1+-2x)^3*(3+5x)^-2, x) == :(-1331*(1875+3125x)^-1+-726//625*log(3+5x)+-4//25*x^2+108//125*x)
@test integrate((1+-2x)^3*(2+3x)^-1*(3+5x)^-2, x) == :(-1331*(375+625x)^-1+-4719//125*log(3+5x)+-8//75*x+343//9*log(2+3x))
@test integrate((1+-2x)^3*(2+3x)^-2*(3+5x)^-2, x) == :(-1331*(75+125x)^-1+-343*(18+27x)^-1+-8712//25*log(3+5x)+3136//9*log(2+3x))
@test integrate((1+-2x)^3*(2+3x)^-3*(3+5x)^-2, x) == :(-3136*(18+27x)^-1+-2541*log(3+5x)+-1331*(15+25x)^-1+2541*log(2+3x)+-343//18*(2+3x)^-2)
@test integrate((1+-2x)^3*(2+3x)^-4*(3+5x)^-2, x) == :(-16698*log(3+5x)+-2541*(2+3x)^-1+-1331*(3+5x)^-1+16698*log(2+3x)+-1568//9*(2+3x)^-2+-343//27*(2+3x)^-3)
@test integrate((1+-2x)^3*(2+3x)^-5*(3+5x)^-2, x) == :(-103455*log(3+5x)+-16698*(2+3x)^-1+-6655*(3+5x)^-1+103455*log(2+3x)+-3136//27*(2+3x)^-3+-2541//2*(2+3x)^-2+-343//36*(2+3x)^-4)
@test integrate((1+-2x)^3*(2+3x)^-6*(3+5x)^-2, x) == :(-617100*log(3+5x)+-103455*(2+3x)^-1+-33275*(3+5x)^-1+-8349*(2+3x)^-2+-847*(2+3x)^-3+617100*log(2+3x)+-784//9*(2+3x)^-4+-343//45*(2+3x)^-5)
@test integrate((1+-2x)^3*(2+3x)^-7*(3+5x)^-2, x) == :(-3584625*log(3+5x)+-617100*(2+3x)^-1+-166375*(3+5x)^-1+-5566*(2+3x)^-3+3584625*log(2+3x)+-103455//2*(2+3x)^-2+-3136//45*(2+3x)^-5+-2541//4*(2+3x)^-4+-343//54*(2+3x)^-6)
@test integrate((1+-2x)^3*(2+3x)^-8*(3+5x)^-2, x) == :(-20418750*log(3+5x)+-3584625*(2+3x)^-1+-831875*(3+5x)^-1+-308550*(2+3x)^-2+-34485*(2+3x)^-3+20418750*log(2+3x)+-8349//2*(2+3x)^-4+-2541//5*(2+3x)^-5+-1568//27*(2+3x)^-6+-49//9*(2+3x)^-7)
@test integrate((1+-2x)^3*(2+3x)^7*(3+5x)^-3, x) == :(-1089*(5859375+9765625x)^-1+-5918904//390625*x^3+-2300646//1953125*x^2+-119556//4375*x^7+-2187//125*x^8+-1331//97656250*(3+5x)^-2+6507//62500*x^4+33291//3125*x^6+47289//9765625*log(3+5x)+491913//15625*x^5+46214407//9765625*x)
@test integrate((1+-2x)^3*(2+3x)^6*(3+5x)^-3, x) == :(-23232*(29296875+48828125x)^-1+-915777//390625*x^2+-81747//15625*x^3+-5832//875*x^7+-3402//625*x^6+-1331//19531250*(3+5x)^-2+74223//12500*x^4+134622//15625*x^5+166749//9765625*log(3+5x)+4571416//1953125*x)
@test integrate((1+-2x)^3*(2+3x)^5*(3+5x)^-3, x) == :(-19239*(5859375+9765625x)^-1+-62097//31250*x^2+-1331//3906250*(3+5x)^-2+-393//625*x^3+-324//125*x^6+-324//3125*x^5+22977//6250*x^4+109032//1953125*log(3+5x)+424432//390625*x)
@test integrate((1+-2x)^3*(2+3x)^4*(3+5x)^-3, x) == :(-15246*(1171875+1953125x)^-1+-7617//6250*x^2+-1331//781250*(3+5x)^-2+-648//625*x^5+513//625*x^4+2826//3125*x^3+4691//15625*x+63294//390625*log(3+5x))
@test integrate((1+-2x)^3*(2+3x)^3*(3+5x)^-3, x) == :(-11253*(234375+390625x)^-1+-1331//156250*(3+5x)^-2+-1303//3125*x+-927//3125*x^2+-54//125*x^4+468//625*x^3+5907//15625*log(3+5x))
@test integrate((1+-2x)^3*(2+3x)^2*(3+5x)^-3, x) == :(-1452*(9375+15625x)^-1+-2978//3125*x+-1331//31250*(3+5x)^-2+-24//125*x^3+354//625*x^2+1551//3125*log(3+5x))
@test integrate((1+-2x)^3*(3+5x)^-3*(2+3x), x) == :(-3267*(9375+15625x)^-1+-2046//3125*log(3+5x)+-1331//6250*(3+5x)^-2+-12//125*x^2+316//625*x)
@test integrate((1+-2x)^3*(3+5x)^-3, x) == :(726*(1875+3125x)^-1+-1331//1250*(3+5x)^-2+-8//125*x+132//625*log(3+5x))
@test integrate((1+-2x)^3*(2+3x)^-1*(3+5x)^-3, x) == :(4719*(375+625x)^-1+-1331//250*(3+5x)^-2+-343//3*log(2+3x)+14289//125*log(3+5x))
@test integrate((1+-2x)^3*(2+3x)^-2*(3+5x)^-3, x) == :(-1617*log(2+3x)+343*(6+9x)^-1+1617*log(3+5x)+8712*(75+125x)^-1+-1331//50*(3+5x)^-2)
@test integrate((1+-2x)^3*(2+3x)^-3*(3+5x)^-3, x) == :(-15708*log(2+3x)+1617*(2+3x)^-1+2541*(3+5x)^-1+15708*log(3+5x)+-1331//10*(3+5x)^-2+343//6*(2+3x)^-2)
@test integrate((1+-2x)^3*(2+3x)^-4*(3+5x)^-3, x) == :(-128634*log(2+3x)+15708*(2+3x)^-1+16698*(3+5x)^-1+128634*log(3+5x)+-1331//2*(3+5x)^-2+343//9*(2+3x)^-3+1617//2*(2+3x)^-2)
@test integrate((1+-2x)^3*(2+3x)^-5*(3+5x)^-3, x) == :(-953535*log(2+3x)+539*(2+3x)^-3+7854*(2+3x)^-2+103455*(3+5x)^-1+128634*(2+3x)^-1+953535*log(3+5x)+-6655//2*(3+5x)^-2+343//12*(2+3x)^-4)
@test integrate((1+-2x)^3*(2+3x)^-6*(3+5x)^-3, x) == :(-6618975*log(2+3x)+5236*(2+3x)^-3+64317*(2+3x)^-2+617100*(3+5x)^-1+953535*(2+3x)^-1+6618975*log(3+5x)+-33275//2*(3+5x)^-2+343//15*(2+3x)^-5+1617//4*(2+3x)^-4)
@test integrate((1+-2x)^3*(2+3x)^-7*(3+5x)^-3, x) == :(-43848750*log(2+3x)+3927*(2+3x)^-4+42878*(2+3x)^-3+3584625*(3+5x)^-1+6618975*(2+3x)^-1+43848750*log(3+5x)+-166375//2*(3+5x)^-2+343//18*(2+3x)^-6+1617//5*(2+3x)^-5+953535//2*(2+3x)^-2)
@test integrate((1+-2x)^3*(2+3x)^-8*(3+5x)^-3, x) == :(-280500000*log(2+3x)+317845*(2+3x)^-3+20418750*(3+5x)^-1+43848750*(2+3x)^-1+280500000*log(3+5x)+-831875//2*(3+5x)^-2+49//3*(2+3x)^-7+539//2*(2+3x)^-6+15708//5*(2+3x)^-5+64317//2*(2+3x)^-4+6618975//2*(2+3x)^-2)
@test integrate((1+-2x)^-1*(2+3x)^8*(3+5x), x) == :(-63412811//1024*log(1+-2x)+-63019595//512*x+-60332619//512*x^2+-37722699//256*x^4+-21272139//160*x^5+-17391129//128*x^3+-2929689//32*x^6+-422091//32*x^8+-353565//8*x^7+-3645//2*x^9)
@test integrate((1+-2x)^-1*(2+3x)^7*(3+5x), x) == :(-9058973//512*log(1+-2x)+-8960669//256*x+-8362653//256*x^2+-4352157//128*x^4+-2257119//64*x^3+-2053917//80*x^5+-218943//16*x^6+-126117//28*x^7+-10935//16*x^8)
@test integrate((1+-2x)^-1*(2+3x)^6*(3+5x), x) == :(-1294139//256*log(1+-2x)+-1269563//128*x+-1138491//128*x^2+-458811//64*x^4+-279657//32*x^3+-169371//40*x^5+-12393//8*x^6+-3645//14*x^7)
@test integrate((1+-2x)^-1*(2+3x)^5*(3+5x), x) == :(-184877//128*log(1+-2x)+-178733//64*x+-150573//64*x^2+-42093//32*x^4+-32271//16*x^3+-10773//20*x^5+-405//4*x^6)
@test integrate((1+-2x)^-1*(2+3x)^4*(3+5x), x) == :(-26411//64*log(1+-2x)+-24875//32*x+-18987//32*x^2+-3321//8*x^3+-3051//16*x^4+-81//2*x^5)
@test integrate((1+-2x)^-1*(2+3x)^3*(3+5x), x) == :(-3773//32*log(1+-2x)+-3389//16*x+-2205//16*x^2+-279//4*x^3+-135//8*x^4)
@test integrate((1+-2x)^-1*(2+3x)^2*(3+5x), x) == :(-539//16*log(1+-2x)+-443//8*x+-219//8*x^2+-15//2*x^3)
@test integrate((1+-2x)^-1*(2+3x)*(3+5x), x) == :(-77//8*log(1+-2x)+-53//4*x+-15//4*x^2)
@test integrate((1+-2x)^-1*(3+5x), x) == :(-11//4*log(1+-2x)+-5//2*x)
@test integrate((1+-2x)^-1*(2+3x)^-1*(3+5x), x) == :(-11//14*log(1+-2x)+-1//21*log(2+3x))
@test integrate((1+-2x)^-1*(2+3x)^-2*(3+5x), x) == :((42+63x)^-1+-11//49*log(1+-2x)+11//49*log(2+3x))
@test integrate((1+-2x)^-1*(2+3x)^-3*(3+5x), x) == :(-11*(98+147x)^-1+-22//343*log(1+-2x)+1//42*(2+3x)^-2+22//343*log(2+3x))
@test integrate((1+-2x)^-1*(2+3x)^-4*(3+5x), x) == :(-22*(686+1029x)^-1+-44//2401*log(1+-2x)+-11//98*(2+3x)^-2+1//63*(2+3x)^-3+44//2401*log(2+3x))
@test integrate((1+-2x)^-1*(2+3x)^-5*(3+5x), x) == :(-44*(4802+7203x)^-1+-88//16807*log(1+-2x)+-11//147*(2+3x)^-3+-11//343*(2+3x)^-2+1//84*(2+3x)^-4+88//16807*log(2+3x))
@test integrate((1+-2x)^-1*(2+3x)^-6*(3+5x), x) == :(-88*(33614+50421x)^-1+-176//117649*log(1+-2x)+-22//1029*(2+3x)^-3+-22//2401*(2+3x)^-2+-11//196*(2+3x)^-4+1//105*(2+3x)^-5+176//117649*log(2+3x))
@test integrate((1+-2x)^-1*(2+3x)^-7*(3+5x), x) == :(-176*(235298+352947x)^-1+-352//823543*log(1+-2x)+-44//7203*(2+3x)^-3+-44//16807*(2+3x)^-2+-11//245*(2+3x)^-5+-11//686*(2+3x)^-4+1//126*(2+3x)^-6+352//823543*log(2+3x))
@test integrate((1+-2x)^-1*(2+3x)^-8*(3+5x), x) == :(-352*(1647086+2470629x)^-1+-704//5764801*log(1+-2x)+-88//50421*(2+3x)^-3+-88//117649*(2+3x)^-2+-22//1715*(2+3x)^-5+-11//294*(2+3x)^-6+-11//2401*(2+3x)^-4+1//147*(2+3x)^-7+704//5764801*log(2+3x))
@test integrate((1+-2x)^-1*(2+3x)^8*(3+5x)^2, x) == :(-697540921//2048*log(1+-2x)+-695181625//1024*x+-677093689//1024*x^2+-487203129//512*x^4+-316246329//320*x^5+-204901139//256*x^3+-53031699//64*x^6+-14907321//64*x^8+-8399295//16*x^7+-256365//4*x^9+-32805//4*x^10)
@test integrate((1+-2x)^-1*(2+3x)^7*(3+5x)^2, x) == :(-99648703//1024*log(1+-2x)+-99058879//512*x+-94979263//512*x^2+-59969727//256*x^4+-34084287//160*x^5+-27480469//128*x^3+-4736853//32*x^6+-4040847//56*x^7+-696195//32*x^8+-6075//2*x^9)
@test integrate((1+-2x)^-1*(2+3x)^6*(3+5x)^2, x) == :(-14235529//512*log(1+-2x)+-14088073//256*x+-13178761//256*x^2+-6947721//128*x^4+-3575427//64*x^3+-3310281//80*x^5+-356643//16*x^6+-207765//28*x^7+-18225//16*x^8)
@test integrate((1+-2x)^-1*(2+3x)^5*(3+5x)^2, x) == :(-2033647//256*log(1+-2x)+-1996783//128*x+-1797103//128*x^2+-736623//64*x^4+-444581//32*x^3+-275103//40*x^5+-20385//8*x^6+-6075//14*x^7)
@test integrate((1+-2x)^-1*(2+3x)^4*(3+5x)^2, x) == :(-290521//128*log(1+-2x)+-281305//64*x+-238297//64*x^2+-68121//32*x^4+-51571//16*x^3+-3537//4*x^5+-675//4*x^6)
@test integrate((1+-2x)^-1*(2+3x)^3*(3+5x)^2, x) == :(-41503//64*log(1+-2x)+-39199//32*x+-30175//32*x^2+-5349//8*x^3+-4995//16*x^4+-135//2*x^5)
@test integrate((1+-2x)^-1*(2+3x)^2*(3+5x)^2, x) == :(-5929//32*log(1+-2x)+-5353//16*x+-3529//16*x^2+-455//4*x^3+-225//8*x^4)
@test integrate((1+-2x)^-1*(3+5x)^2*(2+3x), x) == :(-847//16*log(1+-2x)+-703//8*x+-355//8*x^2+-25//2*x^3)
@test integrate((1+-2x)^-1*(3+5x)^2, x) == :(-121//8*log(1+-2x)+-85//4*x+-25//4*x^2)
@test integrate((1+-2x)^-1*(2+3x)^-1*(3+5x)^2, x) == :(-121//28*log(1+-2x)+-25//6*x+1//63*log(2+3x))
@test integrate((1+-2x)^-1*(2+3x)^-2*(3+5x)^2, x) == :(-1*(126+189x)^-1+-121//98*log(1+-2x)+-68//441*log(2+3x))
@test integrate((1+-2x)^-1*(2+3x)^-3*(3+5x)^2, x) == :(68*(882+1323x)^-1+-121//343*log(1+-2x)+-1//126*(2+3x)^-2+121//343*log(2+3x))
@test integrate((1+-2x)^-1*(2+3x)^-4*(3+5x)^2, x) == :(-121*(686+1029x)^-1+-242//2401*log(1+-2x)+-1//189*(2+3x)^-3+34//441*(2+3x)^-2+242//2401*log(2+3x))
@test integrate((1+-2x)^-1*(2+3x)^-5*(3+5x)^2, x) == :(-242*(4802+7203x)^-1+-484//16807*log(1+-2x)+-121//686*(2+3x)^-2+-1//252*(2+3x)^-4+68//1323*(2+3x)^-3+484//16807*log(2+3x))
@test integrate((1+-2x)^-1*(2+3x)^-6*(3+5x)^2, x) == :(-484*(33614+50421x)^-1+-968//117649*log(1+-2x)+-121//1029*(2+3x)^-3+-121//2401*(2+3x)^-2+-1//315*(2+3x)^-5+17//441*(2+3x)^-4+968//117649*log(2+3x))
@test integrate((1+-2x)^-1*(2+3x)^-7*(3+5x)^2, x) == :(-968*(235298+352947x)^-1+-1936//823543*log(1+-2x)+-242//7203*(2+3x)^-3+-242//16807*(2+3x)^-2+-121//1372*(2+3x)^-4+-1//378*(2+3x)^-6+68//2205*(2+3x)^-5+1936//823543*log(2+3x))
@test integrate((1+-2x)^-1*(2+3x)^-8*(3+5x)^2, x) == :(-1936*(1647086+2470629x)^-1+-3872//5764801*log(1+-2x)+-484//50421*(2+3x)^-3+-484//117649*(2+3x)^-2+-121//1715*(2+3x)^-5+-121//4802*(2+3x)^-4+-1//441*(2+3x)^-7+34//1323*(2+3x)^-6+3872//5764801*log(2+3x))
@test integrate((1+-2x)^-1*(2+3x)^7*(3+5x)^3, x) == :(-1096135733//2048*log(1+-2x)+-1092596789//1024*x+-1065169973//1024*x^2+-969544757//768*x^3+-772025397//512*x^4+-504354357//320*x^5+-95297877//112*x^7+-85228263//64*x^6+-24381405//64*x^8+-423225//4*x^9+-54675//4*x^10)
@test integrate((1+-2x)^-1*(2+3x)^6*(3+5x)^3, x) == :(-156590819//1024*log(1+-2x)+-155706083//512*x+-149512931//512*x^2+-130251491//384*x^3+-95317731//256*x^4+-54600291//160*x^5+-7656993//32*x^6+-6596235//56*x^7+-1148175//32*x^8+-10125//2*x^9)
@test integrate((1+-2x)^-1*(2+3x)^5*(3+5x)^3, x) == :(-22370117//512*log(1+-2x)+-22148933//256*x+-20766533//256*x^2+-16987973//192*x^3+-11088453//128*x^4+-5333733//80*x^5+-580815//16*x^6+-342225//28*x^7+-30375//16*x^8)
@test integrate((1+-2x)^-1*(2+3x)^4*(3+5x)^3, x) == :(-3195731//256*log(1+-2x)+-3140435//128*x+-2836307//128*x^2+-2119763//96*x^3+-1182291//64*x^4+-89343//8*x^5+-33525//8*x^6+-10125//14*x^7)
@test integrate((1+-2x)^-1*(2+3x)^3*(3+5x)^3, x) == :(-456533//128*log(1+-2x)+-442709//64*x+-377045//64*x^2+-247157//48*x^3+-110205//32*x^4+-5805//4*x^5+-1125//4*x^6)
@test integrate((1+-2x)^-1*(2+3x)^2*(3+5x)^3, x) == :(-65219//64*log(1+-2x)+-61763//32*x+-47939//32*x^2+-25835//24*x^3+-8175//16*x^4+-225//2*x^5)
@test integrate((1+-2x)^-1*(3+5x)^3*(2+3x), x) == :(-9317//32*log(1+-2x)+-8453//16*x+-5645//16*x^2+-2225//12*x^3+-375//8*x^4)
@test integrate((1+-2x)^-1*(3+5x)^3, x) == :(-1331//16*log(1+-2x)+-1115//8*x+-575//8*x^2+-125//6*x^3)
@test integrate((1+-2x)^-1*(2+3x)^-1*(3+5x)^3, x) == :(-1331//56*log(1+-2x)+-1225//36*x+-125//12*x^2+-1//189*log(2+3x))
@test integrate((1+-2x)^-1*(2+3x)^-2*(3+5x)^3, x) == :((378+567x)^-1+-1331//196*log(1+-2x)+-125//18*x+103//1323*log(2+3x))
@test integrate((1+-2x)^-1*(2+3x)^-3*(3+5x)^3, x) == :(-103*(2646+3969x)^-1+-3469//9261*log(2+3x)+-1331//686*log(1+-2x)+1//378*(2+3x)^-2)
@test integrate((1+-2x)^-1*(2+3x)^-4*(3+5x)^3, x) == :(3469*(18522+27783x)^-1+-1331//2401*log(1+-2x)+-103//2646*(2+3x)^-2+1//567*(2+3x)^-3+1331//2401*log(2+3x))
@test integrate((1+-2x)^-1*(2+3x)^-5*(3+5x)^3, x) == :(-1331*(4802+7203x)^-1+-2662//16807*log(1+-2x)+-103//3969*(2+3x)^-3+1//756*(2+3x)^-4+2662//16807*log(2+3x)+3469//18522*(2+3x)^-2)
@test integrate((1+-2x)^-1*(2+3x)^-6*(3+5x)^3, x) == :(-2662*(33614+50421x)^-1+-5324//117649*log(1+-2x)+-1331//4802*(2+3x)^-2+-103//5292*(2+3x)^-4+1//945*(2+3x)^-5+3469//27783*(2+3x)^-3+5324//117649*log(2+3x))
@test integrate((1+-2x)^-1*(2+3x)^-7*(3+5x)^3, x) == :(-5324*(235298+352947x)^-1+-10648//823543*log(1+-2x)+-1331//7203*(2+3x)^-3+-1331//16807*(2+3x)^-2+-103//6615*(2+3x)^-5+1//1134*(2+3x)^-6+3469//37044*(2+3x)^-4+10648//823543*log(2+3x))
@test integrate((1+-2x)^-1*(2+3x)^-8*(3+5x)^3, x) == :(-10648*(1647086+2470629x)^-1+-21296//5764801*log(1+-2x)+-2662//50421*(2+3x)^-3+-2662//117649*(2+3x)^-2+-1331//9604*(2+3x)^-4+-103//7938*(2+3x)^-6+1//1323*(2+3x)^-7+3469//46305*(2+3x)^-5+21296//5764801*log(2+3x))
@test integrate((a+b*x)^3*(c+d*x)^-1*(e+f*x)^-1, x) == :(f^-3*(b*e+-1*a*f)^3*(d*e+-1*c*f)^-1*log(e+f*x)+(1/2)*b^3*d^-1*f^-1*x^2+-1*d^-3*(b*c+-1*a*d)^3*(d*e+-1*c*f)^-1*log(c+d*x)+-1*x*b^2*d^-2*f^-2*(b*c*f+b*d*e+-3*a*d*f))
@test integrate((1+-2x)^-1*(2+3x)^8*(3+5x)^-1, x) == :(-40089855591//10000000*x+-7136193339//2000000*x^2+-345533877//100000*x^3+-111146499//40000*x^4+-8018271//5000*x^5+-5764801//2816*log(1+-2x)+-114453//200*x^6+-6561//70*x^7+1//4296875*log(3+5x))
@test integrate((1+-2x)^-1*(2+3x)^7*(3+5x)^-1, x) == :(-1127138733//1000000*x+-187738857//200000*x^2+-7889751//10000*x^3+-2006937//4000*x^4+-823543//1408*log(1+-2x)+-99873//500*x^5+-729//20*x^6+1//859375*log(3+5x))
@test integrate((1+-2x)^-1*(2+3x)^6*(3+5x)^-1, x) == :(-31289679//100000*x+-4693491//20000*x^2+-159813//1000*x^3+-117649//704*log(1+-2x)+-28431//400*x^4+-729//50*x^5+1//171875*log(3+5x))
@test integrate((1+-2x)^-1*(2+3x)^5*(3+5x)^-1, x) == :(-848277//10000*x+-107433//2000*x^2+-16807//352*log(1+-2x)+-2619//100*x^3+-243//40*x^4+1//34375*log(3+5x))
@test integrate((1+-2x)^-1*(2+3x)^4*(3+5x)^-1, x) == :(-21951//1000*x+-2401//176*log(1+-2x)+-2079//200*x^2+-27//10*x^3+1//6875*log(3+5x))
@test integrate((1+-2x)^-1*(2+3x)^3*(3+5x)^-1, x) == :(-513//100*x+-343//88*log(1+-2x)+-27//20*x^2+1//1375*log(3+5x))
@test integrate((1+-2x)^-1*(2+3x)^2*(3+5x)^-1, x) == :(-49//44*log(1+-2x)+-9//10*x+1//275*log(3+5x))
@test integrate((1+-2x)^-1*(3+5x)^-1*(2+3x), x) == :(-7//22*log(1+-2x)+1//55*log(3+5x))
@test integrate((1+-2x)^-1*(3+5x)^-1, x) == :(-1//11*log(1+-2x)+1//11*log(3+5x))
@test integrate((1+-2x)^-1*(2+3x)^-1*(3+5x)^-1, x) == :(-3//7*log(2+3x)+-2//77*log(1+-2x)+5//11*log(3+5x))
@test integrate((1+-2x)^-1*(2+3x)^-2*(3+5x)^-1, x) == :(3*(14+21x)^-1+-111//49*log(2+3x)+-4//539*log(1+-2x)+25//11*log(3+5x))
@test integrate((1+-2x)^-1*(2+3x)^-3*(3+5x)^-1, x) == :(111*(98+147x)^-1+-3897//343*log(2+3x)+-8//3773*log(1+-2x)+3//14*(2+3x)^-2+125//11*log(3+5x))
@test integrate((1+-2x)^-1*(2+3x)^-4*(3+5x)^-1, x) == :(3897*(686+1029x)^-1+-136419//2401*log(2+3x)+-16//26411*log(1+-2x)+1//7*(2+3x)^-3+111//98*(2+3x)^-2+625//11*log(3+5x))
@test integrate((1+-2x)^-1*(2+3x)^-5*(3+5x)^-1, x) == :(136419*(4802+7203x)^-1+-4774713//16807*log(2+3x)+-32//184877*log(1+-2x)+3//28*(2+3x)^-4+37//49*(2+3x)^-3+3125//11*log(3+5x)+3897//686*(2+3x)^-2)
@test integrate((1+-2x)^-1*(2+3x)^-6*(3+5x)^-1, x) == :(4774713*(33614+50421x)^-1+-167115051//117649*log(2+3x)+-64//1294139*log(1+-2x)+3//35*(2+3x)^-5+111//196*(2+3x)^-4+1299//343*(2+3x)^-3+15625//11*log(3+5x)+136419//4802*(2+3x)^-2)
@test integrate((1+-2x)^-1*(2+3x)^-7*(3+5x)^-1, x) == :(167115051*(235298+352947x)^-1+-5849026977//823543*log(2+3x)+-128//9058973*log(1+-2x)+1//14*(2+3x)^-6+111//245*(2+3x)^-5+3897//1372*(2+3x)^-4+45473//2401*(2+3x)^-3+78125//11*log(3+5x)+4774713//33614*(2+3x)^-2)
@test integrate((1+-2x)^-1*(2+3x)^8*(3+5x)^-2, x) == :(-1*(12890625+21484375x)^-1+-3579885909//5000000*x+-118543581//200000*x^2+-24660207//50000*x^3+-6194313//20000*x^4+-5764801//15488*log(1+-2x)+-303993//2500*x^5+-2187//100*x^6+266//47265625*log(3+5x))
@test integrate((1+-2x)^-1*(2+3x)^7*(3+5x)^-2, x) == :(-1*(2578125+4296875x)^-1+-19846971//100000*x+-14750667//100000*x^2+-823543//7744*log(1+-2x)+-495477//5000*x^3+-86751//2000*x^4+-2187//250*x^5+233//9453125*log(3+5x))
@test integrate((1+-2x)^-1*(2+3x)^6*(3+5x)^-2, x) == :(-1*(515625+859375x)^-1+-2682909//50000*x+-335097//10000*x^2+-117649//3872*log(1+-2x)+-8019//500*x^3+-729//200*x^4+8//75625*log(3+5x))
@test integrate((1+-2x)^-1*(2+3x)^5*(3+5x)^-2, x) == :(-1*(103125+171875x)^-1+-69039//5000*x+-16807//1936*log(1+-2x)+-6399//1000*x^2+-81//50*x^3+167//378125*log(3+5x))
@test integrate((1+-2x)^-1*(2+3x)^4*(3+5x)^-2, x) == :(-1*(20625+34375x)^-1+-2401//968*log(1+-2x)+-1593//500*x+-81//100*x^2+134//75625*log(3+5x))
@test integrate((1+-2x)^-1*(2+3x)^3*(3+5x)^-2, x) == :(-1*(4125+6875x)^-1+-343//484*log(1+-2x)+-27//50*x+101//15125*log(3+5x))
@test integrate((1+-2x)^-1*(2+3x)^2*(3+5x)^-2, x) == :(-1*(825+1375x)^-1+-49//242*log(1+-2x)+68//3025*log(3+5x))
@test integrate((1+-2x)^-1*(3+5x)^-2*(2+3x), x) == :(-1*(165+275x)^-1+-7//121*log(1+-2x)+7//121*log(3+5x))
@test integrate((1+-2x)^-1*(3+5x)^-2, x) == :(-1*(33+55x)^-1+-2//121*log(1+-2x)+2//121*log(3+5x))
@test integrate((1+-2x)^-1*(2+3x)^-1*(3+5x)^-2, x) == :(-5*(33+55x)^-1+-155//121*log(3+5x)+-4//847*log(1+-2x)+9//7*log(2+3x))
@test integrate((1+-2x)^-1*(2+3x)^-2*(3+5x)^-2, x) == :(-25*(33+55x)^-1+-9*(14+21x)^-1+-1600//121*log(3+5x)+-8//5929*log(1+-2x)+648//49*log(2+3x))
@test integrate((1+-2x)^-1*(2+3x)^-3*(3+5x)^-2, x) == :(-648*(98+147x)^-1+-125*(33+55x)^-1+-12125//121*log(3+5x)+-16//41503*log(1+-2x)+-9//14*(2+3x)^-2+34371//343*log(2+3x))
@test integrate((1+-2x)^-1*(2+3x)^-4*(3+5x)^-2, x) == :(-34371*(686+1029x)^-1+-625*(33+55x)^-1+-81250//121*log(3+5x)+-324//49*(2+3x)^-2+-32//290521*log(1+-2x)+-3//7*(2+3x)^-3+1612242//2401*log(2+3x))
@test integrate((1+-2x)^-1*(2+3x)^-5*(3+5x)^-2, x) == :(-1612242*(4802+7203x)^-1+-3125*(33+55x)^-1+-509375//121*log(3+5x)+-34371//686*(2+3x)^-2+-216//49*(2+3x)^-3+-64//2033647*log(1+-2x)+-9//28*(2+3x)^-4+70752609//16807*log(2+3x))
@test integrate((1+-2x)^-1*(2+3x)^-6*(3+5x)^-2, x) == :(-70752609*(33614+50421x)^-1+-15625*(33+55x)^-1+-3062500//121*log(3+5x)+-806121//2401*(2+3x)^-2+-11457//343*(2+3x)^-3+-162//49*(2+3x)^-4+-128//14235529*log(1+-2x)+-9//35*(2+3x)^-5+2977686468//117649*log(2+3x))
@test integrate((1+-2x)^-1*(2+3x)^8*(3+5x)^-3, x) == :(-266*(141796875+236328125x)^-1+-62934003//500000*x+-9268263//100000*x^2+-5764801//85184*log(1+-2x)+-1535517//25000*x^3+-264627//10000*x^4+-6561//1250*x^5+-1//8593750*(3+5x)^-2+31024//519921875*log(3+5x))
@test integrate((1+-2x)^-1*(2+3x)^7*(3+5x)^-3, x) == :(-233*(28359375+47265625x)^-1+-1044657//50000*x^2+-823543//42592*log(1+-2x)+-339309//10000*x+-24543//2500*x^3+-2187//1000*x^4+-1//1718750*(3+5x)^-2+4667//20796875*log(3+5x))
@test integrate((1+-2x)^-1*(2+3x)^6*(3+5x)^-3, x) == :(-8*(226875+378125x)^-1+-216999//25000*x+-117649//21296*log(1+-2x)+-19683//5000*x^2+-243//250*x^3+-1//343750*(3+5x)^-2+3347//4159375*log(3+5x))
@test integrate((1+-2x)^-1*(2+3x)^5*(3+5x)^-3, x) == :(-167*(1134375+1890625x)^-1+-16807//10648*log(1+-2x)+-4941//2500*x+-243//500*x^2+-1//68750*(3+5x)^-2+11224//4159375*log(3+5x))
@test integrate((1+-2x)^-1*(2+3x)^4*(3+5x)^-3, x) == :(-134*(226875+378125x)^-1+-2401//5324*log(1+-2x)+-81//250*x+-1//13750*(3+5x)^-2+6802//831875*log(3+5x))
@test integrate((1+-2x)^-1*(2+3x)^3*(3+5x)^-3, x) == :(-101*(45375+75625x)^-1+-343//2662*log(1+-2x)+-1//2750*(3+5x)^-2+3469//166375*log(3+5x))
@test integrate((1+-2x)^-1*(2+3x)^2*(3+5x)^-3, x) == :(-68*(9075+15125x)^-1+-49//1331*log(1+-2x)+-1//550*(3+5x)^-2+49//1331*log(3+5x))
@test integrate((1+-2x)^-1*(3+5x)^-3*(2+3x), x) == :(-7*(363+605x)^-1+-14//1331*log(1+-2x)+-1//110*(3+5x)^-2+14//1331*log(3+5x))
@test integrate((1+-2x)^-1*(3+5x)^-3, x) == :(-2*(363+605x)^-1+-4//1331*log(1+-2x)+-1//22*(3+5x)^-2+4//1331*log(3+5x))
@test integrate((1+-2x)^-1*(2+3x)^-1*(3+5x)^-3, x) == :(155*(363+605x)^-1+-27//7*log(2+3x)+-8//9317*log(1+-2x)+-5//22*(3+5x)^-2+5135//1331*log(3+5x))
@test integrate((1+-2x)^-1*(2+3x)^-2*(3+5x)^-3, x) == :(27*(14+21x)^-1+1600*(363+605x)^-1+-2889//49*log(2+3x)+-25//22*(3+5x)^-2+-16//65219*log(1+-2x)+78475//1331*log(3+5x))
@test integrate((1+-2x)^-1*(2+3x)^-3*(3+5x)^-3, x) == :(2889*(98+147x)^-1+12125*(363+605x)^-1+-204228//343*log(2+3x)+-125//22*(3+5x)^-2+-32//456533*log(1+-2x)+27//14*(2+3x)^-2+792500//1331*log(3+5x))
@test integrate((1+-2x)^-1*(2+3x)^-4*(3+5x)^-3, x) == :(81250*(363+605x)^-1+204228*(686+1029x)^-1+-11984706//2401*log(2+3x)+-625//22*(3+5x)^-2+-64//3195731*log(1+-2x)+9//7*(2+3x)^-3+2889//98*(2+3x)^-2+6643750//1331*log(3+5x))
@test integrate((1+-2x)^-1*(2+3x)^-5*(3+5x)^-3, x) == :(509375*(363+605x)^-1+11984706*(4802+7203x)^-1+-631722537//16807*log(2+3x)+-3125//22*(3+5x)^-2+-128//22370117*log(1+-2x)+27//28*(2+3x)^-4+963//49*(2+3x)^-3+102114//343*(2+3x)^-2+50028125//1331*log(3+5x))
@test integrate((a+b*x)^-1*(a+-1*b*x)^-1*(c+d*x)^4, x) == :(-1//3*b^-2*d^4*x^3+(1/2)*a^-1*b^-5*(b*c+-1*a*d)^4*log(a+b*x)+-1*x*b^-4*d^2*(a^2*d^2+6*b^2*c^2)+-2*c*b^-2*d^3*x^2+-1//2*a^-1*b^-5*(a*d+b*c)^4*log(a+-1*b*x))
@test integrate((a+b*x)^-1*(a+-1*b*x)^-1*(c+d*x)^3, x) == :(-1//2*b^-2*d^3*x^2+(1/2)*a^-1*b^-4*(b*c+-1*a*d)^3*log(a+b*x)+-3*c*x*b^-2*d^2+-1//2*a^-1*b^-4*(a*d+b*c)^3*log(a+-1*b*x))
@test integrate((a+b*x)^-1*(a+-1*b*x)^-1*(c+d*x)^2, x) == :(-1*x*b^-2*d^2+(1/2)*a^-1*b^-3*(b*c+-1*a*d)^2*log(a+b*x)+-1//2*a^-1*b^-3*(a*d+b*c)^2*log(a+-1*b*x))
@test integrate((a+b*x)^-1*(a+-1*b*x)^-1*(c+d*x), x) == :((1/2)*a^-1*b^-2*(b*c+-1*a*d)*log(a+b*x)+-1//2*a^-1*b^-2*(a*d+b*c)*log(a+-1*b*x))
@test integrate((a+b*x)^-1*(a+-1*b*x)^-1, x) == :(a^-1*b^-1*arctanh(b*x*a^-1))
@test integrate((a+b*x)^-1*(a+-1*b*x)^-1*(c+d*x)^-1, x) == :((1/2)*a^-1*(b*c+-1*a*d)^-1*log(a+b*x)+-1*d*(b^2*c^2+-1*a^2*d^2)^-1*log(c+d*x)+-1//2*a^-1*(a*d+b*c)^-1*log(a+-1*b*x))
@test integrate((a+b*x)^-1*(a+-1*b*x)^-1*(c+d*x)^-2, x) == :(d*(c+d*x)^-1*(b^2*c^2+-1*a^2*d^2)^-1+(1/2)*b*a^-1*(b*c+-1*a*d)^-2*log(a+b*x)+-1//2*b*a^-1*(a*d+b*c)^-2*log(a+-1*b*x)+-2*c*d*b^2*(b^2*c^2+-1*a^2*d^2)^-2*log(c+d*x))
@test integrate((a+b*x)^-1*(a+-1*b*x)^-1*(c+d*x)^-3, x) == :(d*(c+d*x)^-2*(-2*a^2*d^2+2*b^2*c^2)^-1+(1/2)*a^-1*b^2*(b*c+-1*a*d)^-3*log(a+b*x)+-1//2*a^-1*b^2*(a*d+b*c)^-3*log(a+-1*b*x)+-1*d*b^2*(b^2*c^2+-1*a^2*d^2)^-3*(a^2*d^2+3*b^2*c^2)*log(c+d*x)+2*c*d*b^2*(c+d*x)^-1*(b^2*c^2+-1*a^2*d^2)^-2)
@test integrate((1+-2x)^-2*(2+3x)^8*(3+5x), x) == :(63412811*(1024+-2048x)^-1+32805//32*x^8+56862//7*x^7+976617//32*x^6+5859459//80*x^5+5892813//32*x^3+32991057//256*x^4+91609881//256*x+122887143//512*x^2+246239357//1024*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^7*(3+5x), x) == :(9058973*(512+-1024x)^-1+10935//28*x^7+11421//4*x^6+793881//80*x^5+873207//16*x^2+1423899//64*x^4+2399985//64*x^3+15647317//256*log(1+-2x)+22333965//256*x)
@test integrate((1+-2x)^-2*(2+3x)^6*(3+5x), x) == :(1294139*(256+-512x)^-1+1215//8*x^6+5103//5*x^5+111501//16*x^3+210195//64*x^4+661617//32*x+1507977//128*x^2+3916031//256*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^5*(3+5x), x) == :(184877*(128+-256x)^-1+243//4*x^5+2997//8*x^4+18027//16*x^3+60025//16*log(1+-2x)+75447//32*x^2+301467//64*x)
@test integrate((1+-2x)^-2*(2+3x)^4*(3+5x), x) == :(144*x^3+26411*(64+-128x)^-1+405//16*x^4+13419//32*x^2+16203//16*x+57281//64*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^3*(3+5x), x) == :(3773*(32+-64x)^-1+45//4*x^3+243//4*x^2+3177//16*x+3283//16*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^2*(3+5x), x) == :(33x+539*(16+-32x)^-1+45//8*x^2+707//16*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)*(3+5x), x) == :(77*(8+-16x)^-1+15//4*x+17//2*log(1+-2x))
@test integrate((1+-2x)^-2*(3+5x), x) == :(11*(4+-8x)^-1+5//4*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^-1*(3+5x), x) == :(11*(14+-28x)^-1+-1//49*log(2+3x)+1//49*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^-2*(3+5x), x) == :((98+147x)^-1+11*(49+-98x)^-1+-31//343*log(1+-2x)+31//343*log(2+3x))
@test integrate((1+-2x)^-2*(2+3x)^-3*(3+5x), x) == :(-31*(686+1029x)^-1+22*(343+-686x)^-1+-128//2401*log(1+-2x)+1//98*(2+3x)^-2+128//2401*log(2+3x))
@test integrate((1+-2x)^-2*(2+3x)^-4*(3+5x), x) == :(-128*(4802+7203x)^-1+44*(2401+-4802x)^-1+-388//16807*log(1+-2x)+-31//686*(2+3x)^-2+1//147*(2+3x)^-3+388//16807*log(2+3x))
@test integrate((1+-2x)^-2*(2+3x)^-5*(3+5x), x) == :(-388*(33614+50421x)^-1+88*(16807+-33614x)^-1+-1040//117649*log(1+-2x)+-64//2401*(2+3x)^-2+-31//1029*(2+3x)^-3+1//196*(2+3x)^-4+1040//117649*log(2+3x))
@test integrate((1+-2x)^-2*(2+3x)^-6*(3+5x), x) == :(-1040*(235298+352947x)^-1+176*(117649+-235298x)^-1+-2608//823543*log(1+-2x)+-194//16807*(2+3x)^-2+-128//7203*(2+3x)^-3+-31//1372*(2+3x)^-4+1//245*(2+3x)^-5+2608//823543*log(2+3x))
@test integrate((1+-2x)^-2*(2+3x)^-7*(3+5x), x) == :(-2608*(1647086+2470629x)^-1+352*(823543+-1647086x)^-1+-520//117649*(2+3x)^-2+-388//50421*(2+3x)^-3+-128//117649*log(1+-2x)+-32//2401*(2+3x)^-4+-31//1715*(2+3x)^-5+1//294*(2+3x)^-6+128//117649*log(2+3x))
@test integrate((1+-2x)^-2*(2+3x)^8*(3+5x)^2, x) == :(396738*x^6+697540921*(2048+-4096x)^-1+18225//4*x^9+1235655//32*x^8+17378631//112*x^7+235268793//320*x^5+275757561//256*x^4+346239417//256*x^3+413355417//256*x^2+1512848491//1024*log(1+-2x)+2330515357//1024*x)
@test integrate((1+-2x)^-2*(2+3x)^7*(3+5x)^2, x) == :(99648703*(1024+-2048x)^-1+54675//32*x^8+375435//28*x^7+1597239//32*x^6+4750569//40*x^5+9077405//16*x+18842715//64*x^3+53086563//256*x^4+195497697//512*x^2+389535839//1024*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^6*(3+5x)^2, x) == :(14235529*(512+-1024x)^-1+18225//28*x^7+37665//8*x^6+575775//16*x^4+1295919//80*x^5+3851307//64*x^3+11140101//128*x^2+12386759//128*log(1+-2x)+35458963//256*x)
@test integrate((1+-2x)^-2*(2+3x)^5*(3+5x)^2, x) == :(2033647*(256+-512x)^-1+2025//8*x^6+6723//4*x^5+89913//8*x^3+342333//64*x^4+2104901//64*x+2412699//128*x^2+6206585//256*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^4*(3+5x)^2, x) == :(290521*(128+-256x)^-1+405//4*x^5+9855//16*x^4+15159//4*x^2+29277//16*x^3+381073//64*log(1+-2x)+480841//64*x)
@test integrate((1+-2x)^-2*(2+3x)^3*(3+5x)^2, x) == :(41503*(64+-128x)^-1+675//16*x^4+945//4*x^3+12973//8*x+21717//32*x^2+91091//64*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^2*(3+5x)^2, x) == :(5929*(32+-64x)^-1+75//4*x^3+795//8*x^2+1309//4*log(1+-2x)+5119//16*x)
@test integrate((1+-2x)^-2*(3+5x)^2*(2+3x), x) == :(847*(16+-32x)^-1+75//8*x^2+215//4*x+1133//16*log(1+-2x))
@test integrate((1+-2x)^-2*(3+5x)^2, x) == :(121*(8+-16x)^-1+25//4*x+55//4*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^-1*(3+5x)^2, x) == :(121*(28+-56x)^-1+1//147*log(2+3x)+407//196*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^-2*(3+5x)^2, x) == :(-1*(294+441x)^-1+121*(98+-196x)^-1+-22//343*log(2+3x)+22//343*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^-3*(3+5x)^2, x) == :(22*(686+1029x)^-1+121*(343+-686x)^-1+-319//2401*log(1+-2x)+-1//294*(2+3x)^-2+319//2401*log(2+3x))
@test integrate((1+-2x)^-2*(2+3x)^-4*(3+5x)^2, x) == :(-319*(4802+7203x)^-1+242*(2401+-4802x)^-1+-1364//16807*log(1+-2x)+-1//441*(2+3x)^-3+11//343*(2+3x)^-2+1364//16807*log(2+3x))
@test integrate((1+-2x)^-2*(2+3x)^-5*(3+5x)^2, x) == :(-1364*(33614+50421x)^-1+484*(16807+-33614x)^-1+-4180//117649*log(1+-2x)+-319//4802*(2+3x)^-2+-1//588*(2+3x)^-4+22//1029*(2+3x)^-3+4180//117649*log(2+3x))
@test integrate((1+-2x)^-2*(2+3x)^-6*(3+5x)^2, x) == :(-4180*(235298+352947x)^-1+968*(117649+-235298x)^-1+-11264//823543*log(1+-2x)+-682//16807*(2+3x)^-2+-319//7203*(2+3x)^-3+-1//735*(2+3x)^-5+11//686*(2+3x)^-4+11264//823543*log(2+3x))
@test integrate((1+-2x)^-2*(2+3x)^-7*(3+5x)^2, x) == :(-11264*(1647086+2470629x)^-1+1936*(823543+-1647086x)^-1+-4048//823543*log(1+-2x)+-2090//117649*(2+3x)^-2+-1364//50421*(2+3x)^-3+-319//9604*(2+3x)^-4+-1//882*(2+3x)^-6+22//1715*(2+3x)^-5+4048//823543*log(2+3x))
@test integrate((1+-2x)^-2*(2+3x)^-8*(3+5x)^2, x) == :(-4048*(1647086+2470629x)^-1+3872*(5764801+-11529602x)^-1+-68288//40353607*log(1+-2x)+-5632//823543*(2+3x)^-2+-4180//352947*(2+3x)^-3+-341//16807*(2+3x)^-4+-319//12005*(2+3x)^-5+-1//1029*(2+3x)^-7+11//1029*(2+3x)^-6+68288//40353607*log(2+3x))
@test integrate((1+-2x)^-2*(2+3x)^8*(3+5x)^3, x) == :(7672950131*(4096+-8192x)^-1+164025//8*x^10+370575//2*x^9+101721015//128*x^8+242570133//112*x^7+260574273//40*x^5+544462047//128*x^6+2416569641//256*x^3+7277894263//512*x+8502681987//1024*x^4+21573106793//2048*x^2+36770371407//4096*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^7*(3+5x)^3, x) == :(1096135733*(2048+-4096x)^-1+30375//4*x^9+127575//2*x^8+20626947//32*x^6+28463805//112*x^7+220950207//128*x^4+298946109//128*log(1+-2x)+379446471//320*x^5+551942075//256*x^3+1312685491//512*x^2+3690540955//1024*x)
@test integrate((1+-2x)^-2*(2+3x)^6*(3+5x)^3, x) == :(156590819*(1024+-2048x)^-1+91125//32*x^8+309825//14*x^7+2611845//32*x^6+7530189//16*x^3+15403257//80*x^5+85406805//256*x^4+230244479//256*x+310976027//512*x^2+616195041//1024*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^5*(3+5x)^3, x) == :(22370117*(512+-1024x)^-1+15525//2*x^6+30375//28*x^7+423009//16*x^5+3724389//64*x^4+6179077//64*x^3+8881301//64*x^2+39220335//256*log(1+-2x)+56291737//256*x)
@test integrate((1+-2x)^-2*(2+3x)^4*(3+5x)^3, x) == :(3195731*(256+-512x)^-1+3375//8*x^6+5535//2*x^5+209243//4*x+289951//16*x^3+557415//64*x^4+3859469//128*x^2+9836211//256*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^3*(3+5x)^3, x) == :(456533*(128+-256x)^-1+675//4*x^5+2025//2*x^4+47535//16*x^3+194881//32*x^2+302379//32*log(1+-2x)+766807//64*x)
@test integrate((1+-2x)^-2*(2+3x)^2*(3+5x)^3, x) == :(65219*(64+-128x)^-1+775//2*x^3+1125//16*x^4+35135//32*x^2+41537//16*x+144837//64*log(1+-2x))
@test integrate((1+-2x)^-2*(3+5x)^3*(2+3x), x) == :(9317*(32+-64x)^-1+125//4*x^3+325//2*x^2+8245//16*x+8349//16*log(1+-2x))
@test integrate((1+-2x)^-2*(3+5x)^3, x) == :(1331*(16+-32x)^-1+125//8*x^2+175//2*x+1815//16*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^-1*(3+5x)^3, x) == :(1331*(56+-112x)^-1+-1//441*log(2+3x)+125//12*x+1089//49*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^-2*(3+5x)^3, x) == :((882+1323x)^-1+1331*(196+-392x)^-1+101//3087*log(2+3x)+4719//1372*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^-3*(3+5x)^3, x) == :(-101*(6174+9261x)^-1+1331*(686+-1372x)^-1+-363//2401*log(2+3x)+1//882*(2+3x)^-2+363//2401*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^-4*(3+5x)^3, x) == :(363*(4802+7203x)^-1+1331*(2401+-4802x)^-1+-3267//16807*log(1+-2x)+-101//6174*(2+3x)^-2+1//1323*(2+3x)^-3+3267//16807*log(2+3x))
@test integrate((1+-2x)^-2*(2+3x)^-5*(3+5x)^3, x) == :(-3267*(33614+50421x)^-1+2662*(16807+-33614x)^-1+-14520//117649*log(1+-2x)+-101//9261*(2+3x)^-3+1//1764*(2+3x)^-4+363//4802*(2+3x)^-2+14520//117649*log(2+3x))
@test integrate((1+-2x)^-2*(2+3x)^-6*(3+5x)^3, x) == :(-14520*(235298+352947x)^-1+5324*(117649+-235298x)^-1+-45012//823543*log(1+-2x)+-3267//33614*(2+3x)^-2+-101//12348*(2+3x)^-4+1//2205*(2+3x)^-5+121//2401*(2+3x)^-3+45012//823543*log(2+3x))
@test integrate((1+-2x)^-2*(2+3x)^-7*(3+5x)^3, x) == :(-45012*(1647086+2470629x)^-1+10648*(823543+-1647086x)^-1+-17424//823543*log(1+-2x)+-7260//117649*(2+3x)^-2+-1089//16807*(2+3x)^-3+-101//15435*(2+3x)^-5+1//2646*(2+3x)^-6+363//9604*(2+3x)^-4+17424//823543*log(2+3x))
@test integrate((1+-2x)^-2*(2+3x)^-8*(3+5x)^3, x) == :(-17424*(1647086+2470629x)^-1+21296*(5764801+-11529602x)^-1+-307824//40353607*log(1+-2x)+-22506//823543*(2+3x)^-2+-4840//117649*(2+3x)^-3+-3267//67228*(2+3x)^-4+-101//18522*(2+3x)^-6+1//3087*(2+3x)^-7+363//12005*(2+3x)^-5+307824//40353607*log(2+3x))
@test integrate((1+-2x)^-2*(2+3x)^8*(3+5x)^-1, x) == :(5764801*(2816+-5632x)^-1+1//9453125*log(3+5x)+2187//40*x^6+94041//250*x^5+9899091//8000*x^4+26773659//10000*x^3+188591347//30976*log(1+-2x)+1839811401//400000*x^2+2041906293//250000*x)
@test integrate((1+-2x)^-2*(2+3x)^7*(3+5x)^-1, x) == :(823543*(1408+-2816x)^-1+1//1890625*log(3+5x)+2187//100*x^5+13851//100*x^4+853659//2000*x^3+5764801//3872*log(1+-2x)+18237069//20000*x^2+370109547//200000*x)
@test integrate((1+-2x)^-2*(2+3x)^6*(3+5x)^-1, x) == :(117649*(704+-1408x)^-1+1//378125*log(3+5x)+729//80*x^4+2673//50*x^3+639819//4000*x^2+2739541//7744*log(1+-2x)+3946293//10000*x)
@test integrate((1+-2x)^-2*(2+3x)^5*(3+5x)^-1, x) == :(16807*(352+-704x)^-1+1//75625*log(3+5x)+81//20*x^3+567//25*x^2+152793//2000*x+156065//1936*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^4*(3+5x)^-1, x) == :(2401*(176+-352x)^-1+1//15125*log(3+5x)+81//40*x^2+621//50*x+33271//1936*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^3*(3+5x)^-1, x) == :(343*(88+-176x)^-1+1//3025*log(3+5x)+27//20*x+392//121*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^2*(3+5x)^-1, x) == :(49*(44+-88x)^-1+1//605*log(3+5x)+217//484*log(1+-2x))
@test integrate((1+-2x)^-2*(3+5x)^-1*(2+3x), x) == :(7*(22+-44x)^-1+-1//121*log(1+-2x)+1//121*log(3+5x))
@test integrate((1+-2x)^-2*(3+5x)^-1, x) == :((11+-22x)^-1+-5//121*log(1+-2x)+5//121*log(3+5x))
@test integrate((1+-2x)^-2*(2+3x)^-1*(3+5x)^-1, x) == :(2*(77+-154x)^-1+-136//5929*log(1+-2x)+-9//49*log(2+3x)+25//121*log(3+5x))
@test integrate((1+-2x)^-2*(2+3x)^-2*(3+5x)^-1, x) == :(4*(539+-1078x)^-1+9*(98+147x)^-1+-404//41503*log(1+-2x)+-351//343*log(2+3x)+125//121*log(3+5x))
@test integrate((1+-2x)^-2*(2+3x)^-3*(3+5x)^-1, x) == :(8*(3773+-7546x)^-1+351*(686+1029x)^-1+-12393//2401*log(2+3x)+-1072//290521*log(1+-2x)+9//98*(2+3x)^-2+625//121*log(3+5x))
@test integrate((1+-2x)^-2*(2+3x)^-4*(3+5x)^-1, x) == :(16*(26411+-52822x)^-1+12393*(4802+7203x)^-1+-434043//16807*log(2+3x)+-2672//2033647*log(1+-2x)+3//49*(2+3x)^-3+351//686*(2+3x)^-2+3125//121*log(3+5x))
@test integrate((1+-2x)^-2*(2+3x)^-5*(3+5x)^-1, x) == :(32*(184877+-369754x)^-1+434043*(33614+50421x)^-1+-15192225//117649*log(2+3x)+-6400//14235529*log(1+-2x)+9//196*(2+3x)^-4+117//343*(2+3x)^-3+12393//4802*(2+3x)^-2+15625//121*log(3+5x))
@test integrate((1+-2x)^-2*(2+3x)^-6*(3+5x)^-1, x) == :(64*(1294139+-2588278x)^-1+15192225*(235298+352947x)^-1+-531729603//823543*log(2+3x)+-14912//99648703*log(1+-2x)+9//245*(2+3x)^-5+351//1372*(2+3x)^-4+4131//2401*(2+3x)^-3+78125//121*log(3+5x)+434043//33614*(2+3x)^-2)
@test integrate((1+-2x)^-2*(2+3x)^8*(3+5x)^-2, x) == :(-1*(28359375+47265625x)^-1+5764801*(15488+-30976x)^-1+268//103984375*log(3+5x)+6561//500*x^5+168399//2000*x^4+2626101//10000*x^3+14171517//25000*x^2+79883671//85184*log(1+-2x)+231915717//200000*x)
@test integrate((1+-2x)^-2*(2+3x)^7*(3+5x)^-2, x) == :(-1*(5671875+9453125x)^-1+823543*(7744+-15488x)^-1+47//4159375*log(3+5x)+2187//400*x^4+16281//500*x^3+1974861//20000*x^2+6156243//25000*x+18941489//85184*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^6*(3+5x)^-2, x) == :(-1*(1134375+1890625x)^-1+117649*(3872+-7744x)^-1+202//4159375*log(3+5x)+243//100*x^3+13851//1000*x^2+67228//1331*log(1+-2x)+473607//10000*x)
@test integrate((1+-2x)^-2*(2+3x)^5*(3+5x)^-2, x) == :(-1*(226875+378125x)^-1+16807*(1936+-3872x)^-1+169//831875*log(3+5x)+243//200*x^2+3807//500*x+228095//21296*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^4*(3+5x)^-2, x) == :(-1*(45375+75625x)^-1+2401*(968+-1936x)^-1+81//100*x+136//166375*log(3+5x)+10633//5324*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^3*(3+5x)^-2, x) == :(-1*(9075+15125x)^-1+343*(484+-968x)^-1+103//33275*log(3+5x)+1421//5324*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^2*(3+5x)^-2, x) == :(-1*(1815+3025x)^-1+49*(242+-484x)^-1+-14//1331*log(1+-2x)+14//1331*log(3+5x))
@test integrate((1+-2x)^-2*(3+5x)^-2*(2+3x), x) == :(-1*(363+605x)^-1+7*(121+-242x)^-1+-37//1331*log(1+-2x)+37//1331*log(3+5x))
@test integrate((1+-2x)^-2*(3+5x)^-2, x) == :(-5*(363+605x)^-1+2*(121+-242x)^-1+-20//1331*log(1+-2x)+20//1331*log(3+5x))
@test integrate((1+-2x)^-2*(2+3x)^-1*(3+5x)^-2, x) == :(-25*(363+605x)^-1+4*(847+-1694x)^-1+-725//1331*log(3+5x)+-412//65219*log(1+-2x)+27//49*log(2+3x))
@test integrate((1+-2x)^-2*(2+3x)^-2*(3+5x)^-2, x) == :(-125*(363+605x)^-1+-27*(98+147x)^-1+8*(5929+-11858x)^-1+-7750//1331*log(3+5x)+-1088//456533*log(1+-2x)+1998//343*log(2+3x))
@test integrate((1+-2x)^-2*(2+3x)^-3*(3+5x)^-2, x) == :(-1998*(686+1029x)^-1+-625*(363+605x)^-1+16*(41503+-83006x)^-1+-59375//1331*log(3+5x)+-2704//3195731*log(1+-2x)+-27//98*(2+3x)^-2+107109//2401*log(2+3x))
@test integrate((1+-2x)^-2*(2+3x)^-4*(3+5x)^-2, x) == :(-107109*(4802+7203x)^-1+-3125*(363+605x)^-1+32*(290521+-581042x)^-1+-400000//1331*log(3+5x)+-6464//22370117*log(1+-2x)+-999//343*(2+3x)^-2+-9//49*(2+3x)^-3+5050944//16807*log(2+3x))
@test integrate((1+-2x)^-2*(2+3x)^-5*(3+5x)^-2, x) == :(-5050944*(33614+50421x)^-1+-15625*(363+605x)^-1+64*(2033647+-4067294x)^-1+-2515625//1331*log(3+5x)+-107109//4802*(2+3x)^-2+-15040//156590819*log(1+-2x)+-666//343*(2+3x)^-3+-27//196*(2+3x)^-4+222359715//117649*log(2+3x))
@test integrate((1+-2x)^-2*(2+3x)^8*(3+5x)^-3, x) == :(-268*(311953125+519921875x)^-1+5764801*(85184+-170368x)^-1+-1//18906250*(3+5x)^-2+6312//228765625*log(3+5x)+6561//2000*x^4+12393//625*x^3+6093711//100000*x^2+7680987//50000*x+130943337//937024*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^7*(3+5x)^-3, x) == :(-47*(12478125+20796875x)^-1+823543*(42592+-85184x)^-1+-1//3781250*(3+5x)^-2+729//500*x^3+4761//45753125*log(3+5x)+21141//2500*x^2+1467477//50000*x+7411887//234256*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^6*(3+5x)^-3, x) == :(-202*(12478125+20796875x)^-1+117649*(21296+-42592x)^-1+-1//756250*(3+5x)^-2+729//1000*x^2+2916//625*x+17139//45753125*log(3+5x)+1563051//234256*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^5*(3+5x)^-3, x) == :(-169*(2495625+4159375x)^-1+16807*(10648+-21296x)^-1+-1//151250*(3+5x)^-2+243//500*x+11562//9150625*log(3+5x)+36015//29282*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^4*(3+5x)^-3, x) == :(-136*(499125+831875x)^-1+2401*(5324+-10648x)^-1+-1//30250*(3+5x)^-2+7074//1830125*log(3+5x)+9261//58564*log(1+-2x))
@test integrate((1+-2x)^-2*(2+3x)^3*(3+5x)^-3, x) == :(-103*(99825+166375x)^-1+343*(2662+-5324x)^-1+-147//14641*log(1+-2x)+-1//6050*(3+5x)^-2+147//14641*log(3+5x))
@test integrate((1+-2x)^-2*(2+3x)^2*(3+5x)^-3, x) == :(-14*(3993+6655x)^-1+49*(1331+-2662x)^-1+-273//14641*log(1+-2x)+-1//1210*(3+5x)^-2+273//14641*log(3+5x))
@test integrate((1+-2x)^-2*(3+5x)^-3*(2+3x), x) == :(-37*(3993+6655x)^-1+14*(1331+-2662x)^-1+-144//14641*log(1+-2x)+-1//242*(3+5x)^-2+144//14641*log(3+5x))
@test integrate((1+-2x)^-2*(3+5x)^-3, x) == :(-20*(3993+6655x)^-1+4*(1331+-2662x)^-1+-60//14641*log(1+-2x)+-5//242*(3+5x)^-2+60//14641*log(3+5x))
@test integrate((1+-2x)^-2*(2+3x)^-1*(3+5x)^-3, x) == :(8*(9317+-18634x)^-1+725*(3993+6655x)^-1+-1104//717409*log(1+-2x)+-81//49*log(2+3x)+-25//242*(3+5x)^-2+24225//14641*log(3+5x))
@test integrate((1+-2x)^-2*(2+3x)^-2*(3+5x)^-3, x) == :(16*(65219+-130438x)^-1+81*(98+147x)^-1+7750*(3993+6655x)^-1+-8829//343*log(2+3x)+-2736//5021863*log(1+-2x)+-125//242*(3+5x)^-2+376875//14641*log(3+5x))
@test integrate((1+-2x)^-2*(2+3x)^-3*(3+5x)^-3, x) == :(32*(456533+-913066x)^-1+8829*(686+1029x)^-1+59375*(3993+6655x)^-1+-630342//2401*log(2+3x)+-6528//35153041*log(1+-2x)+-625//242*(3+5x)^-2+81//98*(2+3x)^-2+3843750//14641*log(3+5x))
@test integrate((1+-2x)^-2*(2+3x)^-4*(3+5x)^-3, x) == :(64*(3195731+-6391462x)^-1+400000*(3993+6655x)^-1+630342*(4802+7203x)^-1+-37214802//16807*log(2+3x)+-15168//246071287*log(1+-2x)+-3125//242*(3+5x)^-2+27//49*(2+3x)^-3+8829//686*(2+3x)^-2+32418750//14641*log(3+5x))
@test integrate((1+-2x)^-3*(2+3x)^8*(3+5x), x) == :(-246239357*(1024+-2048x)^-1+-120864213//256*x+-118841283//512*x^2+-106237047//256*log(1+-2x)+-16042509//128*x^3+-7568235//128*x^4+-213597//10*x^5+-162567//32*x^6+-32805//56*x^7+63412811//2048*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^7*(3+5x), x) == :(-15647317*(256+-512x)^-1+-24960933//256*x+-23647449//256*log(1+-2x)+-10989621//256*x^2+-631611//32*x^3+-235467//32*x^4+-147987//80*x^5+-3645//16*x^6+9058973//1024*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^6*(3+5x), x) == :(-3916031*(256+-512x)^-1+-5078115//256*log(1+-2x)+-2431647//128*x+-461835//64*x^2+-44469//64*x^4+-10611//4*x^3+-729//8*x^5+1294139//512*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^5*(3+5x), x) == :(-60025*(16+-32x)^-1+-519645//128*log(1+-2x)+-109089//32*x+-16821//16*x^2+-4401//16*x^3+-1215//32*x^4+184877//256*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^4*(3+5x), x) == :(-57281*(64+-128x)^-1+-540x+-24843//32*log(1+-2x)+-3861//32*x^2+-135//8*x^3+26411//128*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^3*(3+5x), x) == :(-3283*(16+-32x)^-1+-1107//16*x+-1071//8*log(1+-2x)+-135//16*x^2+3773//64*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^2*(3+5x), x) == :(-707*(16+-32x)^-1+-309//16*log(1+-2x)+-45//8*x+539//32*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)*(3+5x), x) == :(-17*(2+-4x)^-1+-15//8*log(1+-2x)+77//16*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(3+5x), x) == :(1//22*(1+-2x)^-2*(3+5x)^2)
@test integrate((1+-2x)^-3*(2+3x)^-1*(3+5x), x) == :(-1*(49+-98x)^-1+-3//343*log(2+3x)+3//343*log(1+-2x)+11//28*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^-2*(3+5x), x) == :(3*(686+1029x)^-1+31*(343+-686x)^-1+-87//2401*log(1+-2x)+11//98*(1+-2x)^-2+87//2401*log(2+3x))
@test integrate((1+-2x)^-3*(2+3x)^-3*(3+5x), x) == :(-87*(4802+7203x)^-1+128*(2401+-4802x)^-1+-558//16807*log(1+-2x)+3//686*(2+3x)^-2+11//343*(1+-2x)^-2+558//16807*log(2+3x))
@test integrate((1+-2x)^-3*(2+3x)^-4*(3+5x), x) == :(-558*(33614+50421x)^-1+388*(16807+-33614x)^-1+-2280//117649*log(1+-2x)+-87//4802*(2+3x)^-2+1//343*(2+3x)^-3+22//2401*(1+-2x)^-2+2280//117649*log(2+3x))
@test integrate((1+-2x)^-3*(2+3x)^-5*(3+5x), x) == :(-2280*(235298+352947x)^-1+1040*(117649+-235298x)^-1+-7680//823543*log(1+-2x)+-279//16807*(2+3x)^-2+-29//2401*(2+3x)^-3+3//1372*(2+3x)^-4+44//16807*(1+-2x)^-2+7680//823543*log(2+3x))
@test integrate((1+-2x)^-3*(2+3x)^-6*(3+5x), x) == :(-7680*(1647086+2470629x)^-1+2608*(823543+-1647086x)^-1+-3312//823543*log(1+-2x)+-1140//117649*(2+3x)^-2+-186//16807*(2+3x)^-3+-87//9604*(2+3x)^-4+3//1715*(2+3x)^-5+88//117649*(1+-2x)^-2+3312//823543*log(2+3x))
@test integrate((1+-2x)^-3*(2+3x)^7*(3+5x)^2, x) == :(-389535839*(1024+-2048x)^-1+-190742391//512*x^2+-84589631//128*log(1+-2x)+-48280011//64*x+-25895367//128*x^3+-12299769//128*x^4+-2798631//80*x^5+-268515//32*x^6+-54675//56*x^7+99648703//2048*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^6*(3+5x)^2, x) == :(-12386759*(128+-256x)^-1+-39980457//256*x+-18859855//128*log(1+-2x)+-17700255//256*x^2+-1024389//32*x^3+-770067//64*x^4+-48843//16*x^5+-6075//16*x^6+14235529//1024*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^5*(3+5x)^2, x) == :(-6206585*(256+-512x)^-1+-8117095//256*log(1+-2x)+-3907293//128*x+-747297//64*x^2+-73305//64*x^4+-69273//16*x^3+-1215//8*x^5+2033647//512*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^4*(3+5x)^2, x) == :(-381073*(64+-128x)^-1+-832951//128*log(1+-2x)+-176055//32*x+-54783//32*x^2+-7245//16*x^3+-2025//32*x^4+290521//256*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^3*(3+5x)^2, x) == :(-91091*(64+-128x)^-1+-39977//32*log(1+-2x)+-14031//16*x+-6345//32*x^2+-225//8*x^3+41503//128*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^2*(3+5x)^2, x) == :(-1309*(4+-8x)^-1+-3467//16*log(1+-2x)+-1815//16*x+-225//16*x^2+5929//64*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(3+5x)^2*(2+3x), x) == :(-1133*(16+-32x)^-1+-505//16*log(1+-2x)+-75//8*x+847//32*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(3+5x)^2, x) == :(-55*(4+-8x)^-1+-25//8*log(1+-2x)+121//16*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^-1*(3+5x)^2, x) == :(-407*(196+-392x)^-1+-1//343*log(1+-2x)+1//343*log(2+3x)+121//56*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^-2*(3+5x)^2, x) == :(-1*(686+1029x)^-1+-22*(343+-686x)^-1+-64//2401*log(2+3x)+64//2401*log(1+-2x)+121//196*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^-3*(3+5x)^2, x) == :(64*(4802+7203x)^-1+319*(2401+-4802x)^-1+-829//16807*log(1+-2x)+-1//686*(2+3x)^-2+121//686*(1+-2x)^-2+829//16807*log(2+3x))
@test integrate((1+-2x)^-3*(2+3x)^-4*(3+5x)^2, x) == :(-829*(33614+50421x)^-1+1364*(16807+-33614x)^-1+-5750//117649*log(1+-2x)+-1//1029*(2+3x)^-3+32//2401*(2+3x)^-2+121//2401*(1+-2x)^-2+5750//117649*log(2+3x))
@test integrate((1+-2x)^-3*(2+3x)^-5*(3+5x)^2, x) == :(-5750*(235298+352947x)^-1+4180*(117649+-235298x)^-1+-24040//823543*log(1+-2x)+-829//33614*(2+3x)^-2+-1//1372*(2+3x)^-4+64//7203*(2+3x)^-3+242//16807*(1+-2x)^-2+24040//823543*log(2+3x))
@test integrate((1+-2x)^-3*(2+3x)^-6*(3+5x)^2, x) == :(-24040*(1647086+2470629x)^-1+11264*(823543+-1647086x)^-1+-11696//823543*log(1+-2x)+-2875//117649*(2+3x)^-2+-829//50421*(2+3x)^-3+-1//1715*(2+3x)^-5+16//2401*(2+3x)^-4+484//117649*(1+-2x)^-2+11696//823543*log(2+3x))
@test integrate((1+-2x)^-3*(2+3x)^6*(3+5x)^3, x) == :(-616195041*(1024+-2048x)^-1+-308539921//256*x+-306103815//512*x^2+-41793093//128*x^3+-33674025//32*log(1+-2x)+-19986237//128*x^4+-443475//32*x^6+-229149//4*x^5+-91125//56*x^7+156590819//2048*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^5*(3+5x)^3, x) == :(-39220335*(256+-512x)^-1+-64029233//256*x+-60160485//256*log(1+-2x)+-28504029//256*x^2+-1661133//32*x^3+-629505//32*x^4+-80595//16*x^5+-10125//16*x^6+22370117//1024*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^4*(3+5x)^3, x) == :(-9836211*(256+-512x)^-1+-7065*x^3+-12973191//256*log(1+-2x)+-6277415//128*x+-1208973//64*x^2+-120825//64*x^4+-2025//8*x^5+3195731//512*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^3*(3+5x)^3, x) == :(-302379*(32+-64x)^-1+-1334949//128*log(1+-2x)+-284071//32*x+-44595//16*x^2+-11925//16*x^3+-3375//32*x^4+456533//256*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^2*(3+5x)^3, x) == :(-144837*(64+-128x)^-1+-64317//32*log(1+-2x)+-10425//32*x^2+-5695//4*x+-375//8*x^3+65219//128*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(3+5x)^3*(2+3x), x) == :(-8349*(16+-32x)^-1+-2975//16*x+-2805//8*log(1+-2x)+-375//16*x^2+9317//64*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(3+5x)^3, x) == :(-1815*(16+-32x)^-1+-825//16*log(1+-2x)+-125//8*x+1331//32*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^-1*(3+5x)^3, x) == :(-1089*(49+-98x)^-1+-14289//2744*log(1+-2x)+-1//1029*log(2+3x)+1331//112*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^-2*(3+5x)^3, x) == :((2058+3087x)^-1+-4719*(1372+-2744x)^-1+-33//2401*log(1+-2x)+33//2401*log(2+3x)+1331//392*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^-3*(3+5x)^3, x) == :(-363*(2401+-4802x)^-1+-33*(4802+7203x)^-1+-1023//16807*log(2+3x)+1//2058*(2+3x)^-2+1023//16807*log(1+-2x)+1331//1372*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^-4*(3+5x)^3, x) == :(1023*(33614+50421x)^-1+3267*(16807+-33614x)^-1+-7755//117649*log(1+-2x)+-33//4802*(2+3x)^-2+1//3087*(2+3x)^-3+1331//4802*(1+-2x)^-2+7755//117649*log(2+3x))
@test integrate((1+-2x)^-3*(2+3x)^-5*(3+5x)^3, x) == :(-7755*(235298+352947x)^-1+14520*(117649+-235298x)^-1+-59070//823543*log(1+-2x)+-11//2401*(2+3x)^-3+1//4116*(2+3x)^-4+1023//33614*(2+3x)^-2+1331//16807*(1+-2x)^-2+59070//823543*log(2+3x))
@test integrate((1+-2x)^-3*(2+3x)^8*(3+5x)^-1, x) == :(-188591347*(30976+-61952x)^-1+-2941619571//400000*x+-2644396573//340736*log(1+-2x)+-110180817//40000*x^2+-408969//1600*x^4+-124416//125*x^3+-6561//200*x^5+1//20796875*log(3+5x)+5764801//5632*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^7*(3+5x)^-1, x) == :(-5764801*(3872+-7744x)^-1+-269063263//170368*log(1+-2x)+-26161299//20000*x+-792423//2000*x^2+-40581//400*x^3+-2187//160*x^4+1//4159375*log(3+5x)+823543//2816*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^6*(3+5x)^-1, x) == :(-2739541*(7744+-15488x)^-1+-12761315//42592*log(1+-2x)+-102303//500*x+-35721//800*x^2+-243//40*x^3+1//831875*log(3+5x)+117649//1408*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^5*(3+5x)^-1, x) == :(-156065*(1936+-3872x)^-1+-543655//10648*log(1+-2x)+-10287//400*x+-243//80*x^2+1//166375*log(3+5x)+16807//704*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^4*(3+5x)^-1, x) == :(-33271*(1936+-3872x)^-1+-153811//21296*log(1+-2x)+-81//40*x+1//33275*log(3+5x)+2401//352*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^3*(3+5x)^-1, x) == :(-392*(121+-242x)^-1+-7189//10648*log(1+-2x)+1//6655*log(3+5x)+343//176*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^2*(3+5x)^-1, x) == :(-217*(484+-968x)^-1+-1//1331*log(1+-2x)+1//1331*log(3+5x)+49//88*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(3+5x)^-1*(2+3x), x) == :((121+-242x)^-1+-5//1331*log(1+-2x)+5//1331*log(3+5x)+7//44*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(3+5x)^-1, x) == :(5*(121+-242x)^-1+-25//1331*log(1+-2x)+1//22*(1+-2x)^-2+25//1331*log(3+5x))
@test integrate((1+-2x)^-3*(2+3x)^-1*(3+5x)^-1, x) == :(136*(5929+-11858x)^-1+-6938//456533*log(1+-2x)+-27//343*log(2+3x)+1//77*(1+-2x)^-2+125//1331*log(3+5x))
@test integrate((1+-2x)^-3*(2+3x)^-2*(3+5x)^-1, x) == :(27*(686+1029x)^-1+404*(41503+-83006x)^-1+-27208//3195731*log(1+-2x)+-1107//2401*log(2+3x)+2//539*(1+-2x)^-2+625//1331*log(3+5x))
@test integrate((1+-2x)^-3*(2+3x)^-3*(3+5x)^-1, x) == :(1072*(290521+-581042x)^-1+1107*(4802+7203x)^-1+-89792//22370117*log(1+-2x)+-39393//16807*log(2+3x)+4//3773*(1+-2x)^-2+27//686*(2+3x)^-2+3125//1331*log(3+5x))
@test integrate((1+-2x)^-3*(2+3x)^-4*(3+5x)^-1, x) == :(2672*(2033647+-4067294x)^-1+39393*(33614+50421x)^-1+-1380915//117649*log(2+3x)+-267760//156590819*log(1+-2x)+8//26411*(1+-2x)^-2+9//343*(2+3x)^-3+1107//4802*(2+3x)^-2+15625//1331*log(3+5x))
@test integrate((1+-2x)^-3*(2+3x)^8*(3+5x)^-2, x) == :(-1*(62390625+103984375x)^-1+-79883671*(85184+-170368x)^-1+-1845559863//1874048*log(1+-2x)+-81001863//100000*x+-4863159//20000*x^2+-123201//2000*x^3+-6561//800*x^4+54//45753125*log(3+5x)+5764801//30976*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^7*(3+5x)^-2, x) == :(-1*(12478125+20796875x)^-1+-18941489*(85184+-170368x)^-1+-87177909//468512*log(1+-2x)+-1258983//10000*x+-108621//4000*x^2+-729//200*x^3+237//45753125*log(3+5x)+823543//15488*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^6*(3+5x)^-2, x) == :(-1*(2495625+4159375x)^-1+-67228*(1331+-2662x)^-1+-7383075//234256*log(1+-2x)+-31347//2000*x+-729//400*x^2+204//9150625*log(3+5x)+117649//7744*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^5*(3+5x)^-2, x) == :(-1*(499125+831875x)^-1+-228095*(21296+-42592x)^-1+-1034145//234256*log(1+-2x)+-243//200*x+171//1830125*log(3+5x)+16807//3872*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^4*(3+5x)^-2, x) == :(-1*(99825+166375x)^-1+-10633*(5324+-10648x)^-1+-47481//117128*log(1+-2x)+138//366025*log(3+5x)+2401//1936*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^3*(3+5x)^-2, x) == :(-1*(19965+33275x)^-1+-1421*(5324+-10648x)^-1+-21//14641*log(1+-2x)+21//14641*log(3+5x)+343//968*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^2*(3+5x)^-2, x) == :(-1*(3993+6655x)^-1+14*(1331+-2662x)^-1+-72//14641*log(1+-2x)+49//484*(1+-2x)^-2+72//14641*log(3+5x))
@test integrate((1+-2x)^-3*(3+5x)^-2*(2+3x), x) == :(-5*(3993+6655x)^-1+37*(1331+-2662x)^-1+-195//14641*log(1+-2x)+7//242*(1+-2x)^-2+195//14641*log(3+5x))
@test integrate((1+-2x)^-3*(3+5x)^-2, x) == :(-25*(3993+6655x)^-1+20*(1331+-2662x)^-1+-150//14641*log(1+-2x)+1//121*(1+-2x)^-2+150//14641*log(3+5x))
@test integrate((1+-2x)^-3*(2+3x)^-1*(3+5x)^-2, x) == :(-125*(3993+6655x)^-1+412*(65219+-130438x)^-1+-28296//5021863*log(1+-2x)+-3375//14641*log(3+5x)+2//847*(1+-2x)^-2+81//343*log(2+3x))
@test integrate((1+-2x)^-3*(2+3x)^-2*(3+5x)^-2, x) == :(-625*(3993+6655x)^-1+-81*(686+1029x)^-1+1088*(456533+-913066x)^-1+-92496//35153041*log(1+-2x)+-37500//14641*log(3+5x)+4//5929*(1+-2x)^-2+6156//2401*log(2+3x))
@test integrate((1+-2x)^-3*(2+3x)^-3*(3+5x)^-2, x) == :(-6156*(4802+7203x)^-1+-3125*(3993+6655x)^-1+2704*(3195731+-6391462x)^-1+-290625//14641*log(3+5x)+-274224//246071287*log(1+-2x)+-81//686*(2+3x)^-2+8//41503*(1+-2x)^-2+333639//16807*log(2+3x))
@test integrate((1+-2x)^-3*(2+3x)^-4*(3+5x)^-2, x) == :(-333639*(33614+50421x)^-1+-15625*(3993+6655x)^-1+6464*(22370117+-44740234x)^-1+-1968750//14641*log(3+5x)+-761760//1722499009*log(1+-2x)+-3078//2401*(2+3x)^-2+-27//343*(2+3x)^-3+16//290521*(1+-2x)^-2+15820110//117649*log(2+3x))
@test integrate((1+-2x)^-3*(2+3x)^9*(3+5x)^-3, x) == :(-17294403*(29282+-58564x)^-1+-303*(3431484375+5719140625x)^-1+-12657032367//20614528*log(1+-2x)+-50150097//100000*x+-7459857//50000*x^2+-373977//10000*x^3+-19683//4000*x^4+-1//207968750*(3+5x)^-2+8202//2516421875*log(3+5x)+40353607//340736*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^8*(3+5x)^-3, x) == :(-130943337*(937024+-1874048x)^-1+-54*(137259375+228765625x)^-1+-595421589//5153632*log(1+-2x)+-330237//20000*x^2+-242028//3125*x+-2187//1000*x^3+-1//41593750*(3+5x)^-2+1284//100656875*log(3+5x)+5764801//170368*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^7*(3+5x)^-3, x) == :(-7411887*(234256+-468512x)^-1+-237*(137259375+228765625x)^-1+-25059237//1288408*log(1+-2x)+-95499//10000*x+-2187//2000*x^2+-1//8318750*(3+5x)^-2+24279//503284375*log(3+5x)+823543//85184*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^6*(3+5x)^-3, x) == :(-1563051*(234256+-468512x)^-1+-204*(27451875+45753125x)^-1+-6950895//2576816*log(1+-2x)+-729//1000*x+-1//1663750*(3+5x)^-2+17547//100656875*log(3+5x)+117649//42592*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^5*(3+5x)^-3, x) == :(-36015*(29282+-58564x)^-1+-171*(5490375+9150625x)^-1+-313845//1288408*log(1+-2x)+-1//332750*(3+5x)^-2+11904//20131375*log(3+5x)+16807//21296*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^4*(3+5x)^-3, x) == :(-9261*(58564+-117128x)^-1+-138*(1098075+1830125x)^-1+-294//161051*log(1+-2x)+-1//66550*(3+5x)^-2+294//161051*log(3+5x)+2401//10648*(1+-2x)^-2)
@test integrate((1+-2x)^-3*(2+3x)^3*(3+5x)^-3, x) == :(-21*(43923+73205x)^-1+147*(14641+-29282x)^-1+-777//161051*log(1+-2x)+-1//13310*(3+5x)^-2+343//5324*(1+-2x)^-2+777//161051*log(3+5x))
@test integrate((1+-2x)^-3*(2+3x)^2*(3+5x)^-3, x) == :(-72*(43923+73205x)^-1+273*(14641+-29282x)^-1+-1509//161051*log(1+-2x)+-1//2662*(3+5x)^-2+49//2662*(1+-2x)^-2+1509//161051*log(3+5x))
@test integrate((1+-2x)^-3*(3+5x)^-3*(2+3x), x) == :(-195*(43923+73205x)^-1+144*(14641+-29282x)^-1+-1110//161051*log(1+-2x)+-5//2662*(3+5x)^-2+7//1331*(1+-2x)^-2+1110//161051*log(3+5x))
@test integrate((1+-2x)^-3*(3+5x)^-3, x) == :(-150*(43923+73205x)^-1+60*(14641+-29282x)^-1+-600//161051*log(1+-2x)+-25//2662*(3+5x)^-2+2//1331*(1+-2x)^-2+600//161051*log(3+5x))
@test integrate((1+-2x)^-3*(2+3x)^-1*(3+5x)^-3, x) == :(1104*(717409+-1434818x)^-1+3375*(43923+73205x)^-1+-95232//55240493*log(1+-2x)+-243//343*log(2+3x)+-125//2662*(3+5x)^-2+4//9317*(1+-2x)^-2+114375//161051*log(3+5x))
@test integrate((1+-2x)^-3*(2+3x)^-2*(3+5x)^-3, x) == :(243*(686+1029x)^-1+2736*(5021863+-10043726x)^-1+37500*(43923+73205x)^-1+-280752//386683451*log(1+-2x)+-26973//2401*log(2+3x)+-625//2662*(3+5x)^-2+8//65219*(1+-2x)^-2+1809375//161051*log(3+5x))
@test integrate((1+-2x)^-3*(2+3x)^-3*(3+5x)^-3, x) == :(6528*(35153041+-70306082x)^-1+26973*(4802+7203x)^-1+290625*(43923+73205x)^-1+-1944972//16807*log(2+3x)+-776928//2706784157*log(1+-2x)+-3125//2662*(3+5x)^-2+16//456533*(1+-2x)^-2+243//686*(2+3x)^-2+18637500//161051*log(3+5x))
@test integrate((1+-2x)^-3*(2+3x)^-4*(3+5x)^-3, x) == :(15168*(246071287+-492142574x)^-1+1944972*(33614+50421x)^-1+1968750*(43923+73205x)^-1+-115534350//117649*log(2+3x)+-2054400//18947489099*log(1+-2x)+-15625//2662*(3+5x)^-2+32//3195731*(1+-2x)^-2+81//343*(2+3x)^-3+26973//4802*(2+3x)^-2+158156250//161051*log(3+5x))
@test integrate((a+b*x)^3*(c+d*x)^3*(e+f*x)^3, x) == :(1//4*b^-7*(a+b*x)^4*(b*c+-1*a*d)^3*(b*e+-1*a*f)^3+1//7*b^-7*(a+b*x)^7*(b^2*(c^2*f^2+d^2*e^2+8*c*d*e*f)+10*a^2*d^2*f^2+-10*a*b*d*f*(c*f+d*e))*(b*c*f+b*d*e+-2*a*d*f)+1//10*b^-7*d^3*f^3*(a+b*x)^10+(1/2)*b^-7*(a+b*x)^6*(b*c+-1*a*d)*(b*e+-1*a*f)*(b^2*(c^2*f^2+d^2*e^2+3*c*d*e*f)+5*a^2*d^2*f^2+-5*a*b*d*f*(c*f+d*e))+1//3*b^-7*d^2*f^2*(a+b*x)^9*(b*c*f+b*d*e+-2*a*d*f)+3//5*b^-7*(a+b*x)^5*(b*c+-1*a*d)^2*(b*e+-1*a*f)^2*(b*c*f+b*d*e+-2*a*d*f)+3//8*d*f*b^-7*(a+b*x)^8*(b^2*(c^2*f^2+d^2*e^2+3*c*d*e*f)+5*a^2*d^2*f^2+-5*a*b*d*f*(c*f+d*e)))
@test integrate((a+b*x)^2*(c+d*x)^2*(e+f*x)^2, x) == :(1//5*b^-5*(a+b*x)^5*(b^2*(c^2*f^2+d^2*e^2+4*c*d*e*f)+6*a^2*d^2*f^2+-6*a*b*d*f*(c*f+d*e))+1//3*b^-5*(a+b*x)^3*(b*c+-1*a*d)^2*(b*e+-1*a*f)^2+1//7*b^-5*d^2*f^2*(a+b*x)^7+(1/2)*b^-5*(a+b*x)^4*(b*c+-1*a*d)*(b*e+-1*a*f)*(b*c*f+b*d*e+-2*a*d*f)+1//3*d*f*b^-5*(a+b*x)^6*(b*c*f+b*d*e+-2*a*d*f))
@test integrate((a+b*x)*(c+d*x)*(e+f*x), x) == :(x^2*((1/2)*a*c*f+(1/2)*a*d*e+(1/2)*b*c*e)+x^3*(1//3*a*d*f+1//3*b*c*f+1//3*b*d*e)+a*c*e*x+1//4*b*d*f*x^4)
@test integrate((a+b*x)^-1*(c+d*x)^-1*(e+f*x)^-1, x) == :(b*(b*c+-1*a*d)^-1*(b*e+-1*a*f)^-1*log(a+b*x)+f*(b*e+-1*a*f)^-1*(d*e+-1*c*f)^-1*log(e+f*x)+-1*d*(b*c+-1*a*d)^-1*(d*e+-1*c*f)^-1*log(c+d*x))
@test integrate((a+b*x)^-2*(c+d*x)^-2*(e+f*x)^-2, x) == :(-1*b^3*(a+b*x)^-1*(b*c+-1*a*d)^-2*(b*e+-1*a*f)^-2+-1*d^3*(c+d*x)^-1*(b*c+-1*a*d)^-2*(d*e+-1*c*f)^-2+-1*f^3*(e+f*x)^-1*(b*e+-1*a*f)^-2*(d*e+-1*c*f)^-2+-2*b^3*(b*c+-1*a*d)^-3*(b*e+-1*a*f)^-3*(b*c*f+b*d*e+-2*a*d*f)*log(a+b*x)+2*d^3*(b*c+-1*a*d)^-3*(d*e+-1*c*f)^-3*(a*d*f+b*d*e+-2*b*c*f)*log(c+d*x)+2*f^3*(b*e+-1*a*f)^-3*(d*e+-1*c*f)^-3*(-1*a*d*f+-1*b*c*f+2*b*d*e)*log(e+f*x))
@test integrate((a+b*x)^-3*(c+d*x)^-3*(e+f*x)^-3, x) == :((1/2)*d^5*(c+d*x)^-2*(b*c+-1*a*d)^-3*(d*e+-1*c*f)^-3+-1//2*b^5*(a+b*x)^-2*(b*c+-1*a*d)^-3*(b*e+-1*a*f)^-3+-1//2*f^5*(e+f*x)^-2*(b*e+-1*a*f)^-3*(d*e+-1*c*f)^-3+-3*d^5*(b*c+-1*a*d)^-5*(d*e+-1*c*f)^-5*(b^2*(2*d^2*e^2+7*c^2*f^2+-7*c*d*e*f)+2*a^2*d^2*f^2+a*b*d*f*(-7*c*f+3*d*e))*log(c+d*x)+-3*f^5*(e+f*x)^-1*(b*e+-1*a*f)^-4*(d*e+-1*c*f)^-4*(-1*a*d*f+-1*b*c*f+2*b*d*e)+3*b^5*(a+b*x)^-1*(b*c+-1*a*d)^-4*(b*e+-1*a*f)^-4*(b*c*f+b*d*e+-2*a*d*f)+3*b^5*(b*c+-1*a*d)^-5*(b*e+-1*a*f)^-5*(b^2*(2*c^2*f^2+2*d^2*e^2+3*c*d*e*f)+7*a^2*d^2*f^2+-7*a*b*d*f*(c*f+d*e))*log(a+b*x)+3*d^5*(c+d*x)^-1*(b*c+-1*a*d)^-4*(d*e+-1*c*f)^-4*(a*d*f+b*d*e+-2*b*c*f)+3*f^5*(b*e+-1*a*f)^-5*(d*e+-1*c*f)^-5*(b^2*(2*c^2*f^2+7*d^2*e^2+-7*c*d*e*f)+2*a^2*d^2*f^2+-1*a*b*d*f*(-3*c*f+7*d*e))*log(e+f*x))
@test integrate((a+b*x)^-2*(c+d*x)^3//2*(e+f*x)^-1, x) == :(2*f^-1//2*(b*e+-1*a*f)^-2*(d*e+-1*c*f)^3//2*arctan(f^(1/2)*(c+d*x)^(1/2)*(d*e+-1*c*f)^-1//2)+-1*b^-1*(a+b*x)^-1*(c+d*x)^(1/2)*(b*e+-1*a*f)^-1*(b*c+-1*a*d)+-1*b^-3//2*(b*c+-1*a*d)^(1/2)*(b*e+-1*a*f)^-2*(-1*a*d*f+-2*b*c*f+3*b*d*e)*arctanh(b^(1/2)*(c+d*x)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((d+e*x)^7//2*(A+B*x)*(a+b*x), x) == :(-1//11*e^-3*(d+e*x)^11//2*(-2*A*b*e+-2*B*a*e+4*B*b*d)+1//9*e^-3*(d+e*x)^9//2*(B*d+-1*A*e)*(-2*a*e+2*b*d)+2//13*B*b*e^-3*(d+e*x)^13//2)
@test integrate((d+e*x)^5//2*(A+B*x)*(a+b*x), x) == :(-1//9*e^-3*(d+e*x)^9//2*(-2*A*b*e+-2*B*a*e+4*B*b*d)+1//7*e^-3*(d+e*x)^7//2*(B*d+-1*A*e)*(-2*a*e+2*b*d)+2//11*B*b*e^-3*(d+e*x)^11//2)
@test integrate((d+e*x)^3//2*(A+B*x)*(a+b*x), x) == :(-1//7*e^-3*(d+e*x)^7//2*(-2*A*b*e+-2*B*a*e+4*B*b*d)+1//5*e^-3*(d+e*x)^5//2*(B*d+-1*A*e)*(-2*a*e+2*b*d)+2//9*B*b*e^-3*(d+e*x)^9//2)
@test integrate((d+e*x)^(1/2)*(A+B*x)*(a+b*x), x) == :(-1//5*e^-3*(d+e*x)^5//2*(-2*A*b*e+-2*B*a*e+4*B*b*d)+1//3*e^-3*(d+e*x)^3//2*(B*d+-1*A*e)*(-2*a*e+2*b*d)+2//7*B*b*e^-3*(d+e*x)^7//2)
@test integrate((d+e*x)^-1//2*(A+B*x)*(a+b*x), x) == :(-1//3*e^-3*(d+e*x)^3//2*(-2*A*b*e+-2*B*a*e+4*B*b*d)+e^-3*(d+e*x)^(1/2)*(B*d+-1*A*e)*(-2*a*e+2*b*d)+2//5*B*b*e^-3*(d+e*x)^5//2)
@test integrate((d+e*x)^-3//2*(A+B*x)*(a+b*x), x) == :(-1*e^-3*(d+e*x)^(1/2)*(-2*A*b*e+-2*B*a*e+4*B*b*d)+e^-3*(d+e*x)^-1//2*(B*d+-1*A*e)*(-2*b*d+2*a*e)+2//3*B*b*e^-3*(d+e*x)^3//2)
@test integrate((d+e*x)^-5//2*(A+B*x)*(a+b*x), x) == :(e^-3*(d+e*x)^-1//2*(-2*A*b*e+-2*B*a*e+4*B*b*d)+2*B*b*e^-3*(d+e*x)^(1/2)+1//3*e^-3*(d+e*x)^-3//2*(B*d+-1*A*e)*(-2*b*d+2*a*e))
@test integrate((d+e*x)^-7//2*(A+B*x)*(a+b*x), x) == :(1//3*e^-3*(d+e*x)^-3//2*(-2*A*b*e+-2*B*a*e+4*B*b*d)+-2*B*b*e^-3*(d+e*x)^-1//2+1//5*e^-3*(d+e*x)^-5//2*(B*d+-1*A*e)*(-2*b*d+2*a*e))
@test integrate((a+b*x)^2*(d+e*x)^7//2*(A+B*x), x) == :(-2//9*e^-4*(d+e*x)^9//2*(b*d+-1*a*e)^2*(B*d+-1*A*e)+-2//13*b*e^-4*(d+e*x)^13//2*(-1*A*b*e+-2*B*a*e+3*B*b*d)+1//11*e^-4*(d+e*x)^11//2*(-2*a*e+2*b*d)*(-1*B*a*e+-2*A*b*e+3*B*b*d)+2//15*B*b^2*e^-4*(d+e*x)^15//2)
@test integrate((a+b*x)^2*(d+e*x)^5//2*(A+B*x), x) == :(-2//7*e^-4*(d+e*x)^7//2*(b*d+-1*a*e)^2*(B*d+-1*A*e)+-2//11*b*e^-4*(d+e*x)^11//2*(-1*A*b*e+-2*B*a*e+3*B*b*d)+1//9*e^-4*(d+e*x)^9//2*(-2*a*e+2*b*d)*(-1*B*a*e+-2*A*b*e+3*B*b*d)+2//13*B*b^2*e^-4*(d+e*x)^13//2)
@test integrate((a+b*x)^2*(d+e*x)^3//2*(A+B*x), x) == :(-2//5*e^-4*(d+e*x)^5//2*(b*d+-1*a*e)^2*(B*d+-1*A*e)+-2//9*b*e^-4*(d+e*x)^9//2*(-1*A*b*e+-2*B*a*e+3*B*b*d)+1//7*e^-4*(d+e*x)^7//2*(-2*a*e+2*b*d)*(-1*B*a*e+-2*A*b*e+3*B*b*d)+2//11*B*b^2*e^-4*(d+e*x)^11//2)
@test integrate((a+b*x)^2*(d+e*x)^(1/2)*(A+B*x), x) == :(-2//3*e^-4*(d+e*x)^3//2*(b*d+-1*a*e)^2*(B*d+-1*A*e)+-2//7*b*e^-4*(d+e*x)^7//2*(-1*A*b*e+-2*B*a*e+3*B*b*d)+1//5*e^-4*(d+e*x)^5//2*(-2*a*e+2*b*d)*(-1*B*a*e+-2*A*b*e+3*B*b*d)+2//9*B*b^2*e^-4*(d+e*x)^9//2)
@test integrate((a+b*x)^2*(d+e*x)^-1//2*(A+B*x), x) == :(-2*e^-4*(d+e*x)^(1/2)*(b*d+-1*a*e)^2*(B*d+-1*A*e)+-2//5*b*e^-4*(d+e*x)^5//2*(-1*A*b*e+-2*B*a*e+3*B*b*d)+1//3*e^-4*(d+e*x)^3//2*(-2*a*e+2*b*d)*(-1*B*a*e+-2*A*b*e+3*B*b*d)+2//7*B*b^2*e^-4*(d+e*x)^7//2)
@test integrate((a+b*x)^2*(d+e*x)^-3//2*(A+B*x), x) == :(e^-4*(d+e*x)^(1/2)*(-2*a*e+2*b*d)*(-1*B*a*e+-2*A*b*e+3*B*b*d)+2*e^-4*(d+e*x)^-1//2*(b*d+-1*a*e)^2*(B*d+-1*A*e)+-2//3*b*e^-4*(d+e*x)^3//2*(-1*A*b*e+-2*B*a*e+3*B*b*d)+2//5*B*b^2*e^-4*(d+e*x)^5//2)
@test integrate((a+b*x)^2*(d+e*x)^-5//2*(A+B*x), x) == :(-1*e^-4*(d+e*x)^-1//2*(-2*a*e+2*b*d)*(-1*B*a*e+-2*A*b*e+3*B*b*d)+-2*b*e^-4*(d+e*x)^(1/2)*(-1*A*b*e+-2*B*a*e+3*B*b*d)+2//3*B*b^2*e^-4*(d+e*x)^3//2+2//3*e^-4*(d+e*x)^-3//2*(b*d+-1*a*e)^2*(B*d+-1*A*e))
@test integrate((a+b*x)^2*(d+e*x)^-7//2*(A+B*x), x) == :(2*B*b^2*e^-4*(d+e*x)^(1/2)+2*b*e^-4*(d+e*x)^-1//2*(-1*A*b*e+-2*B*a*e+3*B*b*d)+-1//3*e^-4*(d+e*x)^-3//2*(-2*a*e+2*b*d)*(-1*B*a*e+-2*A*b*e+3*B*b*d)+2//5*e^-4*(d+e*x)^-5//2*(b*d+-1*a*e)^2*(B*d+-1*A*e))
@test integrate((a+b*x)^3*(d+e*x)^7//2*(A+B*x), x) == :(-2//11*e^-5*(d+e*x)^11//2*(b*d+-1*a*e)^2*(-1*B*a*e+-3*A*b*e+4*B*b*d)+-2//15*b^2*e^-5*(d+e*x)^15//2*(-1*A*b*e+-3*B*a*e+4*B*b*d)+2//9*e^-5*(d+e*x)^9//2*(b*d+-1*a*e)^3*(B*d+-1*A*e)+2//17*B*b^3*e^-5*(d+e*x)^17//2+6//13*b*e^-5*(d+e*x)^13//2*(b*d+-1*a*e)*(-1*A*b*e+-1*B*a*e+2*B*b*d))
@test integrate((a+b*x)^3*(d+e*x)^5//2*(A+B*x), x) == :(-2//9*e^-5*(d+e*x)^9//2*(b*d+-1*a*e)^2*(-1*B*a*e+-3*A*b*e+4*B*b*d)+-2//13*b^2*e^-5*(d+e*x)^13//2*(-1*A*b*e+-3*B*a*e+4*B*b*d)+2//7*e^-5*(d+e*x)^7//2*(b*d+-1*a*e)^3*(B*d+-1*A*e)+2//15*B*b^3*e^-5*(d+e*x)^15//2+6//11*b*e^-5*(d+e*x)^11//2*(b*d+-1*a*e)*(-1*A*b*e+-1*B*a*e+2*B*b*d))
@test integrate((a+b*x)^3*(d+e*x)^3//2*(A+B*x), x) == :(-2//7*e^-5*(d+e*x)^7//2*(b*d+-1*a*e)^2*(-1*B*a*e+-3*A*b*e+4*B*b*d)+-2//11*b^2*e^-5*(d+e*x)^11//2*(-1*A*b*e+-3*B*a*e+4*B*b*d)+2//5*e^-5*(d+e*x)^5//2*(b*d+-1*a*e)^3*(B*d+-1*A*e)+2//13*B*b^3*e^-5*(d+e*x)^13//2+2//3*b*e^-5*(d+e*x)^9//2*(b*d+-1*a*e)*(-1*A*b*e+-1*B*a*e+2*B*b*d))
@test integrate((a+b*x)^3*(d+e*x)^(1/2)*(A+B*x), x) == :(-2//5*e^-5*(d+e*x)^5//2*(b*d+-1*a*e)^2*(-1*B*a*e+-3*A*b*e+4*B*b*d)+-2//9*b^2*e^-5*(d+e*x)^9//2*(-1*A*b*e+-3*B*a*e+4*B*b*d)+2//3*e^-5*(d+e*x)^3//2*(b*d+-1*a*e)^3*(B*d+-1*A*e)+2//11*B*b^3*e^-5*(d+e*x)^11//2+6//7*b*e^-5*(d+e*x)^7//2*(b*d+-1*a*e)*(-1*A*b*e+-1*B*a*e+2*B*b*d))
@test integrate((a+b*x)^3*(d+e*x)^-1//2*(A+B*x), x) == :(2*e^-5*(d+e*x)^(1/2)*(b*d+-1*a*e)^3*(B*d+-1*A*e)+-2//3*e^-5*(d+e*x)^3//2*(b*d+-1*a*e)^2*(-1*B*a*e+-3*A*b*e+4*B*b*d)+-2//7*b^2*e^-5*(d+e*x)^7//2*(-1*A*b*e+-3*B*a*e+4*B*b*d)+2//9*B*b^3*e^-5*(d+e*x)^9//2+6//5*b*e^-5*(d+e*x)^5//2*(b*d+-1*a*e)*(-1*A*b*e+-1*B*a*e+2*B*b*d))
@test integrate((a+b*x)^3*(d+e*x)^-3//2*(A+B*x), x) == :(-2*e^-5*(d+e*x)^(1/2)*(b*d+-1*a*e)^2*(-1*B*a*e+-3*A*b*e+4*B*b*d)+-2*e^-5*(d+e*x)^-1//2*(b*d+-1*a*e)^3*(B*d+-1*A*e)+-2//5*b^2*e^-5*(d+e*x)^5//2*(-1*A*b*e+-3*B*a*e+4*B*b*d)+2//7*B*b^3*e^-5*(d+e*x)^7//2+2*b*e^-5*(d+e*x)^3//2*(b*d+-1*a*e)*(-1*A*b*e+-1*B*a*e+2*B*b*d))
@test integrate((a+b*x)^3*(d+e*x)^-5//2*(A+B*x), x) == :(2*e^-5*(d+e*x)^-1//2*(b*d+-1*a*e)^2*(-1*B*a*e+-3*A*b*e+4*B*b*d)+-2//3*b^2*e^-5*(d+e*x)^3//2*(-1*A*b*e+-3*B*a*e+4*B*b*d)+-2//3*e^-5*(d+e*x)^-3//2*(b*d+-1*a*e)^3*(B*d+-1*A*e)+2//5*B*b^3*e^-5*(d+e*x)^5//2+6*b*e^-5*(d+e*x)^(1/2)*(b*d+-1*a*e)*(-1*A*b*e+-1*B*a*e+2*B*b*d))
@test integrate((a+b*x)^3*(d+e*x)^-7//2*(A+B*x), x) == :(-2*b^2*e^-5*(d+e*x)^(1/2)*(-1*A*b*e+-3*B*a*e+4*B*b*d)+-2//5*e^-5*(d+e*x)^-5//2*(b*d+-1*a*e)^3*(B*d+-1*A*e)+2//3*B*b^3*e^-5*(d+e*x)^3//2+2//3*e^-5*(d+e*x)^-3//2*(b*d+-1*a*e)^2*(-1*B*a*e+-3*A*b*e+4*B*b*d)+-6*b*e^-5*(d+e*x)^-1//2*(b*d+-1*a*e)*(-1*A*b*e+-1*B*a*e+2*B*b*d))
@test integrate((a+b*x)^-1*(d+e*x)^7//2*(A+B*x), x) == :(1//7*b^-2*(d+e*x)^7//2*(-2*B*a+2*A*b)+b^-5*(d+e*x)^(1/2)*(b*d+-1*a*e)^3*(-2*B*a+2*A*b)+-1*b^-11//2*(b*d+-1*a*e)^7//2*(-2*B*a+2*A*b)*arctanh(b^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1//2)+1//3*b^-4*(d+e*x)^3//2*(b*d+-1*a*e)^2*(-2*B*a+2*A*b)+1//5*b^-3*(d+e*x)^5//2*(b*d+-1*a*e)*(-2*B*a+2*A*b)+2//9*B*b^-1*e^-1*(d+e*x)^9//2)
@test integrate((a+b*x)^-1*(d+e*x)^5//2*(A+B*x), x) == :(1//5*b^-2*(d+e*x)^5//2*(-2*B*a+2*A*b)+b^-4*(d+e*x)^(1/2)*(b*d+-1*a*e)^2*(-2*B*a+2*A*b)+-1*b^-9//2*(b*d+-1*a*e)^5//2*(-2*B*a+2*A*b)*arctanh(b^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1//2)+1//3*b^-3*(d+e*x)^3//2*(b*d+-1*a*e)*(-2*B*a+2*A*b)+2//7*B*b^-1*e^-1*(d+e*x)^7//2)
@test integrate((a+b*x)^-1*(d+e*x)^3//2*(A+B*x), x) == :(1//3*b^-2*(d+e*x)^3//2*(-2*B*a+2*A*b)+b^-3*(d+e*x)^(1/2)*(b*d+-1*a*e)*(-2*B*a+2*A*b)+-1*b^-7//2*(b*d+-1*a*e)^3//2*(-2*B*a+2*A*b)*arctanh(b^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1//2)+2//5*B*b^-1*e^-1*(d+e*x)^5//2)
@test integrate((a+b*x)^-1*(d+e*x)^(1/2)*(A+B*x), x) == :(b^-2*(d+e*x)^(1/2)*(-2*B*a+2*A*b)+-1*b^-5//2*(b*d+-1*a*e)^(1/2)*(-2*B*a+2*A*b)*arctanh(b^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1//2)+2//3*B*b^-1*e^-1*(d+e*x)^3//2)
@test integrate((a+b*x)^-1*(d+e*x)^-1//2*(A+B*x), x) == :(-1*b^-3//2*(b*d+-1*a*e)^-1//2*(-2*B*a+2*A*b)*arctanh(b^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1//2)+2*B*b^-1*e^-1*(d+e*x)^(1/2))
@test integrate((a+b*x)^-1*(d+e*x)^-3//2*(A+B*x), x) == :(e^-1*(d+e*x)^-1//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e)+-1*b^-1//2*(b*d+-1*a*e)^-3//2*(-2*B*a+2*A*b)*arctanh(b^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1//2))
@test integrate((a+b*x)^-1*(d+e*x)^-5//2*(A+B*x), x) == :((d+e*x)^-1//2*(b*d+-1*a*e)^-2*(-2*B*a+2*A*b)+-2*b^(1/2)*(b*d+-1*a*e)^-5//2*(A*b+-1*B*a)*arctanh(b^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1//2)+1//3*e^-1*(d+e*x)^-3//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e))
@test integrate((a+b*x)^-1*(d+e*x)^-7//2*(A+B*x), x) == :(1//3*(d+e*x)^-3//2*(b*d+-1*a*e)^-2*(-2*B*a+2*A*b)+-2*b^3//2*(b*d+-1*a*e)^-7//2*(A*b+-1*B*a)*arctanh(b^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1//2)+2*b*(d+e*x)^-1//2*(b*d+-1*a*e)^-3*(A*b+-1*B*a)+1//5*e^-1*(d+e*x)^-5//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e))
@test integrate((a+b*x)^-2*(d+e*x)^7//2*(A+B*x), x) == :(1//5*b^-3*(d+e*x)^5//2*(-9*B*a*e+2*B*b*d+7*A*b*e)+b^-5*(d+e*x)^(1/2)*(b*d+-1*a*e)^2*(-9*B*a*e+2*B*b*d+7*A*b*e)+-1*b^-11//2*(b*d+-1*a*e)^5//2*(-9*B*a*e+2*B*b*d+7*A*b*e)*arctanh(b^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1//2)+1//3*b^-4*(d+e*x)^3//2*(b*d+-1*a*e)*(-9*B*a*e+2*B*b*d+7*A*b*e)+1//7*b^-2*(d+e*x)^7//2*(b*d+-1*a*e)^-1*(-9*B*a*e+2*B*b*d+7*A*b*e)+-1*b^-1*(a+b*x)^-1*(d+e*x)^9//2*(b*d+-1*a*e)^-1*(A*b+-1*B*a))
@test integrate((a+b*x)^-2*(d+e*x)^5//2*(A+B*x), x) == :(1//3*b^-3*(d+e*x)^3//2*(-7*B*a*e+2*B*b*d+5*A*b*e)+b^-4*(d+e*x)^(1/2)*(b*d+-1*a*e)*(-7*B*a*e+2*B*b*d+5*A*b*e)+-1*b^-9//2*(b*d+-1*a*e)^3//2*(-7*B*a*e+2*B*b*d+5*A*b*e)*arctanh(b^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1//2)+1//5*b^-2*(d+e*x)^5//2*(b*d+-1*a*e)^-1*(-7*B*a*e+2*B*b*d+5*A*b*e)+-1*b^-1*(a+b*x)^-1*(d+e*x)^7//2*(b*d+-1*a*e)^-1*(A*b+-1*B*a))
@test integrate((a+b*x)^-2*(d+e*x)^3//2*(A+B*x), x) == :(b^-3*(d+e*x)^(1/2)*(-5*B*a*e+2*B*b*d+3*A*b*e)+-1*b^-7//2*(b*d+-1*a*e)^(1/2)*(-5*B*a*e+2*B*b*d+3*A*b*e)*arctanh(b^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1//2)+1//3*b^-2*(d+e*x)^3//2*(b*d+-1*a*e)^-1*(-5*B*a*e+2*B*b*d+3*A*b*e)+-1*b^-1*(a+b*x)^-1*(d+e*x)^5//2*(b*d+-1*a*e)^-1*(A*b+-1*B*a))
@test integrate((a+b*x)^-2*(d+e*x)^(1/2)*(A+B*x), x) == :(b^-2*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1*(A*b*e+-3*B*a*e+2*B*b*d)+-1*b^-5//2*(b*d+-1*a*e)^-1//2*(A*b*e+-3*B*a*e+2*B*b*d)*arctanh(b^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1//2)+-1*b^-1*(a+b*x)^-1*(d+e*x)^3//2*(b*d+-1*a*e)^-1*(A*b+-1*B*a))
@test integrate((a+b*x)^-2*(d+e*x)^-1//2*(A+B*x), x) == :(-1*b^-3//2*(b*d+-1*a*e)^-3//2*(-1*A*b*e+-1*B*a*e+2*B*b*d)*arctanh(b^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1//2)+-1*b^-1*(a+b*x)^-1*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1*(A*b+-1*B*a))
@test integrate((a+b*x)^-2*(d+e*x)^-3//2*(A+B*x), x) == :(b^-1*(d+e*x)^-1//2*(b*d+-1*a*e)^-2*(B*a*e+-3*A*b*e+2*B*b*d)+-1*b^-1//2*(b*d+-1*a*e)^-5//2*(B*a*e+-3*A*b*e+2*B*b*d)*arctanh(b^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1//2)+-1*b^-1*(a+b*x)^-1*(d+e*x)^-1//2*(b*d+-1*a*e)^-1*(A*b+-1*B*a))
@test integrate((a+b*x)^-2*(d+e*x)^-5//2*(A+B*x), x) == :((d+e*x)^-1//2*(b*d+-1*a*e)^-3*(-5*A*b*e+2*B*b*d+3*B*a*e)+-1*b^(1/2)*(b*d+-1*a*e)^-7//2*(-5*A*b*e+2*B*b*d+3*B*a*e)*arctanh(b^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1//2)+1//3*b^-1*(d+e*x)^-3//2*(b*d+-1*a*e)^-2*(-5*A*b*e+2*B*b*d+3*B*a*e)+-1*b^-1*(a+b*x)^-1*(d+e*x)^-3//2*(b*d+-1*a*e)^-1*(A*b+-1*B*a))
@test integrate((a+b*x)^-2*(d+e*x)^-7//2*(A+B*x), x) == :(1//3*(d+e*x)^-3//2*(b*d+-1*a*e)^-3*(-7*A*b*e+2*B*b*d+5*B*a*e)+b*(d+e*x)^-1//2*(b*d+-1*a*e)^-4*(-7*A*b*e+2*B*b*d+5*B*a*e)+-1*b^3//2*(b*d+-1*a*e)^-9//2*(-7*A*b*e+2*B*b*d+5*B*a*e)*arctanh(b^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1//2)+1//5*b^-1*(d+e*x)^-5//2*(b*d+-1*a*e)^-2*(-7*A*b*e+2*B*b*d+5*B*a*e)+-1*b^-1*(a+b*x)^-1*(d+e*x)^-5//2*(b*d+-1*a*e)^-1*(A*b+-1*B*a))
@test integrate((a+b*x)^-3*(d+e*x)^7//2*(A+B*x), x) == :(7//12*e*b^-4*(d+e*x)^3//2*(-9*B*a*e+4*B*b*d+5*A*b*e)+-7//4*e*b^-11//2*(b*d+-1*a*e)^3//2*(-9*B*a*e+4*B*b*d+5*A*b*e)*arctanh(b^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1//2)+-1//2*b^-1*(a+b*x)^-2*(d+e*x)^9//2*(b*d+-1*a*e)^-1*(A*b+-1*B*a)+-1//4*b^-2*(a+b*x)^-1*(d+e*x)^7//2*(b*d+-1*a*e)^-1*(-9*B*a*e+4*B*b*d+5*A*b*e)+7//4*e*b^-5*(d+e*x)^(1/2)*(b*d+-1*a*e)*(-9*B*a*e+4*B*b*d+5*A*b*e)+7//20*e*b^-3*(d+e*x)^5//2*(b*d+-1*a*e)^-1*(-9*B*a*e+4*B*b*d+5*A*b*e))
@test integrate((a+b*x)^-3*(d+e*x)^5//2*(A+B*x), x) == :(5//4*e*b^-4*(d+e*x)^(1/2)*(-7*B*a*e+3*A*b*e+4*B*b*d)+-5//4*e*b^-9//2*(b*d+-1*a*e)^(1/2)*(-7*B*a*e+3*A*b*e+4*B*b*d)*arctanh(b^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1//2)+-1//2*b^-1*(a+b*x)^-2*(d+e*x)^7//2*(b*d+-1*a*e)^-1*(A*b+-1*B*a)+-1//4*b^-2*(a+b*x)^-1*(d+e*x)^5//2*(b*d+-1*a*e)^-1*(-7*B*a*e+3*A*b*e+4*B*b*d)+5//12*e*b^-3*(d+e*x)^3//2*(b*d+-1*a*e)^-1*(-7*B*a*e+3*A*b*e+4*B*b*d))
@test integrate((a+b*x)^-3*(d+e*x)^3//2*(A+B*x), x) == :(-3//4*e*b^-7//2*(b*d+-1*a*e)^-1//2*(A*b*e+-5*B*a*e+4*B*b*d)*arctanh(b^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1//2)+-1//2*b^-1*(a+b*x)^-2*(d+e*x)^5//2*(b*d+-1*a*e)^-1*(A*b+-1*B*a)+-1//4*b^-2*(a+b*x)^-1*(d+e*x)^3//2*(b*d+-1*a*e)^-1*(A*b*e+-5*B*a*e+4*B*b*d)+3//4*e*b^-3*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1*(A*b*e+-5*B*a*e+4*B*b*d))
@test integrate((a+b*x)^-3*(d+e*x)^(1/2)*(A+B*x), x) == :(-1//2*b^-1*(a+b*x)^-2*(d+e*x)^3//2*(b*d+-1*a*e)^-1*(A*b+-1*B*a)+-1//4*e*b^-5//2*(b*d+-1*a*e)^-3//2*(-1*A*b*e+-3*B*a*e+4*B*b*d)*arctanh(b^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1//2)+-1//4*b^-2*(a+b*x)^-1*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1*(-1*A*b*e+-3*B*a*e+4*B*b*d))
@test integrate((a+b*x)^-3*(d+e*x)^-1//2*(A+B*x), x) == :(-1//2*b^-1*(a+b*x)^-2*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1*(A*b+-1*B*a)+-1//4*b^-1*(a+b*x)^-1*(d+e*x)^(1/2)*(b*d+-1*a*e)^-2*(-1*B*a*e+-3*A*b*e+4*B*b*d)+1//4*e*b^-3//2*(b*d+-1*a*e)^-5//2*(-1*B*a*e+-3*A*b*e+4*B*b*d)*arctanh(b^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1//2))
@test integrate((a+b*x)^-3*(d+e*x)^-3//2*(A+B*x), x) == :(-3//4*e*b^-1*(d+e*x)^-1//2*(b*d+-1*a*e)^-3*(B*a*e+-5*A*b*e+4*B*b*d)+-1//2*b^-1*(a+b*x)^-2*(d+e*x)^-1//2*(b*d+-1*a*e)^-1*(A*b+-1*B*a)+-1//4*b^-1*(a+b*x)^-1*(d+e*x)^-1//2*(b*d+-1*a*e)^-2*(B*a*e+-5*A*b*e+4*B*b*d)+3//4*e*b^-1//2*(b*d+-1*a*e)^-7//2*(B*a*e+-5*A*b*e+4*B*b*d)*arctanh(b^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1//2))
@test integrate((a+b*x)^-3*(d+e*x)^-5//2*(A+B*x), x) == :(-5//4*e*(d+e*x)^-1//2*(b*d+-1*a*e)^-4*(-7*A*b*e+3*B*a*e+4*B*b*d)+-5//12*e*b^-1*(d+e*x)^-3//2*(b*d+-1*a*e)^-3*(-7*A*b*e+3*B*a*e+4*B*b*d)+-1//2*b^-1*(a+b*x)^-2*(d+e*x)^-3//2*(b*d+-1*a*e)^-1*(A*b+-1*B*a)+-1//4*b^-1*(a+b*x)^-1*(d+e*x)^-3//2*(b*d+-1*a*e)^-2*(-7*A*b*e+3*B*a*e+4*B*b*d)+5//4*e*b^(1/2)*(b*d+-1*a*e)^-9//2*(-7*A*b*e+3*B*a*e+4*B*b*d)*arctanh(b^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1//2))
@test integrate((a+b*x)^-3*(d+e*x)^-7//2*(A+B*x), x) == :(-7//12*e*(d+e*x)^-3//2*(b*d+-1*a*e)^-4*(-9*A*b*e+4*B*b*d+5*B*a*e)+-7//4*b*e*(d+e*x)^-1//2*(b*d+-1*a*e)^-5*(-9*A*b*e+4*B*b*d+5*B*a*e)+-7//20*e*b^-1*(d+e*x)^-5//2*(b*d+-1*a*e)^-3*(-9*A*b*e+4*B*b*d+5*B*a*e)+-1//2*b^-1*(a+b*x)^-2*(d+e*x)^-5//2*(b*d+-1*a*e)^-1*(A*b+-1*B*a)+-1//4*b^-1*(a+b*x)^-1*(d+e*x)^-5//2*(b*d+-1*a*e)^-2*(-9*A*b*e+4*B*b*d+5*B*a*e)+7//4*e*b^3//2*(b*d+-1*a*e)^-11//2*(-9*A*b*e+4*B*b*d+5*B*a*e)*arctanh(b^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1//2))
@test integrate((c+d*x)^-1*(e+f*x)^5//2*(a+b*x), x) == :(-1//5*d^-2*(e+f*x)^5//2*(-2*a*d+2*b*c)+d^-9//2*(d*e+-1*c*f)^5//2*(-2*a*d+2*b*c)*arctanh(d^(1/2)*(e+f*x)^(1/2)*(d*e+-1*c*f)^-1//2)+-1*d^-4*(e+f*x)^(1/2)*(d*e+-1*c*f)^2*(-2*a*d+2*b*c)+-1//3*d^-3*(e+f*x)^3//2*(d*e+-1*c*f)*(-2*a*d+2*b*c)+2//7*b*d^-1*f^-1*(e+f*x)^7//2)
@test integrate((c+d*x)^-1*(e+f*x)^3//2*(a+b*x), x) == :(-1//3*d^-2*(e+f*x)^3//2*(-2*a*d+2*b*c)+d^-7//2*(d*e+-1*c*f)^3//2*(-2*a*d+2*b*c)*arctanh(d^(1/2)*(e+f*x)^(1/2)*(d*e+-1*c*f)^-1//2)+-1*d^-3*(e+f*x)^(1/2)*(d*e+-1*c*f)*(-2*a*d+2*b*c)+2//5*b*d^-1*f^-1*(e+f*x)^5//2)
@test integrate((c+d*x)^-1*(e+f*x)^(1/2)*(a+b*x), x) == :(-1*d^-2*(e+f*x)^(1/2)*(-2*a*d+2*b*c)+d^-5//2*(d*e+-1*c*f)^(1/2)*(-2*a*d+2*b*c)*arctanh(d^(1/2)*(e+f*x)^(1/2)*(d*e+-1*c*f)^-1//2)+2//3*b*d^-1*f^-1*(e+f*x)^3//2)
@test integrate((c+d*x)^-1*(e+f*x)^-1//2*(a+b*x), x) == :(d^-3//2*(d*e+-1*c*f)^-1//2*(-2*a*d+2*b*c)*arctanh(d^(1/2)*(e+f*x)^(1/2)*(d*e+-1*c*f)^-1//2)+2*b*d^-1*f^-1*(e+f*x)^(1/2))
@test integrate((c+d*x)^-1*(e+f*x)^-3//2*(a+b*x), x) == :(d^-1//2*(d*e+-1*c*f)^-3//2*(-2*a*d+2*b*c)*arctanh(d^(1/2)*(e+f*x)^(1/2)*(d*e+-1*c*f)^-1//2)+-1*f^-1*(e+f*x)^-1//2*(d*e+-1*c*f)^-1*(-2*a*f+2*b*e))
@test integrate((c+d*x)^-1*(e+f*x)^-5//2*(a+b*x), x) == :(-1*(e+f*x)^-1//2*(d*e+-1*c*f)^-2*(-2*a*d+2*b*c)+2*d^(1/2)*(d*e+-1*c*f)^-5//2*(b*c+-1*a*d)*arctanh(d^(1/2)*(e+f*x)^(1/2)*(d*e+-1*c*f)^-1//2)+-1//3*f^-1*(e+f*x)^-3//2*(d*e+-1*c*f)^-1*(-2*a*f+2*b*e))
@test integrate((c+d*x)^-1*(e+f*x)^-7//2*(a+b*x), x) == :(-1//3*(e+f*x)^-3//2*(d*e+-1*c*f)^-2*(-2*a*d+2*b*c)+-2*d*(e+f*x)^-1//2*(d*e+-1*c*f)^-3*(b*c+-1*a*d)+2*d^3//2*(d*e+-1*c*f)^-7//2*(b*c+-1*a*d)*arctanh(d^(1/2)*(e+f*x)^(1/2)*(d*e+-1*c*f)^-1//2)+-1//5*f^-1*(e+f*x)^-5//2*(d*e+-1*c*f)^-1*(-2*a*f+2*b*e))
@test integrate((c+d*x)^-1*(e+f*x)^-9//2*(a+b*x), x) == :(-1//5*(e+f*x)^-5//2*(d*e+-1*c*f)^-2*(-2*a*d+2*b*c)+-2*d^2*(e+f*x)^-1//2*(d*e+-1*c*f)^-4*(b*c+-1*a*d)+2*d^5//2*(d*e+-1*c*f)^-9//2*(b*c+-1*a*d)*arctanh(d^(1/2)*(e+f*x)^(1/2)*(d*e+-1*c*f)^-1//2)+-2//3*d*(e+f*x)^-3//2*(d*e+-1*c*f)^-3*(b*c+-1*a*d)+-1//7*f^-1*(e+f*x)^-7//2*(d*e+-1*c*f)^-1*(-2*a*f+2*b*e))
@test integrate((a+b*x)^2*(c+d*x)^-1*(e+f*x)^5//2, x) == :(2//5*d^-3*(e+f*x)^5//2*(b*c+-1*a*d)^2+-2*d^-11//2*(b*c+-1*a*d)^2*(d*e+-1*c*f)^5//2*arctanh(d^(1/2)*(e+f*x)^(1/2)*(d*e+-1*c*f)^-1//2)+2*d^-5*(e+f*x)^(1/2)*(b*c+-1*a*d)^2*(d*e+-1*c*f)^2+2//3*d^-4*(e+f*x)^3//2*(b*c+-1*a*d)^2*(d*e+-1*c*f)+2//9*b^2*d^-1*f^-2*(e+f*x)^9//2+-2//7*b*d^-2*f^-2*(e+f*x)^7//2*(b*c*f+b*d*e+-2*a*d*f))
@test integrate((a+b*x)^2*(c+d*x)^-1*(e+f*x)^3//2, x) == :(2//3*d^-3*(e+f*x)^3//2*(b*c+-1*a*d)^2+-2*d^-9//2*(b*c+-1*a*d)^2*(d*e+-1*c*f)^3//2*arctanh(d^(1/2)*(e+f*x)^(1/2)*(d*e+-1*c*f)^-1//2)+2*d^-4*(e+f*x)^(1/2)*(b*c+-1*a*d)^2*(d*e+-1*c*f)+2//7*b^2*d^-1*f^-2*(e+f*x)^7//2+-2//5*b*d^-2*f^-2*(e+f*x)^5//2*(b*c*f+b*d*e+-2*a*d*f))
@test integrate((a+b*x)^2*(c+d*x)^-1*(e+f*x)^(1/2), x) == :(2*d^-3*(e+f*x)^(1/2)*(b*c+-1*a*d)^2+-2*d^-7//2*(b*c+-1*a*d)^2*(d*e+-1*c*f)^(1/2)*arctanh(d^(1/2)*(e+f*x)^(1/2)*(d*e+-1*c*f)^-1//2)+2//5*b^2*d^-1*f^-2*(e+f*x)^5//2+-2//3*b*d^-2*f^-2*(e+f*x)^3//2*(b*c*f+b*d*e+-2*a*d*f))
@test integrate((a+b*x)^2*(c+d*x)^-1*(e+f*x)^-1//2, x) == :(-2*d^-5//2*(b*c+-1*a*d)^2*(d*e+-1*c*f)^-1//2*arctanh(d^(1/2)*(e+f*x)^(1/2)*(d*e+-1*c*f)^-1//2)+2//3*b^2*d^-1*f^-2*(e+f*x)^3//2+-2*b*d^-2*f^-2*(e+f*x)^(1/2)*(b*c*f+b*d*e+-2*a*d*f))
@test integrate((a+b*x)^2*(c+d*x)^-1*(e+f*x)^-3//2, x) == :(-2*d^-3//2*(b*c+-1*a*d)^2*(d*e+-1*c*f)^-3//2*arctanh(d^(1/2)*(e+f*x)^(1/2)*(d*e+-1*c*f)^-1//2)+2*b^2*d^-1*f^-2*(e+f*x)^(1/2)+2*f^-2*(e+f*x)^-1//2*(b*e+-1*a*f)^2*(d*e+-1*c*f)^-1)
@test integrate((a+b*x)^2*(c+d*x)^-1*(e+f*x)^-5//2, x) == :(-2*d^-1//2*(b*c+-1*a*d)^2*(d*e+-1*c*f)^-5//2*arctanh(d^(1/2)*(e+f*x)^(1/2)*(d*e+-1*c*f)^-1//2)+2//3*f^-2*(e+f*x)^-3//2*(b*e+-1*a*f)^2*(d*e+-1*c*f)^-1+-1*f^-2*(e+f*x)^-1//2*(d*e+-1*c*f)^-2*(-2*a*f+2*b*e)*(a*d*f+b*d*e+-2*b*c*f))
@test integrate((a+b*x)^2*(c+d*x)^-1*(e+f*x)^-7//2, x) == :(2*(e+f*x)^-1//2*(b*c+-1*a*d)^2*(d*e+-1*c*f)^-3+-2*d^(1/2)*(b*c+-1*a*d)^2*(d*e+-1*c*f)^-7//2*arctanh(d^(1/2)*(e+f*x)^(1/2)*(d*e+-1*c*f)^-1//2)+2//5*f^-2*(e+f*x)^-5//2*(b*e+-1*a*f)^2*(d*e+-1*c*f)^-1+-1//3*f^-2*(e+f*x)^-3//2*(d*e+-1*c*f)^-2*(-2*a*f+2*b*e)*(a*d*f+b*d*e+-2*b*c*f))
@test integrate((a+b*x)^2*(c+d*x)^-1*(e+f*x)^-9//2, x) == :(2//3*(e+f*x)^-3//2*(b*c+-1*a*d)^2*(d*e+-1*c*f)^-3+-2*d^3//2*(b*c+-1*a*d)^2*(d*e+-1*c*f)^-9//2*arctanh(d^(1/2)*(e+f*x)^(1/2)*(d*e+-1*c*f)^-1//2)+2*d*(e+f*x)^-1//2*(b*c+-1*a*d)^2*(d*e+-1*c*f)^-4+2//7*f^-2*(e+f*x)^-7//2*(b*e+-1*a*f)^2*(d*e+-1*c*f)^-1+-1//5*f^-2*(e+f*x)^-5//2*(d*e+-1*c*f)^-2*(-2*a*f+2*b*e)*(a*d*f+b*d*e+-2*b*c*f))
@test integrate((a+b*x)^3*(c+d*x)^-1*(e+f*x)^5//2, x) == :(-2//5*d^-4*(e+f*x)^5//2*(b*c+-1*a*d)^3+-2*d^-6*(e+f*x)^(1/2)*(b*c+-1*a*d)^3*(d*e+-1*c*f)^2+2*d^-13//2*(b*c+-1*a*d)^3*(d*e+-1*c*f)^5//2*arctanh(d^(1/2)*(e+f*x)^(1/2)*(d*e+-1*c*f)^-1//2)+-2//3*d^-5*(e+f*x)^3//2*(b*c+-1*a*d)^3*(d*e+-1*c*f)+2//11*b^3*d^-1*f^-3*(e+f*x)^11//2+-2//9*b^2*d^-2*f^-3*(e+f*x)^9//2*(b*c*f+-3*a*d*f+2*b*d*e)+2//7*b*d^-3*f^-3*(e+f*x)^7//2*(b^2*(c^2*f^2+d^2*e^2+c*d*e*f)+3*a^2*d^2*f^2+-3*a*b*d*f*(c*f+d*e)))
@test integrate((a+b*x)^3*(c+d*x)^-1*(e+f*x)^3//2, x) == :(-2//3*d^-4*(e+f*x)^3//2*(b*c+-1*a*d)^3+-2*d^-5*(e+f*x)^(1/2)*(b*c+-1*a*d)^3*(d*e+-1*c*f)+2*d^-11//2*(b*c+-1*a*d)^3*(d*e+-1*c*f)^3//2*arctanh(d^(1/2)*(e+f*x)^(1/2)*(d*e+-1*c*f)^-1//2)+2//9*b^3*d^-1*f^-3*(e+f*x)^9//2+-2//7*b^2*d^-2*f^-3*(e+f*x)^7//2*(b*c*f+-3*a*d*f+2*b*d*e)+2//5*b*d^-3*f^-3*(e+f*x)^5//2*(b^2*(c^2*f^2+d^2*e^2+c*d*e*f)+3*a^2*d^2*f^2+-3*a*b*d*f*(c*f+d*e)))
@test integrate((a+b*x)^3*(c+d*x)^-1*(e+f*x)^(1/2), x) == :(-2*d^-4*(e+f*x)^(1/2)*(b*c+-1*a*d)^3+2*d^-9//2*(b*c+-1*a*d)^3*(d*e+-1*c*f)^(1/2)*arctanh(d^(1/2)*(e+f*x)^(1/2)*(d*e+-1*c*f)^-1//2)+2//7*b^3*d^-1*f^-3*(e+f*x)^7//2+-2//5*b^2*d^-2*f^-3*(e+f*x)^5//2*(b*c*f+-3*a*d*f+2*b*d*e)+2//3*b*d^-3*f^-3*(e+f*x)^3//2*(b^2*(c^2*f^2+d^2*e^2+c*d*e*f)+3*a^2*d^2*f^2+-3*a*b*d*f*(c*f+d*e)))
@test integrate((a+b*x)^3*(c+d*x)^-1*(e+f*x)^-1//2, x) == :(2*d^-7//2*(b*c+-1*a*d)^3*(d*e+-1*c*f)^-1//2*arctanh(d^(1/2)*(e+f*x)^(1/2)*(d*e+-1*c*f)^-1//2)+2//5*b^3*d^-1*f^-3*(e+f*x)^5//2+2*b*d^-3*f^-3*(e+f*x)^(1/2)*(b^2*(c^2*f^2+d^2*e^2+c*d*e*f)+3*a^2*d^2*f^2+-3*a*b*d*f*(c*f+d*e))+-2//3*b^2*d^-2*f^-3*(e+f*x)^3//2*(b*c*f+-3*a*d*f+2*b*d*e))
@test integrate((a+b*x)^3*(c+d*x)^-1*(e+f*x)^-5//2, x) == :(2*b^3*d^-1*f^-3*(e+f*x)^(1/2)+2*d^-3//2*(b*c+-1*a*d)^3*(d*e+-1*c*f)^-5//2*arctanh(d^(1/2)*(e+f*x)^(1/2)*(d*e+-1*c*f)^-1//2)+-2//3*f^-3*(e+f*x)^-3//2*(b*e+-1*a*f)^3*(d*e+-1*c*f)^-1+2*f^-3*(e+f*x)^-1//2*(b*e+-1*a*f)^2*(d*e+-1*c*f)^-2*(a*d*f+-3*b*c*f+2*b*d*e))
@test integrate((a+b*x)^3*(c+d*x)^-1*(e+f*x)^-7//2, x) == :(2*d^-1//2*(b*c+-1*a*d)^3*(d*e+-1*c*f)^-7//2*arctanh(d^(1/2)*(e+f*x)^(1/2)*(d*e+-1*c*f)^-1//2)+-2//5*f^-3*(e+f*x)^-5//2*(b*e+-1*a*f)^3*(d*e+-1*c*f)^-1+-1*f^-3*(e+f*x)^-1//2*(d*e+-1*c*f)^-3*(-2*a*f+2*b*e)*(b^2*(d^2*e^2+3*c^2*f^2+-3*c*d*e*f)+a^2*d^2*f^2+a*b*d*f*(d*e+-3*c*f))+2//3*f^-3*(e+f*x)^-3//2*(b*e+-1*a*f)^2*(d*e+-1*c*f)^-2*(a*d*f+-3*b*c*f+2*b*d*e))
@test integrate((a+b*x)^3*(c+d*x)^-1*(e+f*x)^-9//2, x) == :(-2*(e+f*x)^-1//2*(b*c+-1*a*d)^3*(d*e+-1*c*f)^-4+2*d^(1/2)*(b*c+-1*a*d)^3*(d*e+-1*c*f)^-9//2*arctanh(d^(1/2)*(e+f*x)^(1/2)*(d*e+-1*c*f)^-1//2)+-2//7*f^-3*(e+f*x)^-7//2*(b*e+-1*a*f)^3*(d*e+-1*c*f)^-1+-1//3*f^-3*(e+f*x)^-3//2*(d*e+-1*c*f)^-3*(-2*a*f+2*b*e)*(b^2*(d^2*e^2+3*c^2*f^2+-3*c*d*e*f)+a^2*d^2*f^2+a*b*d*f*(d*e+-3*c*f))+2//5*f^-3*(e+f*x)^-5//2*(b*e+-1*a*f)^2*(d*e+-1*c*f)^-2*(a*d*f+-3*b*c*f+2*b*d*e))
@test integrate((1+-2x)^(1/2)*(2+3x)^6*(3+5x), x) == :(-1580985//1408*(1+-2x)^11//2+-1294139//384*(1+-2x)^3//2+-725445//128*(1+-2x)^7//2+-19683//640*(1+-2x)^15//2+3645//2176*(1+-2x)^17//2+406455//128*(1+-2x)^9//2+409941//1664*(1+-2x)^13//2+3916031//640*(1+-2x)^5//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^5*(3+5x), x) == :(-184877//192*(1+-2x)^3//2+-97335//704*(1+-2x)^11//2+-74235//64*(1+-2x)^7//2+-81//64*(1+-2x)^15//2+81//4*(1+-2x)^13//2+4165//8*(1+-2x)^9//2+12005//8*(1+-2x)^5//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^4*(3+5x), x) == :(-26411//96*(1+-2x)^3//2+-4671//352*(1+-2x)^11//2+-3549//16*(1+-2x)^7//2+405//416*(1+-2x)^13//2+1197//16*(1+-2x)^9//2+57281//160*(1+-2x)^5//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^3*(3+5x), x) == :(-3773//48*(1+-2x)^3//2+-153//4*(1+-2x)^7//2+-135//176*(1+-2x)^11//2+69//8*(1+-2x)^9//2+3283//40*(1+-2x)^5//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^2*(3+5x), x) == :(-539//24*(1+-2x)^3//2+-309//56*(1+-2x)^7//2+5//8*(1+-2x)^9//2+707//40*(1+-2x)^5//2)
@test integrate((1+-2x)^(1/2)*(2+3x)*(3+5x), x) == :(-77//12*(1+-2x)^3//2+-15//28*(1+-2x)^7//2+17//5*(1+-2x)^5//2)
@test integrate((1+-2x)^(1/2)*(3+5x), x) == :((1/2)*(1+-2x)^5//2+-11//6*(1+-2x)^3//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-1*(3+5x), x) == :(-5//9*(1+-2x)^3//2+-2//9*(1+-2x)^(1/2)+2//27*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^-2*(3+5x), x) == :(8//7*(1+-2x)^(1/2)+(1+-2x)^3//2*(42+63x)^-1+-8//21*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^-3*(3+5x), x) == :(-23*(1+-2x)^(1/2)*(84+126x)^-1+1//42*(1+-2x)^3//2*(2+3x)^-2+23//441*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^-4*(3+5x), x) == :(17*(1+-2x)^(1/2)*(882+1323x)^-1+-17//63*(1+-2x)^(1/2)*(2+3x)^-2+1//63*(1+-2x)^3//2*(2+3x)^-3+34//9261*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^-5*(3+5x), x) == :(15*(1+-2x)^(1/2)*(5488+8232x)^-1+-5//28*(1+-2x)^(1/2)*(2+3x)^-3+1//84*(1+-2x)^3//2*(2+3x)^-4+5//392*(1+-2x)^(1/2)*(2+3x)^-2+5//9604*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^-6*(3+5x), x) == :((1+-2x)^(1/2)*(2058+3087x)^-1+-2//15*(1+-2x)^(1/2)*(2+3x)^-4+1//105*(1+-2x)^3//2*(2+3x)^-5+1//441*(1+-2x)^(1/2)*(2+3x)^-2+2//315*(1+-2x)^(1/2)*(2+3x)^-3+2//21609*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^4*(3+5x)^2, x) == :(-290521//192*(1+-2x)^3//2+-159111//704*(1+-2x)^11//2+-118993//64*(1+-2x)^7//2+-135//64*(1+-2x)^15//2+13905//416*(1+-2x)^13//2+40453//48*(1+-2x)^9//2+381073//160*(1+-2x)^5//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^3*(3+5x)^2, x) == :(-41503//96*(1+-2x)^3//2+-7695//352*(1+-2x)^11//2+-5711//16*(1+-2x)^7//2+675//416*(1+-2x)^13//2+1949//16*(1+-2x)^9//2+91091//160*(1+-2x)^5//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^2*(3+5x)^2, x) == :(-5929//48*(1+-2x)^3//2+-3467//56*(1+-2x)^7//2+-225//176*(1+-2x)^11//2+85//6*(1+-2x)^9//2+1309//10*(1+-2x)^5//2)
@test integrate((1+-2x)^(1/2)*(3+5x)^2*(2+3x), x) == :(-847//24*(1+-2x)^3//2+-505//56*(1+-2x)^7//2+25//24*(1+-2x)^9//2+1133//40*(1+-2x)^5//2)
@test integrate((1+-2x)^(1/2)*(3+5x)^2, x) == :(-121//12*(1+-2x)^3//2+-25//28*(1+-2x)^7//2+11//2*(1+-2x)^5//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-1*(3+5x)^2, x) == :(-155//54*(1+-2x)^3//2+2//27*(1+-2x)^(1/2)+5//6*(1+-2x)^5//2+-2//81*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^2, x) == :(-142//189*(1+-2x)^(1/2)+-25//27*(1+-2x)^3//2+-1*(1+-2x)^3//2*(126+189x)^-1+142//567*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^2, x) == :(863//441*(1+-2x)^(1/2)+139*(1+-2x)^3//2*(1764+2646x)^-1+-863//1323*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-1//126*(1+-2x)^3//2*(2+3x)^-2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^2, x) == :(-2381*(1+-2x)^(1/2)*(5292+7938x)^-1+-1//189*(1+-2x)^3//2*(2+3x)^-3+23//294*(1+-2x)^3//2*(2+3x)^-2+2381//27783*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^-5*(3+5x)^2, x) == :(4625*(1+-2x)^(1/2)*(148176+222264x)^-1+-4625//10584*(1+-2x)^(1/2)*(2+3x)^-2+-1//252*(1+-2x)^3//2*(2+3x)^-4+275//5292*(1+-2x)^3//2*(2+3x)^-3+4625//777924*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^-6*(3+5x)^2, x) == :(31*(1+-2x)^(1/2)*(7056+10584x)^-1+-31//108*(1+-2x)^(1/2)*(2+3x)^-3+-1//315*(1+-2x)^3//2*(2+3x)^-5+7//180*(1+-2x)^3//2*(2+3x)^-4+31//1512*(1+-2x)^(1/2)*(2+3x)^-2+31//37044*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^-7*(3+5x)^2, x) == :(1613*(1+-2x)^(1/2)*(2074464+3111696x)^-1+-1613//7560*(1+-2x)^(1/2)*(2+3x)^-4+-1//378*(1+-2x)^3//2*(2+3x)^-6+137//4410*(1+-2x)^3//2*(2+3x)^-5+1613//158760*(1+-2x)^(1/2)*(2+3x)^-3+1613//444528*(1+-2x)^(1/2)*(2+3x)^-2+1613//10890936*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^4*(3+5x)^3, x) == :(-4177401//1408*(1+-2x)^11//2+-3195731//384*(1+-2x)^3//2+-1853313//128*(1+-2x)^7//2+-10755//128*(1+-2x)^15//2+10125//2176*(1+-2x)^17//2+1101465//1664*(1+-2x)^13//2+9504551//1152*(1+-2x)^9//2+9836211//640*(1+-2x)^5//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^3*(3+5x)^3, x) == :(-456533//192*(1+-2x)^3//2+-260055//704*(1+-2x)^11//2+-190707//64*(1+-2x)^7//2+-225//64*(1+-2x)^15//2+11475//208*(1+-2x)^13//2+98209//72*(1+-2x)^9//2+302379//80*(1+-2x)^5//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^2*(3+5x)^3, x) == :(-65219//96*(1+-2x)^3//2+-64317//112*(1+-2x)^7//2+-12675//352*(1+-2x)^11//2+1125//416*(1+-2x)^13//2+28555//144*(1+-2x)^9//2+144837//160*(1+-2x)^5//2)
@test integrate((1+-2x)^(1/2)*(3+5x)^3*(2+3x), x) == :(-9317//48*(1+-2x)^3//2+-2805//28*(1+-2x)^7//2+-375//176*(1+-2x)^11//2+1675//72*(1+-2x)^9//2+8349//40*(1+-2x)^5//2)
@test integrate((1+-2x)^(1/2)*(3+5x)^3, x) == :(-1331//24*(1+-2x)^3//2+-825//56*(1+-2x)^7//2+125//72*(1+-2x)^9//2+363//8*(1+-2x)^5//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-1*(3+5x)^3, x) == :(-5135//324*(1+-2x)^3//2+-125//84*(1+-2x)^7//2+-2//81*(1+-2x)^(1/2)+80//9*(1+-2x)^5//2+2//243*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3, x) == :(-212//1701*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-2//81*(1+-2x)^(1/2)*(211+170x)+7//9*(1+-2x)^(1/2)*(3+5x)^2+-1*(1+-2x)^(1/2)*(3+5x)^3*(6+9x)^-1)
@test integrate((1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^3, x) == :(5//1134*(1+-2x)^(1/2)*(323+2815x)+7559//11907*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-53*(1+-2x)^(1/2)*(3+5x)^2*(126+189x)^-1+-1//6*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3)
@test integrate((1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^3, x) == :(-92996//83349*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+2*(1+-2x)^(1/2)*(7938+11907x)^-1*(18016+26075x)+-53//189*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^2+-1//9*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^3)
@test integrate((1+-2x)^(1/2)*(2+3x)^-5*(3+5x)^3, x) == :(328715//2333772*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-53//378*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^2+-5//222264*(1+-2x)^(1/2)*(2+3x)^-2*(70429+110981x)+-1//12*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^3)
@test integrate((1+-2x)^(1/2)*(2+3x)^-6*(3+5x)^3, x) == :(11237*(1+-2x)^(1/2)*(222264+333396x)^-1+11237//1166886*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-53//630*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^2+-1//15*(1+-2x)^(1/2)*(2+3x)^-5*(3+5x)^3+-1//79380*(1+-2x)^(1/2)*(2+3x)^-3*(37224+59665x))
@test integrate((1+-2x)^(1/2)*(2+3x)^-7*(3+5x)^3, x) == :(43957*(1+-2x)^(1/2)*(6223392+9335088x)^-1+43957//1333584*(1+-2x)^(1/2)*(2+3x)^-2+43957//32672808*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-53//945*(1+-2x)^(1/2)*(2+3x)^-5*(3+5x)^2+-1//18*(1+-2x)^(1/2)*(2+3x)^-6*(3+5x)^3+-1//476280*(1+-2x)^(1/2)*(2+3x)^-4*(98995+160029x))
@test integrate((1+-2x)^(1/2)*(2+3x)^-8*(3+5x)^3, x) == :(23717*(1+-2x)^(1/2)*(19059138+28588707x)^-1+23717//4084101*(1+-2x)^(1/2)*(2+3x)^-2+47434//2917215*(1+-2x)^(1/2)*(2+3x)^-3+47434//200120949*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-53//1323*(1+-2x)^(1/2)*(2+3x)^-6*(3+5x)^2+-2//972405*(1+-2x)^(1/2)*(2+3x)^-5*(54227+88099x)+-1//21*(1+-2x)^(1/2)*(2+3x)^-7*(3+5x)^3)
@test integrate((1+-2x)^(1/2)*(2+3x)^4*(3+5x)^-1, x) == :(-45473//5000*(1+-2x)^3//2+-2889//1400*(1+-2x)^7//2+2//3125*(1+-2x)^(1/2)+9//40*(1+-2x)^9//2+34371//5000*(1+-2x)^5//2+-2//15625*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^3*(3+5x)^-1, x) == :(-1299//500*(1+-2x)^3//2+-27//140*(1+-2x)^7//2+2//625*(1+-2x)^(1/2)+162//125*(1+-2x)^5//2+-2//3125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^2*(3+5x)^-1, x) == :(-37//50*(1+-2x)^3//2+2//125*(1+-2x)^(1/2)+9//50*(1+-2x)^5//2+-2//625*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(3+5x)^-1*(2+3x), x) == :(-1//5*(1+-2x)^3//2+2//25*(1+-2x)^(1/2)+-2//125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(3+5x)^-1, x) == :(2//5*(1+-2x)^(1/2)+-2//25*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^-1*(3+5x)^-1, x) == :(-2//5*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+2//3*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-1, x) == :((1+-2x)^(1/2)*(2+3x)^-1+-2*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+68//21*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^-1, x) == :((1/2)*(1+-2x)^(1/2)*(2+3x)^-2+-10*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+69*(1+-2x)^(1/2)*(28+42x)^-1+793//49*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^-1, x) == :(-50*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+1207*(1+-2x)^(1/2)*(98+147x)^-1+1//3*(1+-2x)^(1/2)*(2+3x)^-3+52//21*(1+-2x)^(1/2)*(2+3x)^-2+83264//1029*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^-5*(3+5x)^-1, x) == :(-250*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+337955*(1+-2x)^(1/2)*(5488+8232x)^-1+1//4*(1+-2x)^(1/2)*(2+3x)^-4+139//84*(1+-2x)^(1/2)*(2+3x)^-3+14555//1176*(1+-2x)^(1/2)*(2+3x)^-2+11656955//28812*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^5*(3+5x)^-2, x) == :(-328//859375*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-172//3125*(1+-2x)^(1/2)*(2+3x)^2+-4//15625*(1+-2x)^(1/2)*(10998+3625x)+11//75*(1+-2x)^(1/2)*(2+3x)^4+64//2625*(1+-2x)^(1/2)*(2+3x)^3+-1*(1+-2x)^(1/2)*(2+3x)^5*(15+25x)^-1)
@test integrate((1+-2x)^(1/2)*(2+3x)^4*(3+5x)^-2, x) == :(-262//171875*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-3//3125*(1+-2x)^(1/2)*(1256+375x)+12//625*(1+-2x)^(1/2)*(2+3x)^2+27//175*(1+-2x)^(1/2)*(2+3x)^3+-1*(1+-2x)^(1/2)*(2+3x)^4*(15+25x)^-1)
@test integrate((1+-2x)^(1/2)*(2+3x)^3*(3+5x)^-2, x) == :(-294//625*(1+-2x)^(1/2)+-196//34375*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+21//125*(1+-2x)^(1/2)*(2+3x)^2+-1*(1+-2x)^(1/2)*(2+3x)^3*(15+25x)^-1)
@test integrate((1+-2x)^(1/2)*(2+3x)^2*(3+5x)^-2, x) == :(-3//25*(1+-2x)^3//2+26//275*(1+-2x)^(1/2)+-1*(1+-2x)^3//2*(825+1375x)^-1+-26//1375*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(3+5x)^-2*(2+3x), x) == :(64//275*(1+-2x)^(1/2)+-1*(1+-2x)^3//2*(165+275x)^-1+-64//1375*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(3+5x)^-2, x) == :(-1*(1+-2x)^(1/2)*(15+25x)^-1+2//275*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^-1*(3+5x)^-2, x) == :(-1*(1+-2x)^(1/2)*(3+5x)^-1+-2*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+68//55*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-2, x) == :(-10*(1+-2x)^(1/2)*(3+5x)^-1+-138//7*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+134//11*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+(1+-2x)^(1/2)*(2+3x)^-1*(3+5x)^-1)
@test integrate((1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^-2, x) == :(-1045*(1+-2x)^(1/2)*(42+70x)^-1+-7209//49*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+1000//11*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+(1/2)*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-1+52*(1+-2x)^(1/2)*(3+5x)^-1*(14+21x)^-1)
@test integrate((1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^-2, x) == :(-48645*(1+-2x)^(1/2)*(294+490x)^-1+-335579//343*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+6650//11*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+7261*(1+-2x)^(1/2)*(3+5x)^-1*(294+441x)^-1+1//3*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^-1+139//42*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-1)
@test integrate((1+-2x)^(1/2)*(2+3x)^4*(3+5x)^-3, x) == :(-12803//1890625*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-1//68750*(1+-2x)^(1/2)*(14784+-7875x)+1428//6875*(1+-2x)^(1/2)*(2+3x)^2+-131*(1+-2x)^(1/2)*(2+3x)^3*(1650+2750x)^-1+-1//10*(1+-2x)^(1/2)*(2+3x)^4*(3+5x)^-2)
@test integrate((1+-2x)^(1/2)*(2+3x)^3*(3+5x)^-3, x) == :(-1267//75625*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+21//2750*(1+-2x)^(1/2)*(44+75x)+-49*(1+-2x)^(1/2)*(2+3x)^2*(825+1375x)^-1+-1//10*(1+-2x)^(1/2)*(2+3x)^3*(3+5x)^-2)
@test integrate((1+-2x)^(1/2)*(2+3x)^2*(3+5x)^-3, x) == :(409//3025*(1+-2x)^(1/2)+-133*(1+-2x)^3//2*(18150+30250x)^-1+-409//15125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-1//550*(1+-2x)^3//2*(3+5x)^-2)
@test integrate((1+-2x)^(1/2)*(3+5x)^-3*(2+3x), x) == :(-67*(1+-2x)^(1/2)*(1650+2750x)^-1+-1//110*(1+-2x)^3//2*(3+5x)^-2+67//15125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(3+5x)^-3, x) == :((1+-2x)^(1/2)*(330+550x)^-1+-1//10*(1+-2x)^(1/2)*(3+5x)^-2+1//3025*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^-1*(3+5x)^-3, x) == :(6*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+67*(1+-2x)^(1/2)*(66+110x)^-1+-2243//605*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-1//2*(1+-2x)^(1/2)*(3+5x)^-2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-3, x) == :(995*(1+-2x)^(1/2)*(66+110x)^-1+-6665//121*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-15//2*(1+-2x)^(1/2)*(3+5x)^-2+624//7*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+(1+-2x)^(1/2)*(2+3x)^-1*(3+5x)^-2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^-3, x) == :(34655*(1+-2x)^(1/2)*(231+385x)^-1+-66325//121*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-1045//14*(1+-2x)^(1/2)*(3+5x)^-2+43467//49*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+(1/2)*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-2+139*(1+-2x)^(1/2)*(3+5x)^-2*(28+42x)^-1)
@test integrate((1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^-3, x) == :(4031135*(1+-2x)^(1/2)*(3234+5390x)^-1+-551075//121*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-182335//294*(1+-2x)^(1/2)*(3+5x)^-2+2528082//343*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+4042*(1+-2x)^(1/2)*(3+5x)^-2*(98+147x)^-1+1//3*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^-2+29//7*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-2)
@test integrate((1+-2x)^3//2*(2+3x)^6*(3+5x), x) == :(-1580985//1664*(1+-2x)^13//2+-1294139//640*(1+-2x)^5//2+-564235//128*(1+-2x)^9//2+-59049//2176*(1+-2x)^17//2+3645//2432*(1+-2x)^19//2+136647//640*(1+-2x)^15//2+559433//128*(1+-2x)^7//2+3658095//1408*(1+-2x)^11//2)
@test integrate((1+-2x)^3//2*(2+3x)^5*(3+5x), x) == :(-184877//320*(1+-2x)^5//2+-173215//192*(1+-2x)^9//2+-97335//832*(1+-2x)^13//2+-1215//1088*(1+-2x)^17//2+351//20*(1+-2x)^15//2+8575//8*(1+-2x)^7//2+37485//88*(1+-2x)^11//2)
@test integrate((1+-2x)^3//2*(2+3x)^4*(3+5x), x) == :(-26411//160*(1+-2x)^5//2+-8281//48*(1+-2x)^9//2+-4671//416*(1+-2x)^13//2+27//32*(1+-2x)^15//2+8183//32*(1+-2x)^7//2+10773//176*(1+-2x)^11//2)
@test integrate((1+-2x)^3//2*(2+3x)^3*(3+5x), x) == :(-3773//80*(1+-2x)^5//2+-135//208*(1+-2x)^13//2+-119//4*(1+-2x)^9//2+469//8*(1+-2x)^7//2+621//88*(1+-2x)^11//2)
@test integrate((1+-2x)^3//2*(2+3x)^2*(3+5x), x) == :(-539//40*(1+-2x)^5//2+-103//24*(1+-2x)^9//2+45//88*(1+-2x)^11//2+101//8*(1+-2x)^7//2)
@test integrate((1+-2x)^3//2*(2+3x)*(3+5x), x) == :(-77//20*(1+-2x)^5//2+-5//12*(1+-2x)^9//2+17//7*(1+-2x)^7//2)
@test integrate((1+-2x)^3//2*(3+5x), x) == :(-11//10*(1+-2x)^5//2+5//14*(1+-2x)^7//2)
@test integrate((1+-2x)^3//2*(2+3x)^-1*(3+5x), x) == :(-14//27*(1+-2x)^(1/2)+-2//27*(1+-2x)^3//2+-1//3*(1+-2x)^5//2+14//81*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^3//2*(2+3x)^-2*(3+5x), x) == :(76//27*(1+-2x)^(1/2)+76//189*(1+-2x)^3//2+(1+-2x)^5//2*(42+63x)^-1+-76//81*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^3//2*(2+3x)^-3*(3+5x), x) == :(-71//63*(1+-2x)^(1/2)+-71*(1+-2x)^3//2*(252+378x)^-1+1//42*(1+-2x)^5//2*(2+3x)^-2+71//189*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^3//2*(2+3x)^-4*(3+5x), x) == :(52*(1+-2x)^(1/2)*(378+567x)^-1+-104//3969*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-52//189*(1+-2x)^3//2*(2+3x)^-2+1//63*(1+-2x)^5//2*(2+3x)^-3)
@test integrate((1+-2x)^3//2*(2+3x)^-5*(3+5x), x) == :(-137*(1+-2x)^(1/2)*(21168+31752x)^-1+-137//756*(1+-2x)^3//2*(2+3x)^-3+-137//111132*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+1//84*(1+-2x)^5//2*(2+3x)^-4+137//1512*(1+-2x)^(1/2)*(2+3x)^-2)
@test integrate((1+-2x)^3//2*(2+3x)^-6*(3+5x), x) == :(-17*(1+-2x)^(1/2)*(24696+37044x)^-1+-17//126*(1+-2x)^3//2*(2+3x)^-4+-17//5292*(1+-2x)^(1/2)*(2+3x)^-2+-17//129654*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+1//105*(1+-2x)^5//2*(2+3x)^-5+17//378*(1+-2x)^(1/2)*(2+3x)^-3)
@test integrate((1+-2x)^3//2*(2+3x)^4*(3+5x)^2, x) == :(-832951//576*(1+-2x)^9//2+-290521//320*(1+-2x)^5//2+-159111//832*(1+-2x)^13//2+-2025//1088*(1+-2x)^17//2+927//32*(1+-2x)^15//2+54439//32*(1+-2x)^7//2+121359//176*(1+-2x)^11//2)
@test integrate((1+-2x)^3//2*(2+3x)^3*(3+5x)^2, x) == :(-41503//160*(1+-2x)^5//2+-39977//144*(1+-2x)^9//2+-7695//416*(1+-2x)^13//2+45//32*(1+-2x)^15//2+13013//32*(1+-2x)^7//2+17541//176*(1+-2x)^11//2)
@test integrate((1+-2x)^3//2*(2+3x)^2*(3+5x)^2, x) == :(-5929//80*(1+-2x)^5//2+-3467//72*(1+-2x)^9//2+-225//208*(1+-2x)^13//2+187//2*(1+-2x)^7//2+255//22*(1+-2x)^11//2)
@test integrate((1+-2x)^3//2*(3+5x)^2*(2+3x), x) == :(-847//40*(1+-2x)^5//2+-505//72*(1+-2x)^9//2+75//88*(1+-2x)^11//2+1133//56*(1+-2x)^7//2)
@test integrate((1+-2x)^3//2*(3+5x)^2, x) == :(-121//20*(1+-2x)^5//2+-25//36*(1+-2x)^9//2+55//14*(1+-2x)^7//2)
@test integrate((1+-2x)^3//2*(2+3x)^-1*(3+5x)^2, x) == :(-31//18*(1+-2x)^5//2+2//81*(1+-2x)^3//2+14//81*(1+-2x)^(1/2)+25//42*(1+-2x)^7//2+-14//243*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^3//2*(2+3x)^-2*(3+5x)^2, x) == :(-146//81*(1+-2x)^(1/2)+-146//567*(1+-2x)^3//2+-5//9*(1+-2x)^5//2+-1*(1+-2x)^5//2*(126+189x)^-1+146//243*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^3//2*(2+3x)^-3*(3+5x)^2, x) == :(2873//567*(1+-2x)^(1/2)+2873//3969*(1+-2x)^3//2+47*(1+-2x)^5//2*(588+882x)^-1+-2873//1701*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-1//126*(1+-2x)^5//2*(2+3x)^-2)
@test integrate((1+-2x)^3//2*(2+3x)^-4*(3+5x)^2, x) == :(-7559//3969*(1+-2x)^(1/2)+-7559*(1+-2x)^3//2*(15876+23814x)^-1+-1//189*(1+-2x)^5//2*(2+3x)^-3+209//2646*(1+-2x)^5//2*(2+3x)^-2+7559//11907*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^3//2*(2+3x)^-5*(3+5x)^2, x) == :(14423*(1+-2x)^(1/2)*(63504+95256x)^-1+-14423//31752*(1+-2x)^3//2*(2+3x)^-2+-14423//333396*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-1//252*(1+-2x)^5//2*(2+3x)^-4+277//5292*(1+-2x)^5//2*(2+3x)^-3)
@test integrate((1+-2x)^3//2*(2+3x)^-6*(3+5x)^2, x) == :(-4693*(1+-2x)^(1/2)*(444528+666792x)^-1+-4693//15876*(1+-2x)^3//2*(2+3x)^-3+-4693//2333772*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-1//315*(1+-2x)^5//2*(2+3x)^-5+23//588*(1+-2x)^5//2*(2+3x)^-4+4693//31752*(1+-2x)^(1/2)*(2+3x)^-2)
@test integrate((1+-2x)^3//2*(2+3x)^-7*(3+5x)^2, x) == :(-991*(1+-2x)^(1/2)*(889056+1333584x)^-1+-991//4536*(1+-2x)^3//2*(2+3x)^-4+-991//190512*(1+-2x)^(1/2)*(2+3x)^-2+-991//4667544*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-1//378*(1+-2x)^5//2*(2+3x)^-6+59//1890*(1+-2x)^5//2*(2+3x)^-5+991//13608*(1+-2x)^(1/2)*(2+3x)^-3)
@test integrate((1+-2x)^3//2*(2+3x)^4*(3+5x)^3, x) == :(-4324397//384*(1+-2x)^9//2+-4177401//1664*(1+-2x)^13//2+-3195731//640*(1+-2x)^5//2+-161325//2176*(1+-2x)^17//2+10125//2432*(1+-2x)^19//2+73431//128*(1+-2x)^15//2+1405173//128*(1+-2x)^7//2+9504551//1408*(1+-2x)^11//2)
@test integrate((1+-2x)^3//2*(2+3x)^3*(3+5x)^3, x) == :(-456533//320*(1+-2x)^5//2+-444983//192*(1+-2x)^9//2+-260055//832*(1+-2x)^13//2+-3375//1088*(1+-2x)^17//2+765//16*(1+-2x)^15//2+43197//16*(1+-2x)^7//2+98209//88*(1+-2x)^11//2)
@test integrate((1+-2x)^3//2*(2+3x)^2*(3+5x)^3, x) == :(-65219//160*(1+-2x)^5//2+-21439//48*(1+-2x)^9//2+-975//32*(1+-2x)^13//2+75//32*(1+-2x)^15//2+20691//32*(1+-2x)^7//2+28555//176*(1+-2x)^11//2)
@test integrate((1+-2x)^3//2*(3+5x)^3*(2+3x), x) == :(-9317//80*(1+-2x)^5//2+-935//12*(1+-2x)^9//2+-375//208*(1+-2x)^13//2+1675//88*(1+-2x)^11//2+8349//56*(1+-2x)^7//2)
@test integrate((1+-2x)^3//2*(3+5x)^3, x) == :(-1331//40*(1+-2x)^5//2+-275//24*(1+-2x)^9//2+125//88*(1+-2x)^11//2+1815//56*(1+-2x)^7//2)
@test integrate((1+-2x)^3//2*(2+3x)^-1*(3+5x)^3, x) == :(-1027//108*(1+-2x)^5//2+-125//108*(1+-2x)^9//2+-14//243*(1+-2x)^(1/2)+-2//243*(1+-2x)^3//2+400//63*(1+-2x)^7//2+14//729*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^3//2*(2+3x)^-2*(3+5x)^3, x) == :(8//9*(1+-2x)^(1/2)+-10//63*(1+-2x)^3//2*(22+27x)+-8//27*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+5//7*(1+-2x)^3//2*(3+5x)^2+-1*(1+-2x)^3//2*(3+5x)^3*(6+9x)^-1)
@test integrate((1+-2x)^3//2*(2+3x)^-3*(3+5x)^3, x) == :(-31//3*(1+-2x)^(1/2)*(3+5x)^2+1//54*(1+-2x)^(1/2)*(367+1715x)+887//567*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+6*(1+-2x)^(1/2)*(2+3x)^-1*(3+5x)^3+-1//6*(1+-2x)^3//2*(2+3x)^-2*(3+5x)^3)
@test integrate((1+-2x)^3//2*(2+3x)^-4*(3+5x)^3, x) == :(-36038//11907*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-5//567*(1+-2x)^(1/2)*(2323+7265x)+2*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3+251*(1+-2x)^(1/2)*(3+5x)^2*(126+189x)^-1+-1//9*(1+-2x)^3//2*(2+3x)^-3*(3+5x)^3)
@test integrate((1+-2x)^3//2*(2+3x)^-5*(3+5x)^3, x) == :(13243//12348*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^3+-1*(1+-2x)^(1/2)*(2352+3528x)^-1*(18187+26775x)+-1//12*(1+-2x)^3//2*(2+3x)^-4*(3+5x)^3+13//56*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^2)
@test integrate((1+-2x)^3//2*(2+3x)^-6*(3+5x)^3, x) == :(-13892//194481*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-67//315*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^2+-2//9261*(1+-2x)^(1/2)*(2+3x)^-2*(9529+15074x)+-1//15*(1+-2x)^3//2*(2+3x)^-5*(3+5x)^3+3//5*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^3)
@test integrate((1+-2x)^3//2*(2+3x)^-7*(3+5x)^3, x) == :(-15313*(1+-2x)^(1/2)*(889056+1333584x)^-1+-15313//4667544*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-653//2520*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^2+-1//18*(1+-2x)^3//2*(2+3x)^-6*(3+5x)^3+-1//317520*(1+-2x)^(1/2)*(2+3x)^-3*(413424+664915x)+2//5*(1+-2x)^(1/2)*(2+3x)^-5*(3+5x)^3)
@test integrate((1+-2x)^3//2*(2+3x)^-8*(3+5x)^3, x) == :(-4369*(1+-2x)^(1/2)*(2420208+3630312x)^-1+-4369//518616*(1+-2x)^(1/2)*(2+3x)^-2+-4369//12706092*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-173//735*(1+-2x)^(1/2)*(2+3x)^-5*(3+5x)^2+-1//21*(1+-2x)^3//2*(2+3x)^-7*(3+5x)^3+-1//185220*(1+-2x)^(1/2)*(2+3x)^-4*(146585+237807x)+2//7*(1+-2x)^(1/2)*(2+3x)^-6*(3+5x)^3)
@test integrate((1+-2x)^3//2*(2+3x)^6*(3+5x)^-1, x) == :(-167115051//2500000*(1+-2x)^5//2+-665817//10000*(1+-2x)^9//2+-43011//10400*(1+-2x)^13//2+2//234375*(1+-2x)^3//2+22//390625*(1+-2x)^(1/2)+243//800*(1+-2x)^15//2+507627//22000*(1+-2x)^11//2+70752609//700000*(1+-2x)^7//2+-22//1953125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^3//2*(2+3x)^5*(3+5x)^-1, x) == :(-4774713//250000*(1+-2x)^5//2+-5673//500*(1+-2x)^9//2+-243//1040*(1+-2x)^13//2+2//46875*(1+-2x)^3//2+22//78125*(1+-2x)^(1/2)+5751//2200*(1+-2x)^11//2+806121//35000*(1+-2x)^7//2+-22//390625*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^3//2*(2+3x)^4*(3+5x)^-1, x) == :(-136419//25000*(1+-2x)^5//2+-321//200*(1+-2x)^9//2+2//9375*(1+-2x)^3//2+22//15625*(1+-2x)^(1/2)+81//440*(1+-2x)^11//2+34371//7000*(1+-2x)^7//2+-22//78125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^3//2*(2+3x)^3*(3+5x)^-1, x) == :(-3897//2500*(1+-2x)^5//2+-3//20*(1+-2x)^9//2+2//1875*(1+-2x)^3//2+22//3125*(1+-2x)^(1/2)+162//175*(1+-2x)^7//2+-22//15625*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^3//2*(2+3x)^2*(3+5x)^-1, x) == :(-111//250*(1+-2x)^5//2+2//375*(1+-2x)^3//2+9//70*(1+-2x)^7//2+22//625*(1+-2x)^(1/2)+-22//3125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^3//2*(3+5x)^-1*(2+3x), x) == :(-3//25*(1+-2x)^5//2+2//75*(1+-2x)^3//2+22//125*(1+-2x)^(1/2)+-22//625*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^3//2*(3+5x)^-1, x) == :(2//15*(1+-2x)^3//2+22//25*(1+-2x)^(1/2)+-22//125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^3//2*(2+3x)^-1*(3+5x)^-1, x) == :(-4//15*(1+-2x)^(1/2)+-22//25*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+14//9*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^3//2*(2+3x)^-2*(3+5x)^-1, x) == :(7*(1+-2x)^(1/2)*(6+9x)^-1+-22//5*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+64//9*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^3//2*(2+3x)^-3*(3+5x)^-1, x) == :(-22*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+65*(1+-2x)^(1/2)*(12+18x)^-1+7//6*(1+-2x)^(1/2)*(2+3x)^-2+2243//63*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^3//2*(2+3x)^-4*(3+5x)^-1, x) == :(-110*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+1138*(1+-2x)^(1/2)*(42+63x)^-1+7//9*(1+-2x)^(1/2)*(2+3x)^-3+49//9*(1+-2x)^(1/2)*(2+3x)^-2+78506//441*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^3//2*(2+3x)^-5*(3+5x)^-1, x) == :(-550*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+318643*(1+-2x)^(1/2)*(2352+3528x)^-1+7//12*(1+-2x)^(1/2)*(2+3x)^-4+131//36*(1+-2x)^(1/2)*(2+3x)^-3+13723//504*(1+-2x)^(1/2)*(2+3x)^-2+10990843//12348*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^3//2*(2+3x)^-6*(3+5x)^-1, x) == :(-2750*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+2788127*(1+-2x)^(1/2)*(4116+6174x)^-1+7//15*(1+-2x)^(1/2)*(2+3x)^-5+41//15*(1+-2x)^(1/2)*(2+3x)^-4+5732//315*(1+-2x)^(1/2)*(2+3x)^-3+120077//882*(1+-2x)^(1/2)*(2+3x)^-2+96169877//21609*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^3//2*(2+3x)^5*(3+5x)^-2, x) == :(324//78125*(1+-2x)^(1/2)+-4016//48125*(1+-2x)^3//2*(2+3x)^2+-324//390625*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-2//515625*(1+-2x)^3//2*(298462+204777x)+38//4125*(1+-2x)^3//2*(2+3x)^3+39//275*(1+-2x)^3//2*(2+3x)^4+-1*(1+-2x)^3//2*(2+3x)^5*(15+25x)^-1)
@test integrate((1+-2x)^3//2*(2+3x)^4*(3+5x)^-2, x) == :(258//15625*(1+-2x)^(1/2)+-258//78125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-2//875*(1+-2x)^3//2*(2+3x)^2+-1//9375*(1+-2x)^3//2*(5678+3663x)+11//75*(1+-2x)^3//2*(2+3x)^3+-1*(1+-2x)^3//2*(2+3x)^4*(15+25x)^-1)
@test integrate((1+-2x)^3//2*(2+3x)^3*(3+5x)^-2, x) == :(192//3125*(1+-2x)^(1/2)+-192//15625*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-6//625*(1+-2x)^3//2*(29+9x)+27//175*(1+-2x)^3//2*(2+3x)^2+-1*(1+-2x)^3//2*(2+3x)^3*(15+25x)^-1)
@test integrate((1+-2x)^3//2*(2+3x)^2*(3+5x)^-2, x) == :(-9//125*(1+-2x)^5//2+42//1375*(1+-2x)^3//2+126//625*(1+-2x)^(1/2)+-1*(1+-2x)^5//2*(825+1375x)^-1+-126//3125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^3//2*(3+5x)^-2*(2+3x), x) == :(4//55*(1+-2x)^3//2+12//25*(1+-2x)^(1/2)+-1*(1+-2x)^5//2*(165+275x)^-1+-12//125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^3//2*(3+5x)^-2, x) == :(-6//25*(1+-2x)^(1/2)+-1*(1+-2x)^3//2*(15+25x)^-1+6//125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^3//2*(2+3x)^-1*(3+5x)^-2, x) == :(-11*(1+-2x)^(1/2)*(15+25x)^-1+-14//3*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+72//25*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^3//2*(2+3x)^-2*(3+5x)^-2, x) == :(-68*(1+-2x)^(1/2)*(9+15x)^-1+-134//3*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+138//5*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+7*(1+-2x)^(1/2)*(3+5x)^-1*(6+9x)^-1)
@test integrate((1+-2x)^3//2*(2+3x)^-3*(3+5x)^-2, x) == :(-335*(1+-2x)^(1/2)*(6+10x)^-1+204*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-2311//7*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+50*(1+-2x)^(1/2)*(3+5x)^-1*(6+9x)^-1+7//6*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-1)
@test integrate((1+-2x)^3//2*(2+3x)^-4*(3+5x)^-2, x) == :(-46555*(1+-2x)^(1/2)*(126+210x)^-1+1350*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-321161//147*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+6949*(1+-2x)^(1/2)*(3+5x)^-1*(126+189x)^-1+7//9*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^-1+133//18*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-1)
@test integrate((1+-2x)^3//2*(2+3x)^-5*(3+5x)^-2, x) == :(-8110915*(1+-2x)^(1/2)*(3528+5880x)^-1+8400*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-55953383//4116*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+302668*(1+-2x)^(1/2)*(3+5x)^-1*(882+1323x)^-1+7//12*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^-1+83//18*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^-1+23173//504*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-1)
@test integrate((1+-2x)^3//2*(2+3x)^4*(3+5x)^-3, x) == :(-12279//859375*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+9//31250*(1+-2x)^(1/2)*(32+1375x)+1404//3125*(1+-2x)^(1/2)*(2+3x)^2+2643//1750*(1+-2x)^(1/2)*(2+3x)^3+-129*(1+-2x)^(1/2)*(2+3x)^4*(150+250x)^-1+-1//10*(1+-2x)^3//2*(2+3x)^4*(3+5x)^-2)
@test integrate((1+-2x)^3//2*(2+3x)^3*(3+5x)^-3, x) == :(-5943//171875*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+63//6250*(1+-2x)^(1/2)*(92+125x)+693//625*(1+-2x)^(1/2)*(2+3x)^2+-48*(1+-2x)^(1/2)*(2+3x)^3*(75+125x)^-1+-1//10*(1+-2x)^3//2*(2+3x)^3*(3+5x)^-2)
@test integrate((1+-2x)^3//2*(2+3x)^2*(3+5x)^-3, x) == :(119//3025*(1+-2x)^3//2+357//1375*(1+-2x)^(1/2)+-131*(1+-2x)^5//2*(18150+30250x)^-1+-357//6875*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-1//550*(1+-2x)^5//2*(3+5x)^-2)
@test integrate((1+-2x)^3//2*(3+5x)^-3*(2+3x), x) == :(-39//275*(1+-2x)^(1/2)+-13*(1+-2x)^3//2*(330+550x)^-1+-1//110*(1+-2x)^5//2*(3+5x)^-2+39//1375*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^3//2*(3+5x)^-3, x) == :(3*(1+-2x)^(1/2)*(150+250x)^-1+-3//1375*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-1//10*(1+-2x)^3//2*(3+5x)^-2)
@test integrate((1+-2x)^3//2*(2+3x)^-1*(3+5x)^-3, x) == :(14*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+71*(1+-2x)^(1/2)*(30+50x)^-1+-2379//275*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-11//10*(1+-2x)^(1/2)*(3+5x)^-2)
@test integrate((1+-2x)^3//2*(2+3x)^-2*(3+5x)^-3, x) == :(204*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+207*(1+-2x)^(1/2)*(6+10x)^-1+-6933//55*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-103//6*(1+-2x)^(1/2)*(3+5x)^-2+7*(1+-2x)^(1/2)*(3+5x)^-2*(6+9x)^-1)
@test integrate((1+-2x)^3//2*(2+3x)^-3*(3+5x)^-3, x) == :(1020*(1+-2x)^(1/2)*(3+5x)^-1+-13665//11*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-1015//6*(1+-2x)^(1/2)*(3+5x)^-2+14073//7*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+45*(1+-2x)^(1/2)*(3+5x)^-2*(4+6x)^-1+7//6*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-2)
@test integrate((1+-2x)^3//2*(2+3x)^-4*(3+5x)^-3, x) == :(117955*(1+-2x)^(1/2)*(42+70x)^-1+-176065//126*(1+-2x)^(1/2)*(3+5x)^-2+-112875//11*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+813716//49*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+1301*(1+-2x)^(1/2)*(3+5x)^-2*(14+21x)^-1+7//9*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^-2+28//3*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-2)
@test integrate((1+-2x)^5//2*(2+3x)^6*(3+5x), x) == :(-5078115//1408*(1+-2x)^11//2+-184877//128*(1+-2x)^7//2+-105399//128*(1+-2x)^15//2+-59049//2432*(1+-2x)^19//2+1215//896*(1+-2x)^21//2+409941//2176*(1+-2x)^17//2+3658095//1664*(1+-2x)^13//2+3916031//1152*(1+-2x)^9//2)
@test integrate((1+-2x)^5//2*(2+3x)^5*(3+5x), x) == :(-519645//704*(1+-2x)^11//2+-26411//64*(1+-2x)^7//2+-6489//64*(1+-2x)^15//2+-1215//1216*(1+-2x)^19//2+1053//68*(1+-2x)^17//2+37485//104*(1+-2x)^13//2+60025//72*(1+-2x)^9//2)
@test integrate((1+-2x)^5//2*(2+3x)^4*(3+5x), x) == :(-24843//176*(1+-2x)^11//2+-3773//32*(1+-2x)^7//2+-1557//160*(1+-2x)^15//2+405//544*(1+-2x)^17//2+10773//208*(1+-2x)^13//2+57281//288*(1+-2x)^9//2)
@test integrate((1+-2x)^5//2*(2+3x)^3*(3+5x), x) == :(-1071//44*(1+-2x)^11//2+-539//16*(1+-2x)^7//2+-9//16*(1+-2x)^15//2+621//104*(1+-2x)^13//2+3283//72*(1+-2x)^9//2)
@test integrate((1+-2x)^5//2*(2+3x)^2*(3+5x), x) == :(-309//88*(1+-2x)^11//2+-77//8*(1+-2x)^7//2+45//104*(1+-2x)^13//2+707//72*(1+-2x)^9//2)
@test integrate((1+-2x)^5//2*(2+3x)*(3+5x), x) == :(-15//44*(1+-2x)^11//2+-11//4*(1+-2x)^7//2+17//9*(1+-2x)^9//2)
@test integrate((1+-2x)^5//2*(3+5x), x) == :(-11//14*(1+-2x)^7//2+5//18*(1+-2x)^9//2)
@test integrate((1+-2x)^5//2*(2+3x)^-1*(3+5x), x) == :(-98//81*(1+-2x)^(1/2)+-14//81*(1+-2x)^3//2+-5//21*(1+-2x)^7//2+-2//45*(1+-2x)^5//2+98//243*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^-2*(3+5x), x) == :(16//63*(1+-2x)^5//2+80//81*(1+-2x)^3//2+560//81*(1+-2x)^(1/2)+(1+-2x)^7//2*(42+63x)^-1+-560//243*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^-3*(3+5x), x) == :(-365//81*(1+-2x)^(1/2)+-365//567*(1+-2x)^3//2+-73*(1+-2x)^5//2*(252+378x)^-1+1//42*(1+-2x)^7//2*(2+3x)^-2+365//243*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^-4*(3+5x), x) == :(530//567*(1+-2x)^(1/2)+265*(1+-2x)^3//2*(1134+1701x)^-1+-530//1701*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-53//189*(1+-2x)^5//2*(2+3x)^-2+1//63*(1+-2x)^7//2*(2+3x)^-3)
@test integrate((1+-2x)^5//2*(2+3x)^-5*(3+5x), x) == :(-695*(1+-2x)^(1/2)*(9072+13608x)^-1+-139//756*(1+-2x)^5//2*(2+3x)^-3+1//84*(1+-2x)^7//2*(2+3x)^-4+695//4536*(1+-2x)^3//2*(2+3x)^-2+695//47628*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^-6*(3+5x), x) == :(43*(1+-2x)^(1/2)*(15876+23814x)^-1+-43//315*(1+-2x)^5//2*(2+3x)^-4+-43//1134*(1+-2x)^(1/2)*(2+3x)^-2+1//105*(1+-2x)^7//2*(2+3x)^-5+43//567*(1+-2x)^3//2*(2+3x)^-3+43//83349*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^-7*(3+5x), x) == :(205*(1+-2x)^(1/2)*(889056+1333584x)^-1+-205//13608*(1+-2x)^(1/2)*(2+3x)^-3+-41//378*(1+-2x)^5//2*(2+3x)^-5+1//126*(1+-2x)^7//2*(2+3x)^-6+205//4536*(1+-2x)^3//2*(2+3x)^-4+205//190512*(1+-2x)^(1/2)*(2+3x)^-2+205//4667544*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^4*(3+5x)^2, x) == :(-832951//704*(1+-2x)^11//2+-53037//320*(1+-2x)^15//2+-41503//64*(1+-2x)^7//2+-2025//1216*(1+-2x)^19//2+13905//544*(1+-2x)^17//2+121359//208*(1+-2x)^13//2+381073//288*(1+-2x)^9//2)
@test integrate((1+-2x)^5//2*(2+3x)^3*(3+5x)^2, x) == :(-39977//176*(1+-2x)^11//2+-5929//32*(1+-2x)^7//2+-513//32*(1+-2x)^15//2+675//544*(1+-2x)^17//2+17541//208*(1+-2x)^13//2+91091//288*(1+-2x)^9//2)
@test integrate((1+-2x)^5//2*(2+3x)^2*(3+5x)^2, x) == :(-3467//88*(1+-2x)^11//2+-847//16*(1+-2x)^7//2+-15//16*(1+-2x)^15//2+255//26*(1+-2x)^13//2+1309//18*(1+-2x)^9//2)
@test integrate((1+-2x)^5//2*(3+5x)^2*(2+3x), x) == :(-505//88*(1+-2x)^11//2+-121//8*(1+-2x)^7//2+75//104*(1+-2x)^13//2+1133//72*(1+-2x)^9//2)
@test integrate((1+-2x)^5//2*(3+5x)^2, x) == :(-121//28*(1+-2x)^7//2+-25//44*(1+-2x)^11//2+55//18*(1+-2x)^9//2)
@test integrate((1+-2x)^5//2*(2+3x)^-1*(3+5x)^2, x) == :(-155//126*(1+-2x)^7//2+2//135*(1+-2x)^5//2+14//243*(1+-2x)^3//2+25//54*(1+-2x)^9//2+98//243*(1+-2x)^(1/2)+-98//729*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^-2*(3+5x)^2, x) == :(-350//81*(1+-2x)^(1/2)+-50//81*(1+-2x)^3//2+-25//63*(1+-2x)^7//2+-10//63*(1+-2x)^5//2+-1*(1+-2x)^7//2*(126+189x)^-1+350//243*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^-3*(3+5x)^2, x) == :(211//441*(1+-2x)^5//2+1055//81*(1+-2x)^(1/2)+1055//567*(1+-2x)^3//2+143*(1+-2x)^7//2*(1764+2646x)^-1+-1055//243*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-1//126*(1+-2x)^7//2*(2+3x)^-2)
@test integrate((1+-2x)^5//2*(2+3x)^-4*(3+5x)^2, x) == :(-4435//567*(1+-2x)^(1/2)+-4435//3969*(1+-2x)^3//2+-887*(1+-2x)^5//2*(1764+2646x)^-1+-1//189*(1+-2x)^7//2*(2+3x)^-3+211//2646*(1+-2x)^7//2*(2+3x)^-2+4435//1701*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^-5*(3+5x)^2, x) == :(24965//15876*(1+-2x)^(1/2)+24965*(1+-2x)^3//2*(63504+95256x)^-1+-24965//47628*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-4993//10584*(1+-2x)^5//2*(2+3x)^-2+-1//252*(1+-2x)^7//2*(2+3x)^-4+31//588*(1+-2x)^7//2*(2+3x)^-3)
@test integrate((1+-2x)^5//2*(2+3x)^-6*(3+5x)^2, x) == :(-8051*(1+-2x)^(1/2)*(63504+95256x)^-1+-8051//26460*(1+-2x)^5//2*(2+3x)^-3+-1//315*(1+-2x)^7//2*(2+3x)^-5+347//8820*(1+-2x)^7//2*(2+3x)^-4+8051//31752*(1+-2x)^3//2*(2+3x)^-2+8051//333396*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^-7*(3+5x)^2, x) == :(1315*(1+-2x)^(1/2)*(296352+444528x)^-1+-1315//21168*(1+-2x)^(1/2)*(2+3x)^-2+-263//1176*(1+-2x)^5//2*(2+3x)^-4+-1//378*(1+-2x)^7//2*(2+3x)^-6+83//2646*(1+-2x)^7//2*(2+3x)^-5+1315//10584*(1+-2x)^3//2*(2+3x)^-3+1315//1555848*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^-8*(3+5x)^2, x) == :(2335*(1+-2x)^(1/2)*(6223392+9335088x)^-1+-2335//95256*(1+-2x)^(1/2)*(2+3x)^-3+-467//2646*(1+-2x)^5//2*(2+3x)^-5+-1//441*(1+-2x)^7//2*(2+3x)^-7+23//882*(1+-2x)^7//2*(2+3x)^-6+2335//31752*(1+-2x)^3//2*(2+3x)^-4+2335//1333584*(1+-2x)^(1/2)*(2+3x)^-2+2335//32672808*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^4*(3+5x)^3, x) == :(-1392467//640*(1+-2x)^15//2+-1179381//128*(1+-2x)^11//2+-456533//128*(1+-2x)^7//2+-161325//2432*(1+-2x)^19//2+3375//896*(1+-2x)^21//2+1101465//2176*(1+-2x)^17//2+3278737//384*(1+-2x)^9//2+9504551//1664*(1+-2x)^13//2)
@test integrate((1+-2x)^5//2*(2+3x)^3*(3+5x)^3, x) == :(-121359//64*(1+-2x)^11//2+-65219//64*(1+-2x)^7//2+-17337//64*(1+-2x)^15//2+-3375//1216*(1+-2x)^19//2+675//16*(1+-2x)^17//2+98209//104*(1+-2x)^13//2+100793//48*(1+-2x)^9//2)
@test integrate((1+-2x)^5//2*(2+3x)^2*(3+5x)^3, x) == :(-9317//32*(1+-2x)^7//2+-5847//16*(1+-2x)^11//2+-845//32*(1+-2x)^15//2+1125//544*(1+-2x)^17//2+16093//32*(1+-2x)^9//2+28555//208*(1+-2x)^13//2)
@test integrate((1+-2x)^5//2*(3+5x)^3*(2+3x), x) == :(-1331//16*(1+-2x)^7//2+-255//4*(1+-2x)^11//2+-25//16*(1+-2x)^15//2+1675//104*(1+-2x)^13//2+2783//24*(1+-2x)^9//2)
@test integrate((1+-2x)^5//2*(3+5x)^3, x) == :(-1331//56*(1+-2x)^7//2+-75//8*(1+-2x)^11//2+125//104*(1+-2x)^13//2+605//24*(1+-2x)^9//2)
@test integrate((1+-2x)^5//2*(2+3x)^-1*(3+5x)^3, x) == :(-5135//756*(1+-2x)^7//2+-125//132*(1+-2x)^11//2+-98//729*(1+-2x)^(1/2)+-14//729*(1+-2x)^3//2+-2//405*(1+-2x)^5//2+400//81*(1+-2x)^9//2+98//2187*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^-2*(3+5x)^3, x) == :(220//729*(1+-2x)^3//2+1540//729*(1+-2x)^(1/2)+-1540//2187*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-22//567*(1+-2x)^5//2*(69+100x)+55//81*(1+-2x)^5//2*(3+5x)^2+-1*(1+-2x)^5//2*(3+5x)^3*(6+9x)^-1)
@test integrate((1+-2x)^5//2*(2+3x)^-3*(3+5x)^3, x) == :(-935//81*(1+-2x)^(1/2)+-220//21*(1+-2x)^3//2*(3+5x)^2+55//1134*(1+-2x)^3//2*(209+603x)+935//243*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+55*(1+-2x)^3//2*(3+5x)^3*(18+27x)^-1+-1//6*(1+-2x)^5//2*(2+3x)^-2*(3+5x)^3)
@test integrate((1+-2x)^5//2*(2+3x)^-4*(3+5x)^3, x) == :(-41360//5103*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-22//243*(1+-2x)^(1/2)*(578+1885x)+1441//27*(1+-2x)^(1/2)*(3+5x)^2+-275*(1+-2x)^(1/2)*(3+5x)^3*(18+27x)^-1+-1//9*(1+-2x)^5//2*(2+3x)^-3*(3+5x)^3+55//27*(1+-2x)^3//2*(2+3x)^-2*(3+5x)^3)
@test integrate((1+-2x)^5//2*(2+3x)^-5*(3+5x)^3, x) == :(275//13608*(1+-2x)^(1/2)*(1123+4595x)+645865//142884*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-2255*(1+-2x)^(1/2)*(3+5x)^2*(756+1134x)^-1+-55//24*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3+-1//12*(1+-2x)^5//2*(2+3x)^-4*(3+5x)^3+55//54*(1+-2x)^3//2*(2+3x)^-3*(3+5x)^3)
@test integrate((1+-2x)^5//2*(2+3x)^-6*(3+5x)^3, x) == :(-146971//166698*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-11*(1+-2x)^(1/2)*(31752+47628x)^-1*(3911+6475x)+-209//756*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^2+-1//15*(1+-2x)^5//2*(2+3x)^-5*(3+5x)^3+11//9*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^3+11//18*(1+-2x)^3//2*(2+3x)^-4*(3+5x)^3)
@test integrate((1+-2x)^5//2*(2+3x)^-7*(3+5x)^3, x) == :(559625*(1+-2x)^(1/2)*(2667168+4000752x)^-1+-559625//190512*(1+-2x)^(1/2)*(2+3x)^-2+-121//4536*(1+-2x)^3//2*(2+3x)^-4+33275//95256*(1+-2x)^3//2*(2+3x)^-3+559625//14002632*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-1//18*(1+-2x)^5//2*(2+3x)^-6*(3+5x)^3+11//27*(1+-2x)^3//2*(2+3x)^-5*(3+5x)^3)
@test integrate((1+-2x)^5//2*(2+3x)^-8*(3+5x)^3, x) == :(33935*(1+-2x)^(1/2)*(4667544+7001316x)^-1+33935//24504606*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-3223//2646*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^2+-11//333396*(1+-2x)^(1/2)*(2+3x)^-3*(187704+301765x)+-1//21*(1+-2x)^5//2*(2+3x)^-7*(3+5x)^3+11//7*(1+-2x)^(1/2)*(2+3x)^-5*(3+5x)^3+55//189*(1+-2x)^3//2*(2+3x)^-6*(3+5x)^3)
@test integrate((1+-2x)^5//2*(2+3x)^4*(3+5x)^-1, x) == :(-136419//35000*(1+-2x)^7//2+-2889//2200*(1+-2x)^11//2+2//15625*(1+-2x)^5//2+22//46875*(1+-2x)^3//2+81//520*(1+-2x)^13//2+242//78125*(1+-2x)^(1/2)+3819//1000*(1+-2x)^9//2+-242//390625*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^3*(3+5x)^-1, x) == :(-3897//3500*(1+-2x)^7//2+-27//220*(1+-2x)^11//2+2//3125*(1+-2x)^5//2+18//25*(1+-2x)^9//2+22//9375*(1+-2x)^3//2+242//15625*(1+-2x)^(1/2)+-242//78125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^2*(3+5x)^-1, x) == :(-111//350*(1+-2x)^7//2+1//10*(1+-2x)^9//2+2//625*(1+-2x)^5//2+22//1875*(1+-2x)^3//2+242//3125*(1+-2x)^(1/2)+-242//15625*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(3+5x)^-1*(2+3x), x) == :(-3//35*(1+-2x)^7//2+2//125*(1+-2x)^5//2+22//375*(1+-2x)^3//2+242//625*(1+-2x)^(1/2)+-242//3125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(3+5x)^-1, x) == :(2//25*(1+-2x)^5//2+22//75*(1+-2x)^3//2+242//125*(1+-2x)^(1/2)+-242//625*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^-1*(3+5x)^-1, x) == :(-272//225*(1+-2x)^(1/2)+-4//45*(1+-2x)^3//2+-242//125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+98//27*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^-2*(3+5x)^-1, x) == :(26//15*(1+-2x)^(1/2)+7*(1+-2x)^3//2*(6+9x)^-1+-242//25*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+140//9*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^-3*(3+5x)^-1, x) == :(49*(1+-2x)^(1/2)*(4+6x)^-1+-242//5*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+7//6*(1+-2x)^3//2*(2+3x)^-2+235//3*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^-4*(3+5x)^-1, x) == :(-242*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+1073*(1+-2x)^(1/2)*(18+27x)^-1+7//9*(1+-2x)^3//2*(2+3x)^-3+112//9*(1+-2x)^(1/2)*(2+3x)^-2+74020//189*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^-5*(3+5x)^-1, x) == :(-1210*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+100145*(1+-2x)^(1/2)*(336+504x)^-1+7//12*(1+-2x)^3//2*(2+3x)^-4+301//36*(1+-2x)^(1/2)*(2+3x)^-3+4313//72*(1+-2x)^(1/2)*(2+3x)^-2+3454265//1764*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^-6*(3+5x)^-1, x) == :(-6050*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+584179*(1+-2x)^(1/2)*(392+588x)^-1+7//15*(1+-2x)^3//2*(2+3x)^-5+63//10*(1+-2x)^(1/2)*(2+3x)^-4+1201//30*(1+-2x)^(1/2)*(2+3x)^-3+25159//84*(1+-2x)^(1/2)*(2+3x)^-2+20149879//2058*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^-7*(3+5x)^-1, x) == :(-30250*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+736065535*(1+-2x)^(1/2)*(98784+148176x)^-1+7//18*(1+-2x)^3//2*(2+3x)^-6+91//18*(1+-2x)^(1/2)*(2+3x)^-5+2165//72*(1+-2x)^(1/2)*(2+3x)^-4+302651//1512*(1+-2x)^(1/2)*(2+3x)^-3+31700335//21168*(1+-2x)^(1/2)*(2+3x)^-2+25388847535//518616*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^4*(3+5x)^-2, x) == :(254//46875*(1+-2x)^3//2+2794//78125*(1+-2x)^(1/2)+-2794//390625*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-32//4125*(1+-2x)^5//2*(2+3x)^2+-1//3609375*(1+-2x)^5//2*(1347116+1110975x)+39//275*(1+-2x)^5//2*(2+3x)^3+-1*(1+-2x)^5//2*(2+3x)^4*(15+25x)^-1)
@test integrate((1+-2x)^5//2*(2+3x)^3*(3+5x)^-2, x) == :(188//9375*(1+-2x)^3//2+2068//15625*(1+-2x)^(1/2)+-2068//78125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-2//65625*(1+-2x)^5//2*(6191+2850x)+11//75*(1+-2x)^5//2*(2+3x)^2+-1*(1+-2x)^5//2*(2+3x)^3*(15+25x)^-1)
@test integrate((1+-2x)^5//2*(2+3x)^2*(3+5x)^-2, x) == :(-9//175*(1+-2x)^7//2+122//1875*(1+-2x)^3//2+122//6875*(1+-2x)^5//2+1342//3125*(1+-2x)^(1/2)+-1*(1+-2x)^7//2*(825+1375x)^-1+-1342//15625*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(3+5x)^-2*(2+3x), x) == :(56//375*(1+-2x)^3//2+56//1375*(1+-2x)^5//2+616//625*(1+-2x)^(1/2)+-1*(1+-2x)^7//2*(165+275x)^-1+-616//3125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(3+5x)^-2, x) == :(-22//25*(1+-2x)^(1/2)+-2//15*(1+-2x)^3//2+-1*(1+-2x)^5//2*(15+25x)^-1+22//125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^-1*(3+5x)^-2, x) == :(-58//75*(1+-2x)^(1/2)+-11*(1+-2x)^3//2*(15+25x)^-1+-98//9*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+836//125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^-2*(3+5x)^-2, x) == :(-748*(1+-2x)^(1/2)*(45+75x)^-1+-910//9*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+1562//25*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+7*(1+-2x)^3//2*(3+5x)^-1*(6+9x)^-1)
@test integrate((1+-2x)^5//2*(2+3x)^-3*(3+5x)^-2, x) == :(-6763*(1+-2x)^(1/2)*(54+90x)^-1+-6665//9*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+2288//5*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+343*(1+-2x)^(1/2)*(3+5x)^-1*(18+27x)^-1+7//6*(1+-2x)^3//2*(2+3x)^-2*(3+5x)^-1)
@test integrate((1+-2x)^5//2*(2+3x)^-4*(3+5x)^-2, x) == :(-44545*(1+-2x)^(1/2)*(54+90x)^-1+3014*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-307295//63*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+6649*(1+-2x)^(1/2)*(3+5x)^-1*(54+81x)^-1+7//9*(1+-2x)^3//2*(2+3x)^-3*(3+5x)^-1+917//54*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-1)
@test integrate((1+-2x)^5//2*(2+3x)^-5*(3+5x)^-2, x) == :(-7738475*(1+-2x)^(1/2)*(1512+2520x)^-1+18700*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-53384095//1764*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+288770*(1+-2x)^(1/2)*(3+5x)^-1*(378+567x)^-1+7//12*(1+-2x)^3//2*(2+3x)^-4*(3+5x)^-1+287//27*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^-1+22109//216*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-1)
@test integrate((1+-2x)^5//2*(2+3x)^-6*(3+5x)^-2, x) == :(-323422735*(1+-2x)^(1/2)*(10584+17640x)^-1+111650*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-2231141147//12348*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+12068887*(1+-2x)^(1/2)*(3+5x)^-1*(2646+3969x)^-1+7//15*(1+-2x)^3//2*(2+3x)^-5*(3+5x)^-1+1379//180*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^-1+16549//270*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^-1+924025//1512*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-1)
@test integrate((1+-2x)^5//2*(2+3x)^4*(3+5x)^-3, x) == :(11763//78125*(1+-2x)^(1/2)+-11763//390625*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+1//93750*(1+-2x)^3//2*(734+24939x)+1117//750*(1+-2x)^3//2*(2+3x)^3+1903//4375*(1+-2x)^3//2*(2+3x)^2+-127*(1+-2x)^3//2*(2+3x)^4*(150+250x)^-1+-1//10*(1+-2x)^5//2*(2+3x)^4*(3+5x)^-2)
@test integrate((1+-2x)^5//2*(2+3x)^3*(3+5x)^-3, x) == :(5559//15625*(1+-2x)^(1/2)+-5559//78125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+3//6250*(1+-2x)^3//2*(1618+2403x)+954//875*(1+-2x)^3//2*(2+3x)^2+-47*(1+-2x)^3//2*(2+3x)^3*(75+125x)^-1+-1//10*(1+-2x)^5//2*(2+3x)^3*(3+5x)^-2)
@test integrate((1+-2x)^5//2*(2+3x)^2*(3+5x)^-3, x) == :(511//6875*(1+-2x)^3//2+1533//3125*(1+-2x)^(1/2)+1533//75625*(1+-2x)^5//2+-129*(1+-2x)^7//2*(18150+30250x)^-1+-1533//15625*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-1//550*(1+-2x)^7//2*(3+5x)^-2)
@test integrate((1+-2x)^5//2*(3+5x)^-3*(2+3x), x) == :(-63//125*(1+-2x)^(1/2)+-21//275*(1+-2x)^3//2+-63*(1+-2x)^5//2*(1650+2750x)^-1+-1//110*(1+-2x)^7//2*(3+5x)^-2+63//625*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(3+5x)^-3, x) == :(3//25*(1+-2x)^(1/2)+(1+-2x)^3//2*(30+50x)^-1+-3//125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-1//10*(1+-2x)^5//2*(3+5x)^-2)
@test integrate((1+-2x)^5//2*(2+3x)^-1*(3+5x)^-3, x) == :(803*(1+-2x)^(1/2)*(150+250x)^-1+-2523//125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-11//10*(1+-2x)^3//2*(3+5x)^-2+98//3*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^-2*(3+5x)^-3, x) == :(7103*(1+-2x)^(1/2)*(90+150x)^-1+-7209//25*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-1133//30*(1+-2x)^(1/2)*(3+5x)^-2+1400//3*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+7*(1+-2x)^3//2*(3+5x)^-2*(6+9x)^-1)
@test integrate((1+-2x)^5//2*(2+3x)^-3*(3+5x)^-3, x) == :(2311*(1+-2x)^(1/2)*(3+5x)^-1+4555*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-14073//5*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-6899//18*(1+-2x)^(1/2)*(3+5x)^-2+931*(1+-2x)^(1/2)*(3+5x)^-2*(36+54x)^-1+7//6*(1+-2x)^3//2*(2+3x)^-2*(3+5x)^-2)
@test integrate((1+-2x)^5//2*(2+3x)^-4*(3+5x)^-3, x) == :(-23115*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+113875*(1+-2x)^(1/2)*(18+30x)^-1+-169975//54*(1+-2x)^(1/2)*(3+5x)^-2+785570//21*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+1256*(1+-2x)^(1/2)*(3+5x)^-2*(6+9x)^-1+7//9*(1+-2x)^3//2*(2+3x)^-3*(3+5x)^-2+581//27*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-2)
@test integrate((1+-2x)^5//2*(2+3x)^-5*(3+5x)^-3, x) == :(-171675*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+23680975*(1+-2x)^(1/2)*(504+840x)^-1+-8836825//378*(1+-2x)^(1/2)*(3+5x)^-2+163363895//588*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+522385*(1+-2x)^(1/2)*(3+5x)^-2*(336+504x)^-1+7//12*(1+-2x)^3//2*(2+3x)^-4*(3+5x)^-2+1393//108*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^-2+11243//72*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-2)
@test integrate((1+-2x)^-1//2*(2+3x)^5*(3+5x), x) == :(-184877//64*(1+-2x)^(1/2)+-103929//64*(1+-2x)^5//2+-10815//64*(1+-2x)^9//2+-1215//832*(1+-2x)^13//2+1053//44*(1+-2x)^11//2+5355//8*(1+-2x)^7//2+60025//24*(1+-2x)^3//2)
@test integrate((1+-2x)^-1//2*(2+3x)^4*(3+5x), x) == :(-26411//32*(1+-2x)^(1/2)+-24843//80*(1+-2x)^5//2+-519//32*(1+-2x)^9//2+405//352*(1+-2x)^11//2+1539//16*(1+-2x)^7//2+57281//96*(1+-2x)^3//2)
@test integrate((1+-2x)^-1//2*(2+3x)^3*(3+5x), x) == :(-3773//16*(1+-2x)^(1/2)+-1071//20*(1+-2x)^5//2+-15//16*(1+-2x)^9//2+621//56*(1+-2x)^7//2+3283//24*(1+-2x)^3//2)
@test integrate((1+-2x)^-1//2*(2+3x)^2*(3+5x), x) == :(-539//8*(1+-2x)^(1/2)+-309//40*(1+-2x)^5//2+45//56*(1+-2x)^7//2+707//24*(1+-2x)^3//2)
@test integrate((1+-2x)^-1//2*(2+3x)*(3+5x), x) == :(-77//4*(1+-2x)^(1/2)+-3//4*(1+-2x)^5//2+17//3*(1+-2x)^3//2)
@test integrate((1+-2x)^-1//2*(3+5x), x) == :(-11//2*(1+-2x)^(1/2)+5//6*(1+-2x)^3//2)
@test integrate((1+-2x)^-1//2*(2+3x)^-1*(3+5x), x) == :(-5//3*(1+-2x)^(1/2)+2//63*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-1//2*(2+3x)^-2*(3+5x), x) == :((1+-2x)^(1/2)*(42+63x)^-1+-68//441*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-1//2*(2+3x)^-3*(3+5x), x) == :(-67*(1+-2x)^(1/2)*(588+882x)^-1+-67//3087*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+1//42*(1+-2x)^(1/2)*(2+3x)^-2)
@test integrate((1+-2x)^-1//2*(2+3x)^-4*(3+5x), x) == :(-50*(1+-2x)^(1/2)*(2058+3087x)^-1+-100//21609*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-50//441*(1+-2x)^(1/2)*(2+3x)^-2+1//63*(1+-2x)^(1/2)*(2+3x)^-3)
@test integrate((1+-2x)^-1//2*(2+3x)^-5*(3+5x), x) == :(-95*(1+-2x)^(1/2)*(16464+24696x)^-1+-95//3528*(1+-2x)^(1/2)*(2+3x)^-2+-95//86436*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-19//252*(1+-2x)^(1/2)*(2+3x)^-3+1//84*(1+-2x)^(1/2)*(2+3x)^-4)
@test integrate((1+-2x)^-1//2*(2+3x)^5*(3+5x)^2, x) == :(-2033647//128*(1+-2x)^(1/2)+-1623419//128*(1+-2x)^5//2+-285565//128*(1+-2x)^9//2+-97605//1664*(1+-2x)^13//2+405//128*(1+-2x)^15//2+672003//1408*(1+-2x)^11//2+842415//128*(1+-2x)^7//2+6206585//384*(1+-2x)^3//2)
@test integrate((1+-2x)^-1//2*(2+3x)^4*(3+5x)^2, x) == :(-832951//320*(1+-2x)^5//2+-290521//64*(1+-2x)^(1/2)+-17679//64*(1+-2x)^9//2+-2025//832*(1+-2x)^13//2+13905//352*(1+-2x)^11//2+17337//16*(1+-2x)^7//2+381073//96*(1+-2x)^3//2)
@test integrate((1+-2x)^-1//2*(2+3x)^3*(3+5x)^2, x) == :(-41503//32*(1+-2x)^(1/2)+-39977//80*(1+-2x)^5//2+-855//32*(1+-2x)^9//2+675//352*(1+-2x)^11//2+17541//112*(1+-2x)^7//2+91091//96*(1+-2x)^3//2)
@test integrate((1+-2x)^-1//2*(2+3x)^2*(3+5x)^2, x) == :(-5929//16*(1+-2x)^(1/2)+-3467//40*(1+-2x)^5//2+-25//16*(1+-2x)^9//2+255//14*(1+-2x)^7//2+1309//6*(1+-2x)^3//2)
@test integrate((1+-2x)^-1//2*(3+5x)^2*(2+3x), x) == :(-847//8*(1+-2x)^(1/2)+-101//8*(1+-2x)^5//2+75//56*(1+-2x)^7//2+1133//24*(1+-2x)^3//2)
@test integrate((1+-2x)^-1//2*(3+5x)^2, x) == :(-121//4*(1+-2x)^(1/2)+-5//4*(1+-2x)^5//2+55//6*(1+-2x)^3//2)
@test integrate((1+-2x)^-1//2*(2+3x)^-1*(3+5x)^2, x) == :(-155//18*(1+-2x)^(1/2)+25//18*(1+-2x)^3//2+-2//189*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-1//2*(2+3x)^-2*(3+5x)^2, x) == :(-25//9*(1+-2x)^(1/2)+-1*(1+-2x)^(1/2)*(126+189x)^-1+46//441*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-1//2*(2+3x)^-3*(3+5x)^2, x) == :(137*(1+-2x)^(1/2)*(1764+2646x)^-1+-257//1029*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-1//126*(1+-2x)^(1/2)*(2+3x)^-2)
@test integrate((1+-2x)^-1//2*(2+3x)^-4*(3+5x)^2, x) == :(-2245*(1+-2x)^(1/2)*(12348+18522x)^-1+-2245//64827*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-1//189*(1+-2x)^(1/2)*(2+3x)^-3+205//2646*(1+-2x)^(1/2)*(2+3x)^-2)
@test integrate((1+-2x)^-1//2*(2+3x)^-5*(3+5x)^2, x) == :(-635*(1+-2x)^(1/2)*(16464+24696x)^-1+-635//3528*(1+-2x)^(1/2)*(2+3x)^-2+-635//86436*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-1//252*(1+-2x)^(1/2)*(2+3x)^-4+13//252*(1+-2x)^(1/2)*(2+3x)^-3)
@test integrate((1+-2x)^-1//2*(2+3x)^-6*(3+5x)^2, x) == :(-351*(1+-2x)^(1/2)*(38416+57624x)^-1+-117//980*(1+-2x)^(1/2)*(2+3x)^-3+-117//2744*(1+-2x)^(1/2)*(2+3x)^-2+-117//67228*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-1//315*(1+-2x)^(1/2)*(2+3x)^-5+341//8820*(1+-2x)^(1/2)*(2+3x)^-4)
@test integrate((1+-2x)^-1//2*(2+3x)^4*(3+5x)^3, x) == :(-12973191//640*(1+-2x)^5//2+-3195731//128*(1+-2x)^(1/2)+-1392467//384*(1+-2x)^9//2+-161325//1664*(1+-2x)^13//2+675//128*(1+-2x)^15//2+1101465//1408*(1+-2x)^11//2+1357793//128*(1+-2x)^7//2+3278737//128*(1+-2x)^3//2)
@test integrate((1+-2x)^-1//2*(2+3x)^3*(3+5x)^3, x) == :(-1334949//320*(1+-2x)^5//2+-456533//64*(1+-2x)^(1/2)+-28895//64*(1+-2x)^9//2+-3375//832*(1+-2x)^13//2+11475//176*(1+-2x)^11//2+98209//56*(1+-2x)^7//2+100793//16*(1+-2x)^3//2)
@test integrate((1+-2x)^-1//2*(2+3x)^2*(3+5x)^3, x) == :(-65219//32*(1+-2x)^(1/2)+-64317//80*(1+-2x)^5//2+-4225//96*(1+-2x)^9//2+1125//352*(1+-2x)^11//2+28555//112*(1+-2x)^7//2+48279//32*(1+-2x)^3//2)
@test integrate((1+-2x)^-1//2*(3+5x)^3*(2+3x), x) == :(-9317//16*(1+-2x)^(1/2)+-561//4*(1+-2x)^5//2+-125//48*(1+-2x)^9//2+1675//56*(1+-2x)^7//2+2783//8*(1+-2x)^3//2)
@test integrate((1+-2x)^-1//2*(3+5x)^3, x) == :(-1331//8*(1+-2x)^(1/2)+-165//8*(1+-2x)^5//2+125//56*(1+-2x)^7//2+605//8*(1+-2x)^3//2)
@test integrate((1+-2x)^-1//2*(2+3x)^-1*(3+5x)^3, x) == :(-5135//108*(1+-2x)^(1/2)+-25//12*(1+-2x)^5//2+400//27*(1+-2x)^3//2+2//567*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-1//2*(2+3x)^-2*(3+5x)^3, x) == :(-208//3969*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-10//189*(1+-2x)^(1/2)*(214+95x)+(1+-2x)^(1/2)*(3+5x)^2*(42+63x)^-1)
@test integrate((1+-2x)^-1//2*(2+3x)^-3*(3+5x)^3, x) == :(2381//9261*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-1*(1+-2x)^(1/2)*(1764+2646x)^-1*(8329+12425x)+1//42*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^2)
@test integrate((1+-2x)^-1//2*(2+3x)^-4*(3+5x)^3, x) == :(-78710//194481*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+1//63*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^2+5//9261*(1+-2x)^(1/2)*(2+3x)^-2*(1205+1867x))
@test integrate((1+-2x)^-1//2*(2+3x)^-5*(3+5x)^3, x) == :(-42995*(1+-2x)^(1/2)*(148176+222264x)^-1+-42995//777924*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+1//84*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^2+1//10584*(1+-2x)^(1/2)*(2+3x)^-3*(3168+4955x))
@test integrate((1+-2x)^-1//2*(2+3x)^-6*(3+5x)^3, x) == :(-5293*(1+-2x)^(1/2)*(86436+129654x)^-1+-5293//18522*(1+-2x)^(1/2)*(2+3x)^-2+-5293//453789*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+1//105*(1+-2x)^(1/2)*(2+3x)^-5*(3+5x)^2+1//6615*(1+-2x)^(1/2)*(2+3x)^-4*(1255+1971x))
@test integrate((a+b*x)^2*(c+d*x)^-2*(e+f*x)^-1//2, x) == :(2*b^2*d^-2*f^-1*(e+f*x)^(1/2)+d^-5//2*(d*e+-1*c*f)^-3//2*(b*c+-1*a*d)*(-1*a*d*f+-3*b*c*f+4*b*d*e)*arctanh(d^(1/2)*(e+f*x)^(1/2)*(d*e+-1*c*f)^-1//2)+-1*d^-2*(c+d*x)^-1*(e+f*x)^(1/2)*(b*c+-1*a*d)^2*(d*e+-1*c*f)^-1)
@test integrate((1+-2x)^-1//2*(2+3x)^5*(3+5x)^-1, x) == :(-4774713//50000*(1+-2x)^(1/2)+-51057//2500*(1+-2x)^5//2+-27//80*(1+-2x)^9//2+5751//1400*(1+-2x)^7//2+268707//5000*(1+-2x)^3//2+-2//171875*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-1//2*(2+3x)^4*(3+5x)^-1, x) == :(-136419//5000*(1+-2x)^(1/2)+-2889//1000*(1+-2x)^5//2+81//280*(1+-2x)^7//2+11457//1000*(1+-2x)^3//2+-2//34375*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-1//2*(2+3x)^3*(3+5x)^-1, x) == :(-3897//500*(1+-2x)^(1/2)+-27//100*(1+-2x)^5//2+54//25*(1+-2x)^3//2+-2//6875*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-1//2*(2+3x)^2*(3+5x)^-1, x) == :(-111//50*(1+-2x)^(1/2)+3//10*(1+-2x)^3//2+-2//1375*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-1//2*(3+5x)^-1*(2+3x), x) == :(-3//5*(1+-2x)^(1/2)+-2//275*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-1//2*(3+5x)^-1, x) == :(-2//55*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-1//2*(2+3x)^-1*(3+5x)^-1, x) == :(-2//11*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+2//7*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-1//2*(2+3x)^-2*(3+5x)^-1, x) == :(3*(1+-2x)^(1/2)*(14+21x)^-1+-10//11*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+72//49*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-1//2*(2+3x)^-3*(3+5x)^-1, x) == :(219*(1+-2x)^(1/2)*(196+294x)^-1+-50//11*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+3//14*(1+-2x)^(1/2)*(2+3x)^-2+2523//343*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-1//2*(2+3x)^-4*(3+5x)^-1, x) == :(3840*(1+-2x)^(1/2)*(686+1029x)^-1+-250//11*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+1//7*(1+-2x)^(1/2)*(2+3x)^-3+55//49*(1+-2x)^(1/2)*(2+3x)^-2+88310//2401*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-1//2*(2+3x)^-5*(3+5x)^-1, x) == :(3135*(1+-2x)^(1/2)*(112+168x)^-1+-1250//11*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+3//4*(1+-2x)^(1/2)*(2+3x)^-3+3//28*(1+-2x)^(1/2)*(2+3x)^-4+45//8*(1+-2x)^(1/2)*(2+3x)^-2+36045//196*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-1//2*(2+3x)^6*(3+5x)^-2, x) == :(-26352//34375*(1+-2x)^(1/2)*(2+3x)^2+-1717//9625*(1+-2x)^(1/2)*(2+3x)^3+-398//9453125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-8//275*(1+-2x)^(1/2)*(2+3x)^4+-3//171875*(1+-2x)^(1/2)*(1847824+615875x)+-1*(1+-2x)^(1/2)*(2+3x)^5*(165+275x)^-1)
@test integrate((1+-2x)^-1//2*(2+3x)^5*(3+5x)^-2, x) == :(-1668//6875*(1+-2x)^(1/2)*(2+3x)^2+-332//1890625*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-78//1925*(1+-2x)^(1/2)*(2+3x)^3+-6//34375*(1+-2x)^(1/2)*(59708+19875x)+-1*(1+-2x)^(1/2)*(2+3x)^4*(165+275x)^-1)
@test integrate((1+-2x)^-1//2*(2+3x)^4*(3+5x)^-2, x) == :(-266//378125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-84//1375*(1+-2x)^(1/2)*(2+3x)^2+-21//6875*(1+-2x)^(1/2)*(1144+375x)+-1*(1+-2x)^(1/2)*(2+3x)^3*(165+275x)^-1)
@test integrate((1+-2x)^-1//2*(2+3x)^3*(3+5x)^-2, x) == :(-8//3025*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-6//55*(1+-2x)^(1/2)*(11+3x)+-1*(1+-2x)^(1/2)*(2+3x)^2*(165+275x)^-1)
@test integrate((1+-2x)^-1//2*(2+3x)^2*(3+5x)^-2, x) == :(-9//25*(1+-2x)^(1/2)+-1*(1+-2x)^(1/2)*(825+1375x)^-1+-134//15125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-1//2*(3+5x)^-2*(2+3x), x) == :(-1*(1+-2x)^(1/2)*(165+275x)^-1+-68//3025*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-1//2*(3+5x)^-2, x) == :(-1*(1+-2x)^(1/2)*(33+55x)^-1+-2//605*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-1//2*(2+3x)^-1*(3+5x)^-2, x) == :(-5*(1+-2x)^(1/2)*(33+55x)^-1+-6//7*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+64//121*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-1//2*(2+3x)^-2*(3+5x)^-2, x) == :(-340*(1+-2x)^(1/2)*(231+385x)^-1+-426//49*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+650//121*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+3*(1+-2x)^(1/2)*(3+5x)^-1*(14+21x)^-1)
@test integrate((1+-2x)^-1//2*(2+3x)^-3*(3+5x)^-2, x) == :(-35845*(1+-2x)^(1/2)*(3234+5390x)^-1+-22479//343*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+4900//121*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+162*(1+-2x)^(1/2)*(3+5x)^-1*(98+147x)^-1+3//14*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-1)
@test integrate((1+-2x)^-1//2*(2+3x)^-4*(3+5x)^-2, x) == :(-1676975*(1+-2x)^(1/2)*(22638+37730x)^-1+-1051695//2401*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+32750//121*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+7585*(1+-2x)^(1/2)*(3+5x)^-1*(686+1029x)^-1+1//7*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^-1+145//98*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-1)
@test integrate((1+-2x)^-1//2*(2+3x)^6*(3+5x)^-3, x) == :(-56556//378125*(1+-2x)^(1/2)*(2+3x)^2+-33069//103984375*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-927//211750*(1+-2x)^(1/2)*(2+3x)^3+-9//3781250*(1+-2x)^(1/2)*(2815648+934875x)+-117*(1+-2x)^(1/2)*(2+3x)^4*(9075+15125x)^-1+-1//110*(1+-2x)^(1/2)*(2+3x)^5*(3+5x)^-2)
@test integrate((1+-2x)^-1//2*(2+3x)^5*(3+5x)^-3, x) == :(-22113//20796875*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-1512//75625*(1+-2x)^(1/2)*(2+3x)^2+-189//756250*(1+-2x)^(1/2)*(8976+2875x)+-201*(1+-2x)^(1/2)*(2+3x)^3*(18150+30250x)^-1+-1//110*(1+-2x)^(1/2)*(2+3x)^4*(3+5x)^-2)
@test integrate((1+-2x)^-1//2*(2+3x)^4*(3+5x)^-3, x) == :(-2667//831875*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-63//30250*(1+-2x)^(1/2)*(352+75x)+-84*(1+-2x)^(1/2)*(2+3x)^2*(9075+15125x)^-1+-1//110*(1+-2x)^(1/2)*(2+3x)^3*(3+5x)^-2)
@test integrate((1+-2x)^-1//2*(2+3x)^3*(3+5x)^-3, x) == :(-1347//166375*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-9*(1+-2x)^(1/2)*(18150+30250x)^-1*(432+715x)+-1//110*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^-2)
@test integrate((1+-2x)^-1//2*(2+3x)^2*(3+5x)^-3, x) == :(-27*(1+-2x)^(1/2)*(3630+6050x)^-1+-2313//166375*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-1//550*(1+-2x)^(1/2)*(3+5x)^-2)
@test integrate((1+-2x)^-1//2*(3+5x)^-3*(2+3x), x) == :(-69*(1+-2x)^(1/2)*(3630+6050x)^-1+-69//33275*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-1//110*(1+-2x)^(1/2)*(3+5x)^-2)
@test integrate((1+-2x)^-1//2*(3+5x)^-3, x) == :(-3*(1+-2x)^(1/2)*(726+1210x)^-1+-3//6655*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-1//22*(1+-2x)^(1/2)*(3+5x)^-2)
@test integrate((1+-2x)^-1//2*(2+3x)^-1*(3+5x)^-3, x) == :(315*(1+-2x)^(1/2)*(726+1210x)^-1+-2115//1331*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-5//22*(1+-2x)^(1/2)*(3+5x)^-2+18//7*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-1//2*(2+3x)^-2*(3+5x)^-3, x) == :(33465*(1+-2x)^(1/2)*(5082+8470x)^-1+-32025//1331*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-505//154*(1+-2x)^(1/2)*(3+5x)^-2+1908//49*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+3*(1+-2x)^(1/2)*(3+5x)^-2*(14+21x)^-1)
@test integrate((1+-2x)^-1//2*(2+3x)^-3*(3+5x)^-3, x) == :(1177080*(1+-2x)^(1/2)*(17787+29645x)^-1+-321825//1331*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-35495//1078*(1+-2x)^(1/2)*(3+5x)^-2+134217//343*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+429*(1+-2x)^(1/2)*(3+5x)^-2*(196+294x)^-1+3//14*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-2)
@test integrate((1+-2x)^-1//2*(2+3x)^-4*(3+5x)^-3, x) == :(137735775*(1+-2x)^(1/2)*(249018+415030x)^-1+-2689875//1331*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-2076675//7546*(1+-2x)^(1/2)*(3+5x)^-2+7852680//2401*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+12555*(1+-2x)^(1/2)*(3+5x)^-2*(686+1029x)^-1+1//7*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^-2+90//49*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-2)
@test integrate((1+-2x)^-3//2*(2+3x)^7*(3+5x), x) == :(-7882483//128*(1+-2x)^3//2+-821583//1408*(1+-2x)^11//2+-787185//64*(1+-2x)^7//2+-729//256*(1+-2x)^15//2+101331//1664*(1+-2x)^13//2+422919//128*(1+-2x)^9//2+4084101//128*(1+-2x)^5//2+9058973//256*(1+-2x)^-1//2+15647317//128*(1+-2x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^6*(3+5x), x) == :(-1692705//128*(1+-2x)^3//2+-225855//128*(1+-2x)^7//2+-59049//1408*(1+-2x)^11//2+3645//1664*(1+-2x)^13//2+45549//128*(1+-2x)^9//2+731619//128*(1+-2x)^5//2+1294139//128*(1+-2x)^-1//2+3916031//128*(1+-2x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^5*(3+5x), x) == :(-173215//64*(1+-2x)^3//2+-13905//64*(1+-2x)^7//2+-1215//704*(1+-2x)^11//2+117//4*(1+-2x)^9//2+7497//8*(1+-2x)^5//2+60025//8*(1+-2x)^(1/2)+184877//64*(1+-2x)^-1//2)
@test integrate((1+-2x)^-3//2*(2+3x)^4*(3+5x), x) == :(-8281//16*(1+-2x)^3//2+-4671//224*(1+-2x)^7//2+45//32*(1+-2x)^9//2+10773//80*(1+-2x)^5//2+26411//32*(1+-2x)^-1//2+57281//32*(1+-2x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^3*(3+5x), x) == :(-357//4*(1+-2x)^3//2+-135//112*(1+-2x)^7//2+621//40*(1+-2x)^5//2+3283//8*(1+-2x)^(1/2)+3773//16*(1+-2x)^-1//2)
@test integrate((1+-2x)^-3//2*(2+3x)^2*(3+5x), x) == :(-103//8*(1+-2x)^3//2+9//8*(1+-2x)^5//2+539//8*(1+-2x)^-1//2+707//8*(1+-2x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)*(3+5x), x) == :(17*(1+-2x)^(1/2)+-5//4*(1+-2x)^3//2+77//4*(1+-2x)^-1//2)
@test integrate((1+-2x)^-3//2*(3+5x), x) == :(5//2*(1+-2x)^(1/2)+11//2*(1+-2x)^-1//2)
@test integrate((1+-2x)^-3//2*(2+3x)^-1*(3+5x), x) == :(11//7*(1+-2x)^-1//2+2//147*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-3//2*(2+3x)^-2*(3+5x), x) == :(64//147*(1+-2x)^-1//2+-64//1029*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+1//21*(1+-2x)^-1//2*(2+3x)^-1)
@test integrate((1+-2x)^-3//2*(2+3x)^-3*(3+5x), x) == :(65//343*(1+-2x)^-1//2+-65//294*(1+-2x)^-1//2*(2+3x)^-1+-65//2401*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+1//42*(1+-2x)^-1//2*(2+3x)^-2)
@test integrate((1+-2x)^-3//2*(2+3x)^-4*(3+5x), x) == :(10//147*(1+-2x)^-1//2+-10//1029*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-5//63*(1+-2x)^-1//2*(2+3x)^-1+-1//9*(1+-2x)^-1//2*(2+3x)^-2+1//63*(1+-2x)^-1//2*(2+3x)^-3)
@test integrate((1+-2x)^-3//2*(2+3x)^-5*(3+5x), x) == :(655//28812*(1+-2x)^-1//2+-655//24696*(1+-2x)^-1//2*(2+3x)^-1+-655//201684*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-131//1764*(1+-2x)^-1//2*(2+3x)^-3+-131//3528*(1+-2x)^-1//2*(2+3x)^-2+1//84*(1+-2x)^-1//2*(2+3x)^-4)
@test integrate((1+-2x)^-3//2*(2+3x)^-6*(3+5x), x) == :(123//16807*(1+-2x)^-1//2+-123//117649*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-41//735*(1+-2x)^-1//2*(2+3x)^-4+-41//1715*(1+-2x)^-1//2*(2+3x)^-3+-41//3430*(1+-2x)^-1//2*(2+3x)^-2+-41//4802*(1+-2x)^-1//2*(2+3x)^-1+1//105*(1+-2x)^-1//2*(2+3x)^-5)
@test integrate((1+-2x)^-3//2*(2+3x)^5*(3+5x)^2, x) == :(-8117095//384*(1+-2x)^3//2+-367155//128*(1+-2x)^7//2+-97605//1408*(1+-2x)^11//2+6075//1664*(1+-2x)^13//2+74667//128*(1+-2x)^9//2+1179381//128*(1+-2x)^5//2+2033647//128*(1+-2x)^-1//2+6206585//128*(1+-2x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^4*(3+5x)^2, x) == :(-832951//192*(1+-2x)^3//2+-159111//448*(1+-2x)^7//2+-2025//704*(1+-2x)^11//2+1545//32*(1+-2x)^9//2+121359//80*(1+-2x)^5//2+290521//64*(1+-2x)^-1//2+381073//32*(1+-2x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^3*(3+5x)^2, x) == :(-39977//48*(1+-2x)^3//2+-7695//224*(1+-2x)^7//2+75//32*(1+-2x)^9//2+17541//80*(1+-2x)^5//2+41503//32*(1+-2x)^-1//2+91091//32*(1+-2x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^2*(3+5x)^2, x) == :(-3467//24*(1+-2x)^3//2+-225//112*(1+-2x)^7//2+51//2*(1+-2x)^5//2+1309//2*(1+-2x)^(1/2)+5929//16*(1+-2x)^-1//2)
@test integrate((1+-2x)^-3//2*(3+5x)^2*(2+3x), x) == :(-505//24*(1+-2x)^3//2+15//8*(1+-2x)^5//2+847//8*(1+-2x)^-1//2+1133//8*(1+-2x)^(1/2))
@test integrate((1+-2x)^-3//2*(3+5x)^2, x) == :(-25//12*(1+-2x)^3//2+55//2*(1+-2x)^(1/2)+121//4*(1+-2x)^-1//2)
@test integrate((1+-2x)^-3//2*(2+3x)^-1*(3+5x)^2, x) == :(25//6*(1+-2x)^(1/2)+121//14*(1+-2x)^-1//2+-2//441*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-3//2*(2+3x)^-2*(3+5x)^2, x) == :(-1091*(1+-2x)^(1/2)*(588+882x)^-1+121//14*(1+-2x)^-1//2*(2+3x)^-1+134//3087*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-3//2*(2+3x)^-3*(3+5x)^2, x) == :(-2045*(1+-2x)^(1/2)*(4116+6174x)^-1+-2045//21609*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-545//147*(1+-2x)^(1/2)*(2+3x)^-2+121//14*(1+-2x)^-1//2*(2+3x)^-2)
@test integrate((1+-2x)^-3//2*(2+3x)^-4*(3+5x)^2, x) == :(-905*(1+-2x)^(1/2)*(4116+6174x)^-1+-905//882*(1+-2x)^(1/2)*(2+3x)^-2+-905//21609*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-467//126*(1+-2x)^(1/2)*(2+3x)^-3+121//14*(1+-2x)^-1//2*(2+3x)^-3)
@test integrate((1+-2x)^-3//2*(2+3x)^-5*(3+5x)^2, x) == :(-9145*(1+-2x)^(1/2)*(115248+172872x)^-1+-9145//24696*(1+-2x)^(1/2)*(2+3x)^-2+-9145//605052*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-2179//588*(1+-2x)^(1/2)*(2+3x)^-4+-1829//1764*(1+-2x)^(1/2)*(2+3x)^-3+121//14*(1+-2x)^-1//2*(2+3x)^-4)
@test integrate((1+-2x)^-3//2*(2+3x)^4*(3+5x)^3, x) == :(-4324397//128*(1+-2x)^3//2+-4177401//896*(1+-2x)^7//2+-161325//1408*(1+-2x)^11//2+10125//1664*(1+-2x)^13//2+122385//128*(1+-2x)^9//2+3195731//128*(1+-2x)^-1//2+9504551//640*(1+-2x)^5//2+9836211//128*(1+-2x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^3*(3+5x)^3, x) == :(-444983//64*(1+-2x)^3//2+-260055//448*(1+-2x)^7//2+-3375//704*(1+-2x)^11//2+1275//16*(1+-2x)^9//2+98209//40*(1+-2x)^5//2+302379//16*(1+-2x)^(1/2)+456533//64*(1+-2x)^-1//2)
@test integrate((1+-2x)^-3//2*(2+3x)^2*(3+5x)^3, x) == :(-21439//16*(1+-2x)^3//2+-12675//224*(1+-2x)^7//2+125//32*(1+-2x)^9//2+5711//16*(1+-2x)^5//2+65219//32*(1+-2x)^-1//2+144837//32*(1+-2x)^(1/2))
@test integrate((1+-2x)^-3//2*(3+5x)^3*(2+3x), x) == :(-935//4*(1+-2x)^3//2+-375//112*(1+-2x)^7//2+335//8*(1+-2x)^5//2+8349//8*(1+-2x)^(1/2)+9317//16*(1+-2x)^-1//2)
@test integrate((1+-2x)^-3//2*(3+5x)^3, x) == :(-275//8*(1+-2x)^3//2+25//8*(1+-2x)^5//2+1331//8*(1+-2x)^-1//2+1815//8*(1+-2x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-1*(3+5x)^3, x) == :(-125//36*(1+-2x)^3//2+400//9*(1+-2x)^(1/2)+1331//28*(1+-2x)^-1//2+2//1323*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-3//2*(2+3x)^-2*(3+5x)^3, x) == :(-68//3087*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+2*(1+-2x)^(1/2)*(294+441x)^-1*(1978+2975x)+11//7*(1+-2x)^-1//2*(2+3x)^-1*(3+5x)^2)
@test integrate((1+-2x)^-3//2*(2+3x)^-3*(3+5x)^3, x) == :(2245//21609*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+5//2058*(1+-2x)^(1/2)*(2+3x)^-2*(541+857x)+11//7*(1+-2x)^-1//2*(2+3x)^-2*(3+5x)^2)
@test integrate((1+-2x)^-3//2*(2+3x)^-4*(3+5x)^3, x) == :(-4660*(1+-2x)^(1/2)*(6174+9261x)^-1+-9320//64827*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+2//441*(1+-2x)^(1/2)*(2+3x)^-3*(297+470x)+11//7*(1+-2x)^-1//2*(2+3x)^-3*(3+5x)^2)
@test integrate((1+-2x)^-3//2*(2+3x)^-5*(3+5x)^3, x) == :(-39185*(1+-2x)^(1/2)*(115248+172872x)^-1+-39185//24696*(1+-2x)^(1/2)*(2+3x)^-2+-39185//605052*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+1//1764*(1+-2x)^(1/2)*(2+3x)^-4*(2395+3789x)+11//7*(1+-2x)^-1//2*(2+3x)^-4*(3+5x)^2)
@test integrate((1+-2x)^-3//2*(2+3x)^6*(3+5x)^-1, x) == :(-1997451//10000*(1+-2x)^3//2+-43011//5600*(1+-2x)^7//2+81//160*(1+-2x)^9//2+117649//352*(1+-2x)^-1//2+507627//10000*(1+-2x)^5//2+70752609//100000*(1+-2x)^(1/2)+-2//1890625*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-3//2*(2+3x)^5*(3+5x)^-1, x) == :(-17019//500*(1+-2x)^3//2+-243//560*(1+-2x)^7//2+5751//1000*(1+-2x)^5//2+16807//176*(1+-2x)^-1//2+806121//5000*(1+-2x)^(1/2)+-2//378125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-3//2*(2+3x)^4*(3+5x)^-1, x) == :(-963//200*(1+-2x)^3//2+81//200*(1+-2x)^5//2+2401//88*(1+-2x)^-1//2+34371//1000*(1+-2x)^(1/2)+-2//75625*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-3//2*(2+3x)^3*(3+5x)^-1, x) == :(-9//20*(1+-2x)^3//2+162//25*(1+-2x)^(1/2)+343//44*(1+-2x)^-1//2+-2//15125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-3//2*(2+3x)^2*(3+5x)^-1, x) == :(9//10*(1+-2x)^(1/2)+49//22*(1+-2x)^-1//2+-2//3025*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-3//2*(3+5x)^-1*(2+3x), x) == :(7//11*(1+-2x)^-1//2+-2//605*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-3//2*(3+5x)^-1, x) == :(2//11*(1+-2x)^-1//2+-2//121*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-3//2*(2+3x)^-1*(3+5x)^-1, x) == :(4//77*(1+-2x)^-1//2+-10//121*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+6//49*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-3//2*(2+3x)^-2*(3+5x)^-1, x) == :(-58//539*(1+-2x)^-1//2+-50//121*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+3//7*(1+-2x)^-1//2*(2+3x)^-1+228//343*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-3//2*(2+3x)^-3*(3+5x)^-1, x) == :(-2525//3773*(1+-2x)^-1//2+-250//121*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+3//14*(1+-2x)^-1//2*(2+3x)^-2+225//98*(1+-2x)^-1//2*(2+3x)^-1+8025//2401*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-3//2*(2+3x)^-4*(3+5x)^-1, x) == :(-12790//3773*(1+-2x)^-1//2+-1250//121*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+1//7*(1+-2x)^-1//2*(2+3x)^-3+8//7*(1+-2x)^-1//2*(2+3x)^-2+565//49*(1+-2x)^-1//2*(2+3x)^-1+40140//2401*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-3//2*(2+3x)^6*(3+5x)^-2, x) == :(-402//20796875*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+9//378125*(1+-2x)^(1/2)*(5065808+1688625x)+14517//21175*(1+-2x)^(1/2)*(2+3x)^3+217152//75625*(1+-2x)^(1/2)*(2+3x)^2+-36*(1+-2x)^(1/2)*(2+3x)^4*(1815+3025x)^-1+7//11*(1+-2x)^-1//2*(2+3x)^5*(3+5x)^-1)
@test integrate((1+-2x)^-3//2*(2+3x)^5*(3+5x)^-2, x) == :(-336//4159375*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+504//75625*(1+-2x)^(1/2)*(4499+1500x)+10836//15125*(1+-2x)^(1/2)*(2+3x)^2+-36*(1+-2x)^(1/2)*(2+3x)^3*(1815+3025x)^-1+7//11*(1+-2x)^-1//2*(2+3x)^4*(3+5x)^-1)
@test integrate((1+-2x)^-3//2*(2+3x)^4*(3+5x)^-2, x) == :(-54//166375*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+27//3025*(1+-2x)^(1/2)*(792+265x)+-36*(1+-2x)^(1/2)*(2+3x)^2*(1815+3025x)^-1+7//11*(1+-2x)^-1//2*(2+3x)^3*(3+5x)^-1)
@test integrate((1+-2x)^-3//2*(2+3x)^3*(3+5x)^-2, x) == :(-204//166375*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+18*(1+-2x)^(1/2)*(9075+15125x)^-1*(559+935x)+7//11*(1+-2x)^-1//2*(2+3x)^2*(3+5x)^-1)
@test integrate((1+-2x)^-3//2*(2+3x)^2*(3+5x)^-2, x) == :(-1227*(1+-2x)^(1/2)*(3630+6050x)^-1+-138//33275*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+49//22*(1+-2x)^-1//2*(3+5x)^-1)
@test integrate((1+-2x)^-3//2*(3+5x)^-2*(2+3x), x) == :(72//605*(1+-2x)^-1//2+-72//6655*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-1//55*(1+-2x)^-1//2*(3+5x)^-1)
@test integrate((1+-2x)^-3//2*(3+5x)^-2, x) == :(6//121*(1+-2x)^-1//2+-6//1331*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-1//11*(1+-2x)^-1//2*(3+5x)^-1)
@test integrate((1+-2x)^-3//2*(2+3x)^-1*(3+5x)^-2, x) == :(78//847*(1+-2x)^-1//2+-18//49*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-5//11*(1+-2x)^-1//2*(3+5x)^-1+300//1331*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-3//2*(2+3x)^-2*(3+5x)^-2, x) == :(4644//5929*(1+-2x)^-1//2+-1314//343*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-340//77*(1+-2x)^-1//2*(3+5x)^-1+3150//1331*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+3//7*(1+-2x)^-1//2*(2+3x)^-1*(3+5x)^-1)
@test integrate((1+-2x)^-3//2*(2+3x)^-3*(3+5x)^-2, x) == :(245865//41503*(1+-2x)^-1//2+-70065//2401*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-36175//1078*(1+-2x)^-1//2*(3+5x)^-1+24000//1331*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+3//14*(1+-2x)^-1//2*(2+3x)^-2*(3+5x)^-1+165//49*(1+-2x)^-1//2*(2+3x)^-1*(3+5x)^-1)
@test integrate((1+-2x)^-3//2*(2+3x)^6*(3+5x)^-3, x) == :(-33873//228765625*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+63//8318750*(1+-2x)^(1/2)*(2492512+831375x)+377748//831875*(1+-2x)^(1/2)*(2+3x)^2+-2721*(1+-2x)^(1/2)*(2+3x)^3*(199650+332750x)^-1+-71//1210*(1+-2x)^(1/2)*(2+3x)^4*(3+5x)^-2+7//11*(1+-2x)^-1//2*(2+3x)^5*(3+5x)^-2)
@test integrate((1+-2x)^-3//2*(2+3x)^5*(3+5x)^-3, x) == :(-4557//9150625*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+441//332750*(1+-2x)^(1/2)*(3344+1125x)+-1344*(1+-2x)^(1/2)*(2+3x)^2*(99825+166375x)^-1+-71//1210*(1+-2x)^(1/2)*(2+3x)^3*(3+5x)^-2+7//11*(1+-2x)^-1//2*(2+3x)^4*(3+5x)^-2)
@test integrate((1+-2x)^-3//2*(2+3x)^4*(3+5x)^-3, x) == :(-111//73205*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+9*(1+-2x)^(1/2)*(39930+66550x)^-1*(3044+5093x)+-71//1210*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^-2+7//11*(1+-2x)^-1//2*(2+3x)^3*(3+5x)^-2)
@test integrate((1+-2x)^-3//2*(2+3x)^3*(3+5x)^-3, x) == :(-7143//1830125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-1//66550*(1+-2x)^(1/2)*(3+5x)^-2*(15676+24825x)+7//11*(1+-2x)^-1//2*(2+3x)^2*(3+5x)^-2)
@test integrate((1+-2x)^-3//2*(2+3x)^2*(3+5x)^-3, x) == :(-2589*(1+-2x)^(1/2)*(39930+66550x)^-1+-2589//366025*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-613//605*(1+-2x)^(1/2)*(3+5x)^-2+49//22*(1+-2x)^-1//2*(3+5x)^-2)
@test integrate((1+-2x)^-3//2*(3+5x)^-3*(2+3x), x) == :(213//6655*(1+-2x)^-1//2+-213//73205*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-71//1210*(1+-2x)^-1//2*(3+5x)^-1+-1//110*(1+-2x)^-1//2*(3+5x)^-2)
@test integrate((1+-2x)^-3//2*(3+5x)^-3, x) == :(15//1331*(1+-2x)^-1//2+-15//14641*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-5//242*(1+-2x)^-1//2*(3+5x)^-1+-1//22*(1+-2x)^-1//2*(3+5x)^-2)
@test integrate((1+-2x)^-3//2*(2+3x)^-1*(3+5x)^-3, x) == :(-2049//9317*(1+-2x)^-1//2+-9975//14641*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-5//22*(1+-2x)^-1//2*(3+5x)^-2+54//49*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+305//242*(1+-2x)^-1//2*(3+5x)^-1)
@test integrate((1+-2x)^-3//2*(2+3x)^-2*(3+5x)^-3, x) == :(-224967//65219*(1+-2x)^-1//2+-153825//14641*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-505//154*(1+-2x)^-1//2*(3+5x)^-2+5832//343*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+33115//1694*(1+-2x)^-1//2*(3+5x)^-1+3//7*(1+-2x)^-1//2*(2+3x)^-1*(3+5x)^-2)
@test integrate((1+-2x)^-3//2*(2+3x)^-3*(3+5x)^-3, x) == :(-15987390//456533*(1+-2x)^-1//2+-1561125//14641*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-35825//1078*(1+-2x)^-1//2*(3+5x)^-2+414315//2401*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+1176400//5929*(1+-2x)^-1//2*(3+5x)^-1+3//14*(1+-2x)^-1//2*(2+3x)^-2*(3+5x)^-2+435//98*(1+-2x)^-1//2*(2+3x)^-1*(3+5x)^-2)
@test integrate((1+-2x)^-5//2*(2+3x)^5*(3+5x), x) == :(-519645//64*(1+-2x)^(1/2)+-60025//8*(1+-2x)^-1//2+-19467//64*(1+-2x)^5//2+-135//64*(1+-2x)^9//2+1053//28*(1+-2x)^7//2+12495//8*(1+-2x)^3//2+184877//192*(1+-2x)^-3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^4*(3+5x), x) == :(-57281//32*(1+-2x)^-1//2+-24843//16*(1+-2x)^(1/2)+-4671//160*(1+-2x)^5//2+405//224*(1+-2x)^7//2+3591//16*(1+-2x)^3//2+26411//96*(1+-2x)^-3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^3*(3+5x), x) == :(-3283//8*(1+-2x)^-1//2+-1071//4*(1+-2x)^(1/2)+-27//16*(1+-2x)^5//2+207//8*(1+-2x)^3//2+3773//48*(1+-2x)^-3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^2*(3+5x), x) == :(-707//8*(1+-2x)^-1//2+-309//8*(1+-2x)^(1/2)+15//8*(1+-2x)^3//2+539//24*(1+-2x)^-3//2)
@test integrate((1+-2x)^-5//2*(2+3x)*(3+5x), x) == :(-17*(1+-2x)^-1//2+-15//4*(1+-2x)^(1/2)+77//12*(1+-2x)^-3//2)
@test integrate((1+-2x)^-5//2*(3+5x), x) == :(-5//2*(1+-2x)^-1//2+11//6*(1+-2x)^-3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^-1*(3+5x), x) == :(-2//49*(1+-2x)^-1//2+11//21*(1+-2x)^-3//2+2//343*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-5//2*(2+3x)^-2*(3+5x), x) == :(20//147*(1+-2x)^-3//2+60//343*(1+-2x)^-1//2+-60//2401*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+1//21*(1+-2x)^-3//2*(2+3x)^-1)
@test integrate((1+-2x)^-5//2*(2+3x)^-3*(3+5x), x) == :(5//49*(1+-2x)^-3//2+45//343*(1+-2x)^-1//2+-45//2401*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-3//14*(1+-2x)^-3//2*(2+3x)^-1+1//42*(1+-2x)^-3//2*(2+3x)^-2)
@test integrate((1+-2x)^-5//2*(2+3x)^-4*(3+5x), x) == :(160//2401*(1+-2x)^-1//2+160//3087*(1+-2x)^-3//2+-160//16807*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-16//147*(1+-2x)^-3//2*(2+3x)^-1+-16//147*(1+-2x)^-3//2*(2+3x)^-2+1//63*(1+-2x)^-3//2*(2+3x)^-3)
@test integrate((1+-2x)^-5//2*(2+3x)^-5*(3+5x), x) == :(215//9604*(1+-2x)^-3//2+1935//67228*(1+-2x)^-1//2+-1935//470596*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-129//2744*(1+-2x)^-3//2*(2+3x)^-1+-129//2744*(1+-2x)^-3//2*(2+3x)^-2+-43//588*(1+-2x)^-3//2*(2+3x)^-3+1//84*(1+-2x)^-3//2*(2+3x)^-4)
@test integrate((1+-2x)^-5//2*(2+3x)^5*(3+5x)^2, x) == :(-8117095//128*(1+-2x)^(1/2)+-6206585//128*(1+-2x)^-1//2+-514017//128*(1+-2x)^5//2+-10845//128*(1+-2x)^9//2+6075//1408*(1+-2x)^11//2+672003//896*(1+-2x)^7//2+1965635//128*(1+-2x)^3//2+2033647//384*(1+-2x)^-3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^4*(3+5x)^2, x) == :(-832951//64*(1+-2x)^(1/2)+-381073//32*(1+-2x)^-1//2+-159111//320*(1+-2x)^5//2+-225//64*(1+-2x)^9//2+13905//224*(1+-2x)^7//2+40453//16*(1+-2x)^3//2+290521//192*(1+-2x)^-3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^3*(3+5x)^2, x) == :(-91091//32*(1+-2x)^-1//2+-39977//16*(1+-2x)^(1/2)+-1539//32*(1+-2x)^5//2+675//224*(1+-2x)^7//2+5847//16*(1+-2x)^3//2+41503//96*(1+-2x)^-3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^2*(3+5x)^2, x) == :(-3467//8*(1+-2x)^(1/2)+-1309//2*(1+-2x)^-1//2+-45//16*(1+-2x)^5//2+85//2*(1+-2x)^3//2+5929//48*(1+-2x)^-3//2)
@test integrate((1+-2x)^-5//2*(3+5x)^2*(2+3x), x) == :(-1133//8*(1+-2x)^-1//2+-505//8*(1+-2x)^(1/2)+25//8*(1+-2x)^3//2+847//24*(1+-2x)^-3//2)
@test integrate((1+-2x)^-5//2*(3+5x)^2, x) == :(-55//2*(1+-2x)^-1//2+-25//4*(1+-2x)^(1/2)+121//12*(1+-2x)^-3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^-1*(3+5x)^2, x) == :(-407//98*(1+-2x)^-1//2+121//42*(1+-2x)^-3//2+-2//1029*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-5//2*(2+3x)^-2*(3+5x)^2, x) == :(-130//1029*(1+-2x)^-1//2+-365//294*(1+-2x)^-1//2*(2+3x)^-1+121//42*(1+-2x)^-3//2*(2+3x)^-1+130//7203*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-5//2*(2+3x)^-3*(3+5x)^2, x) == :(85//343*(1+-2x)^-1//2+-85//294*(1+-2x)^-1//2*(2+3x)^-1+-85//2401*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-26//21*(1+-2x)^-1//2*(2+3x)^-2+121//42*(1+-2x)^-3//2*(2+3x)^-2)
@test integrate((1+-2x)^-5//2*(2+3x)^-4*(3+5x)^2, x) == :(1415//7203*(1+-2x)^-1//2+-1415//6174*(1+-2x)^-1//2*(2+3x)^-1+-1415//50421*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-1091//882*(1+-2x)^-1//2*(2+3x)^-3+-283//882*(1+-2x)^-1//2*(2+3x)^-2+121//42*(1+-2x)^-3//2*(2+3x)^-3)
@test integrate((1+-2x)^-5//2*(2+3x)^-5*(3+5x)^2, x) == :(20465//201684*(1+-2x)^-1//2+-20465//172872*(1+-2x)^-1//2*(2+3x)^-1+-20465//1411788*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-4093//12348*(1+-2x)^-1//2*(2+3x)^-3+-4093//24696*(1+-2x)^-1//2*(2+3x)^-2+-727//588*(1+-2x)^-1//2*(2+3x)^-4+121//42*(1+-2x)^-3//2*(2+3x)^-4)
@test integrate((1+-2x)^-5//2*(2+3x)^5*(3+5x)^3, x) == :(-60160485//128*(1+-2x)^(1/2)+-39220335//128*(1+-2x)^-1//2+-2887773//64*(1+-2x)^5//2+-246315//128*(1+-2x)^9//2+-30375//3328*(1+-2x)^13//2+277425//1408*(1+-2x)^11//2+10121229//896*(1+-2x)^7//2+22370117//768*(1+-2x)^-3//2+52725715//384*(1+-2x)^3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^4*(3+5x)^3, x) == :(-12973191//128*(1+-2x)^(1/2)+-9836211//128*(1+-2x)^-1//2+-4177401//640*(1+-2x)^5//2+-17925//128*(1+-2x)^9//2+10125//1408*(1+-2x)^11//2+1101465//896*(1+-2x)^7//2+3195731//384*(1+-2x)^-3//2+9504551//384*(1+-2x)^3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^3*(3+5x)^3, x) == :(-1334949//64*(1+-2x)^(1/2)+-302379//16*(1+-2x)^-1//2+-52011//64*(1+-2x)^5//2+-375//64*(1+-2x)^9//2+11475//112*(1+-2x)^7//2+98209//24*(1+-2x)^3//2+456533//192*(1+-2x)^-3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^2*(3+5x)^3, x) == :(-144837//32*(1+-2x)^-1//2+-64317//16*(1+-2x)^(1/2)+-2535//32*(1+-2x)^5//2+1125//224*(1+-2x)^7//2+28555//48*(1+-2x)^3//2+65219//96*(1+-2x)^-3//2)
@test integrate((1+-2x)^-5//2*(3+5x)^3*(2+3x), x) == :(-8349//8*(1+-2x)^-1//2+-2805//4*(1+-2x)^(1/2)+-75//16*(1+-2x)^5//2+1675//24*(1+-2x)^3//2+9317//48*(1+-2x)^-3//2)
@test integrate((1+-2x)^-5//2*(3+5x)^3, x) == :(-1815//8*(1+-2x)^-1//2+-825//8*(1+-2x)^(1/2)+125//24*(1+-2x)^3//2+1331//24*(1+-2x)^-3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^-1*(3+5x)^3, x) == :(-2178//49*(1+-2x)^-1//2+-125//12*(1+-2x)^(1/2)+1331//84*(1+-2x)^-3//2+2//3087*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-5//2*(2+3x)^-2*(3+5x)^3, x) == :(-200//21609*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-1//1029*(1+-2x)^-1//2*(2+3x)^-1*(9690+14500x)+11//21*(1+-2x)^-3//2*(2+3x)^-1*(3+5x)^2)
@test integrate((1+-2x)^-5//2*(2+3x)^-3*(3+5x)^3, x) == :(905*(1+-2x)^(1/2)*(4116+6174x)^-1+905//21609*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-1//294*(1+-2x)^-1//2*(2+3x)^-2*(487+720x)+11//21*(1+-2x)^-3//2*(2+3x)^-2*(3+5x)^2)
@test integrate((1+-2x)^-5//2*(2+3x)^-4*(3+5x)^3, x) == :(-3755*(1+-2x)^(1/2)*(14406+21609x)^-1+-7510//151263*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-3755//3087*(1+-2x)^(1/2)*(2+3x)^-2+1//441*(1+-2x)^-1//2*(2+3x)^-3*(2692+4054x)+11//21*(1+-2x)^-3//2*(2+3x)^-3*(3+5x)^2)
@test integrate((1+-2x)^-5//2*(2+3x)^-5*(3+5x)^3, x) == :(-177635*(1+-2x)^(1/2)*(806736+1210104x)^-1+-177635//172872*(1+-2x)^(1/2)*(2+3x)^-2+-177635//4235364*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-35527//12348*(1+-2x)^(1/2)*(2+3x)^-3+1//4116*(1+-2x)^-1//2*(2+3x)^-4*(57069+85754x)+11//21*(1+-2x)^-3//2*(2+3x)^-4*(3+5x)^2)
@test integrate((1+-2x)^-5//2*(2+3x)^-6*(3+5x)^3, x) == :(-81737*(1+-2x)^(1/2)*(705894+1058841x)^-1+-163474//36015*(1+-2x)^(1/2)*(2+3x)^-4+-163474//108045*(1+-2x)^(1/2)*(2+3x)^-3+-163474//7411887*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-81737//151263*(1+-2x)^(1/2)*(2+3x)^-2+1//5145*(1+-2x)^-1//2*(2+3x)^-5*(111266+167088x)+11//21*(1+-2x)^-3//2*(2+3x)^-5*(3+5x)^2)
@test integrate((1+-2x)^-5//2*(2+3x)^6*(3+5x)^-1, x) == :(-5992353//10000*(1+-2x)^(1/2)+-2739541//3872*(1+-2x)^-1//2+-43011//4000*(1+-2x)^5//2+729//1120*(1+-2x)^7//2+117649//1056*(1+-2x)^-3//2+169209//2000*(1+-2x)^3//2+-2//4159375*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-5//2*(2+3x)^5*(3+5x)^-1, x) == :(-156065//968*(1+-2x)^-1//2+-51057//500*(1+-2x)^(1/2)+-243//400*(1+-2x)^5//2+1917//200*(1+-2x)^3//2+16807//528*(1+-2x)^-3//2+-2//831875*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-5//2*(2+3x)^4*(3+5x)^-1, x) == :(-33271//968*(1+-2x)^-1//2+-2889//200*(1+-2x)^(1/2)+27//40*(1+-2x)^3//2+2401//264*(1+-2x)^-3//2+-2//166375*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-5//2*(2+3x)^3*(3+5x)^-1, x) == :(-784//121*(1+-2x)^-1//2+-27//20*(1+-2x)^(1/2)+343//132*(1+-2x)^-3//2+-2//33275*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-5//2*(2+3x)^2*(3+5x)^-1, x) == :(-217//242*(1+-2x)^-1//2+49//66*(1+-2x)^-3//2+-2//6655*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-5//2*(3+5x)^-1*(2+3x), x) == :(2//121*(1+-2x)^-1//2+7//33*(1+-2x)^-3//2+-2//1331*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-5//2*(3+5x)^-1, x) == :(2//33*(1+-2x)^-3//2+10//121*(1+-2x)^-1//2+-10//1331*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-5//2*(2+3x)^-1*(3+5x)^-1, x) == :(4//231*(1+-2x)^-3//2+272//5929*(1+-2x)^-1//2+-50//1331*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+18//343*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-5//2*(2+3x)^-2*(3+5x)^-1, x) == :(-1370//41503*(1+-2x)^-1//2+-190//1617*(1+-2x)^-3//2+-250//1331*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+3//7*(1+-2x)^-3//2*(2+3x)^-1+720//2401*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-5//2*(2+3x)^-3*(3+5x)^-1, x) == :(-12295//41503*(1+-2x)^-1//2+-1115//1617*(1+-2x)^-3//2+-1250//1331*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+3//14*(1+-2x)^-3//2*(2+3x)^-2+33//14*(1+-2x)^-3//2*(2+3x)^-1+3645//2401*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-5//2*(2+3x)^-4*(3+5x)^-1, x) == :(-446660//290521*(1+-2x)^-1//2+-39520//11319*(1+-2x)^-3//2+-6250//1331*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+1//7*(1+-2x)^-3//2*(2+3x)^-3+57//49*(1+-2x)^-3//2*(2+3x)^-2+582//49*(1+-2x)^-3//2*(2+3x)^-1+127710//16807*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-5//2*(2+3x)^6*(3+5x)^-2, x) == :(-463344//166375*(1+-2x)^(1/2)*(2+3x)^2+-10283//6655*(1+-2x)^-1//2*(2+3x)^3+-406//45753125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-21//831875*(1+-2x)^(1/2)*(4633904+1544625x)+-38//1815*(1+-2x)^-1//2*(2+3x)^4*(3+5x)^-1+7//33*(1+-2x)^-3//2*(2+3x)^5*(3+5x)^-1)
@test integrate((1+-2x)^-5//2*(2+3x)^5*(3+5x)^-2, x) == :(-7588//6655*(1+-2x)^-1//2*(2+3x)^2+-68//1830125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-6//33275*(1+-2x)^(1/2)*(114092+38025x)+-38//1815*(1+-2x)^-1//2*(2+3x)^3*(3+5x)^-1+7//33*(1+-2x)^-3//2*(2+3x)^4*(3+5x)^-1)
@test integrate((1+-2x)^-5//2*(2+3x)^4*(3+5x)^-2, x) == :(-274//1830125*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-1//33275*(1+-2x)^-1//2*(122736+-74217x)+-38//1815*(1+-2x)^-1//2*(2+3x)^2*(3+5x)^-1+7//33*(1+-2x)^-3//2*(2+3x)^3*(3+5x)^-1)
@test integrate((1+-2x)^-5//2*(2+3x)^3*(3+5x)^-2, x) == :(-208//366025*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-1//19965*(1+-2x)^-1//2*(3+5x)^-1*(20618+34224x)+7//33*(1+-2x)^-3//2*(2+3x)^2*(3+5x)^-1)
@test integrate((1+-2x)^-5//2*(2+3x)^2*(3+5x)^-2, x) == :(142//6655*(1+-2x)^-1//2+-1231//3630*(1+-2x)^-1//2*(3+5x)^-1+-142//73205*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+49//66*(1+-2x)^-3//2*(3+5x)^-1)
@test integrate((1+-2x)^-5//2*(3+5x)^-2*(2+3x), x) == :(76//1331*(1+-2x)^-1//2+76//1815*(1+-2x)^-3//2+-76//14641*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-1//55*(1+-2x)^-3//2*(3+5x)^-1)
@test integrate((1+-2x)^-5//2*(3+5x)^-2, x) == :(10//363*(1+-2x)^-3//2+50//1331*(1+-2x)^-1//2+-50//14641*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-1//11*(1+-2x)^-3//2*(3+5x)^-1)
@test integrate((1+-2x)^-5//2*(2+3x)^-1*(3+5x)^-2, x) == :(218//2541*(1+-2x)^-3//2+3274//65219*(1+-2x)^-1//2+-54//343*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-5//11*(1+-2x)^-3//2*(3+5x)^-1+1400//14641*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2)))
@test integrate((1+-2x)^-5//2*(2+3x)^-2*(3+5x)^-2, x) == :(13900//17787*(1+-2x)^-3//2+159800//456533*(1+-2x)^-1//2+-4050//2401*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-340//77*(1+-2x)^-3//2*(3+5x)^-1+15250//14641*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+3//7*(1+-2x)^-3//2*(2+3x)^-1*(3+5x)^-1)
@test integrate((1+-2x)^-5//2*(2+3x)^-3*(3+5x)^-2, x) == :(15185//2541*(1+-2x)^-3//2+172105//65219*(1+-2x)^-1//2+-4455//343*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+-745//22*(1+-2x)^-3//2*(3+5x)^-1+117500//14641*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+3//14*(1+-2x)^-3//2*(2+3x)^-2*(3+5x)^-1+24//7*(1+-2x)^-3//2*(2+3x)^-1*(3+5x)^-1)
@test integrate((1+-2x)^-5//2*(2+3x)^6*(3+5x)^-3, x) == :(-256172//366025*(1+-2x)^-1//2*(2+3x)^2+-6937//100656875*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-21//3660250*(1+-2x)^(1/2)*(2211616+736875x)+-3269//199650*(1+-2x)^-1//2*(2+3x)^3*(3+5x)^-1+-73//3630*(1+-2x)^-1//2*(2+3x)^4*(3+5x)^-2+7//33*(1+-2x)^-3//2*(2+3x)^5*(3+5x)^-2)
@test integrate((1+-2x)^-5//2*(2+3x)^5*(3+5x)^-3, x) == :(-4693//20131375*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-1//732050*(1+-2x)^-1//2*(1633704+-999933x)+-317//19965*(1+-2x)^-1//2*(2+3x)^2*(3+5x)^-1+-73//3630*(1+-2x)^-1//2*(2+3x)^3*(3+5x)^-2+7//33*(1+-2x)^-3//2*(2+3x)^4*(3+5x)^-2)
@test integrate((1+-2x)^-5//2*(2+3x)^4*(3+5x)^-3, x) == :(-14423//20131375*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-73//3630*(1+-2x)^-1//2*(2+3x)^2*(3+5x)^-2+-1//2196150*(1+-2x)^-1//2*(3+5x)^-1*(1287116+2133933x)+7//33*(1+-2x)^-3//2*(2+3x)^3*(3+5x)^-2)
@test integrate((1+-2x)^-5//2*(2+3x)^3*(3+5x)^-3, x) == :(-7559*(1+-2x)^(1/2)*(439230+732050x)^-1+-7559//4026275*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+1//39930*(1+-2x)^-1//2*(3+5x)^-2*(10217+17296x)+7//33*(1+-2x)^-3//2*(2+3x)^2*(3+5x)^-2)
@test integrate((1+-2x)^-5//2*(2+3x)^2*(3+5x)^-3, x) == :(2873//73205*(1+-2x)^-1//2+-2873//39930*(1+-2x)^-1//2*(3+5x)^-1+-2873//805255*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-614//1815*(1+-2x)^-1//2*(3+5x)^-2+49//66*(1+-2x)^-3//2*(3+5x)^-2)
@test integrate((1+-2x)^-5//2*(3+5x)^-3*(2+3x), x) == :(73//3993*(1+-2x)^-3//2+365//14641*(1+-2x)^-1//2+-365//161051*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-73//1210*(1+-2x)^-3//2*(3+5x)^-1+-1//110*(1+-2x)^-3//2*(3+5x)^-2)
@test integrate((1+-2x)^-5//2*(3+5x)^-3, x) == :(35//3993*(1+-2x)^-3//2+175//14641*(1+-2x)^-1//2+-175//161051*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-7//242*(1+-2x)^-3//2*(3+5x)^-1+-1//22*(1+-2x)^-3//2*(3+5x)^-2)
@test integrate((1+-2x)^-5//2*(2+3x)^-1*(3+5x)^-3, x) == :(-65167//717409*(1+-2x)^-1//2+-5969//27951*(1+-2x)^-3//2+-47075//161051*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-5//22*(1+-2x)^-3//2*(3+5x)^-2+162//343*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+295//242*(1+-2x)^-3//2*(3+5x)^-1)
@test integrate((1+-2x)^-5//2*(2+3x)^-2*(3+5x)^-3, x) == :(-7554245//5021863*(1+-2x)^-1//2+-667615//195657*(1+-2x)^-3//2+-738625//161051*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-505//154*(1+-2x)^-3//2*(3+5x)^-2+17820//2401*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+32765//1694*(1+-2x)^-3//2*(3+5x)^-1+3//7*(1+-2x)^-3//2*(2+3x)^-1*(3+5x)^-2)
@test integrate((1+-2x)^-5//2*(2+3x)^-3*(3+5x)^-3, x) == :(-77527480//5021863*(1+-2x)^-1//2+-6845810//195657*(1+-2x)^-3//2+-7570625//161051*55^(1/2)*arctanh(1//11*55^(1/2)*(1+-2x)^(1/2))+-5165//154*(1+-2x)^-3//2*(3+5x)^-2+167960//847*(1+-2x)^-3//2*(3+5x)^-1+182655//2401*21^(1/2)*arctanh(1//7*21^(1/2)*(1+-2x)^(1/2))+3//14*(1+-2x)^-3//2*(2+3x)^-2*(3+5x)^-2+9//2*(1+-2x)^-3//2*(2+3x)^-1*(3+5x)^-2)
@test integrate((a+b*x)^(1/2)*(d+e*x)^5//2*(A+B*x), x) == :(-1//40*b^-2*e^-1*(a+b*x)^3//2*(d+e*x)^5//2*(-10*A*b*e+3*B*b*d+7*B*a*e)+1//5*B*b^-1*e^-1*(a+b*x)^3//2*(d+e*x)^7//2+1//128*b^-9//2*e^-5//2*(b*d+-1*a*e)^4*(-10*A*b*e+3*B*b*d+7*B*a*e)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+-1//48*b^-3*e^-1*(a+b*x)^3//2*(d+e*x)^3//2*(b*d+-1*a*e)*(-10*A*b*e+3*B*b*d+7*B*a*e)+-1//64*b^-4*e^-1*(a+b*x)^3//2*(d+e*x)^(1/2)*(b*d+-1*a*e)^2*(-10*A*b*e+3*B*b*d+7*B*a*e)+-1//128*b^-4*e^-2*(a+b*x)^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^3*(-10*A*b*e+3*B*b*d+7*B*a*e))
@test integrate((a+b*x)^(1/2)*(d+e*x)^3//2*(A+B*x), x) == :(-1//24*b^-2*e^-1*(a+b*x)^3//2*(d+e*x)^3//2*(-8*A*b*e+3*B*b*d+5*B*a*e)+1//4*B*b^-1*e^-1*(a+b*x)^3//2*(d+e*x)^5//2+1//64*b^-7//2*e^-5//2*(b*d+-1*a*e)^3*(-8*A*b*e+3*B*b*d+5*B*a*e)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+-1//32*b^-3*e^-1*(a+b*x)^3//2*(d+e*x)^(1/2)*(b*d+-1*a*e)*(-8*A*b*e+3*B*b*d+5*B*a*e)+-1//64*b^-3*e^-2*(a+b*x)^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^2*(-8*A*b*e+3*B*b*d+5*B*a*e))
@test integrate((a+b*x)^(1/2)*(d+e*x)^(1/2)*(A+B*x), x) == :(-1//8*b^-5//2*e^-5//2*(b*d+-1*a*e)^2*(-1*B*(a*e+b*d)+2*A*b*e)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+1//3*B*b^-1*e^-1*(a+b*x)^3//2*(d+e*x)^3//2+1//4*b^-2*e^-1*(a+b*x)^3//2*(d+e*x)^(1/2)*(-1*B*(a*e+b*d)+2*A*b*e)+1//8*b^-2*e^-2*(a+b*x)^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)*(-1*B*(a*e+b*d)+2*A*b*e))
@test integrate((a+b*x)^(1/2)*(d+e*x)^-1//2*(A+B*x), x) == :((1/2)*B*b^-1*e^-1*(a+b*x)^3//2*(d+e*x)^(1/2)+-1//4*b^-1*e^-2*(a+b*x)^(1/2)*(d+e*x)^(1/2)*(B*a*e+-4*A*b*e+3*B*b*d)+1//4*b^-3//2*e^-5//2*(b*d+-1*a*e)*(B*a*e+-4*A*b*e+3*B*b*d)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2))
@test integrate((a+b*x)^(1/2)*(d+e*x)^-3//2*(A+B*x), x) == :(-1*b^-1//2*e^-5//2*(-1*B*a*e+-2*A*b*e+3*B*b*d)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+e^-1*(a+b*x)^3//2*(d+e*x)^-1//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e)+e^-2*(a+b*x)^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1*(-1*B*a*e+-2*A*b*e+3*B*b*d))
@test integrate((a+b*x)^(1/2)*(d+e*x)^-5//2*(A+B*x), x) == :(-2*B*e^-2*(a+b*x)^(1/2)*(d+e*x)^-1//2+2*B*b^(1/2)*e^-5//2*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+1//3*e^-1*(a+b*x)^3//2*(d+e*x)^-3//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e))
@test integrate((a+b*x)^(1/2)*(d+e*x)^-7//2*(A+B*x), x) == :(1//5*e^-1*(a+b*x)^3//2*(d+e*x)^-5//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e)+1//15*e^-1*(a+b*x)^3//2*(d+e*x)^-3//2*(b*d+-1*a*e)^-2*(-10*B*a*e+4*A*b*e+6*B*b*d))
@test integrate((a+b*x)^(1/2)*(d+e*x)^-9//2*(A+B*x), x) == :(1//7*e^-1*(a+b*x)^3//2*(d+e*x)^-7//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e)+1//35*e^-1*(a+b*x)^3//2*(d+e*x)^-5//2*(b*d+-1*a*e)^-2*(-14*B*a*e+6*B*b*d+8*A*b*e)+4//105*b*e^-1*(a+b*x)^3//2*(d+e*x)^-3//2*(b*d+-1*a*e)^-3*(-7*B*a*e+3*B*b*d+4*A*b*e))
@test integrate((a+b*x)^(1/2)*(d+e*x)^-11//2*(A+B*x), x) == :(1//9*e^-1*(a+b*x)^3//2*(d+e*x)^-9//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e)+1//21*e^-1*(a+b*x)^3//2*(d+e*x)^-7//2*(b*d+-1*a*e)^-2*(-6*B*a*e+2*B*b*d+4*A*b*e)+8//105*b*e^-1*(a+b*x)^3//2*(d+e*x)^-5//2*(b*d+-1*a*e)^-3*(B*b*d+-3*B*a*e+2*A*b*e)+16//315*b^2*e^-1*(a+b*x)^3//2*(d+e*x)^-3//2*(b*d+-1*a*e)^-4*(B*b*d+-3*B*a*e+2*A*b*e))
@test integrate((a+b*x)^(1/2)*(d+e*x)^-13//2*(A+B*x), x) == :(1//11*e^-1*(a+b*x)^3//2*(d+e*x)^-11//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e)+1//99*e^-1*(a+b*x)^3//2*(d+e*x)^-9//2*(b*d+-1*a*e)^-2*(-22*B*a*e+6*B*b*d+16*A*b*e)+4//231*b*e^-1*(a+b*x)^3//2*(d+e*x)^-7//2*(b*d+-1*a*e)^-3*(-11*B*a*e+3*B*b*d+8*A*b*e)+16//1155*b^2*e^-1*(a+b*x)^3//2*(d+e*x)^-5//2*(b*d+-1*a*e)^-4*(-11*B*a*e+3*B*b*d+8*A*b*e)+32//3465*b^3*e^-1*(a+b*x)^3//2*(d+e*x)^-3//2*(b*d+-1*a*e)^-5*(-11*B*a*e+3*B*b*d+8*A*b*e))
@test integrate((a+b*x)^(1/2)*(d+e*x)^-15//2*(A+B*x), x) == :(1//13*e^-1*(a+b*x)^3//2*(d+e*x)^-13//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e)+1//143*e^-1*(a+b*x)^3//2*(d+e*x)^-11//2*(b*d+-1*a*e)^-2*(-26*B*a*e+6*B*b*d+20*A*b*e)+16//1287*b*e^-1*(a+b*x)^3//2*(d+e*x)^-9//2*(b*d+-1*a*e)^-3*(-13*B*a*e+3*B*b*d+10*A*b*e)+32//3003*b^2*e^-1*(a+b*x)^3//2*(d+e*x)^-7//2*(b*d+-1*a*e)^-4*(-13*B*a*e+3*B*b*d+10*A*b*e)+128//15015*b^3*e^-1*(a+b*x)^3//2*(d+e*x)^-5//2*(b*d+-1*a*e)^-5*(-13*B*a*e+3*B*b*d+10*A*b*e)+256//45045*b^4*e^-1*(a+b*x)^3//2*(d+e*x)^-3//2*(b*d+-1*a*e)^-6*(-13*B*a*e+3*B*b*d+10*A*b*e))
@test integrate((a+b*x)^3//2*(d+e*x)^5//2*(A+B*x), x) == :(-1//60*b^-2*e^-1*(a+b*x)^5//2*(d+e*x)^5//2*(-12*A*b*e+5*B*b*d+7*B*a*e)+-1//512*b^-9//2*e^-7//2*(b*d+-1*a*e)^5*(-12*A*b*e+5*B*b*d+7*B*a*e)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+1//6*B*b^-1*e^-1*(a+b*x)^5//2*(d+e*x)^7//2+-1//96*b^-3*e^-1*(a+b*x)^5//2*(d+e*x)^3//2*(b*d+-1*a*e)*(-12*A*b*e+5*B*b*d+7*B*a*e)+-1//192*b^-4*e^-1*(a+b*x)^5//2*(d+e*x)^(1/2)*(b*d+-1*a*e)^2*(-12*A*b*e+5*B*b*d+7*B*a*e)+-1//768*b^-4*e^-2*(a+b*x)^3//2*(d+e*x)^(1/2)*(b*d+-1*a*e)^3*(-12*A*b*e+5*B*b*d+7*B*a*e)+1//512*b^-4*e^-3*(a+b*x)^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^4*(-12*A*b*e+5*B*b*d+7*B*a*e))
@test integrate((a+b*x)^3//2*(d+e*x)^3//2*(A+B*x), x) == :(1//5*B*b^-1*e^-1*(a+b*x)^5//2*(d+e*x)^5//2+1//8*b^-2*e^-1*(a+b*x)^5//2*(d+e*x)^3//2*(-1*B*(a*e+b*d)+2*A*b*e)+3//128*b^-7//2*e^-7//2*(b*d+-1*a*e)^4*(-1*B*(a*e+b*d)+2*A*b*e)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+-3//128*b^-3*e^-3*(a+b*x)^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^3*(-1*B*(a*e+b*d)+2*A*b*e)+1//16*b^-3*e^-1*(a+b*x)^5//2*(d+e*x)^(1/2)*(b*d+-1*a*e)*(-1*B*(a*e+b*d)+2*A*b*e)+1//64*b^-3*e^-2*(a+b*x)^3//2*(d+e*x)^(1/2)*(b*d+-1*a*e)^2*(-1*B*(a*e+b*d)+2*A*b*e))
@test integrate((a+b*x)^3//2*(d+e*x)^(1/2)*(A+B*x), x) == :(-1//24*b^-2*e^-1*(a+b*x)^5//2*(d+e*x)^(1/2)*(-8*A*b*e+3*B*a*e+5*B*b*d)+-1//64*b^-5//2*e^-7//2*(b*d+-1*a*e)^3*(-8*A*b*e+3*B*a*e+5*B*b*d)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+1//4*B*b^-1*e^-1*(a+b*x)^5//2*(d+e*x)^3//2+-1//96*b^-2*e^-2*(a+b*x)^3//2*(d+e*x)^(1/2)*(b*d+-1*a*e)*(-8*A*b*e+3*B*a*e+5*B*b*d)+1//64*b^-2*e^-3*(a+b*x)^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^2*(-8*A*b*e+3*B*a*e+5*B*b*d))
@test integrate((a+b*x)^3//2*(d+e*x)^-1//2*(A+B*x), x) == :(-1//8*b^-3//2*e^-7//2*(b*d+-1*a*e)^2*(B*a*e+-6*A*b*e+5*B*b*d)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+-1//12*b^-1*e^-2*(a+b*x)^3//2*(d+e*x)^(1/2)*(B*a*e+-6*A*b*e+5*B*b*d)+1//3*B*b^-1*e^-1*(a+b*x)^5//2*(d+e*x)^(1/2)+1//8*b^-1*e^-3*(a+b*x)^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)*(B*a*e+-6*A*b*e+5*B*b*d))
@test integrate((a+b*x)^3//2*(d+e*x)^-3//2*(A+B*x), x) == :(-1//4*e^-3*(a+b*x)^(1/2)*(d+e*x)^(1/2)*(-12*A*b*e+-3*B*a*e+15*B*b*d)+e^-1*(a+b*x)^5//2*(d+e*x)^-1//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e)+(1/2)*e^-2*(a+b*x)^3//2*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1*(-1*B*a*e+-4*A*b*e+5*B*b*d)+1//4*b^-1//2*e^-7//2*(-3*a*e+3*b*d)*(-1*B*a*e+-4*A*b*e+5*B*b*d)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2))
@test integrate((a+b*x)^3//2*(d+e*x)^-5//2*(A+B*x), x) == :(-1*b^(1/2)*e^-7//2*(-3*B*a*e+-2*A*b*e+5*B*b*d)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+-1//3*e^-2*(a+b*x)^3//2*(d+e*x)^-1//2*(b*d+-1*a*e)^-1*(-6*B*a*e+-4*A*b*e+10*B*b*d)+1//3*e^-1*(a+b*x)^5//2*(d+e*x)^-3//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e)+b*e^-3*(a+b*x)^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1*(-3*B*a*e+-2*A*b*e+5*B*b*d))
@test integrate((a+b*x)^3//2*(d+e*x)^-7//2*(A+B*x), x) == :(2*B*b^3//2*e^-7//2*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+-2//3*B*e^-2*(a+b*x)^3//2*(d+e*x)^-3//2+-2*B*b*e^-3*(a+b*x)^(1/2)*(d+e*x)^-1//2+1//5*e^-1*(a+b*x)^5//2*(d+e*x)^-5//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e))
@test integrate((a+b*x)^3//2*(d+e*x)^-9//2*(A+B*x), x) == :(1//7*e^-1*(a+b*x)^5//2*(d+e*x)^-7//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e)+1//35*e^-1*(a+b*x)^5//2*(d+e*x)^-5//2*(b*d+-1*a*e)^-2*(-14*B*a*e+4*A*b*e+10*B*b*d))
@test integrate((a+b*x)^3//2*(d+e*x)^-11//2*(A+B*x), x) == :(1//9*e^-1*(a+b*x)^5//2*(d+e*x)^-9//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e)+1//63*e^-1*(a+b*x)^5//2*(d+e*x)^-7//2*(b*d+-1*a*e)^-2*(-18*B*a*e+8*A*b*e+10*B*b*d)+4//315*b*e^-1*(a+b*x)^5//2*(d+e*x)^-5//2*(b*d+-1*a*e)^-3*(-9*B*a*e+4*A*b*e+5*B*b*d))
@test integrate((a+b*x)^3//2*(d+e*x)^-13//2*(A+B*x), x) == :(1//11*e^-1*(a+b*x)^5//2*(d+e*x)^-11//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e)+1//99*e^-1*(a+b*x)^5//2*(d+e*x)^-9//2*(b*d+-1*a*e)^-2*(-22*B*a*e+10*B*b*d+12*A*b*e)+8//693*b*e^-1*(a+b*x)^5//2*(d+e*x)^-7//2*(b*d+-1*a*e)^-3*(-11*B*a*e+5*B*b*d+6*A*b*e)+16//3465*b^2*e^-1*(a+b*x)^5//2*(d+e*x)^-5//2*(b*d+-1*a*e)^-4*(-11*B*a*e+5*B*b*d+6*A*b*e))
@test integrate((a+b*x)^3//2*(d+e*x)^-15//2*(A+B*x), x) == :(1//13*e^-1*(a+b*x)^5//2*(d+e*x)^-13//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e)+1//143*e^-1*(a+b*x)^5//2*(d+e*x)^-11//2*(b*d+-1*a*e)^-2*(-26*B*a*e+10*B*b*d+16*A*b*e)+4//429*b*e^-1*(a+b*x)^5//2*(d+e*x)^-9//2*(b*d+-1*a*e)^-3*(-13*B*a*e+5*B*b*d+8*A*b*e)+16//3003*b^2*e^-1*(a+b*x)^5//2*(d+e*x)^-7//2*(b*d+-1*a*e)^-4*(-13*B*a*e+5*B*b*d+8*A*b*e)+32//15015*b^3*e^-1*(a+b*x)^5//2*(d+e*x)^-5//2*(b*d+-1*a*e)^-5*(-13*B*a*e+5*B*b*d+8*A*b*e))
@test integrate((a+b*x)^3//2*(d+e*x)^-17//2*(A+B*x), x) == :(1//15*e^-1*(a+b*x)^5//2*(d+e*x)^-15//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e)+1//39*e^-1*(a+b*x)^5//2*(d+e*x)^-13//2*(b*d+-1*a*e)^-2*(-6*B*a*e+2*B*b*d+4*A*b*e)+16//429*b*e^-1*(a+b*x)^5//2*(d+e*x)^-11//2*(b*d+-1*a*e)^-3*(B*b*d+-3*B*a*e+2*A*b*e)+32//1287*b^2*e^-1*(a+b*x)^5//2*(d+e*x)^-9//2*(b*d+-1*a*e)^-4*(B*b*d+-3*B*a*e+2*A*b*e)+128//9009*b^3*e^-1*(a+b*x)^5//2*(d+e*x)^-7//2*(b*d+-1*a*e)^-5*(B*b*d+-3*B*a*e+2*A*b*e)+256//45045*b^4*e^-1*(a+b*x)^5//2*(d+e*x)^-5//2*(b*d+-1*a*e)^-6*(B*b*d+-3*B*a*e+2*A*b*e))
@test integrate((a+b*x)^5//2*(d+e*x)^5//2*(A+B*x), x) == :(-5//1024*b^-9//2*e^-9//2*(b*d+-1*a*e)^6*(-1*B*(a*e+b*d)+2*A*b*e)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+1//7*B*b^-1*e^-1*(a+b*x)^7//2*(d+e*x)^7//2+1//12*b^-2*e^-1*(a+b*x)^7//2*(d+e*x)^5//2*(-1*B*(a*e+b*d)+2*A*b*e)+-5//1536*b^-4*e^-3*(a+b*x)^3//2*(d+e*x)^(1/2)*(b*d+-1*a*e)^4*(-1*B*(a*e+b*d)+2*A*b*e)+1//24*b^-3*e^-1*(a+b*x)^7//2*(d+e*x)^3//2*(b*d+-1*a*e)*(-1*B*(a*e+b*d)+2*A*b*e)+1//64*b^-4*e^-1*(a+b*x)^7//2*(d+e*x)^(1/2)*(b*d+-1*a*e)^2*(-1*B*(a*e+b*d)+2*A*b*e)+1//384*b^-4*e^-2*(a+b*x)^5//2*(d+e*x)^(1/2)*(b*d+-1*a*e)^3*(-1*B*(a*e+b*d)+2*A*b*e)+5//1024*b^-4*e^-4*(a+b*x)^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^5*(-1*B*(a*e+b*d)+2*A*b*e))
@test integrate((a+b*x)^5//2*(d+e*x)^3//2*(A+B*x), x) == :(-1//60*b^-2*e^-1*(a+b*x)^7//2*(d+e*x)^3//2*(-12*A*b*e+5*B*a*e+7*B*b*d)+1//6*B*b^-1*e^-1*(a+b*x)^7//2*(d+e*x)^5//2+1//512*b^-7//2*e^-9//2*(b*d+-1*a*e)^5*(-12*A*b*e+5*B*a*e+7*B*b*d)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+-1//160*b^-3*e^-1*(a+b*x)^7//2*(d+e*x)^(1/2)*(b*d+-1*a*e)*(-12*A*b*e+5*B*a*e+7*B*b*d)+-1//512*b^-3*e^-4*(a+b*x)^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^4*(-12*A*b*e+5*B*a*e+7*B*b*d)+-1//960*b^-3*e^-2*(a+b*x)^5//2*(d+e*x)^(1/2)*(b*d+-1*a*e)^2*(-12*A*b*e+5*B*a*e+7*B*b*d)+1//768*b^-3*e^-3*(a+b*x)^3//2*(d+e*x)^(1/2)*(b*d+-1*a*e)^3*(-12*A*b*e+5*B*a*e+7*B*b*d))
@test integrate((a+b*x)^5//2*(d+e*x)^(1/2)*(A+B*x), x) == :(-1//40*b^-2*e^-1*(a+b*x)^7//2*(d+e*x)^(1/2)*(-10*A*b*e+3*B*a*e+7*B*b*d)+1//5*B*b^-1*e^-1*(a+b*x)^7//2*(d+e*x)^3//2+1//128*b^-5//2*e^-9//2*(b*d+-1*a*e)^4*(-10*A*b*e+3*B*a*e+7*B*b*d)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+-1//128*b^-2*e^-4*(a+b*x)^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^3*(-10*A*b*e+3*B*a*e+7*B*b*d)+-1//240*b^-2*e^-2*(a+b*x)^5//2*(d+e*x)^(1/2)*(b*d+-1*a*e)*(-10*A*b*e+3*B*a*e+7*B*b*d)+1//192*b^-2*e^-3*(a+b*x)^3//2*(d+e*x)^(1/2)*(b*d+-1*a*e)^2*(-10*A*b*e+3*B*a*e+7*B*b*d))
@test integrate((a+b*x)^5//2*(d+e*x)^-1//2*(A+B*x), x) == :(-1//24*b^-1*e^-2*(a+b*x)^5//2*(d+e*x)^(1/2)*(B*a*e+-8*A*b*e+7*B*b*d)+1//4*B*b^-1*e^-1*(a+b*x)^7//2*(d+e*x)^(1/2)+5//64*b^-3//2*e^-9//2*(b*d+-1*a*e)^3*(B*a*e+-8*A*b*e+7*B*b*d)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+-5//64*b^-1*e^-4*(a+b*x)^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^2*(B*a*e+-8*A*b*e+7*B*b*d)+1//96*b^-1*e^-3*(a+b*x)^3//2*(d+e*x)^(1/2)*(-5*a*e+5*b*d)*(B*a*e+-8*A*b*e+7*B*b*d))
@test integrate((a+b*x)^5//2*(d+e*x)^-3//2*(A+B*x), x) == :(-1//12*e^-3*(a+b*x)^3//2*(d+e*x)^(1/2)*(-30*A*b*e+-5*B*a*e+35*B*b*d)+e^-1*(a+b*x)^7//2*(d+e*x)^-1//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e)+-5//8*b^-1//2*e^-9//2*(b*d+-1*a*e)^2*(-1*B*a*e+-6*A*b*e+7*B*b*d)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+1//3*e^-2*(a+b*x)^5//2*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1*(-1*B*a*e+-6*A*b*e+7*B*b*d)+1//8*e^-4*(a+b*x)^(1/2)*(d+e*x)^(1/2)*(-5*a*e+5*b*d)*(-1*B*a*e+-6*A*b*e+7*B*b*d))
@test integrate((a+b*x)^5//2*(d+e*x)^-5//2*(A+B*x), x) == :(-5//4*b*e^-4*(a+b*x)^(1/2)*(d+e*x)^(1/2)*(-4*A*b*e+-3*B*a*e+7*B*b*d)+-1//3*e^-2*(a+b*x)^5//2*(d+e*x)^-1//2*(b*d+-1*a*e)^-1*(-8*A*b*e+-6*B*a*e+14*B*b*d)+1//3*e^-1*(a+b*x)^7//2*(d+e*x)^-3//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e)+5//4*b^(1/2)*e^-9//2*(b*d+-1*a*e)*(-4*A*b*e+-3*B*a*e+7*B*b*d)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+5//6*b*e^-3*(a+b*x)^3//2*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1*(-4*A*b*e+-3*B*a*e+7*B*b*d))
@test integrate((a+b*x)^5//2*(d+e*x)^-7//2*(A+B*x), x) == :(-1*b^3//2*e^-9//2*(-5*B*a*e+-2*A*b*e+7*B*b*d)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+-1//15*e^-2*(a+b*x)^5//2*(d+e*x)^-3//2*(b*d+-1*a*e)^-1*(-10*B*a*e+-4*A*b*e+14*B*b*d)+1//5*e^-1*(a+b*x)^7//2*(d+e*x)^-5//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e)+b^2*e^-4*(a+b*x)^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1*(-5*B*a*e+-2*A*b*e+7*B*b*d)+-2//3*b*e^-3*(a+b*x)^3//2*(d+e*x)^-1//2*(b*d+-1*a*e)^-1*(-5*B*a*e+-2*A*b*e+7*B*b*d))
@test integrate((a+b*x)^5//2*(d+e*x)^-9//2*(A+B*x), x) == :(2*B*b^5//2*e^-9//2*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+-2//5*B*e^-2*(a+b*x)^5//2*(d+e*x)^-5//2+-2*B*b^2*e^-4*(a+b*x)^(1/2)*(d+e*x)^-1//2+-2//3*B*b*e^-3*(a+b*x)^3//2*(d+e*x)^-3//2+1//7*e^-1*(a+b*x)^7//2*(d+e*x)^-7//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e))
@test integrate((a+b*x)^5//2*(d+e*x)^-11//2*(A+B*x), x) == :(1//9*e^-1*(a+b*x)^7//2*(d+e*x)^-9//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e)+1//63*e^-1*(a+b*x)^7//2*(d+e*x)^-7//2*(b*d+-1*a*e)^-2*(-18*B*a*e+4*A*b*e+14*B*b*d))
@test integrate((a+b*x)^5//2*(d+e*x)^-13//2*(A+B*x), x) == :(1//11*e^-1*(a+b*x)^7//2*(d+e*x)^-11//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e)+1//99*e^-1*(a+b*x)^7//2*(d+e*x)^-9//2*(b*d+-1*a*e)^-2*(-22*B*a*e+8*A*b*e+14*B*b*d)+4//693*b*e^-1*(a+b*x)^7//2*(d+e*x)^-7//2*(b*d+-1*a*e)^-3*(-11*B*a*e+4*A*b*e+7*B*b*d))
@test integrate((a+b*x)^5//2*(d+e*x)^-15//2*(A+B*x), x) == :(1//13*e^-1*(a+b*x)^7//2*(d+e*x)^-13//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e)+1//143*e^-1*(a+b*x)^7//2*(d+e*x)^-11//2*(b*d+-1*a*e)^-2*(-26*B*a*e+12*A*b*e+14*B*b*d)+8//1287*b*e^-1*(a+b*x)^7//2*(d+e*x)^-9//2*(b*d+-1*a*e)^-3*(-13*B*a*e+6*A*b*e+7*B*b*d)+16//9009*b^2*e^-1*(a+b*x)^7//2*(d+e*x)^-7//2*(b*d+-1*a*e)^-4*(-13*B*a*e+6*A*b*e+7*B*b*d))
@test integrate((a+b*x)^5//2*(d+e*x)^-17//2*(A+B*x), x) == :(1//15*e^-1*(a+b*x)^7//2*(d+e*x)^-15//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e)+1//195*e^-1*(a+b*x)^7//2*(d+e*x)^-13//2*(b*d+-1*a*e)^-2*(-30*B*a*e+14*B*b*d+16*A*b*e)+4//715*b*e^-1*(a+b*x)^7//2*(d+e*x)^-11//2*(b*d+-1*a*e)^-3*(-15*B*a*e+7*B*b*d+8*A*b*e)+16//6435*b^2*e^-1*(a+b*x)^7//2*(d+e*x)^-9//2*(b*d+-1*a*e)^-4*(-15*B*a*e+7*B*b*d+8*A*b*e)+32//45045*b^3*e^-1*(a+b*x)^7//2*(d+e*x)^-7//2*(b*d+-1*a*e)^-5*(-15*B*a*e+7*B*b*d+8*A*b*e))
@test integrate((a+b*x)^5//2*(d+e*x)^-19//2*(A+B*x), x) == :(1//17*e^-1*(a+b*x)^7//2*(d+e*x)^-17//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e)+1//255*e^-1*(a+b*x)^7//2*(d+e*x)^-15//2*(b*d+-1*a*e)^-2*(-34*B*a*e+14*B*b*d+20*A*b*e)+16//3315*b*e^-1*(a+b*x)^7//2*(d+e*x)^-13//2*(b*d+-1*a*e)^-3*(-17*B*a*e+7*B*b*d+10*A*b*e)+32//12155*b^2*e^-1*(a+b*x)^7//2*(d+e*x)^-11//2*(b*d+-1*a*e)^-4*(-17*B*a*e+7*B*b*d+10*A*b*e)+128//109395*b^3*e^-1*(a+b*x)^7//2*(d+e*x)^-9//2*(b*d+-1*a*e)^-5*(-17*B*a*e+7*B*b*d+10*A*b*e)+256//765765*b^4*e^-1*(a+b*x)^7//2*(d+e*x)^-7//2*(b*d+-1*a*e)^-6*(-17*B*a*e+7*B*b*d+10*A*b*e))
@test integrate((a+b*x)^-1//2*(d+e*x)^5//2*(A+B*x), x) == :(-5//64*b^-9//2*e^-3//2*(b*d+-1*a*e)^3*(B*b*d+-8*A*b*e+7*B*a*e)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+-1//24*b^-2*e^-1*(a+b*x)^(1/2)*(d+e*x)^5//2*(B*b*d+-8*A*b*e+7*B*a*e)+1//4*B*b^-1*e^-1*(a+b*x)^(1/2)*(d+e*x)^7//2+-5//64*b^-4*e^-1*(a+b*x)^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^2*(B*b*d+-8*A*b*e+7*B*a*e)+-1//96*b^-3*e^-1*(a+b*x)^(1/2)*(d+e*x)^3//2*(-5*a*e+5*b*d)*(B*b*d+-8*A*b*e+7*B*a*e))
@test integrate((a+b*x)^-1//2*(d+e*x)^3//2*(A+B*x), x) == :(-1//8*b^-7//2*e^-3//2*(b*d+-1*a*e)^2*(B*b*d+-6*A*b*e+5*B*a*e)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+-1//12*b^-2*e^-1*(a+b*x)^(1/2)*(d+e*x)^3//2*(B*b*d+-6*A*b*e+5*B*a*e)+1//3*B*b^-1*e^-1*(a+b*x)^(1/2)*(d+e*x)^5//2+-1//8*b^-3*e^-1*(a+b*x)^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)*(B*b*d+-6*A*b*e+5*B*a*e))
@test integrate((a+b*x)^-1//2*(d+e*x)^(1/2)*(A+B*x), x) == :((1/2)*B*b^-1*e^-1*(a+b*x)^(1/2)*(d+e*x)^3//2+-1//4*b^-2*e^-1*(a+b*x)^(1/2)*(d+e*x)^(1/2)*(B*b*d+-4*A*b*e+3*B*a*e)+-1//4*b^-5//2*e^-3//2*(b*d+-1*a*e)*(B*b*d+-4*A*b*e+3*B*a*e)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2))
@test integrate((a+b*x)^-1//2*(d+e*x)^-1//2*(A+B*x), x) == :(b^-3//2*e^-3//2*(-1*B*(a*e+b*d)+2*A*b*e)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+B*b^-1*e^-1*(a+b*x)^(1/2)*(d+e*x)^(1/2))
@test integrate((a+b*x)^-1//2*(d+e*x)^-3//2*(A+B*x), x) == :(2*B*b^-1//2*e^-3//2*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+e^-1*(a+b*x)^(1/2)*(d+e*x)^-1//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e))
@test integrate((a+b*x)^-1//2*(d+e*x)^-5//2*(A+B*x), x) == :(1//3*e^-1*(a+b*x)^(1/2)*(d+e*x)^-3//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e)+1//3*e^-1*(a+b*x)^(1/2)*(d+e*x)^-1//2*(b*d+-1*a*e)^-2*(-6*B*a*e+2*B*b*d+4*A*b*e))
@test integrate((a+b*x)^-1//2*(d+e*x)^-7//2*(A+B*x), x) == :(1//5*e^-1*(a+b*x)^(1/2)*(d+e*x)^-5//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e)+1//15*e^-1*(a+b*x)^(1/2)*(d+e*x)^-3//2*(b*d+-1*a*e)^-2*(-10*B*a*e+2*B*b*d+8*A*b*e)+4//15*b*e^-1*(a+b*x)^(1/2)*(d+e*x)^-1//2*(b*d+-1*a*e)^-3*(B*b*d+-5*B*a*e+4*A*b*e))
@test integrate((a+b*x)^-1//2*(d+e*x)^-9//2*(A+B*x), x) == :(1//7*e^-1*(a+b*x)^(1/2)*(d+e*x)^-7//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e)+1//35*e^-1*(a+b*x)^(1/2)*(d+e*x)^-5//2*(b*d+-1*a*e)^-2*(-14*B*a*e+2*B*b*d+12*A*b*e)+8//105*b*e^-1*(a+b*x)^(1/2)*(d+e*x)^-3//2*(b*d+-1*a*e)^-3*(B*b*d+-7*B*a*e+6*A*b*e)+16//105*b^2*e^-1*(a+b*x)^(1/2)*(d+e*x)^-1//2*(b*d+-1*a*e)^-4*(B*b*d+-7*B*a*e+6*A*b*e))
@test integrate((a+b*x)^-1//2*(d+e*x)^-11//2*(A+B*x), x) == :(1//9*e^-1*(a+b*x)^(1/2)*(d+e*x)^-9//2*(b*d+-1*a*e)^-1*(-2*B*d+2*A*e)+1//63*e^-1*(a+b*x)^(1/2)*(d+e*x)^-7//2*(b*d+-1*a*e)^-2*(-18*B*a*e+2*B*b*d+16*A*b*e)+4//105*b*e^-1*(a+b*x)^(1/2)*(d+e*x)^-5//2*(b*d+-1*a*e)^-3*(B*b*d+-9*B*a*e+8*A*b*e)+16//315*b^2*e^-1*(a+b*x)^(1/2)*(d+e*x)^-3//2*(b*d+-1*a*e)^-4*(B*b*d+-9*B*a*e+8*A*b*e)+32//315*b^3*e^-1*(a+b*x)^(1/2)*(d+e*x)^-1//2*(b*d+-1*a*e)^-5*(B*b*d+-9*B*a*e+8*A*b*e))
@test integrate((a+b*x)^-3//2*(d+e*x)^5//2*(A+B*x), x) == :(1//12*b^-3*(a+b*x)^(1/2)*(d+e*x)^3//2*(-35*B*a*e+5*B*b*d+30*A*b*e)+-1*b^-1*(a+b*x)^-1//2*(d+e*x)^7//2*(b*d+-1*a*e)^-1*(-2*B*a+2*A*b)+1//3*b^-2*(a+b*x)^(1/2)*(d+e*x)^5//2*(b*d+-1*a*e)^-1*(B*b*d+-7*B*a*e+6*A*b*e)+1//8*b^-4*(a+b*x)^(1/2)*(d+e*x)^(1/2)*(-5*a*e+5*b*d)*(B*b*d+-7*B*a*e+6*A*b*e)+5//8*b^-9//2*e^-1//2*(b*d+-1*a*e)^2*(B*b*d+-7*B*a*e+6*A*b*e)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2))
@test integrate((a+b*x)^-3//2*(d+e*x)^3//2*(A+B*x), x) == :(1//4*b^-3*(a+b*x)^(1/2)*(d+e*x)^(1/2)*(-15*B*a*e+3*B*b*d+12*A*b*e)+(1/2)*b^-2*(a+b*x)^(1/2)*(d+e*x)^3//2*(b*d+-1*a*e)^-1*(B*b*d+-5*B*a*e+4*A*b*e)+-1*b^-1*(a+b*x)^-1//2*(d+e*x)^5//2*(b*d+-1*a*e)^-1*(-2*B*a+2*A*b)+1//4*b^-7//2*e^-1//2*(-3*a*e+3*b*d)*(B*b*d+-5*B*a*e+4*A*b*e)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2))
@test integrate((a+b*x)^-3//2*(d+e*x)^(1/2)*(A+B*x), x) == :(b^-5//2*e^-1//2*(B*b*d+-3*B*a*e+2*A*b*e)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+b^-2*(a+b*x)^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1*(B*b*d+-3*B*a*e+2*A*b*e)+-1*b^-1*(a+b*x)^-1//2*(d+e*x)^3//2*(b*d+-1*a*e)^-1*(-2*B*a+2*A*b))
@test integrate((a+b*x)^-3//2*(d+e*x)^-1//2*(A+B*x), x) == :(2*B*b^-3//2*e^-1//2*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+b^-1*(a+b*x)^-1//2*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1*(-2*A*b+2*B*a))
@test integrate((a+b*x)^-3//2*(d+e*x)^-3//2*(A+B*x), x) == :(e^-1*(a+b*x)^-1//2*(d+e*x)^(1/2)*(b*d+-1*a*e)^-2*(-4*A*b*e+2*B*a*e+2*B*b*d)+-1*e^-1*(a+b*x)^-1//2*(d+e*x)^-1//2*(b*d+-1*a*e)^-1*(-2*A*e+2*B*d))
@test integrate((a+b*x)^-3//2*(d+e*x)^-5//2*(A+B*x), x) == :(1//3*(a+b*x)^(1/2)*(d+e*x)^-1//2*(b*d+-1*a*e)^-3*(-16*A*b*e+4*B*b*d+12*B*a*e)+b^-1*(a+b*x)^-1//2*(d+e*x)^-3//2*(b*d+-1*a*e)^-1*(-2*A*b+2*B*a)+1//3*b^-1*(a+b*x)^(1/2)*(d+e*x)^-3//2*(b*d+-1*a*e)^-2*(-8*A*b*e+2*B*b*d+6*B*a*e))
@test integrate((a+b*x)^-3//2*(d+e*x)^-7//2*(A+B*x), x) == :(1//15*(a+b*x)^(1/2)*(d+e*x)^-3//2*(b*d+-1*a*e)^-3*(-48*A*b*e+8*B*b*d+40*B*a*e)+b^-1*(a+b*x)^-1//2*(d+e*x)^-5//2*(b*d+-1*a*e)^-1*(-2*A*b+2*B*a)+1//5*b^-1*(a+b*x)^(1/2)*(d+e*x)^-5//2*(b*d+-1*a*e)^-2*(-12*A*b*e+2*B*b*d+10*B*a*e)+16//15*b*(a+b*x)^(1/2)*(d+e*x)^-1//2*(b*d+-1*a*e)^-4*(B*b*d+-6*A*b*e+5*B*a*e))
@test integrate((a+b*x)^-3//2*(d+e*x)^-9//2*(A+B*x), x) == :(1//35*(a+b*x)^(1/2)*(d+e*x)^-5//2*(b*d+-1*a*e)^-3*(-96*A*b*e+12*B*b*d+84*B*a*e)+b^-1*(a+b*x)^-1//2*(d+e*x)^-7//2*(b*d+-1*a*e)^-1*(-2*A*b+2*B*a)+1//7*b^-1*(a+b*x)^(1/2)*(d+e*x)^-7//2*(b*d+-1*a*e)^-2*(-16*A*b*e+2*B*b*d+14*B*a*e)+16//35*b*(a+b*x)^(1/2)*(d+e*x)^-3//2*(b*d+-1*a*e)^-4*(B*b*d+-8*A*b*e+7*B*a*e)+32//35*b^2*(a+b*x)^(1/2)*(d+e*x)^-1//2*(b*d+-1*a*e)^-5*(B*b*d+-8*A*b*e+7*B*a*e))
@test integrate((a+b*x)^-5//2*(d+e*x)^7//2*(A+B*x), x) == :(-1*b^-2*(a+b*x)^-1//2*(d+e*x)^7//2*(b*d+-1*a*e)^-1*(-6*B*a*e+2*B*b*d+4*A*b*e)+-1//3*b^-1*(a+b*x)^-3//2*(d+e*x)^9//2*(b*d+-1*a*e)^-1*(-2*B*a+2*A*b)+35//8*b^-11//2*e^(1/2)*(b*d+-1*a*e)^2*(B*b*d+-3*B*a*e+2*A*b*e)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+35//12*e*b^-4*(a+b*x)^(1/2)*(d+e*x)^3//2*(B*b*d+-3*B*a*e+2*A*b*e)+7//3*e*b^-3*(a+b*x)^(1/2)*(d+e*x)^5//2*(b*d+-1*a*e)^-1*(B*b*d+-3*B*a*e+2*A*b*e)+35//8*e*b^-5*(a+b*x)^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)*(B*b*d+-3*B*a*e+2*A*b*e))
@test integrate((a+b*x)^-5//2*(d+e*x)^5//2*(A+B*x), x) == :(-1//3*b^-1*(a+b*x)^-3//2*(d+e*x)^7//2*(b*d+-1*a*e)^-1*(-2*B*a+2*A*b)+-1//3*b^-2*(a+b*x)^-1//2*(d+e*x)^5//2*(b*d+-1*a*e)^-1*(-14*B*a*e+6*B*b*d+8*A*b*e)+5//4*e*b^-4*(a+b*x)^(1/2)*(d+e*x)^(1/2)*(-7*B*a*e+3*B*b*d+4*A*b*e)+5//4*b^-9//2*e^(1/2)*(b*d+-1*a*e)*(-7*B*a*e+3*B*b*d+4*A*b*e)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+5//6*e*b^-3*(a+b*x)^(1/2)*(d+e*x)^3//2*(b*d+-1*a*e)^-1*(-7*B*a*e+3*B*b*d+4*A*b*e))
@test integrate((a+b*x)^-5//2*(d+e*x)^3//2*(A+B*x), x) == :(b^-7//2*e^(1/2)*(-5*B*a*e+2*A*b*e+3*B*b*d)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+-1//3*b^-1*(a+b*x)^-3//2*(d+e*x)^5//2*(b*d+-1*a*e)^-1*(-2*B*a+2*A*b)+-1//3*b^-2*(a+b*x)^-1//2*(d+e*x)^3//2*(b*d+-1*a*e)^-1*(-10*B*a*e+4*A*b*e+6*B*b*d)+e*b^-3*(a+b*x)^(1/2)*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1*(-5*B*a*e+2*A*b*e+3*B*b*d))
@test integrate((a+b*x)^-5//2*(d+e*x)^(1/2)*(A+B*x), x) == :(-2*B*b^-2*(a+b*x)^-1//2*(d+e*x)^(1/2)+2*B*b^-5//2*e^(1/2)*arctanh(b^-1//2*e^(1/2)*(a+b*x)^(1/2)*(d+e*x)^-1//2)+-1//3*b^-1*(a+b*x)^-3//2*(d+e*x)^3//2*(b*d+-1*a*e)^-1*(-2*B*a+2*A*b))
@test integrate((a+b*x)^-5//2*(d+e*x)^-1//2*(A+B*x), x) == :(-1//3*b^-1*(a+b*x)^-1//2*(d+e*x)^(1/2)*(b*d+-1*a*e)^-2*(-4*A*b*e+-2*B*a*e+6*B*b*d)+1//3*b^-1*(a+b*x)^-3//2*(d+e*x)^(1/2)*(b*d+-1*a*e)^-1*(-2*A*b+2*B*a))
@test integrate((a+b*x)^-5//2*(d+e*x)^-3//2*(A+B*x), x) == :(-1//3*(a+b*x)^-1//2*(d+e*x)^(1/2)*(b*d+-1*a*e)^-3*(-16*A*b*e+4*B*a*e+12*B*b*d)+-1*e^-1*(a+b*x)^-3//2*(d+e*x)^-1//2*(b*d+-1*a*e)^-1*(-2*A*e+2*B*d)+1//3*e^-1*(a+b*x)^-3//2*(d+e*x)^(1/2)*(b*d+-1*a*e)^-2*(-8*A*b*e+2*B*a*e+6*B*b*d))
@test integrate((a+b*x)^-5//2*(d+e*x)^-5//2*(A+B*x), x) == :(-1//3*(a+b*x)^-1//2*(d+e*x)^-1//2*(b*d+-1*a*e)^-3*(-16*A*b*e+8*B*a*e+8*B*b*d)+-16//3*e*(a+b*x)^(1/2)*(d+e*x)^-1//2*(b*d+-1*a*e)^-4*(B*a*e+B*b*d+-2*A*b*e)+-1//3*e^-1*(a+b*x)^-3//2*(d+e*x)^-3//2*(b*d+-1*a*e)^-1*(-2*A*e+2*B*d)+1//3*e^-1*(a+b*x)^-3//2*(d+e*x)^-1//2*(b*d+-1*a*e)^-2*(-4*A*b*e+2*B*a*e+2*B*b*d))
@test integrate((a+b*x)^-5//2*(d+e*x)^-7//2*(A+B*x), x) == :(-16//15*e*(a+b*x)^(1/2)*(d+e*x)^-3//2*(b*d+-1*a*e)^-4*(-8*A*b*e+3*B*b*d+5*B*a*e)+-1//3*b^-1*(a+b*x)^-1//2*(d+e*x)^-5//2*(b*d+-1*a*e)^-2*(-16*A*b*e+6*B*b*d+10*B*a*e)+1//3*b^-1*(a+b*x)^-3//2*(d+e*x)^-5//2*(b*d+-1*a*e)^-1*(-2*A*b+2*B*a)+-32//15*b*e*(a+b*x)^(1/2)*(d+e*x)^-1//2*(b*d+-1*a*e)^-5*(-8*A*b*e+3*B*b*d+5*B*a*e)+-4//5*e*b^-1*(a+b*x)^(1/2)*(d+e*x)^-5//2*(b*d+-1*a*e)^-3*(-8*A*b*e+3*B*b*d+5*B*a*e))
@test integrate((a+b*x)^-5//2*(d+e*x)^-9//2*(A+B*x), x) == :(-32//35*e*(a+b*x)^(1/2)*(d+e*x)^-5//2*(b*d+-1*a*e)^-4*(-10*A*b*e+3*B*b*d+7*B*a*e)+-1//3*b^-1*(a+b*x)^-1//2*(d+e*x)^-7//2*(b*d+-1*a*e)^-2*(-20*A*b*e+6*B*b*d+14*B*a*e)+1//3*b^-1*(a+b*x)^-3//2*(d+e*x)^-7//2*(b*d+-1*a*e)^-1*(-2*A*b+2*B*a)+-256//105*e*b^2*(a+b*x)^(1/2)*(d+e*x)^-1//2*(b*d+-1*a*e)^-6*(-10*A*b*e+3*B*b*d+7*B*a*e)+-128//105*b*e*(a+b*x)^(1/2)*(d+e*x)^-3//2*(b*d+-1*a*e)^-5*(-10*A*b*e+3*B*b*d+7*B*a*e)+-16//21*e*b^-1*(a+b*x)^(1/2)*(d+e*x)^-7//2*(b*d+-1*a*e)^-3*(-10*A*b*e+3*B*b*d+7*B*a*e))
@test integrate((1+-2x)^(1/2)*(2+3x)^4*(3+5x)^(1/2), x) == :(-34069301//5120000*(1+-2x)^3//2*(3+5x)^(1/2)+374762311//51200000*(1+-2x)^(1/2)*(3+5x)^(1/2)+4122385421//512000000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-333//2000*(1+-2x)^3//2*(2+3x)^2*(3+5x)^3//2+-7//640000*(1+-2x)^3//2*(3+5x)^3//2*(231223+140652x)+-1//20*(1+-2x)^3//2*(2+3x)^3*(3+5x)^3//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^3*(3+5x)^(1/2), x) == :(-323491//128000*(1+-2x)^3//2*(3+5x)^(1/2)+3558401//1280000*(1+-2x)^(1/2)*(3+5x)^(1/2)+39142411//12800000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-21//16000*(1+-2x)^3//2*(3+5x)^3//2*(731+444x)+-3//50*(1+-2x)^3//2*(2+3x)^2*(3+5x)^3//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^2*(3+5x)^(1/2), x) == :(-1313//1280*(1+-2x)^3//2*(3+5x)^(1/2)+-37//160*(1+-2x)^3//2*(3+5x)^3//2+14443//12800*(1+-2x)^(1/2)*(3+5x)^(1/2)+158873//128000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-3//40*(1+-2x)^3//2*(3+5x)^3//2*(2+3x))
@test integrate((1+-2x)^(1/2)*(3+5x)^(1/2)*(2+3x), x) == :(-37//80*(1+-2x)^3//2*(3+5x)^(1/2)+-1//10*(1+-2x)^3//2*(3+5x)^3//2+407//800*(1+-2x)^(1/2)*(3+5x)^(1/2)+4477//8000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(3+5x)^(1/2), x) == :(-1//4*(1+-2x)^3//2*(3+5x)^(1/2)+11//40*(1+-2x)^(1/2)*(3+5x)^(1/2)+121//400*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^-1*(3+5x)^(1/2), x) == :(1//3*(1+-2x)^(1/2)*(3+5x)^(1/2)+2//9*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+37//90*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2), x) == :(-37//63*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-2//9*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-1*(1+-2x)^(1/2)*(3+5x)^(1/2)*(6+9x)^-1)
@test integrate((1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2), x) == :(-121//196*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+(1/2)*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2+-11*(1+-2x)^(1/2)*(3+5x)^(1/2)*(56+84x)^-1)
@test integrate((1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^(1/2), x) == :(-4477//2744*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-407*(1+-2x)^(1/2)*(3+5x)^(1/2)*(784+1176x)^-1+1//7*(1+-2x)^3//2*(2+3x)^-3*(3+5x)^3//2+37//28*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-5*(3+5x)^(1/2), x) == :(-794365//153664*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+625115*(1+-2x)^(1/2)*(3+5x)^(1/2)*(395136+592704x)^-1+-1//12*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^(1/2)+37//504*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+6005//14112*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^-6*(3+5x)^(1/2), x) == :(-5591773//307328*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+1466281*(1+-2x)^(1/2)*(3+5x)^(1/2)*(263424+395136x)^-1+-1//15*(1+-2x)^(1/2)*(2+3x)^-5*(3+5x)^(1/2)+37//840*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^(1/2)+403//1680*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+14023//9408*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^-7*(3+5x)^(1/2), x) == :(-588912203//8605184*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+463266973*(1+-2x)^(1/2)*(3+5x)^(1/2)*(22127616+33191424x)^-1+-1//18*(1+-2x)^(1/2)*(2+3x)^-6*(3+5x)^(1/2)+37//1260*(1+-2x)^(1/2)*(2+3x)^-5*(3+5x)^(1/2)+10921//70560*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^(1/2)+126799//141120*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+4429459//790272*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^4*(3+5x)^3//2, x) == :(-580364059//20480000*(1+-2x)^3//2*(3+5x)^(1/2)+-52760369//7680000*(1+-2x)^3//2*(3+5x)^3//2+6384004649//204800000*(1+-2x)^(1/2)*(3+5x)^(1/2)+70224051139//2048000000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-403//2800*(1+-2x)^3//2*(2+3x)^2*(3+5x)^5//2+-3//70*(1+-2x)^3//2*(2+3x)^3*(3+5x)^5//2+-1//640000*(1+-2x)^3//2*(3+5x)^5//2*(1480103+874608x))
@test integrate((1+-2x)^(1/2)*(2+3x)^3*(3+5x)^3//2, x) == :(-10493791//1024000*(1+-2x)^3//2*(3+5x)^(1/2)+-953981//384000*(1+-2x)^3//2*(3+5x)^3//2+115431701//10240000*(1+-2x)^(1/2)*(3+5x)^(1/2)+1269748711//102400000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-7//32000*(1+-2x)^3//2*(3+5x)^5//2*(3821+2256x)+-1//20*(1+-2x)^3//2*(2+3x)^2*(3+5x)^5//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^2*(3+5x)^3//2, x) == :(-99077//25600*(1+-2x)^3//2*(3+5x)^(1/2)+-9007//9600*(1+-2x)^3//2*(3+5x)^3//2+-153//800*(1+-2x)^3//2*(3+5x)^5//2+1089847//256000*(1+-2x)^(1/2)*(3+5x)^(1/2)+11988317//2560000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-3//50*(1+-2x)^3//2*(3+5x)^5//2*(2+3x))
@test integrate((1+-2x)^(1/2)*(3+5x)^3//2*(2+3x), x) == :(-1991//1280*(1+-2x)^3//2*(3+5x)^(1/2)+-181//480*(1+-2x)^3//2*(3+5x)^3//2+-3//40*(1+-2x)^3//2*(3+5x)^5//2+21901//12800*(1+-2x)^(1/2)*(3+5x)^(1/2)+240911//128000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(3+5x)^3//2, x) == :(-11//16*(1+-2x)^3//2*(3+5x)^(1/2)+-1//6*(1+-2x)^3//2*(3+5x)^3//2+121//160*(1+-2x)^(1/2)*(3+5x)^(1/2)+1331//1600*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^-1*(3+5x)^3//2, x) == :(-41//72*(1+-2x)^(1/2)*(3+5x)^(1/2)+-2//27*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+1//6*(1+-2x)^(1/2)*(3+5x)^3//2+793//2160*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2, x) == :(10//9*(1+-2x)^(1/2)*(3+5x)^(1/2)+41//54*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+107//189*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-1*(1+-2x)^(1/2)*(3+5x)^3//2*(6+9x)^-1)
@test integrate((1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^3//2, x) == :(-4091//5292*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-10//27*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-107*(1+-2x)^(1/2)*(3+5x)^(1/2)*(504+756x)^-1+-1//6*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^3//2, x) == :(-1331//2744*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-121*(1+-2x)^(1/2)*(3+5x)^(1/2)*(784+1176x)^-1+-11//84*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2+1//3*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^5//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-5*(3+5x)^3//2, x) == :(-153065//153664*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-13915*(1+-2x)^(1/2)*(3+5x)^(1/2)*(43904+65856x)^-1+-1265//4704*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2+3//28*(1+-2x)^3//2*(2+3x)^-4*(3+5x)^5//2+115//168*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^5//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-6*(3+5x)^3//2, x) == :(-783959//307328*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+1852307*(1+-2x)^(1/2)*(3+5x)^(1/2)*(2370816+3556224x)^-1+-107//2520*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^(1/2)+-1//15*(1+-2x)^(1/2)*(2+3x)^-5*(3+5x)^3//2+641//15120*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+17981//84672*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^-7*(3+5x)^3//2, x) == :(-64645339//8605184*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+152571047*(1+-2x)^(1/2)*(3+5x)^(1/2)*(66382848+99574272x)^-1+-107//3780*(1+-2x)^(1/2)*(2+3x)^-5*(3+5x)^(1/2)+-1//18*(1+-2x)^(1/2)*(2+3x)^-6*(3+5x)^3//2+4619//211680*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^(1/2)+42461//423360*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+1460201//2370816*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^4*(3+5x)^5//2, x) == :(-16433930689//131072000*(1+-2x)^3//2*(3+5x)^(1/2)+-1493993699//49152000*(1+-2x)^3//2*(3+5x)^3//2+-135817609//20480000*(1+-2x)^3//2*(3+5x)^5//2+180773237579//1310720000*(1+-2x)^(1/2)*(3+5x)^(1/2)+1988505613369//13107200000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-1419//11200*(1+-2x)^3//2*(2+3x)^2*(3+5x)^7//2+-3//80*(1+-2x)^3//2*(2+3x)^3*(3+5x)^7//2+-3//1280000*(1+-2x)^3//2*(3+5x)^7//2*(899099+522420x))
@test integrate((1+-2x)^(1/2)*(2+3x)^3*(3+5x)^5//2, x) == :(-35892593//819200*(1+-2x)^3//2*(3+5x)^(1/2)+-3262963//307200*(1+-2x)^3//2*(3+5x)^3//2+-296633//128000*(1+-2x)^3//2*(3+5x)^5//2+394818523//8192000*(1+-2x)^(1/2)*(3+5x)^(1/2)+4343003753//81920000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-3//70*(1+-2x)^3//2*(2+3x)^2*(3+5x)^7//2+-3//8000*(1+-2x)^3//2*(3+5x)^7//2*(1963+1140x))
@test integrate((1+-2x)^(1/2)*(2+3x)^2*(3+5x)^5//2, x) == :(-129349//8192*(1+-2x)^3//2*(3+5x)^(1/2)+-11759//3072*(1+-2x)^3//2*(3+5x)^3//2+-1069//1280*(1+-2x)^3//2*(3+5x)^5//2+-13//80*(1+-2x)^3//2*(3+5x)^7//2+1422839//81920*(1+-2x)^(1/2)*(3+5x)^(1/2)+15651229//819200*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-1//20*(1+-2x)^3//2*(3+5x)^7//2*(2+3x))
@test integrate((1+-2x)^(1/2)*(3+5x)^5//2*(2+3x), x) == :(-30371//5120*(1+-2x)^3//2*(3+5x)^(1/2)+-2761//1920*(1+-2x)^3//2*(3+5x)^3//2+-251//800*(1+-2x)^3//2*(3+5x)^5//2+-3//50*(1+-2x)^3//2*(3+5x)^7//2+334081//51200*(1+-2x)^(1/2)*(3+5x)^(1/2)+3674891//512000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(3+5x)^5//2, x) == :(-605//256*(1+-2x)^3//2*(3+5x)^(1/2)+-55//96*(1+-2x)^3//2*(3+5x)^3//2+-1//8*(1+-2x)^3//2*(3+5x)^5//2+1331//512*(1+-2x)^(1/2)*(3+5x)^(1/2)+14641//5120*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^-1*(3+5x)^5//2, x) == :(-925//864*(1+-2x)^(1/2)*(3+5x)^(1/2)+-5//24*(1+-2x)^(1/2)*(3+5x)^3//2+1//9*(1+-2x)^(1/2)*(3+5x)^5//2+2//81*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+6553//5184*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^5//2, x) == :(-95//72*(1+-2x)^(1/2)*(3+5x)^(1/2)+-59//189*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+5//6*(1+-2x)^(1/2)*(3+5x)^3//2+155//432*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-1*(1+-2x)^(1/2)*(3+5x)^5//2*(6+9x)^-1)
@test integrate((1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^5//2, x) == :(25//18*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+215//84*(1+-2x)^(1/2)*(3+5x)^(1/2)+2119//1764*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-59*(1+-2x)^(1/2)*(3+5x)^3//2*(168+252x)^-1+-1//6*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^5//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^5//2, x) == :(-250433//222264*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-50//81*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-6401*(1+-2x)^(1/2)*(3+5x)^(1/2)*(21168+31752x)^-1+-59//252*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2+-1//9*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^5//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-5*(3+5x)^5//2, x) == :(-73205//153664*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-6655*(1+-2x)^(1/2)*(3+5x)^(1/2)*(43904+65856x)^-1+-605//4704*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2+-11//168*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^5//2+1//4*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^7//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-6*(3+5x)^5//2, x) == :(-248897//307328*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-22627*(1+-2x)^(1/2)*(3+5x)^(1/2)*(87808+131712x)^-1+-2057//9408*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2+-187//1680*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^5//2+3//35*(1+-2x)^3//2*(2+3x)^-5*(3+5x)^7//2+17//40*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^7//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-7*(3+5x)^5//2, x) == :(-15036307//8605184*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+106751933*(1+-2x)^(1/2)*(3+5x)^(1/2)*(199148544+298722816x)^-1+-6533//211680*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^(1/2)+-59//1260*(1+-2x)^(1/2)*(2+3x)^-5*(3+5x)^3//2+-1//18*(1+-2x)^(1/2)*(2+3x)^-6*(3+5x)^5//2+47279//1270080*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+1057139//7112448*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^-8*(3+5x)^5//2, x) == :(-3735929329//843308032*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+8818415317*(1+-2x)^(1/2)*(3+5x)^(1/2)*(6505519104+9758278656x)^-1+-6577//370440*(1+-2x)^(1/2)*(2+3x)^-5*(3+5x)^(1/2)+-59//1764*(1+-2x)^(1/2)*(2+3x)^-6*(3+5x)^3//2+-1//21*(1+-2x)^(1/2)*(2+3x)^-7*(3+5x)^5//2+369409//20744640*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^(1/2)+2524471//41489280*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+84539611//232339968*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((a+b*x)^(1/2)*(c+d*x)^-1//2*(e+f*x)^-1, x) == :(-2*f^-1*(b*e+-1*a*f)^(1/2)*(d*e+-1*c*f)^-1//2*arctanh((a+b*x)^(1/2)*(c+d*x)^-1//2*(b*e+-1*a*f)^-1//2*(d*e+-1*c*f)^(1/2))+2*b^(1/2)*d^-1//2*f^-1*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate((a+b*x)^-1//2*(c+d*x)^(1/2)*(e+f*x)^-1, x) == :(-2*f^-1*(b*e+-1*a*f)^-1//2*(d*e+-1*c*f)^(1/2)*arctanh((a+b*x)^(1/2)*(c+d*x)^-1//2*(b*e+-1*a*f)^-1//2*(d*e+-1*c*f)^(1/2))+2*b^-1//2*d^(1/2)*f^-1*arctanh(b^-1//2*d^(1/2)*(a+b*x)^(1/2)*(c+d*x)^-1//2))
@test integrate((1+-2x)^(1/2)*(2+3x)^3*(3+5x)^-1//2, x) == :(47761//64000*(1+-2x)^(1/2)*(3+5x)^(1/2)+525371//640000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-21//6400*(1+-2x)^3//2*(3+5x)^(1/2)*(335+216x)+-3//40*(1+-2x)^3//2*(2+3x)^2*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^2*(3+5x)^-1//2, x) == :(-23//80*(1+-2x)^3//2*(3+5x)^(1/2)+277//800*(1+-2x)^(1/2)*(3+5x)^(1/2)+3047//8000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-1//10*(1+-2x)^3//2*(3+5x)^(1/2)*(2+3x))
@test integrate((1+-2x)^(1/2)*(3+5x)^-1//2*(2+3x), x) == :(-3//20*(1+-2x)^3//2*(3+5x)^(1/2)+41//200*(1+-2x)^(1/2)*(3+5x)^(1/2)+451//2000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(3+5x)^-1//2, x) == :(1//5*(1+-2x)^(1/2)*(3+5x)^(1/2)+11//50*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^-1*(3+5x)^-1//2, x) == :(-2//3*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-2//15*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-1//2, x) == :(-11//7*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+(1+-2x)^(1/2)*(2+3x)^-1*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^-1//2, x) == :(-1177//196*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+107*(1+-2x)^(1/2)*(3+5x)^(1/2)*(56+84x)^-1+3//14*(1+-2x)^3//2*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^-1//2, x) == :(-68959//2744*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+18083*(1+-2x)^(1/2)*(3+5x)^(1/2)*(2352+3528x)^-1+1//3*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+173//84*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^-5*(3+5x)^-1//2, x) == :(-16925425//153664*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+1479375*(1+-2x)^(1/2)*(3+5x)^(1/2)*(43904+65856x)^-1+1//4*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^(1/2)+81//56*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+14145//1568*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^3*(3+5x)^-3//2, x) == :(10409//40000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-2//5*(1+-2x)^(1/2)*(2+3x)^3*(3+5x)^-1//2+-1//4000*(1+-2x)^(1/2)*(3+5x)^(1/2)*(511+-420x)+7//25*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^2*(3+5x)^-3//2, x) == :(-9//100*(1+-2x)^3//2*(3+5x)^(1/2)+-2//275*(1+-2x)^3//2*(3+5x)^-1//2+317//2000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+317//2200*(1+-2x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(3+5x)^-3//2*(2+3x), x) == :(-2//55*(1+-2x)^3//2*(3+5x)^-1//2+29//250*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+29//275*(1+-2x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(3+5x)^-3//2, x) == :(-2//5*(1+-2x)^(1/2)*(3+5x)^-1//2+-2//25*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^(1/2)*(2+3x)^-1*(3+5x)^-3//2, x) == :(-2*(1+-2x)^(1/2)*(3+5x)^-1//2+2*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2))
@test integrate((1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-3//2, x) == :(-103//7*(1+-2x)^(1/2)*(3+5x)^-1//2+103//7*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+3*(1+-2x)^3//2*(3+5x)^-1//2*(14+21x)^-1)
@test integrate((1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^-3//2, x) == :(-2615//28*(1+-2x)^(1/2)*(3+5x)^-1//2+17951//196*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+(1/2)*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-1//2+173*(1+-2x)^(1/2)*(3+5x)^-1//2*(56+84x)^-1)
@test integrate((1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^-3//2, x) == :(-639565//1176*(1+-2x)^(1/2)*(3+5x)^-1//2+1463447//2744*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+14101*(1+-2x)^(1/2)*(3+5x)^-1//2*(784+1176x)^-1+1//3*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^-1//2+81//28*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-1//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^4*(3+5x)^-5//2, x) == :(35511//200000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-524//825*(1+-2x)^(1/2)*(2+3x)^3*(3+5x)^-1//2+-2//15*(1+-2x)^(1/2)*(2+3x)^4*(3+5x)^-3//2+7//220000*(1+-2x)^(1/2)*(3+5x)^(1/2)*(2563+8940x)+623//1375*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^3*(3+5x)^-5//2, x) == :(1071//10000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-392//825*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^-1//2+-2//15*(1+-2x)^(1/2)*(2+3x)^3*(3+5x)^-3//2+7//11000*(1+-2x)^(1/2)*(3+5x)^(1/2)*(1243+1740x))
@test integrate((1+-2x)^(1/2)*(2+3x)^2*(3+5x)^-5//2, x) == :(-12//275*(1+-2x)^3//2*(3+5x)^-1//2+-2//825*(1+-2x)^3//2*(3+5x)^-3//2+3//50*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+3//55*(1+-2x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(3+5x)^-5//2*(2+3x), x) == :(-6//25*(1+-2x)^(1/2)*(3+5x)^-1//2+-6//125*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-2//165*(1+-2x)^3//2*(3+5x)^-3//2)
@test integrate((1+-2x)^(1/2)*(3+5x)^-5//2, x) == :(-2//33*(1+-2x)^3//2*(3+5x)^-3//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-1*(3+5x)^-5//2, x) == :(-6*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+6*(1+-2x)^(1/2)*(3+5x)^-1//2+-10//33*(1+-2x)^3//2*(3+5x)^-3//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-5//2, x) == :(-519//7*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-25//3*(1+-2x)^(1/2)*(3+5x)^-3//2+2495//33*(1+-2x)^(1/2)*(3+5x)^-1//2+(1+-2x)^(1/2)*(2+3x)^-1*(3+5x)^-3//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^-5//2, x) == :(-126513//196*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-6095//84*(1+-2x)^(1/2)*(3+5x)^-3//2+608185//924*(1+-2x)^(1/2)*(3+5x)^-1//2+(1/2)*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-3//2+243*(1+-2x)^(1/2)*(3+5x)^-3//2*(56+84x)^-1)
@test integrate((1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^-5//2, x) == :(-13246251//2744*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-638165//1176*(1+-2x)^(1/2)*(3+5x)^-3//2+63678595//12936*(1+-2x)^(1/2)*(3+5x)^-1//2+25441*(1+-2x)^(1/2)*(3+5x)^-3//2*(784+1176x)^-1+1//3*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^-3//2+313//84*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-3//2)
@test integrate((1+-2x)^3//2*(2+3x)^3*(3+5x)^(1/2), x) == :(-339983//384000*(1+-2x)^5//2*(3+5x)^(1/2)+3739813//7680000*(1+-2x)^3//2*(3+5x)^(1/2)+41137943//25600000*(1+-2x)^(1/2)*(3+5x)^(1/2)+452517373//256000000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-1//20*(1+-2x)^5//2*(2+3x)^2*(3+5x)^3//2+-1//160000*(1+-2x)^5//2*(3+5x)^3//2*(88987+63120x))
@test integrate((1+-2x)^3//2*(2+3x)^2*(3+5x)^(1/2), x) == :(-4123//9600*(1+-2x)^5//2*(3+5x)^(1/2)+-567//4000*(1+-2x)^5//2*(3+5x)^3//2+45353//192000*(1+-2x)^3//2*(3+5x)^(1/2)+498883//640000*(1+-2x)^(1/2)*(3+5x)^(1/2)+5487713//6400000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-3//50*(1+-2x)^5//2*(3+5x)^3//2*(2+3x))
@test integrate((1+-2x)^3//2*(3+5x)^(1/2)*(2+3x), x) == :(-23//96*(1+-2x)^5//2*(3+5x)^(1/2)+-3//40*(1+-2x)^5//2*(3+5x)^3//2+253//1920*(1+-2x)^3//2*(3+5x)^(1/2)+2783//6400*(1+-2x)^(1/2)*(3+5x)^(1/2)+30613//64000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^3//2*(3+5x)^(1/2), x) == :(-1//6*(1+-2x)^5//2*(3+5x)^(1/2)+11//120*(1+-2x)^3//2*(3+5x)^(1/2)+121//400*(1+-2x)^(1/2)*(3+5x)^(1/2)+1331//4000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^3//2*(2+3x)^-1*(3+5x)^(1/2), x) == :(1//6*(1+-2x)^3//2*(3+5x)^(1/2)+14//27*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+107//180*(1+-2x)^(1/2)*(3+5x)^(1/2)+4091//5400*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^3//2*(2+3x)^-2*(3+5x)^(1/2), x) == :(-107//135*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-41//27*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-4//9*(1+-2x)^(1/2)*(3+5x)^(1/2)+-1*(1+-2x)^3//2*(3+5x)^(1/2)*(6+9x)^-1)
@test integrate((1+-2x)^3//2*(2+3x)^-3*(3+5x)^(1/2), x) == :(-793//756*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+4//27*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+41*(1+-2x)^(1/2)*(3+5x)^(1/2)*(72+108x)^-1+-1//6*(1+-2x)^3//2*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^-4*(3+5x)^(1/2), x) == :(-1331//392*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-121*(1+-2x)^(1/2)*(3+5x)^(1/2)*(112+168x)^-1+1//3*(1+-2x)^3//2*(2+3x)^-3*(3+5x)^3//2+11//4*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2)
@test integrate((1+-2x)^3//2*(2+3x)^-5*(3+5x)^(1/2), x) == :(-240911//21952*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-21901*(1+-2x)^(1/2)*(3+5x)^(1/2)*(6272+9408x)^-1+3//28*(1+-2x)^5//2*(2+3x)^-4*(3+5x)^3//2+181//168*(1+-2x)^3//2*(2+3x)^-3*(3+5x)^3//2+1991//224*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2)
@test integrate((1+-2x)^3//2*(2+3x)^-6*(3+5x)^(1/2), x) == :(-11988317//307328*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+28291441*(1+-2x)^(1/2)*(3+5x)^(1/2)*(2370816+3556224x)^-1+-1//15*(1+-2x)^3//2*(2+3x)^-5*(3+5x)^(1/2)+41//360*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^(1/2)+7723//15120*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+270463//84672*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^3*(3+5x)^3//2, x) == :(-1557589//512000*(1+-2x)^5//2*(3+5x)^(1/2)+-141599//128000*(1+-2x)^5//2*(3+5x)^3//2+17133479//10240000*(1+-2x)^3//2*(3+5x)^(1/2)+565404807//102400000*(1+-2x)^(1/2)*(3+5x)^(1/2)+6219452877//1024000000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-3//70*(1+-2x)^5//2*(2+3x)^2*(3+5x)^5//2+-3//280000*(1+-2x)^5//2*(3+5x)^5//2*(49829+33300x))
@test integrate((1+-2x)^3//2*(2+3x)^2*(3+5x)^3//2, x) == :(-34111//25600*(1+-2x)^5//2*(3+5x)^(1/2)+-3101//6400*(1+-2x)^5//2*(3+5x)^3//2+-259//2000*(1+-2x)^5//2*(3+5x)^5//2+375221//512000*(1+-2x)^3//2*(3+5x)^(1/2)+12382293//5120000*(1+-2x)^(1/2)*(3+5x)^(1/2)+136205223//51200000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-1//20*(1+-2x)^5//2*(3+5x)^5//2*(2+3x))
@test integrate((1+-2x)^3//2*(3+5x)^3//2*(2+3x), x) == :(-407//640*(1+-2x)^5//2*(3+5x)^(1/2)+-37//160*(1+-2x)^5//2*(3+5x)^3//2+-3//50*(1+-2x)^5//2*(3+5x)^5//2+4477//12800*(1+-2x)^3//2*(3+5x)^(1/2)+147741//128000*(1+-2x)^(1/2)*(3+5x)^(1/2)+1625151//1280000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^3//2*(3+5x)^3//2, x) == :(-11//32*(1+-2x)^5//2*(3+5x)^(1/2)+-1//8*(1+-2x)^5//2*(3+5x)^3//2+121//640*(1+-2x)^3//2*(3+5x)^(1/2)+3993//6400*(1+-2x)^(1/2)*(3+5x)^(1/2)+43923//64000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^3//2*(2+3x)^-1*(3+5x)^3//2, x) == :(-1781//2160*(1+-2x)^(1/2)*(3+5x)^(1/2)+-14//81*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+1//9*(1+-2x)^3//2*(3+5x)^3//2+37//180*(1+-2x)^(1/2)*(3+5x)^3//2+19573//64800*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^3//2*(2+3x)^-2*(3+5x)^3//2, x) == :(-1//3*(1+-2x)^(1/2)*(3+5x)^3//2+37//27*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+107//36*(1+-2x)^(1/2)*(3+5x)^(1/2)+1649//1080*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-1*(1+-2x)^3//2*(3+5x)^3//2*(6+9x)^-1)
@test integrate((1+-2x)^3//2*(2+3x)^-3*(3+5x)^3//2, x) == :(-1649//756*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-205//36*(1+-2x)^(1/2)*(3+5x)^(1/2)+-37//27*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+37*(1+-2x)^(1/2)*(3+5x)^3//2*(24+36x)^-1+-1//6*(1+-2x)^3//2*(2+3x)^-2*(3+5x)^3//2)
@test integrate((1+-2x)^3//2*(2+3x)^-4*(3+5x)^3//2, x) == :(-19573//31752*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+20//81*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-661*(1+-2x)^(1/2)*(3+5x)^(1/2)*(3024+4536x)^-1+-1//9*(1+-2x)^3//2*(2+3x)^-3*(3+5x)^3//2+37//36*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2)
@test integrate((1+-2x)^3//2*(2+3x)^-5*(3+5x)^3//2, x) == :(-43923//21952*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-3993*(1+-2x)^(1/2)*(3+5x)^(1/2)*(6272+9408x)^-1+-121//224*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2+1//4*(1+-2x)^3//2*(2+3x)^-4*(3+5x)^5//2+11//8*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^5//2)
@test integrate((1+-2x)^3//2*(2+3x)^-6*(3+5x)^3//2, x) == :(-1625151//307328*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-147741*(1+-2x)^(1/2)*(3+5x)^(1/2)*(87808+131712x)^-1+-4477//3136*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2+3//35*(1+-2x)^5//2*(2+3x)^-5*(3+5x)^5//2+37//56*(1+-2x)^3//2*(2+3x)^-4*(3+5x)^5//2+407//112*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^5//2)
@test integrate((1+-2x)^3//2*(2+3x)^-7*(3+5x)^3//2, x) == :(-19457889//1229312*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+137752591*(1+-2x)^(1/2)*(3+5x)^(1/2)*(28449792+42674688x)^-1+-7591//30240*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^(1/2)+-1//18*(1+-2x)^3//2*(2+3x)^-6*(3+5x)^3//2+37//180*(1+-2x)^(1/2)*(2+3x)^-5*(3+5x)^3//2+37333//181440*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+1316353//1016064*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^-8*(3+5x)^3//2, x) == :(-6219452877//120472576*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+14677525921*(1+-2x)^(1/2)*(3+5x)^(1/2)*(929359872+1394039808x)^-1+-9901//52920*(1+-2x)^(1/2)*(2+3x)^-5*(3+5x)^(1/2)+-1//21*(1+-2x)^3//2*(2+3x)^-7*(3+5x)^3//2+37//252*(1+-2x)^(1/2)*(2+3x)^-6*(3+5x)^3//2+341917//2963520*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^(1/2)+4014523//5927040*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+140331343//33191424*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^3*(3+5x)^5//2, x) == :(-37029509//3276800*(1+-2x)^5//2*(3+5x)^(1/2)+-3366319//819200*(1+-2x)^5//2*(3+5x)^3//2+-306029//256000*(1+-2x)^5//2*(3+5x)^5//2+407324599//65536000*(1+-2x)^3//2*(3+5x)^(1/2)+13441711767//655360000*(1+-2x)^(1/2)*(3+5x)^(1/2)+147858829437//6553600000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-9//448000*(1+-2x)^5//2*(3+5x)^7//2*(25043+16120x)+-3//80*(1+-2x)^5//2*(2+3x)^2*(3+5x)^7//2)
@test integrate((1+-2x)^3//2*(2+3x)^2*(3+5x)^5//2, x) == :(-94743//20480*(1+-2x)^5//2*(3+5x)^(1/2)+-8613//5120*(1+-2x)^5//2*(3+5x)^3//2+-783//1600*(1+-2x)^5//2*(3+5x)^5//2+-47//400*(1+-2x)^5//2*(3+5x)^7//2+1042173//409600*(1+-2x)^3//2*(3+5x)^(1/2)+34391709//4096000*(1+-2x)^(1/2)*(3+5x)^(1/2)+378308799//40960000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-3//70*(1+-2x)^5//2*(3+5x)^7//2*(2+3x))
@test integrate((1+-2x)^3//2*(3+5x)^5//2*(2+3x), x) == :(-2057//1024*(1+-2x)^5//2*(3+5x)^(1/2)+-187//256*(1+-2x)^5//2*(3+5x)^3//2+-17//80*(1+-2x)^5//2*(3+5x)^5//2+-1//20*(1+-2x)^5//2*(3+5x)^7//2+22627//20480*(1+-2x)^3//2*(3+5x)^(1/2)+746691//204800*(1+-2x)^(1/2)*(3+5x)^(1/2)+8213601//2048000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^3//2*(3+5x)^5//2, x) == :(-121//128*(1+-2x)^5//2*(3+5x)^(1/2)+-11//32*(1+-2x)^5//2*(3+5x)^3//2+-1//10*(1+-2x)^5//2*(3+5x)^5//2+1331//2560*(1+-2x)^3//2*(3+5x)^(1/2)+43923//25600*(1+-2x)^(1/2)*(3+5x)^(1/2)+483153//256000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^3//2*(2+3x)^-1*(3+5x)^5//2, x) == :(-15863//20736*(1+-2x)^(1/2)*(3+5x)^(1/2)+-53//192*(1+-2x)^(1/2)*(3+5x)^3//2+1//12*(1+-2x)^3//2*(3+5x)^5//2+14//243*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+23//216*(1+-2x)^(1/2)*(3+5x)^5//2+648919//622080*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^3//2*(2+3x)^-2*(3+5x)^5//2, x) == :(-3065//1296*(1+-2x)^(1/2)*(3+5x)^(1/2)+-181//243*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-43//7776*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-8//27*(1+-2x)^(1/2)*(3+5x)^5//2+25//12*(1+-2x)^(1/2)*(3+5x)^3//2+-1*(1+-2x)^3//2*(3+5x)^5//2*(6+9x)^-1)
@test integrate((1+-2x)^3//2*(2+3x)^-3*(3+5x)^5//2, x) == :(-35//4*(1+-2x)^(1/2)*(3+5x)^3//2+185//27*(1+-2x)^(1/2)*(3+5x)^(1/2)+1945//648*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+6829//2268*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+181*(1+-2x)^(1/2)*(3+5x)^5//2*(72+108x)^-1+-1//6*(1+-2x)^3//2*(2+3x)^-2*(3+5x)^5//2)
@test integrate((1+-2x)^3//2*(2+3x)^-4*(3+5x)^5//2, x) == :(-326717//95256*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-39745//4536*(1+-2x)^(1/2)*(3+5x)^(1/2)+-575//243*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+331*(1+-2x)^(1/2)*(3+5x)^3//2*(336+504x)^-1+-1//9*(1+-2x)^3//2*(2+3x)^-3*(3+5x)^5//2+181//108*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^5//2)
@test integrate((1+-2x)^3//2*(2+3x)^-5*(3+5x)^5//2, x) == :(-1922677//5334336*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+100//243*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-77269*(1+-2x)^(1/2)*(3+5x)^(1/2)*(508032+762048x)^-1+-871//6048*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2+-1//12*(1+-2x)^3//2*(2+3x)^-4*(3+5x)^5//2+181//216*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^5//2)
@test integrate((1+-2x)^3//2*(2+3x)^-6*(3+5x)^5//2, x) == :(-483153//307328*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-43923*(1+-2x)^(1/2)*(3+5x)^(1/2)*(87808+131712x)^-1+-1331//3136*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2+-121//560*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^5//2+1//5*(1+-2x)^3//2*(2+3x)^-5*(3+5x)^7//2+33//40*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^7//2)
@test integrate((1+-2x)^3//2*(2+3x)^-7*(3+5x)^5//2, x) == :(-4348377//1229312*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-395307*(1+-2x)^(1/2)*(3+5x)^(1/2)*(351232+526848x)^-1+-11979//12544*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2+-1089//2240*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^5//2+1//14*(1+-2x)^5//2*(2+3x)^-6*(3+5x)^7//2+9//20*(1+-2x)^3//2*(2+3x)^-5*(3+5x)^7//2+297//160*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^7//2)
@test integrate((1+-2x)^3//2*(2+3x)^-8*(3+5x)^5//2, x) == :(-1104970911//120472576*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+23466191827*(1+-2x)^(1/2)*(3+5x)^(1/2)*(8364238848+12546358272x)^-1+-1289227//8890560*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^(1/2)+-12421//52920*(1+-2x)^(1/2)*(2+3x)^-5*(3+5x)^3//2+-1//21*(1+-2x)^3//2*(2+3x)^-7*(3+5x)^5//2+181//756*(1+-2x)^(1/2)*(2+3x)^-6*(3+5x)^5//2+6249601//53343360*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+224018941//298722816*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^3*(3+5x)^-1//2, x) == :(51373//320000*(1+-2x)^3//2*(3+5x)^(1/2)+1695309//3200000*(1+-2x)^(1/2)*(3+5x)^(1/2)+18648399//32000000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-3//50*(1+-2x)^5//2*(2+3x)^2*(3+5x)^(1/2)+-3//80000*(1+-2x)^5//2*(3+5x)^(1/2)*(14629+11580x))
@test integrate((1+-2x)^3//2*(2+3x)^2*(3+5x)^-1//2, x) == :(-119//800*(1+-2x)^5//2*(3+5x)^(1/2)+301//3200*(1+-2x)^3//2*(3+5x)^(1/2)+9933//32000*(1+-2x)^(1/2)*(3+5x)^(1/2)+109263//320000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-3//40*(1+-2x)^5//2*(3+5x)^(1/2)*(2+3x))
@test integrate((1+-2x)^3//2*(3+5x)^-1//2*(2+3x), x) == :(-1//10*(1+-2x)^5//2*(3+5x)^(1/2)+3//40*(1+-2x)^3//2*(3+5x)^(1/2)+99//400*(1+-2x)^(1/2)*(3+5x)^(1/2)+1089//4000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^3//2*(3+5x)^-1//2, x) == :(1//10*(1+-2x)^3//2*(3+5x)^(1/2)+33//100*(1+-2x)^(1/2)*(3+5x)^(1/2)+363//1000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^3//2*(2+3x)^-1*(3+5x)^-1//2, x) == :(-103//225*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-14//9*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-2//15*(1+-2x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^-2*(3+5x)^-1//2, x) == :(-29//9*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+4//45*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+7*(1+-2x)^(1/2)*(3+5x)^(1/2)*(6+9x)^-1)
@test integrate((1+-2x)^3//2*(2+3x)^-3*(3+5x)^-1//2, x) == :(-363//28*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+(1/2)*(1+-2x)^3//2*(2+3x)^-2*(3+5x)^(1/2)+33*(1+-2x)^(1/2)*(3+5x)^(1/2)*(8+12x)^-1)
@test integrate((1+-2x)^3//2*(2+3x)^-4*(3+5x)^-1//2, x) == :(-21417//392*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+1947*(1+-2x)^(1/2)*(3+5x)^(1/2)*(112+168x)^-1+1//7*(1+-2x)^5//2*(2+3x)^-3*(3+5x)^(1/2)+59//28*(1+-2x)^3//2*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^-5*(3+5x)^-1//2, x) == :(-5274027//21952*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+4148797*(1+-2x)^(1/2)*(3+5x)^(1/2)*(56448+84672x)^-1+7//12*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^(1/2)+227//72*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+39667//2016*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^-6*(3+5x)^-1//2, x) == :(-333216939//307328*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+87374783*(1+-2x)^(1/2)*(3+5x)^(1/2)*(263424+395136x)^-1+7//15*(1+-2x)^(1/2)*(2+3x)^-5*(3+5x)^(1/2)+293//120*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^(1/2)+23909//1680*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+835409//9408*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^3*(3+5x)^-3//2, x) == :(35511//160000*(1+-2x)^(1/2)*(3+5x)^(1/2)+390621//1600000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-2//5*(1+-2x)^3//2*(2+3x)^3*(3+5x)^-1//2+-1//16000*(1+-2x)^3//2*(3+5x)^(1/2)*(2205+-504x)+27//100*(1+-2x)^3//2*(2+3x)^2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^2*(3+5x)^-3//2, x) == :(-3//50*(1+-2x)^5//2*(3+5x)^(1/2)+-2//275*(1+-2x)^5//2*(3+5x)^-1//2+119//2200*(1+-2x)^3//2*(3+5x)^(1/2)+357//2000*(1+-2x)^(1/2)*(3+5x)^(1/2)+3927//20000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^3//2*(3+5x)^-3//2*(2+3x), x) == :(-2//55*(1+-2x)^5//2*(3+5x)^-1//2+1//22*(1+-2x)^3//2*(3+5x)^(1/2)+3//20*(1+-2x)^(1/2)*(3+5x)^(1/2)+33//200*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^3//2*(3+5x)^-3//2, x) == :(-33//125*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-6//25*(1+-2x)^(1/2)*(3+5x)^(1/2)+-2//5*(1+-2x)^3//2*(3+5x)^-1//2)
@test integrate((1+-2x)^3//2*(2+3x)^-1*(3+5x)^-3//2, x) == :(-22//5*(1+-2x)^(1/2)*(3+5x)^-1//2+4//75*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+14//3*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2))
@test integrate((1+-2x)^3//2*(2+3x)^-2*(3+5x)^-3//2, x) == :(-33*(1+-2x)^(1/2)*(3+5x)^-1//2+33*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+(1+-2x)^3//2*(2+3x)^-1*(3+5x)^-1//2)
@test integrate((1+-2x)^3//2*(2+3x)^-3*(3+5x)^-3//2, x) == :(-5709//28*(1+-2x)^(1/2)*(3+5x)^-1//2+5709//28*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+173*(1+-2x)^3//2*(3+5x)^-1//2*(56+84x)^-1+3//14*(1+-2x)^5//2*(2+3x)^-2*(3+5x)^-1//2)
@test integrate((1+-2x)^3//2*(2+3x)^-4*(3+5x)^-3//2, x) == :(-608185//504*(1+-2x)^(1/2)*(3+5x)^-1//2+463881//392*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+13409*(1+-2x)^(1/2)*(3+5x)^-1//2*(336+504x)^-1+7//9*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^-1//2+77//12*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-1//2)
@test integrate((1+-2x)^3//2*(2+3x)^-5*(3+5x)^-3//2, x) == :(-63678595//9408*(1+-2x)^(1/2)*(3+5x)^-1//2+145708761//21952*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+1403963*(1+-2x)^(1/2)*(3+5x)^-1//2*(6272+9408x)^-1+7//12*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^-1//2+33//8*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^-1//2+8063//224*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-1//2)
@test integrate((1+-2x)^3//2*(2+3x)^3*(3+5x)^-5//2, x) == :(13153//100000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-128//25*(1+-2x)^(1/2)*(2+3x)^3*(3+5x)^-1//2+-2//15*(1+-2x)^3//2*(2+3x)^3*(3+5x)^-3//2+21//10000*(1+-2x)^(1/2)*(3+5x)^(1/2)*(853+1140x)+378//125*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^2*(3+5x)^-5//2, x) == :(-388//9075*(1+-2x)^5//2*(3+5x)^-1//2+-2//825*(1+-2x)^5//2*(3+5x)^-3//2+343//5000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+343//5500*(1+-2x)^(1/2)*(3+5x)^(1/2)+343//18150*(1+-2x)^3//2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(3+5x)^-5//2*(2+3x), x) == :(-38//165*(1+-2x)^3//2*(3+5x)^-1//2+-38//275*(1+-2x)^(1/2)*(3+5x)^(1/2)+-19//125*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-2//165*(1+-2x)^5//2*(3+5x)^-3//2)
@test integrate((1+-2x)^3//2*(3+5x)^-5//2, x) == :(-2//15*(1+-2x)^3//2*(3+5x)^-3//2+4//25*(1+-2x)^(1/2)*(3+5x)^-1//2+4//125*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^3//2*(2+3x)^-1*(3+5x)^-5//2, x) == :(-14*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+14*(1+-2x)^(1/2)*(3+5x)^-1//2+-2//3*(1+-2x)^3//2*(3+5x)^-3//2)
@test integrate((1+-2x)^3//2*(2+3x)^-2*(3+5x)^-5//2, x) == :(-169*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+169*(1+-2x)^(1/2)*(3+5x)^-1//2+-169//21*(1+-2x)^3//2*(3+5x)^-3//2+3*(1+-2x)^5//2*(3+5x)^-3//2*(14+21x)^-1)
@test integrate((1+-2x)^3//2*(2+3x)^-3*(3+5x)^-5//2, x) == :(-40787//28*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-655//4*(1+-2x)^(1/2)*(3+5x)^-3//2+17825//12*(1+-2x)^(1/2)*(3+5x)^-1//2+235*(1+-2x)^(1/2)*(3+5x)^-3//2*(24+36x)^-1+7//6*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-3//2)
@test integrate((1+-2x)^3//2*(2+3x)^-4*(3+5x)^-5//2, x) == :(-4246733//392*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-204595//168*(1+-2x)^(1/2)*(3+5x)^-3//2+618645//56*(1+-2x)^(1/2)*(3+5x)^-1//2+24469*(1+-2x)^(1/2)*(3+5x)^-3//2*(336+504x)^-1+7//9*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^-3//2+301//36*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-3//2)
@test integrate((1+-2x)^5//2*(2+3x)^3*(3+5x)^(1/2), x) == :(-255169//640000*(1+-2x)^7//2*(3+5x)^(1/2)+2806859//19200000*(1+-2x)^5//2*(3+5x)^(1/2)+30875449//76800000*(1+-2x)^3//2*(3+5x)^(1/2)+339629939//256000000*(1+-2x)^(1/2)*(3+5x)^(1/2)+3735929329//2560000000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-3//70*(1+-2x)^7//2*(2+3x)^2*(3+5x)^3//2+-3//280000*(1+-2x)^7//2*(3+5x)^3//2*(33857+26700x))
@test integrate((1+-2x)^5//2*(2+3x)^2*(3+5x)^(1/2), x) == :(-7189//32000*(1+-2x)^7//2*(3+5x)^(1/2)+-193//2000*(1+-2x)^7//2*(3+5x)^3//2+79079//960000*(1+-2x)^5//2*(3+5x)^(1/2)+869869//3840000*(1+-2x)^3//2*(3+5x)^(1/2)+9568559//12800000*(1+-2x)^(1/2)*(3+5x)^(1/2)+105254149//128000000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-1//20*(1+-2x)^7//2*(3+5x)^3//2*(2+3x))
@test integrate((1+-2x)^5//2*(3+5x)^(1/2)*(2+3x), x) == :(-119//800*(1+-2x)^7//2*(3+5x)^(1/2)+-3//50*(1+-2x)^7//2*(3+5x)^3//2+1309//24000*(1+-2x)^5//2*(3+5x)^(1/2)+14399//96000*(1+-2x)^3//2*(3+5x)^(1/2)+158389//320000*(1+-2x)^(1/2)*(3+5x)^(1/2)+1742279//3200000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^5//2*(3+5x)^(1/2), x) == :(-1//8*(1+-2x)^7//2*(3+5x)^(1/2)+11//240*(1+-2x)^5//2*(3+5x)^(1/2)+121//960*(1+-2x)^3//2*(3+5x)^(1/2)+1331//3200*(1+-2x)^(1/2)*(3+5x)^(1/2)+14641//32000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^-1*(3+5x)^(1/2), x) == :(1//9*(1+-2x)^5//2*(3+5x)^(1/2)+59//180*(1+-2x)^3//2*(3+5x)^(1/2)+98//81*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+6401//5400*(1+-2x)^(1/2)*(3+5x)^(1/2)+250433//162000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^-2*(3+5x)^(1/2), x) == :(-2119//900*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-43//30*(1+-2x)^(1/2)*(3+5x)^(1/2)+-35//9*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-1//3*(1+-2x)^3//2*(3+5x)^(1/2)+-1*(1+-2x)^5//2*(3+5x)^(1/2)*(6+9x)^-1)
@test integrate((1+-2x)^5//2*(2+3x)^-3*(3+5x)^(1/2), x) == :(-155//108*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+19//18*(1+-2x)^(1/2)*(3+5x)^(1/2)+118//135*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+5*(1+-2x)^3//2*(3+5x)^(1/2)*(8+12x)^-1+-1//6*(1+-2x)^5//2*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^-4*(3+5x)^(1/2), x) == :(-32765//4536*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-8//81*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+925*(1+-2x)^(1/2)*(3+5x)^(1/2)*(432+648x)^-1+-1//9*(1+-2x)^5//2*(2+3x)^-3*(3+5x)^(1/2)+5//12*(1+-2x)^3//2*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^-5*(3+5x)^(1/2), x) == :(-73205//3136*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-6655*(1+-2x)^(1/2)*(3+5x)^(1/2)*(896+1344x)^-1+1//4*(1+-2x)^5//2*(2+3x)^-4*(3+5x)^3//2+55//24*(1+-2x)^3//2*(2+3x)^-3*(3+5x)^3//2+605//32*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2)
@test integrate((1+-2x)^5//2*(2+3x)^-6*(3+5x)^(1/2), x) == :(-3674891//43904*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-334081*(1+-2x)^(1/2)*(3+5x)^(1/2)*(12544+18816x)^-1+3//35*(1+-2x)^7//2*(2+3x)^-5*(3+5x)^3//2+251//280*(1+-2x)^5//2*(2+3x)^-4*(3+5x)^3//2+2761//336*(1+-2x)^3//2*(2+3x)^-3*(3+5x)^3//2+30371//448*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2)
@test integrate((1+-2x)^5//2*(2+3x)^-7*(3+5x)^(1/2), x) == :(-391280725//1229312*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+2770202075*(1+-2x)^(1/2)*(3+5x)^(1/2)*(28449792+42674688x)^-1+-1//18*(1+-2x)^5//2*(2+3x)^-6*(3+5x)^(1/2)+1//12*(1+-2x)^3//2*(2+3x)^-5*(3+5x)^(1/2)+647//864*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^(1/2)+151621//36288*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+26486645//1016064*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^3*(3+5x)^3//2, x) == :(-24269487//20480000*(1+-2x)^7//2*(3+5x)^(1/2)+-735439//1280000*(1+-2x)^7//2*(3+5x)^3//2+88988119//204800000*(1+-2x)^5//2*(3+5x)^(1/2)+978869309//819200000*(1+-2x)^3//2*(3+5x)^(1/2)+32302687197//8192000000*(1+-2x)^(1/2)*(3+5x)^(1/2)+355329559167//81920000000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-9//448000*(1+-2x)^7//2*(3+5x)^5//2*(18399+13480x)+-3//80*(1+-2x)^7//2*(2+3x)^2*(3+5x)^5//2)
@test integrate((1+-2x)^5//2*(2+3x)^2*(3+5x)^3//2, x) == :(-75471//128000*(1+-2x)^7//2*(3+5x)^(1/2)+-2287//8000*(1+-2x)^7//2*(3+5x)^3//2+-263//2800*(1+-2x)^7//2*(3+5x)^5//2+276727//1280000*(1+-2x)^5//2*(3+5x)^(1/2)+3043997//5120000*(1+-2x)^3//2*(3+5x)^(1/2)+100451901//51200000*(1+-2x)^(1/2)*(3+5x)^(1/2)+1104970911//512000000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-3//70*(1+-2x)^7//2*(3+5x)^5//2*(2+3x))
@test integrate((1+-2x)^5//2*(3+5x)^3//2*(2+3x), x) == :(-2079//6400*(1+-2x)^7//2*(3+5x)^(1/2)+-63//400*(1+-2x)^7//2*(3+5x)^3//2+-1//20*(1+-2x)^7//2*(3+5x)^5//2+7623//64000*(1+-2x)^5//2*(3+5x)^(1/2)+83853//256000*(1+-2x)^3//2*(3+5x)^(1/2)+2767149//2560000*(1+-2x)^(1/2)*(3+5x)^(1/2)+30438639//25600000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^5//2*(3+5x)^3//2, x) == :(-33//160*(1+-2x)^7//2*(3+5x)^(1/2)+-1//10*(1+-2x)^7//2*(3+5x)^3//2+121//1600*(1+-2x)^5//2*(3+5x)^(1/2)+1331//6400*(1+-2x)^3//2*(3+5x)^(1/2)+43923//64000*(1+-2x)^(1/2)*(3+5x)^(1/2)+483153//640000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^-1*(3+5x)^3//2, x) == :(-390869//259200*(1+-2x)^(1/2)*(3+5x)^(1/2)+-98//243*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+1//12*(1+-2x)^5//2*(3+5x)^3//2+181//1080*(1+-2x)^3//2*(3+5x)^3//2+7093//21600*(1+-2x)^(1/2)*(3+5x)^3//2+1922677//7776000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^-2*(3+5x)^3//2, x) == :(-247//270*(1+-2x)^(1/2)*(3+5x)^3//2+-8//27*(1+-2x)^3//2*(3+5x)^3//2+805//243*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+24251//3240*(1+-2x)^(1/2)*(3+5x)^(1/2)+326717//97200*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-1*(1+-2x)^5//2*(3+5x)^3//2*(6+9x)^-1)
@test integrate((1+-2x)^5//2*(2+3x)^-3*(3+5x)^3//2, x) == :(-6829//1620*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-1945//324*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-1649//108*(1+-2x)^(1/2)*(3+5x)^(1/2)+41//18*(1+-2x)^(1/2)*(3+5x)^3//2+115*(1+-2x)^3//2*(3+5x)^3//2*(72+108x)^-1+-1//6*(1+-2x)^5//2*(2+3x)^-2*(3+5x)^3//2)
@test integrate((1+-2x)^5//2*(2+3x)^-4*(3+5x)^3//2, x) == :(-845//648*(1+-2x)^(1/2)*(3+5x)^(1/2)+215//13608*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+362//243*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+365*(1+-2x)^(1/2)*(3+5x)^3//2*(432+648x)^-1+-1//9*(1+-2x)^5//2*(2+3x)^-3*(3+5x)^3//2+115//108*(1+-2x)^3//2*(2+3x)^-2*(3+5x)^3//2)
@test integrate((1+-2x)^5//2*(2+3x)^-5*(3+5x)^3//2, x) == :(-3244595//762048*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-40//243*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-97235*(1+-2x)^(1/2)*(3+5x)^(1/2)*(72576+108864x)^-1+-1//12*(1+-2x)^5//2*(2+3x)^-4*(3+5x)^3//2+115//216*(1+-2x)^3//2*(2+3x)^-3*(3+5x)^3//2+2675//864*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2)
@test integrate((1+-2x)^5//2*(2+3x)^-6*(3+5x)^3//2, x) == :(-483153//43904*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-43923*(1+-2x)^(1/2)*(3+5x)^(1/2)*(12544+18816x)^-1+-1331//448*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2+1//5*(1+-2x)^5//2*(2+3x)^-5*(3+5x)^5//2+11//8*(1+-2x)^3//2*(2+3x)^-4*(3+5x)^5//2+121//16*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^5//2)
@test integrate((1+-2x)^5//2*(2+3x)^-7*(3+5x)^3//2, x) == :(-41068005//1229312*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-3733455*(1+-2x)^(1/2)*(3+5x)^(1/2)*(351232+526848x)^-1+-113135//12544*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2+1//14*(1+-2x)^7//2*(2+3x)^-6*(3+5x)^5//2+17//28*(1+-2x)^5//2*(2+3x)^-5*(3+5x)^5//2+935//224*(1+-2x)^3//2*(2+3x)^-4*(3+5x)^5//2+10285//448*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^5//2)
@test integrate((1+-2x)^5//2*(2+3x)^-8*(3+5x)^3//2, x) == :(-1891543995//17210368*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+40175505215*(1+-2x)^(1/2)*(3+5x)^(1/2)*(1194891264+1792336896x)^-1+-443563//254016*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^(1/2)+-1//21*(1+-2x)^5//2*(2+3x)^-7*(3+5x)^3//2+115//756*(1+-2x)^3//2*(2+3x)^-6*(3+5x)^3//2+1921//1512*(1+-2x)^(1/2)*(2+3x)^-5*(3+5x)^3//2+2199649//1524096*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+384136145//42674688*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^3*(3+5x)^5//2, x) == :(-63658463//16384000*(1+-2x)^7//2*(3+5x)^(1/2)+-5787133//3072000*(1+-2x)^7//2*(3+5x)^3//2+-526103//768000*(1+-2x)^7//2*(3+5x)^5//2+700243093//491520000*(1+-2x)^5//2*(3+5x)^(1/2)+7702674023//1966080000*(1+-2x)^3//2*(3+5x)^(1/2)+84729414253//6553600000*(1+-2x)^(1/2)*(3+5x)^(1/2)+932023556783//65536000000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-1//30*(1+-2x)^7//2*(2+3x)^2*(3+5x)^7//2+-1//672000*(1+-2x)^7//2*(3+5x)^7//2*(245011+170940x))
@test integrate((1+-2x)^5//2*(2+3x)^2*(3+5x)^5//2, x) == :(-1456961//819200*(1+-2x)^7//2*(3+5x)^(1/2)+-132451//153600*(1+-2x)^7//2*(3+5x)^3//2+-12041//38400*(1+-2x)^7//2*(3+5x)^5//2+-999//11200*(1+-2x)^7//2*(3+5x)^7//2+16026571//24576000*(1+-2x)^5//2*(3+5x)^(1/2)+176292281//98304000*(1+-2x)^3//2*(3+5x)^(1/2)+1939215091//327680000*(1+-2x)^(1/2)*(3+5x)^(1/2)+21331366001//3276800000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-3//80*(1+-2x)^7//2*(3+5x)^7//2*(2+3x))
@test integrate((1+-2x)^5//2*(3+5x)^5//2*(2+3x), x) == :(-4477//5120*(1+-2x)^7//2*(3+5x)^(1/2)+-407//960*(1+-2x)^7//2*(3+5x)^3//2+-37//240*(1+-2x)^7//2*(3+5x)^5//2+-3//70*(1+-2x)^7//2*(3+5x)^7//2+49247//153600*(1+-2x)^5//2*(3+5x)^(1/2)+541717//614400*(1+-2x)^3//2*(3+5x)^(1/2)+5958887//2048000*(1+-2x)^(1/2)*(3+5x)^(1/2)+65547757//20480000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^5//2*(3+5x)^5//2, x) == :(-121//256*(1+-2x)^7//2*(3+5x)^(1/2)+-11//48*(1+-2x)^7//2*(3+5x)^3//2+-1//12*(1+-2x)^7//2*(3+5x)^5//2+1331//7680*(1+-2x)^5//2*(3+5x)^(1/2)+14641//30720*(1+-2x)^3//2*(3+5x)^(1/2)+161051//102400*(1+-2x)^(1/2)*(3+5x)^(1/2)+1771561//1024000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^-1*(3+5x)^5//2, x) == :(-1994287//3110400*(1+-2x)^(1/2)*(3+5x)^(1/2)+-14557//28800*(1+-2x)^(1/2)*(3+5x)^3//2+1//15*(1+-2x)^5//2*(3+5x)^5//2+37//360*(1+-2x)^3//2*(3+5x)^5//2+98//729*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+4783//32400*(1+-2x)^(1/2)*(3+5x)^5//2+109715471//93312000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^-2*(3+5x)^5//2, x) == :(-660959//933120*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-155777//31104*(1+-2x)^(1/2)*(3+5x)^(1/2)+-1295//729*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-247//324*(1+-2x)^(1/2)*(3+5x)^5//2+-5//18*(1+-2x)^3//2*(3+5x)^5//2+1453//288*(1+-2x)^(1/2)*(3+5x)^3//2+-1*(1+-2x)^5//2*(3+5x)^5//2*(6+9x)^-1)
@test integrate((1+-2x)^5//2*(2+3x)^-3*(3+5x)^5//2, x) == :(-785//36*(1+-2x)^(1/2)*(3+5x)^3//2+575//162*(1+-2x)^(1/2)*(3+5x)^5//2+21935//2916*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+34145//1944*(1+-2x)^(1/2)*(3+5x)^(1/2)+81733//11664*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+185*(1+-2x)^3//2*(3+5x)^5//2*(72+108x)^-1+-1//6*(1+-2x)^5//2*(2+3x)^-2*(3+5x)^5//2)
@test integrate((1+-2x)^5//2*(2+3x)^-4*(3+5x)^5//2, x) == :(-408665//40824*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-48625//1944*(1+-2x)^(1/2)*(3+5x)^(1/2)+-21935//2916*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+2075//72*(1+-2x)^(1/2)*(3+5x)^3//2+-10385*(1+-2x)^(1/2)*(3+5x)^5//2*(1296+1944x)^-1+-1//9*(1+-2x)^5//2*(2+3x)^-3*(3+5x)^5//2+185//108*(1+-2x)^3//2*(2+3x)^-2*(3+5x)^5//2)
@test integrate((1+-2x)^5//2*(2+3x)^-5*(3+5x)^5//2, x) == :(1850//729*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+249575//108864*(1+-2x)^(1/2)*(3+5x)^(1/2)+3304795//2286144*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-3485*(1+-2x)^(1/2)*(3+5x)^3//2*(8064+12096x)^-1+-1//12*(1+-2x)^5//2*(2+3x)^-4*(3+5x)^5//2+185//216*(1+-2x)^3//2*(2+3x)^-3*(3+5x)^5//2+1165//2592*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^5//2)
@test integrate((1+-2x)^5//2*(2+3x)^-6*(3+5x)^5//2, x) == :(-109715471//32006016*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-200//729*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-3248687*(1+-2x)^(1/2)*(3+5x)^(1/2)*(3048192+4572288x)^-1+-32453//36288*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2+-1//15*(1+-2x)^5//2*(2+3x)^-5*(3+5x)^5//2+37//72*(1+-2x)^3//2*(2+3x)^-4*(3+5x)^5//2+2543//1296*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^5//2)
@test integrate((1+-2x)^5//2*(2+3x)^-7*(3+5x)^5//2, x) == :(-8857805//1229312*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-805255*(1+-2x)^(1/2)*(3+5x)^(1/2)*(351232+526848x)^-1+-73205//37632*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2+-1331//1344*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^5//2+1//6*(1+-2x)^5//2*(2+3x)^-6*(3+5x)^7//2+11//12*(1+-2x)^3//2*(2+3x)^-5*(3+5x)^7//2+121//32*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^7//2)
@test integrate((1+-2x)^5//2*(2+3x)^-8*(3+5x)^5//2, x) == :(-327738785//17210368*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-29794435*(1+-2x)^(1/2)*(3+5x)^(1/2)*(4917248+7375872x)^-1+-2708585//526848*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2+-49247//18816*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^5//2+3//49*(1+-2x)^7//2*(2+3x)^-7*(3+5x)^7//2+37//84*(1+-2x)^5//2*(2+3x)^-6*(3+5x)^7//2+407//168*(1+-2x)^3//2*(2+3x)^-5*(3+5x)^7//2+4477//448*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^7//2)
@test integrate((1+-2x)^5//2*(2+3x)^-9*(3+5x)^5//2, x) == :(-106656830005//1927561216*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+6796051494355*(1+-2x)^(1/2)*(3+5x)^(1/2)*(401483464704+602225197056x)^-1+-75045071//85349376*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^(1/2)+-720833//508032*(1+-2x)^(1/2)*(2+3x)^-5*(3+5x)^3//2+-1//24*(1+-2x)^5//2*(2+3x)^-8*(3+5x)^5//2+185//1008*(1+-2x)^3//2*(2+3x)^-7*(3+5x)^5//2+47365//36288*(1+-2x)^(1/2)*(2+3x)^-6*(3+5x)^5//2+372439373//512096256*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+64983635965//14338695168*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^4*(3+5x)^-1//2, x) == :(9526549//96000000*(1+-2x)^5//2*(3+5x)^(1/2)+104792039//384000000*(1+-2x)^3//2*(3+5x)^(1/2)+1152712429//1280000000*(1+-2x)^(1/2)*(3+5x)^(1/2)+12679836719//12800000000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-271//2800*(1+-2x)^7//2*(2+3x)^2*(3+5x)^(1/2)+-3//70*(1+-2x)^7//2*(2+3x)^3*(3+5x)^(1/2)+-1//22400000*(1+-2x)^7//2*(3+5x)^(1/2)*(12923401+11603280x))
@test integrate((1+-2x)^5//2*(2+3x)^3*(3+5x)^-1//2, x) == :(276493//4800000*(1+-2x)^5//2*(3+5x)^(1/2)+3041423//19200000*(1+-2x)^3//2*(3+5x)^(1/2)+33455653//64000000*(1+-2x)^(1/2)*(3+5x)^(1/2)+368012183//640000000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-1//20*(1+-2x)^7//2*(2+3x)^2*(3+5x)^(1/2)+-1//160000*(1+-2x)^7//2*(3+5x)^(1/2)*(52951+47280x))
@test integrate((1+-2x)^5//2*(2+3x)^2*(3+5x)^-1//2, x) == :(-369//4000*(1+-2x)^7//2*(3+5x)^(1/2)+4907//120000*(1+-2x)^5//2*(3+5x)^(1/2)+53977//480000*(1+-2x)^3//2*(3+5x)^(1/2)+593747//1600000*(1+-2x)^(1/2)*(3+5x)^(1/2)+6531217//16000000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-3//50*(1+-2x)^7//2*(3+5x)^(1/2)*(2+3x))
@test integrate((1+-2x)^5//2*(3+5x)^-1//2*(2+3x), x) == :(-3//40*(1+-2x)^7//2*(3+5x)^(1/2)+49//1200*(1+-2x)^5//2*(3+5x)^(1/2)+539//4800*(1+-2x)^3//2*(3+5x)^(1/2)+5929//16000*(1+-2x)^(1/2)*(3+5x)^(1/2)+65219//160000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^5//2*(3+5x)^-1//2, x) == :(1//15*(1+-2x)^5//2*(3+5x)^(1/2)+11//60*(1+-2x)^3//2*(3+5x)^(1/2)+121//200*(1+-2x)^(1/2)*(3+5x)^(1/2)+1331//2000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^-1*(3+5x)^-1//2, x) == :(-17687//13500*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-239//450*(1+-2x)^(1/2)*(3+5x)^(1/2)+-98//27*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-1//15*(1+-2x)^3//2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^-2*(3+5x)^-1//2, x) == :(-175//27*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+74//45*(1+-2x)^(1/2)*(3+5x)^(1/2)+346//675*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+7*(1+-2x)^3//2*(3+5x)^(1/2)*(6+9x)^-1)
@test integrate((1+-2x)^5//2*(2+3x)^-3*(3+5x)^-1//2, x) == :(-3035//108*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-8//135*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+637*(1+-2x)^(1/2)*(3+5x)^(1/2)*(72+108x)^-1+7//6*(1+-2x)^3//2*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^-4*(3+5x)^-1//2, x) == :(-6655//56*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+605*(1+-2x)^(1/2)*(3+5x)^(1/2)*(16+24x)^-1+1//3*(1+-2x)^5//2*(2+3x)^-3*(3+5x)^(1/2)+55//12*(1+-2x)^3//2*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^-5*(3+5x)^-1//2, x) == :(-1643785//3136*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+149435*(1+-2x)^(1/2)*(3+5x)^(1/2)*(896+1344x)^-1+3//28*(1+-2x)^7//2*(2+3x)^-4*(3+5x)^(1/2)+247//168*(1+-2x)^5//2*(2+3x)^-3*(3+5x)^(1/2)+13585//672*(1+-2x)^3//2*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^-6*(3+5x)^-1//2, x) == :(-104040277//43904*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+245529161*(1+-2x)^(1/2)*(3+5x)^(1/2)*(338688+508032x)^-1+7//15*(1+-2x)^3//2*(2+3x)^-5*(3+5x)^(1/2)+2023//360*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^(1/2)+67187//2160*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+2347559//12096*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^-7*(3+5x)^-1//2, x) == :(-13391796605//1229312*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+31603880465*(1+-2x)^(1/2)*(3+5x)^(1/2)*(9483264+14224896x)^-1+7//18*(1+-2x)^3//2*(2+3x)^-6*(3+5x)^(1/2)+497//108*(1+-2x)^(1/2)*(2+3x)^-5*(3+5x)^(1/2)+21199//864*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^(1/2)+1729615//12096*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+302171615//338688*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^4*(3+5x)^-3//2, x) == :(3577399//32000000*(1+-2x)^3//2*(3+5x)^(1/2)+118054167//320000000*(1+-2x)^(1/2)*(3+5x)^(1/2)+1298595837//3200000000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-2//5*(1+-2x)^5//2*(2+3x)^4*(3+5x)^-1//2+-1//8000000*(1+-2x)^5//2*(3+5x)^(1/2)*(2725981+1990620x)+13//50*(1+-2x)^5//2*(2+3x)^3*(3+5x)^(1/2)+111//5000*(1+-2x)^5//2*(2+3x)^2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^3*(3+5x)^-3//2, x) == :(66997//800000*(1+-2x)^3//2*(3+5x)^(1/2)+2210901//8000000*(1+-2x)^(1/2)*(3+5x)^(1/2)+24319911//80000000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-2//5*(1+-2x)^5//2*(2+3x)^3*(3+5x)^-1//2+-1//200000*(1+-2x)^5//2*(3+5x)^(1/2)*(19143+-4140x)+33//125*(1+-2x)^5//2*(2+3x)^2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^2*(3+5x)^-3//2, x) == :(-9//200*(1+-2x)^7//2*(3+5x)^(1/2)+-2//275*(1+-2x)^7//2*(3+5x)^-1//2+651//8000*(1+-2x)^3//2*(3+5x)^(1/2)+651//22000*(1+-2x)^5//2*(3+5x)^(1/2)+21483//80000*(1+-2x)^(1/2)*(3+5x)^(1/2)+236313//800000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^5//2*(3+5x)^-3//2*(2+3x), x) == :(-2//55*(1+-2x)^7//2*(3+5x)^-1//2+7//100*(1+-2x)^3//2*(3+5x)^(1/2)+7//275*(1+-2x)^5//2*(3+5x)^(1/2)+231//1000*(1+-2x)^(1/2)*(3+5x)^(1/2)+2541//10000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^5//2*(3+5x)^-3//2, x) == :(-363//500*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-33//50*(1+-2x)^(1/2)*(3+5x)^(1/2)+-2//5*(1+-2x)^5//2*(3+5x)^-1//2+-1//5*(1+-2x)^3//2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^-1*(3+5x)^-3//2, x) == :(-128//75*(1+-2x)^(1/2)*(3+5x)^(1/2)+-22//5*(1+-2x)^3//2*(3+5x)^-1//2+98//9*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+338//1125*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^-2*(3+5x)^-3//2, x) == :(-1111//15*(1+-2x)^(1/2)*(3+5x)^-1//2+-8//225*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+665//9*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+7*(1+-2x)^3//2*(3+5x)^-1//2*(6+9x)^-1)
@test integrate((1+-2x)^5//2*(2+3x)^-3*(3+5x)^-3//2, x) == :(-1815//4*(1+-2x)^(1/2)*(3+5x)^-1//2+1815//4*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+(1/2)*(1+-2x)^5//2*(2+3x)^-2*(3+5x)^-1//2+55*(1+-2x)^3//2*(3+5x)^-1//2*(8+12x)^-1)
@test integrate((1+-2x)^5//2*(2+3x)^-4*(3+5x)^-3//2, x) == :(-147015//56*(1+-2x)^(1/2)*(3+5x)^-1//2+147015//56*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+4455*(1+-2x)^3//2*(3+5x)^-1//2*(112+168x)^-1+1//7*(1+-2x)^7//2*(2+3x)^-3*(3+5x)^-1//2+81//28*(1+-2x)^5//2*(2+3x)^-2*(3+5x)^-1//2)
@test integrate((1+-2x)^5//2*(2+3x)^-5*(3+5x)^-3//2, x) == :(-181304825//12096*(1+-2x)^(1/2)*(3+5x)^-1//2+46095555//3136*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+3997345*(1+-2x)^(1/2)*(3+5x)^-1//2*(8064+12096x)^-1+7//12*(1+-2x)^3//2*(2+3x)^-4*(3+5x)^-1//2+2051//216*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^-1//2+22957//288*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-1//2)
@test integrate((1+-2x)^5//2*(2+3x)^-6*(3+5x)^-3//2, x) == :(-4639661185//56448*(1+-2x)^(1/2)*(3+5x)^-1//2+3538809681//43904*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+102293609*(1+-2x)^(1/2)*(3+5x)^-1//2*(37632+56448x)^-1+7//15*(1+-2x)^3//2*(2+3x)^-5*(3+5x)^-1//2+2513//360*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^-1//2+12023//240*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^-1//2+587477//1344*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-1//2)
@test integrate((1+-2x)^5//2*(2+3x)^4*(3+5x)^-5//2, x) == :(8026963//40000000*(1+-2x)^(1/2)*(3+5x)^(1/2)+88296593//400000000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-508//75*(1+-2x)^3//2*(2+3x)^4*(3+5x)^-1//2+-2//15*(1+-2x)^5//2*(2+3x)^4*(3+5x)^-3//2+21//4000000*(1+-2x)^3//2*(3+5x)^(1/2)*(64435+118392x)+2514//625*(1+-2x)^3//2*(2+3x)^3*(3+5x)^(1/2)+23991//25000*(1+-2x)^3//2*(2+3x)^2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^3*(3+5x)^-5//2, x) == :(69713//400000*(1+-2x)^(1/2)*(3+5x)^(1/2)+766843//4000000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-376//75*(1+-2x)^3//2*(2+3x)^3*(3+5x)^-1//2+-2//15*(1+-2x)^5//2*(2+3x)^3*(3+5x)^-3//2+21//40000*(1+-2x)^3//2*(3+5x)^(1/2)*(3185+4392x)+741//250*(1+-2x)^3//2*(2+3x)^2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^2*(3+5x)^-5//2, x) == :(-76//1815*(1+-2x)^7//2*(3+5x)^-1//2+-2//825*(1+-2x)^7//2*(3+5x)^-3//2+329//5000*(1+-2x)^(1/2)*(3+5x)^(1/2)+329//16500*(1+-2x)^3//2*(3+5x)^(1/2)+329//45375*(1+-2x)^5//2*(3+5x)^(1/2)+3619//50000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^5//2*(3+5x)^-5//2*(2+3x), x) == :(-1001//2500*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-182//825*(1+-2x)^5//2*(3+5x)^-1//2+-91//250*(1+-2x)^(1/2)*(3+5x)^(1/2)+-91//825*(1+-2x)^3//2*(3+5x)^(1/2)+-2//165*(1+-2x)^7//2*(3+5x)^-3//2)
@test integrate((1+-2x)^5//2*(3+5x)^-5//2, x) == :(-2//15*(1+-2x)^5//2*(3+5x)^-3//2+4//15*(1+-2x)^3//2*(3+5x)^-1//2+4//25*(1+-2x)^(1/2)*(3+5x)^(1/2)+22//125*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^5//2*(2+3x)^-1*(3+5x)^-5//2, x) == :(-98//3*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-22//15*(1+-2x)^3//2*(3+5x)^-3//2+-8//375*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+814//25*(1+-2x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^5//2*(2+3x)^-2*(3+5x)^-5//2, x) == :(-385*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+385*(1+-2x)^(1/2)*(3+5x)^-1//2+-55//3*(1+-2x)^3//2*(3+5x)^-3//2+(1+-2x)^5//2*(2+3x)^-1*(3+5x)^-3//2)
@test integrate((1+-2x)^5//2*(2+3x)^-3*(3+5x)^-5//2, x) == :(-13145//4*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-13145//84*(1+-2x)^3//2*(3+5x)^-3//2+13145//4*(1+-2x)^(1/2)*(3+5x)^-1//2+239*(1+-2x)^5//2*(3+5x)^-3//2*(56+84x)^-1+3//14*(1+-2x)^7//2*(2+3x)^-2*(3+5x)^-3//2)
@test integrate((1+-2x)^5//2*(2+3x)^-4*(3+5x)^-5//2, x) == :(-1361195//56*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-196735//72*(1+-2x)^(1/2)*(3+5x)^-3//2+1784635//72*(1+-2x)^(1/2)*(3+5x)^-1//2+7843*(1+-2x)^(1/2)*(3+5x)^-3//2*(48+72x)^-1+7//9*(1+-2x)^3//2*(2+3x)^-3*(3+5x)^-3//2+77//4*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-3//2)
@test integrate((1+-2x)^5//2*(2+3x)^-5*(3+5x)^-5//2, x) == :(-519421265//3136*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-25024175//1344*(1+-2x)^(1/2)*(3+5x)^-3//2+227000875//1344*(1+-2x)^(1/2)*(3+5x)^-1//2+2992825*(1+-2x)^(1/2)*(3+5x)^-3//2*(2688+4032x)^-1+7//12*(1+-2x)^3//2*(2+3x)^-4*(3+5x)^-3//2+847//72*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^-3//2+36817//288*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-3//2)
@test integrate((1+-2x)^5//2*(2+3x)^-6*(3+5x)^-5//2, x) == :(-46975917593//43904*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-754386765//6272*(1+-2x)^(1/2)*(3+5x)^-3//2+20529722435//18816*(1+-2x)^(1/2)*(3+5x)^-1//2+270667969*(1+-2x)^(1/2)*(3+5x)^-3//2*(37632+56448x)^-1+7//15*(1+-2x)^3//2*(2+3x)^-5*(3+5x)^-3//2+1001//120*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^-3//2+53009//720*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^-3//2+3329689//4032*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-3//2)
@test integrate((1+-2x)^-1//2*(2+3x)^4*(3+5x)^(1/2), x) == :(-97032047//2560000*(1+-2x)^(1/2)*(3+5x)^(1/2)+1067352517//25600000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-987//4000*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^3//2+-21//640000*(1+-2x)^(1/2)*(3+5x)^3//2*(194923+92040x)+-3//50*(1+-2x)^(1/2)*(2+3x)^3*(3+5x)^3//2)
@test integrate((1+-2x)^-1//2*(2+3x)^3*(3+5x)^(1/2), x) == :(-61547//5120*(1+-2x)^(1/2)*(3+5x)^(1/2)+677017//51200*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-3//40*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^3//2+-3//1280*(1+-2x)^(1/2)*(3+5x)^3//2*(865+408x))
@test integrate((1+-2x)^-1//2*(2+3x)^2*(3+5x)^(1/2), x) == :(-6269//1600*(1+-2x)^(1/2)*(3+5x)^(1/2)+-181//400*(1+-2x)^(1/2)*(3+5x)^3//2+68959//16000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-1//10*(1+-2x)^(1/2)*(3+5x)^3//2*(2+3x))
@test integrate((1+-2x)^-1//2*(3+5x)^(1/2)*(2+3x), x) == :(-107//80*(1+-2x)^(1/2)*(3+5x)^(1/2)+-3//20*(1+-2x)^(1/2)*(3+5x)^3//2+1177//800*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^-1//2*(3+5x)^(1/2), x) == :(-1//2*(1+-2x)^(1/2)*(3+5x)^(1/2)+11//20*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^-1//2*(2+3x)^-1*(3+5x)^(1/2), x) == :(1//3*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+2//21*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2))
@test integrate((1+-2x)^-1//2*(2+3x)^-2*(3+5x)^(1/2), x) == :(-11//49*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-1*(1+-2x)^(1/2)*(3+5x)^(1/2)*(14+21x)^-1)
@test integrate((1+-2x)^-1//2*(2+3x)^-3*(3+5x)^(1/2), x) == :(-451//1372*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-41*(1+-2x)^(1/2)*(3+5x)^(1/2)*(392+588x)^-1+3//14*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2)
@test integrate((1+-2x)^-1//2*(2+3x)^-4*(3+5x)^(1/2), x) == :(-15235//19208*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+3895*(1+-2x)^(1/2)*(3+5x)^(1/2)*(16464+24696x)^-1+-1//21*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+25//588*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^-5*(3+5x)^(1/2), x) == :(-375265//153664*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+32735*(1+-2x)^(1/2)*(3+5x)^(1/2)*(43904+65856x)^-1+-1//28*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^(1/2)+1//56*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+305//1568*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^3*(3+5x)^3//2, x) == :(-30292449//512000*(1+-2x)^(1/2)*(3+5x)^(1/2)+-917953//128000*(1+-2x)^(1/2)*(3+5x)^3//2+333216939//5120000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-3//50*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^5//2+-3//16000*(1+-2x)^(1/2)*(3+5x)^5//2*(7889+3900x))
@test integrate((1+-2x)^-1//2*(2+3x)^2*(3+5x)^3//2, x) == :(-479457//25600*(1+-2x)^(1/2)*(3+5x)^(1/2)+-14529//6400*(1+-2x)^(1/2)*(3+5x)^3//2+-251//800*(1+-2x)^(1/2)*(3+5x)^5//2+5274027//256000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-3//40*(1+-2x)^(1/2)*(3+5x)^5//2*(2+3x))
@test integrate((1+-2x)^-1//2*(3+5x)^3//2*(2+3x), x) == :(-1947//320*(1+-2x)^(1/2)*(3+5x)^(1/2)+-59//80*(1+-2x)^(1/2)*(3+5x)^3//2+-1//10*(1+-2x)^(1/2)*(3+5x)^5//2+21417//3200*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^-1//2*(3+5x)^3//2, x) == :(-33//16*(1+-2x)^(1/2)*(3+5x)^(1/2)+-1//4*(1+-2x)^(1/2)*(3+5x)^3//2+363//160*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^-1//2*(2+3x)^-1*(3+5x)^3//2, x) == :(-5//6*(1+-2x)^(1/2)*(3+5x)^(1/2)+-2//63*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+29//36*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^-1//2*(2+3x)^-2*(3+5x)^3//2, x) == :(5//9*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+103//441*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+(1+-2x)^(1/2)*(3+5x)^(1/2)*(42+63x)^-1)
@test integrate((1+-2x)^-1//2*(2+3x)^-3*(3+5x)^3//2, x) == :(-363//1372*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-33*(1+-2x)^(1/2)*(3+5x)^(1/2)*(392+588x)^-1+-1//14*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2)
@test integrate((1+-2x)^-1//2*(2+3x)^-4*(3+5x)^3//2, x) == :(-5445//19208*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-495*(1+-2x)^(1/2)*(3+5x)^(1/2)*(5488+8232x)^-1+-15//196*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2+1//7*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^5//2)
@test integrate((1+-2x)^-1//2*(2+3x)^-5*(3+5x)^3//2, x) == :(-78045//153664*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+57595*(1+-2x)^(1/2)*(3+5x)^(1/2)*(395136+592704x)^-1+-43//504*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+1//84*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^(1/2)+85//14112*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^-6*(3+5x)^3//2, x) == :(-2664057//2151296*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+694229*(1+-2x)^(1/2)*(3+5x)^(1/2)*(1843968+2765952x)^-1+-367//5880*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^(1/2)+-73//11760*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+1//105*(1+-2x)^(1/2)*(2+3x)^-5*(3+5x)^(1/2)+6107//65856*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^3*(3+5x)^5//2, x) == :(-243487211//819200*(1+-2x)^(1/2)*(3+5x)^(1/2)+-22135201//614400*(1+-2x)^(1/2)*(3+5x)^3//2+-2012291//384000*(1+-2x)^(1/2)*(3+5x)^5//2+2678359321//8192000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-1//20*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^7//2+-1//32000*(1+-2x)^(1/2)*(3+5x)^7//2*(37439+18960x))
@test integrate((1+-2x)^-1//2*(2+3x)^2*(3+5x)^5//2, x) == :(-9458207//102400*(1+-2x)^(1/2)*(3+5x)^(1/2)+-859837//76800*(1+-2x)^(1/2)*(3+5x)^3//2+-78167//48000*(1+-2x)^(1/2)*(3+5x)^5//2+-963//4000*(1+-2x)^(1/2)*(3+5x)^7//2+104040277//1024000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-3//50*(1+-2x)^(1/2)*(3+5x)^7//2*(2+3x))
@test integrate((1+-2x)^-1//2*(3+5x)^5//2*(2+3x), x) == :(-29887//1024*(1+-2x)^(1/2)*(3+5x)^(1/2)+-2717//768*(1+-2x)^(1/2)*(3+5x)^3//2+-247//480*(1+-2x)^(1/2)*(3+5x)^5//2+-3//40*(1+-2x)^(1/2)*(3+5x)^7//2+328757//10240*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^-1//2*(3+5x)^5//2, x) == :(-605//64*(1+-2x)^(1/2)*(3+5x)^(1/2)+-55//48*(1+-2x)^(1/2)*(3+5x)^3//2+-1//6*(1+-2x)^(1/2)*(3+5x)^5//2+1331//128*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^-1//2*(2+3x)^-1*(3+5x)^5//2, x) == :(-455//144*(1+-2x)^(1/2)*(3+5x)^(1/2)+-5//12*(1+-2x)^(1/2)*(3+5x)^3//2+2//189*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+3035//864*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^-1//2*(2+3x)^-2*(3+5x)^5//2, x) == :(-185//126*(1+-2x)^(1/2)*(3+5x)^(1/2)+-173//1323*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+125//108*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+(1+-2x)^(1/2)*(3+5x)^3//2*(42+63x)^-1)
@test integrate((1+-2x)^-1//2*(2+3x)^-3*(3+5x)^5//2, x) == :(25//27*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+17687//37044*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+239*(1+-2x)^(1/2)*(3+5x)^(1/2)*(3528+5292x)^-1+1//42*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2)
@test integrate((1+-2x)^-1//2*(2+3x)^-4*(3+5x)^5//2, x) == :(-6655//19208*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-605*(1+-2x)^(1/2)*(3+5x)^(1/2)*(5488+8232x)^-1+-55//588*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2+-1//21*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^5//2)
@test integrate((1+-2x)^-1//2*(2+3x)^-5*(3+5x)^5//2, x) == :(-6655//21952*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-605*(1+-2x)^(1/2)*(3+5x)^(1/2)*(6272+9408x)^-1+-55//672*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2+-1//24*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^5//2+3//28*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^7//2)
@test integrate((1+-2x)^-1//2*(2+3x)^-6*(3+5x)^5//2, x) == :(-933031//2151296*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+1948963*(1+-2x)^(1/2)*(3+5x)^(1/2)*(16595712+24893568x)^-1+-14831//105840*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+-12371//592704*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2)+1//105*(1+-2x)^(1/2)*(2+3x)^-5*(3+5x)^3//2+437//17640*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^-7*(3+5x)^5//2, x) == :(-52573169//60236288*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+122343637*(1+-2x)^(1/2)*(3+5x)^(1/2)*(464679936+697019904x)^-1+-149951//1481760*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^(1/2)+-71369//2963520*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+1//126*(1+-2x)^(1/2)*(2+3x)^-6*(3+5x)^3//2+503//26460*(1+-2x)^(1/2)*(2+3x)^-5*(3+5x)^(1/2)+958171//16595712*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^4*(3+5x)^-1//2, x) == :(10866247//1280000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-259//800*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^(1/2)+-7//128000*(1+-2x)^(1/2)*(3+5x)^(1/2)*(187559+77820x)+-3//40*(1+-2x)^(1/2)*(2+3x)^3*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^3*(3+5x)^-1//2, x) == :(44437//16000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-1//10*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^(1/2)+-1//1600*(1+-2x)^(1/2)*(3+5x)^(1/2)*(5363+2220x))
@test integrate((1+-2x)^-1//2*(2+3x)^2*(3+5x)^-1//2, x) == :(-333//400*(1+-2x)^(1/2)*(3+5x)^(1/2)+3827//4000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-3//20*(1+-2x)^(1/2)*(3+5x)^(1/2)*(2+3x))
@test integrate((1+-2x)^-1//2*(3+5x)^-1//2*(2+3x), x) == :(-3//10*(1+-2x)^(1/2)*(3+5x)^(1/2)+37//100*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^-1//2*(3+5x)^-1//2, x) == :(1//5*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^-1//2*(2+3x)^-1*(3+5x)^-1//2, x) == :(-2//7*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2))
@test integrate((1+-2x)^-1//2*(2+3x)^-2*(3+5x)^-1//2, x) == :(-37//49*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+3*(1+-2x)^(1/2)*(3+5x)^(1/2)*(14+21x)^-1)
@test integrate((1+-2x)^-1//2*(2+3x)^-3*(3+5x)^-1//2, x) == :(-3827//1372*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+333*(1+-2x)^(1/2)*(3+5x)^(1/2)*(392+588x)^-1+3//14*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^-4*(3+5x)^-1//2, x) == :(-222185//19208*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+19415*(1+-2x)^(1/2)*(3+5x)^(1/2)*(5488+8232x)^-1+1//7*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+185//196*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^4*(3+5x)^-3//2, x) == :(143283//80000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-21//550*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^(1/2)+-21//88000*(1+-2x)^(1/2)*(3+5x)^(1/2)*(8987+3660x)+-2//55*(1+-2x)^(1/2)*(2+3x)^3*(3+5x)^-1//2)
@test integrate((1+-2x)^-1//2*(2+3x)^3*(3+5x)^-3//2, x) == :(2493//4000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-3//4400*(1+-2x)^(1/2)*(3+5x)^(1/2)*(979+300x)+-2//55*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^-1//2)
@test integrate((1+-2x)^-1//2*(2+3x)^2*(3+5x)^-3//2, x) == :(-9//50*(1+-2x)^(1/2)*(3+5x)^(1/2)+-2//275*(1+-2x)^(1/2)*(3+5x)^-1//2+123//500*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^-1//2*(3+5x)^-3//2*(2+3x), x) == :(-2//55*(1+-2x)^(1/2)*(3+5x)^-1//2+3//25*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^-1//2*(3+5x)^-3//2, x) == :(-2//11*(1+-2x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^-1//2*(2+3x)^-1*(3+5x)^-3//2, x) == :(-10//11*(1+-2x)^(1/2)*(3+5x)^-1//2+6//7*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2))
@test integrate((1+-2x)^-1//2*(2+3x)^-2*(3+5x)^-3//2, x) == :(-515//77*(1+-2x)^(1/2)*(3+5x)^-1//2+321//49*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+3*(1+-2x)^(1/2)*(3+5x)^-1//2*(14+21x)^-1)
@test integrate((1+-2x)^-1//2*(2+3x)^-3*(3+5x)^-3//2, x) == :(-90415//2156*(1+-2x)^(1/2)*(3+5x)^-1//2+56421//1372*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+543*(1+-2x)^(1/2)*(3+5x)^-1//2*(392+588x)^-1+3//14*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-1//2)
@test integrate((1+-2x)^-1//2*(2+3x)^-4*(3+5x)^-3//2, x) == :(-7396875//30184*(1+-2x)^(1/2)*(3+5x)^-1//2+4616025//19208*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+44475*(1+-2x)^(1/2)*(3+5x)^-1//2*(5488+8232x)^-1+1//7*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^-1//2+255//196*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-1//2)
@test integrate((1+-2x)^-1//2*(2+3x)^5*(3+5x)^-5//2, x) == :(462357//400000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-734//9075*(1+-2x)^(1/2)*(2+3x)^3*(3+5x)^-1//2+-7//4840000*(1+-2x)^(1/2)*(3+5x)^(1/2)*(938509+366420x)+-2//165*(1+-2x)^(1/2)*(2+3x)^4*(3+5x)^-3//2+511//30250*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^4*(3+5x)^-5//2, x) == :(8127//20000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-602//9075*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^-1//2+-7//242000*(1+-2x)^(1/2)*(3+5x)^(1/2)*(12199+1020x)+-2//165*(1+-2x)^(1/2)*(2+3x)^3*(3+5x)^-3//2)
@test integrate((1+-2x)^-1//2*(2+3x)^3*(3+5x)^-5//2, x) == :(81//500*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-2//165*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^-3//2+-1//18150*(1+-2x)^(1/2)*(3+5x)^-1//2*(5831+9405x))
@test integrate((1+-2x)^-1//2*(2+3x)^2*(3+5x)^-5//2, x) == :(-404//9075*(1+-2x)^(1/2)*(3+5x)^-1//2+-2//825*(1+-2x)^(1/2)*(3+5x)^-3//2+9//125*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^-1//2*(3+5x)^-5//2*(2+3x), x) == :(-206//1815*(1+-2x)^(1/2)*(3+5x)^-1//2+-2//165*(1+-2x)^(1/2)*(3+5x)^-3//2)
@test integrate((1+-2x)^-1//2*(3+5x)^-5//2, x) == :(-8//363*(1+-2x)^(1/2)*(3+5x)^-1//2+-2//33*(1+-2x)^(1/2)*(3+5x)^-3//2)
@test integrate((1+-2x)^-1//2*(2+3x)^-1*(3+5x)^-5//2, x) == :(-18//7*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-10//33*(1+-2x)^(1/2)*(3+5x)^-3//2+950//363*(1+-2x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^-1//2*(2+3x)^-2*(3+5x)^-5//2, x) == :(-1593//49*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-845//231*(1+-2x)^(1/2)*(3+5x)^-3//2+84235//2541*(1+-2x)^(1/2)*(3+5x)^-1//2+3*(1+-2x)^(1/2)*(3+5x)^-3//2*(14+21x)^-1)
@test integrate((1+-2x)^-1//2*(2+3x)^-3*(3+5x)^-5//2, x) == :(-392283//1372*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-207895//6468*(1+-2x)^(1/2)*(3+5x)^-3//2+20743985//71148*(1+-2x)^(1/2)*(3+5x)^-1//2+753*(1+-2x)^(1/2)*(3+5x)^-3//2*(392+588x)^-1+3//14*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-3//2)
@test integrate((1+-2x)^-1//2*(2+3x)^-4*(3+5x)^-5//2, x) == :(-41307885//19208*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-21891025//90552*(1+-2x)^(1/2)*(3+5x)^-3//2+2184369575//996072*(1+-2x)^(1/2)*(3+5x)^-1//2+79335*(1+-2x)^(1/2)*(3+5x)^-3//2*(5488+8232x)^-1+1//7*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^-3//2+325//196*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^-3//2)
@test integrate((a+b*x)^-1//2*(e+f*x)^-1*(-1*a*f+2*b*e+b*f*x)^-1//2, x) == :(f^-1//2*(b*e+-1*a*f)^-1*arctan(f^(1/2)*(a+b*x)^(1/2)*(b*e+-1*a*f)^-1*(-1*a*f+2*b*e+b*f*x)^(1/2)))
@test integrate((1+-2x)^-3//2*(2+3x)^5*(3+5x)^(1/2), x) == :(-35439958001//51200000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+(1+-2x)^-1//2*(2+3x)^5*(3+5x)^(1/2)+33//20*(1+-2x)^(1/2)*(2+3x)^4*(3+5x)^(1/2)+49//5120000*(1+-2x)^(1/2)*(3+5x)^(1/2)*(87394471+36265980x)+10389//1600*(1+-2x)^(1/2)*(2+3x)^3*(3+5x)^(1/2)+847637//32000*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^4*(3+5x)^(1/2), x) == :(-92108287//512000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+(1+-2x)^-1//2*(2+3x)^4*(3+5x)^(1/2)+1//51200*(1+-2x)^(1/2)*(3+5x)^(1/2)*(11129753+4618500x)+27//16*(1+-2x)^(1/2)*(2+3x)^3*(3+5x)^(1/2)+2203//320*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^3*(3+5x)^(1/2), x) == :(-1463447//32000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+(1+-2x)^-1//2*(2+3x)^3*(3+5x)^(1/2)+1//3200*(1+-2x)^(1/2)*(3+5x)^(1/2)*(176833+73380x)+7//4*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^2*(3+5x)^(1/2), x) == :(-17951//1600*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+9//40*(1+-2x)^(1/2)*(3+5x)^3//2+49//22*(1+-2x)^-1//2*(3+5x)^3//2+17951//1760*(1+-2x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(3+5x)^(1/2)*(2+3x), x) == :(-103//40*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+7//11*(1+-2x)^-1//2*(3+5x)^3//2+103//44*(1+-2x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(3+5x)^(1/2), x) == :((1+-2x)^-1//2*(3+5x)^(1/2)+-1//2*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^-3//2*(2+3x)^-1*(3+5x)^(1/2), x) == :(2//7*(1+-2x)^-1//2*(3+5x)^(1/2)+2//49*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2))
@test integrate((1+-2x)^-3//2*(2+3x)^-2*(3+5x)^(1/2), x) == :(-29//343*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-29*(1+-2x)^(1/2)*(3+5x)^(1/2)*(1078+1617x)^-1+4//77*(1+-2x)^-1//2*(2+3x)^-1*(3+5x)^3//2)
@test integrate((1+-2x)^-3//2*(2+3x)^-3*(3+5x)^(1/2), x) == :(-1585//9604*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+15*(1+-2x)^(1/2)*(3+5x)^(1/2)*(2744+4116x)^-1+-15//98*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2)+2//7*(1+-2x)^-1//2*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-4*(3+5x)^(1/2), x) == :(-7435//19208*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+565*(1+-2x)^(1/2)*(3+5x)^(1/2)*(5488+8232x)^-1+-5//196*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2)+-1//7*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+2//7*(1+-2x)^-1//2*(2+3x)^-3*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-5*(3+5x)^(1/2), x) == :(-1244755//1075648*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+107245*(1+-2x)^(1/2)*(3+5x)^(1/2)*(307328+460992x)^-1+-27//196*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^(1/2)+-13//392*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+2//7*(1+-2x)^-1//2*(2+3x)^-4*(3+5x)^(1/2)+835//10976*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^4*(3+5x)^3//2, x) == :(-11199264087//10240000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+1018114917//1024000*(1+-2x)^(1/2)*(3+5x)^(1/2)+(1+-2x)^-1//2*(2+3x)^4*(3+5x)^3//2+9//256000*(1+-2x)^(1/2)*(3+5x)^3//2*(4772357+2253560x)+33//20*(1+-2x)^(1/2)*(2+3x)^3*(3+5x)^3//2+10377//1600*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^3//2)
@test integrate((1+-2x)^-3//2*(2+3x)^3*(3+5x)^3//2, x) == :(-145708761//512000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+13246251//51200*(1+-2x)^(1/2)*(3+5x)^(1/2)+(1+-2x)^-1//2*(2+3x)^3*(3+5x)^3//2+9//12800*(1+-2x)^(1/2)*(3+5x)^3//2*(62091+29320x)+27//16*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^3//2)
@test integrate((1+-2x)^-3//2*(2+3x)^2*(3+5x)^3//2, x) == :(-463881//6400*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+3//20*(1+-2x)^(1/2)*(3+5x)^5//2+49//22*(1+-2x)^-1//2*(3+5x)^5//2+14057//1760*(1+-2x)^(1/2)*(3+5x)^3//2+42171//640*(1+-2x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(3+5x)^3//2*(2+3x), x) == :(-5709//320*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+7//11*(1+-2x)^-1//2*(3+5x)^5//2+173//88*(1+-2x)^(1/2)*(3+5x)^3//2+519//32*(1+-2x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(3+5x)^3//2, x) == :((1+-2x)^-1//2*(3+5x)^3//2+-33//8*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+15//4*(1+-2x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-1*(3+5x)^3//2, x) == :(-5//6*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-2//147*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+11//7*(1+-2x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-2*(3+5x)^3//2, x) == :(33//343*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+3*(1+-2x)^(1/2)*(3+5x)^(1/2)*(98+147x)^-1+2//7*(1+-2x)^-1//2*(2+3x)^-1*(3+5x)^3//2)
@test integrate((1+-2x)^-3//2*(2+3x)^-3*(3+5x)^3//2, x) == :(-825//9604*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-75*(1+-2x)^(1/2)*(3+5x)^(1/2)*(2744+4116x)^-1+-25//1078*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2+4//77*(1+-2x)^-1//2*(2+3x)^-2*(3+5x)^5//2)
@test integrate((1+-2x)^-3//2*(2+3x)^-4*(3+5x)^3//2, x) == :(-2805//19208*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-415*(1+-2x)^(1/2)*(3+5x)^(1/2)*(16464+24696x)^-1+-145//588*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2)+-2//3*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+11//7*(1+-2x)^-1//2*(2+3x)^-3*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-5*(3+5x)^3//2, x) == :(-279015//1075648*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+16985*(1+-2x)^(1/2)*(3+5x)^(1/2)*(307328+460992x)^-1+-745//10976*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2)+-131//196*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^(1/2)+-89//392*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+11//7*(1+-2x)^-1//2*(2+3x)^-4*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^4*(3+5x)^5//2, x) == :(-107121749031//16384000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+295101237//409600*(1+-2x)^(1/2)*(3+5x)^3//2+9738340821//1638400*(1+-2x)^(1/2)*(3+5x)^(1/2)+(1+-2x)^-1//2*(2+3x)^4*(3+5x)^5//2+1//51200*(1+-2x)^(1/2)*(3+5x)^5//2*(7611023+3765060x)+13//8*(1+-2x)^(1/2)*(2+3x)^3*(3+5x)^5//2+999//160*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^5//2)
@test integrate((1+-2x)^-3//2*(2+3x)^3*(3+5x)^5//2, x) == :(-3538809681//2048000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+9748787//51200*(1+-2x)^(1/2)*(3+5x)^3//2+321709971//204800*(1+-2x)^(1/2)*(3+5x)^(1/2)+(1+-2x)^-1//2*(2+3x)^3*(3+5x)^5//2+9//6400*(1+-2x)^(1/2)*(3+5x)^5//2*(27937+13820x)+33//20*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^5//2)
@test integrate((1+-2x)^-3//2*(2+3x)^2*(3+5x)^5//2, x) == :(-9219111//20480*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+9//80*(1+-2x)^(1/2)*(3+5x)^7//2+49//22*(1+-2x)^-1//2*(3+5x)^7//2+25397//512*(1+-2x)^(1/2)*(3+5x)^3//2+25397//3520*(1+-2x)^(1/2)*(3+5x)^5//2+838101//2048*(1+-2x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(3+5x)^5//2*(2+3x), x) == :(-29403//256*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+7//11*(1+-2x)^-1//2*(3+5x)^7//2+81//44*(1+-2x)^(1/2)*(3+5x)^5//2+405//32*(1+-2x)^(1/2)*(3+5x)^3//2+13365//128*(1+-2x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(3+5x)^5//2, x) == :((1+-2x)^-1//2*(3+5x)^5//2+-1815//64*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+25//8*(1+-2x)^(1/2)*(3+5x)^3//2+825//32*(1+-2x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-1*(3+5x)^5//2, x) == :(-475//72*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+2//441*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+11//7*(1+-2x)^-1//2*(3+5x)^3//2+505//84*(1+-2x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-2*(3+5x)^5//2, x) == :(-169//3087*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-25//18*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+32*(1+-2x)^(1/2)*(3+5x)^(1/2)*(294+441x)^-1+11//7*(1+-2x)^-1//2*(2+3x)^-1*(3+5x)^3//2)
@test integrate((1+-2x)^-3//2*(2+3x)^-3*(3+5x)^5//2, x) == :(1815//9604*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+165*(1+-2x)^(1/2)*(3+5x)^(1/2)*(2744+4116x)^-1+2//7*(1+-2x)^-1//2*(2+3x)^-2*(3+5x)^5//2+5//98*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2)
@test integrate((1+-2x)^-3//2*(2+3x)^-4*(3+5x)^5//2, x) == :(-1815//19208*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-165*(1+-2x)^(1/2)*(3+5x)^(1/2)*(5488+8232x)^-1+-5//196*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2+-1//77*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^5//2+4//77*(1+-2x)^-1//2*(2+3x)^-3*(3+5x)^7//2)
@test integrate((1+-2x)^-3//2*(2+3x)^-5*(3+5x)^5//2, x) == :(-168795//1075648*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-167155*(1+-2x)^(1/2)*(3+5x)^(1/2)*(2765952+4148928x)^-1+-38365//98784*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2)+-3653//3528*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+11//7*(1+-2x)^-1//2*(2+3x)^-4*(3+5x)^3//2+131//588*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-6*(3+5x)^5//2, x) == :(-3474273//15059072*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+426781*(1+-2x)^(1/2)*(3+5x)^(1/2)*(12907776+19361664x)^-1+-55277//460992*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^(1/2)+-42863//41160*(1+-2x)^(1/2)*(2+3x)^-4*(3+5x)^(1/2)+-29297//82320*(1+-2x)^(1/2)*(2+3x)^-3*(3+5x)^(1/2)+11//7*(1+-2x)^-1//2*(2+3x)^-5*(3+5x)^3//2+164//735*(1+-2x)^(1/2)*(2+3x)^-5*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^5*(3+5x)^-1//2, x) == :(-291096141//2560000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+7//11*(1+-2x)^-1//2*(2+3x)^4*(3+5x)^(1/2)+21//2816000*(1+-2x)^(1/2)*(3+5x)^(1/2)*(18424549+7645620x)+939//880*(1+-2x)^(1/2)*(2+3x)^3*(3+5x)^(1/2)+76587//17600*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^4*(3+5x)^-1//2, x) == :(-184641//6400*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+7//11*(1+-2x)^-1//2*(2+3x)^3*(3+5x)^(1/2)+9//7040*(1+-2x)^(1/2)*(3+5x)^(1/2)*(27269+11316x)+243//220*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^3*(3+5x)^-1//2, x) == :(-56421//8000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+3//8800*(1+-2x)^(1/2)*(3+5x)^(1/2)*(25003+10380x)+7//11*(1+-2x)^-1//2*(2+3x)^2*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^2*(3+5x)^-1//2, x) == :(-321//200*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+9//20*(1+-2x)^(1/2)*(3+5x)^(1/2)+49//22*(1+-2x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(3+5x)^-1//2*(2+3x), x) == :(-3//10*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+7//11*(1+-2x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(3+5x)^-1//2, x) == :(2//11*(1+-2x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-1*(3+5x)^-1//2, x) == :(-6//49*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+4//77*(1+-2x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-2*(3+5x)^-1//2, x) == :(-123//343*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-58//539*(1+-2x)^-1//2*(3+5x)^(1/2)+3//7*(1+-2x)^-1//2*(2+3x)^-1*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-3*(3+5x)^-1//2, x) == :(-12465//9604*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-3895//7546*(1+-2x)^-1//2*(3+5x)^(1/2)+3//14*(1+-2x)^-1//2*(2+3x)^-2*(3+5x)^(1/2)+345//196*(1+-2x)^-1//2*(2+3x)^-1*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-4*(3+5x)^-1//2, x) == :(-102345//19208*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-32735//15092*(1+-2x)^-1//2*(3+5x)^(1/2)+1//7*(1+-2x)^-1//2*(2+3x)^-3*(3+5x)^(1/2)+27//28*(1+-2x)^-1//2*(2+3x)^-2*(3+5x)^(1/2)+2865//392*(1+-2x)^-1//2*(2+3x)^-1*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-5*(3+5x)^-1//2, x) == :(-24922335//1075648*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-7986105//845152*(1+-2x)^-1//2*(3+5x)^(1/2)+3//28*(1+-2x)^-1//2*(2+3x)^-4*(3+5x)^(1/2)+263//392*(1+-2x)^-1//2*(2+3x)^-3*(3+5x)^(1/2)+6621//1568*(1+-2x)^-1//2*(2+3x)^-2*(3+5x)^(1/2)+698295//21952*(1+-2x)^-1//2*(2+3x)^-1*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^5*(3+5x)^-3//2, x) == :(-2911419//160000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-37//605*(1+-2x)^(1/2)*(2+3x)^3*(3+5x)^-1//2+7//11*(1+-2x)^-1//2*(2+3x)^4*(3+5x)^-1//2+21//1936000*(1+-2x)^(1/2)*(3+5x)^(1/2)*(2027201+841380x)+8463//12100*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^4*(3+5x)^-3//2, x) == :(-35451//8000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-37//605*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^-1//2+3//96800*(1+-2x)^(1/2)*(3+5x)^(1/2)*(173063+72060x)+7//11*(1+-2x)^-1//2*(2+3x)^3*(3+5x)^-1//2)
@test integrate((1+-2x)^-3//2*(2+3x)^3*(3+5x)^-3//2, x) == :(-999//1000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+1//12100*(1+-2x)^(1/2)*(3+5x)^-1//2*(30443+50985x)+7//11*(1+-2x)^-1//2*(2+3x)^2*(3+5x)^-1//2)
@test integrate((1+-2x)^-3//2*(2+3x)^2*(3+5x)^-3//2, x) == :(-1229//1210*(1+-2x)^(1/2)*(3+5x)^-1//2+-9//50*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+49//22*(1+-2x)^-1//2*(3+5x)^-1//2)
@test integrate((1+-2x)^-3//2*(3+5x)^-3//2*(2+3x), x) == :(-2//55*(1+-2x)^-1//2*(3+5x)^-1//2+74//605*(1+-2x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(3+5x)^-3//2, x) == :(-20//121*(1+-2x)^(1/2)*(3+5x)^-1//2+2//11*(1+-2x)^-1//2*(3+5x)^-1//2)
@test integrate((1+-2x)^-3//2*(2+3x)^-1*(3+5x)^-3//2, x) == :(-370//847*(1+-2x)^(1/2)*(3+5x)^-1//2+4//77*(1+-2x)^-1//2*(3+5x)^-1//2+18//49*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2))
@test integrate((1+-2x)^-3//2*(2+3x)^-2*(3+5x)^-3//2, x) == :(-17735//5929*(1+-2x)^(1/2)*(3+5x)^-1//2+-58//539*(1+-2x)^-1//2*(3+5x)^-1//2+999//343*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+3//7*(1+-2x)^-1//2*(2+3x)^-1*(3+5x)^-1//2)
@test integrate((1+-2x)^-3//2*(2+3x)^-3*(3+5x)^-3//2, x) == :(-3125575//166012*(1+-2x)^(1/2)*(3+5x)^-1//2+-6205//7546*(1+-2x)^-1//2*(3+5x)^-1//2+177255//9604*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+3//14*(1+-2x)^-1//2*(2+3x)^-2*(3+5x)^-1//2+555//196*(1+-2x)^-1//2*(2+3x)^-1*(3+5x)^-1//2)
@test integrate((1+-2x)^-3//2*(2+3x)^-4*(3+5x)^-3//2, x) == :(-36657025//332024*(1+-2x)^(1/2)*(3+5x)^-1//2+-73435//15092*(1+-2x)^-1//2*(3+5x)^-1//2+2079585//19208*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+1//7*(1+-2x)^-1//2*(2+3x)^-3*(3+5x)^-1//2+37//28*(1+-2x)^-1//2*(2+3x)^-2*(3+5x)^-1//2+6525//392*(1+-2x)^-1//2*(2+3x)^-1*(3+5x)^-1//2)
@test integrate((1+-2x)^-3//2*(2+3x)^5*(3+5x)^-5//2, x) == :(-111321//40000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-4487//99825*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^-1//2+-107//1815*(1+-2x)^(1/2)*(2+3x)^3*(3+5x)^-3//2+7//11*(1+-2x)^-1//2*(2+3x)^4*(3+5x)^-3//2+7//5324000*(1+-2x)^(1/2)*(3+5x)^(1/2)*(2571547+1078860x))
@test integrate((1+-2x)^-3//2*(2+3x)^4*(3+5x)^-5//2, x) == :(-621//1000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-107//1815*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^-3//2+1//399300*(1+-2x)^(1/2)*(3+5x)^-1//2*(627641+1051875x)+7//11*(1+-2x)^-1//2*(2+3x)^3*(3+5x)^-3//2)
@test integrate((1+-2x)^-3//2*(2+3x)^3*(3+5x)^-5//2, x) == :(-27//250*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-1//99825*(1+-2x)^(1/2)*(3+5x)^-3//2*(24439+38770x)+7//11*(1+-2x)^-1//2*(2+3x)^2*(3+5x)^-3//2)
@test integrate((1+-2x)^-3//2*(2+3x)^2*(3+5x)^-5//2, x) == :(-4091//19965*(1+-2x)^(1/2)*(3+5x)^-1//2+-3679//3630*(1+-2x)^(1/2)*(3+5x)^-3//2+49//22*(1+-2x)^-1//2*(3+5x)^-3//2)
@test integrate((1+-2x)^-3//2*(3+5x)^-5//2*(2+3x), x) == :(-428//3993*(1+-2x)^(1/2)*(3+5x)^-1//2+-107//363*(1+-2x)^(1/2)*(3+5x)^-3//2+7//11*(1+-2x)^-1//2*(3+5x)^-3//2)
@test integrate((1+-2x)^-3//2*(3+5x)^-5//2, x) == :(-160//3993*(1+-2x)^(1/2)*(3+5x)^-1//2+-40//363*(1+-2x)^(1/2)*(3+5x)^-3//2+2//11*(1+-2x)^-1//2*(3+5x)^-3//2)
@test integrate((1+-2x)^-3//2*(2+3x)^-1*(3+5x)^-5//2, x) == :(-410//2541*(1+-2x)^(1/2)*(3+5x)^-3//2+-54//49*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+4//77*(1+-2x)^-1//2*(3+5x)^-3//2+31030//27951*(1+-2x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^-3//2*(2+3x)^-2*(3+5x)^-5//2, x) == :(-28705//17787*(1+-2x)^(1/2)*(3+5x)^-3//2+-4887//343*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-58//539*(1+-2x)^-1//2*(3+5x)^-3//2+2841815//195657*(1+-2x)^(1/2)*(3+5x)^-1//2+3//7*(1+-2x)^-1//2*(2+3x)^-1*(3+5x)^-3//2)
@test integrate((1+-2x)^-3//2*(2+3x)^-3*(3+5x)^-5//2, x) == :(-7090175//498036*(1+-2x)^(1/2)*(3+5x)^-3//2+-1215945//9604*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-8515//7546*(1+-2x)^-1//2*(3+5x)^-3//2+707286025//5478396*(1+-2x)^(1/2)*(3+5x)^-1//2+3//14*(1+-2x)^-1//2*(2+3x)^-2*(3+5x)^-3//2+765//196*(1+-2x)^-1//2*(2+3x)^-1*(3+5x)^-3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^4*(3+5x)^(1/2), x) == :(13246251//64000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-697//88*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^(1/2)+-299//66*(1+-2x)^-1//2*(2+3x)^3*(3+5x)^(1/2)+-1//70400*(1+-2x)^(1/2)*(3+5x)^(1/2)*(17606479+7306140x)+1//3*(1+-2x)^-3//2*(2+3x)^4*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^3*(3+5x)^(1/2), x) == :(126513//3200*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-233//66*(1+-2x)^-1//2*(2+3x)^2*(3+5x)^(1/2)+-1//3520*(1+-2x)^(1/2)*(3+5x)^(1/2)*(168157+69780x)+1//3*(1+-2x)^-3//2*(2+3x)^3*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^2*(3+5x)^(1/2), x) == :(-519//88*(1+-2x)^(1/2)*(3+5x)^(1/2)+-21//11*(1+-2x)^-1//2*(3+5x)^3//2+49//66*(1+-2x)^-3//2*(3+5x)^3//2+519//80*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^-5//2*(3+5x)^(1/2)*(2+3x), x) == :(-3//2*(1+-2x)^-1//2*(3+5x)^(1/2)+3//4*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+7//33*(1+-2x)^-3//2*(3+5x)^3//2)
@test integrate((1+-2x)^-5//2*(3+5x)^(1/2), x) == :(2//33*(1+-2x)^-3//2*(3+5x)^3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^-1*(3+5x)^(1/2), x) == :(4//231*(1+-2x)^-3//2*(3+5x)^3//2+6//49*(1+-2x)^-1//2*(3+5x)^(1/2)+6//343*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2))
@test integrate((1+-2x)^-5//2*(2+3x)^-2*(3+5x)^(1/2), x) == :(-75//2401*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+850//11319*(1+-2x)^-1//2*(3+5x)^(1/2)+-5//49*(1+-2x)^-1//2*(2+3x)^-1*(3+5x)^(1/2)+2//21*(1+-2x)^-3//2*(2+3x)^-1*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^-3*(3+5x)^(1/2), x) == :(-765//9604*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+415//22638*(1+-2x)^-1//2*(3+5x)^(1/2)+-1//14*(1+-2x)^-1//2*(2+3x)^-2*(3+5x)^(1/2)+2//21*(1+-2x)^-3//2*(2+3x)^-2*(3+5x)^(1/2)+5//196*(1+-2x)^-1//2*(2+3x)^-1*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^-4*(3+5x)^(1/2), x) == :(-25365//134456*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-16985//316932*(1+-2x)^-1//2*(3+5x)^(1/2)+-3//49*(1+-2x)^-1//2*(2+3x)^-3*(3+5x)^(1/2)+-1//196*(1+-2x)^-1//2*(2+3x)^-2*(3+5x)^(1/2)+2//21*(1+-2x)^-3//2*(2+3x)^-3*(3+5x)^(1/2)+605//2744*(1+-2x)^-1//2*(2+3x)^-1*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^4*(3+5x)^3//2, x) == :(-1626211523//1126400*(1+-2x)^(1/2)*(3+5x)^(1/2)+1626211523//1024000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-3315//352*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^3//2+-123//22*(1+-2x)^-1//2*(2+3x)^3*(3+5x)^3//2+-3//281600*(1+-2x)^(1/2)*(3+5x)^3//2*(22868329+10798680x)+1//3*(1+-2x)^-3//2*(2+3x)^4*(3+5x)^3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^3*(3+5x)^3//2, x) == :(-4246733//14080*(1+-2x)^(1/2)*(3+5x)^(1/2)+4246733//12800*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-101//22*(1+-2x)^-1//2*(2+3x)^2*(3+5x)^3//2+-3//3520*(1+-2x)^(1/2)*(3+5x)^3//2*(59719+28200x)+1//3*(1+-2x)^-3//2*(2+3x)^3*(3+5x)^3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^2*(3+5x)^3//2, x) == :(-40787//704*(1+-2x)^(1/2)*(3+5x)^(1/2)+-40787//5808*(1+-2x)^(1/2)*(3+5x)^3//2+-938//363*(1+-2x)^-1//2*(3+5x)^5//2+49//66*(1+-2x)^-3//2*(3+5x)^5//2+40787//640*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^-5//2*(3+5x)^3//2*(2+3x), x) == :(-845//88*(1+-2x)^(1/2)*(3+5x)^(1/2)+-169//66*(1+-2x)^-1//2*(3+5x)^3//2+7//33*(1+-2x)^-3//2*(3+5x)^5//2+169//16*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^-5//2*(3+5x)^3//2, x) == :(-5//2*(1+-2x)^-1//2*(3+5x)^(1/2)+1//3*(1+-2x)^-3//2*(3+5x)^3//2+5//4*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^-5//2*(2+3x)^-1*(3+5x)^3//2, x) == :(-2//49*(1+-2x)^-1//2*(3+5x)^(1/2)+-2//343*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+2//21*(1+-2x)^-3//2*(3+5x)^3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^-2*(3+5x)^3//2, x) == :(95//2401*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+95*(1+-2x)^(1/2)*(3+5x)^(1/2)*(7546+11319x)^-1+4//231*(1+-2x)^-3//2*(2+3x)^-1*(3+5x)^5//2+190//1617*(1+-2x)^-1//2*(2+3x)^-1*(3+5x)^3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^-3*(3+5x)^3//2, x) == :(-5//196*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+5//42*(1+-2x)^-1//2*(3+5x)^(1/2)+-5//28*(1+-2x)^-1//2*(2+3x)^-1*(3+5x)^(1/2)+-3//14*(1+-2x)^-1//2*(2+3x)^-2*(3+5x)^(1/2)+11//21*(1+-2x)^-3//2*(2+3x)^-2*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^-4*(3+5x)^3//2, x) == :(-9395//134456*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+465//9604*(1+-2x)^-1//2*(3+5x)^(1/2)+-85//2744*(1+-2x)^-1//2*(2+3x)^-1*(3+5x)^(1/2)+-32//147*(1+-2x)^-1//2*(2+3x)^-3*(3+5x)^(1/2)+-23//196*(1+-2x)^-1//2*(2+3x)^-2*(3+5x)^(1/2)+11//21*(1+-2x)^-3//2*(2+3x)^-3*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^4*(3+5x)^5//2, x) == :(-4270537963//409600*(1+-2x)^(1/2)*(3+5x)^(1/2)+-4270537963//3379200*(1+-2x)^(1/2)*(3+5x)^3//2+46975917593//4096000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-4819//440*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^5//2+-439//66*(1+-2x)^-1//2*(2+3x)^3*(3+5x)^5//2+-1//140800*(1+-2x)^(1/2)*(3+5x)^5//2*(36714139+18161940x)+1//3*(1+-2x)^-3//2*(2+3x)^4*(3+5x)^5//2)
@test integrate((1+-2x)^-5//2*(2+3x)^3*(3+5x)^5//2, x) == :(-9444023//4096*(1+-2x)^(1/2)*(3+5x)^(1/2)+-9444023//33792*(1+-2x)^(1/2)*(3+5x)^3//2+103884253//40960*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-373//66*(1+-2x)^-1//2*(2+3x)^2*(3+5x)^5//2+-1//1408*(1+-2x)^(1/2)*(3+5x)^5//2*(81191+40164x)+1//3*(1+-2x)^-3//2*(2+3x)^3*(3+5x)^5//2)
@test integrate((1+-2x)^-5//2*(2+3x)^2*(3+5x)^5//2, x) == :(-123745//256*(1+-2x)^(1/2)*(3+5x)^(1/2)+-123745//2112*(1+-2x)^(1/2)*(3+5x)^3//2+-24749//2904*(1+-2x)^(1/2)*(3+5x)^5//2+-1183//363*(1+-2x)^-1//2*(3+5x)^7//2+49//66*(1+-2x)^-3//2*(3+5x)^7//2+272239//512*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^-5//2*(3+5x)^5//2*(2+3x), x) == :(-5975//64*(1+-2x)^(1/2)*(3+5x)^(1/2)+-5975//528*(1+-2x)^(1/2)*(3+5x)^3//2+-239//66*(1+-2x)^-1//2*(3+5x)^5//2+7//33*(1+-2x)^-3//2*(3+5x)^7//2+13145//128*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^-5//2*(3+5x)^5//2, x) == :(-125//8*(1+-2x)^(1/2)*(3+5x)^(1/2)+-25//6*(1+-2x)^-1//2*(3+5x)^3//2+1//3*(1+-2x)^-3//2*(3+5x)^5//2+275//16*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^-5//2*(2+3x)^-1*(3+5x)^5//2, x) == :(-407//98*(1+-2x)^-1//2*(3+5x)^(1/2)+2//1029*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+11//21*(1+-2x)^-3//2*(3+5x)^3//2+25//12*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2)))
@test integrate((1+-2x)^-5//2*(2+3x)^-2*(3+5x)^5//2, x) == :(-55//2401*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-5*(1+-2x)^(1/2)*(3+5x)^(1/2)*(686+1029x)^-1+-10//147*(1+-2x)^-1//2*(2+3x)^-1*(3+5x)^3//2+2//21*(1+-2x)^-3//2*(2+3x)^-1*(3+5x)^5//2)
@test integrate((1+-2x)^-5//2*(2+3x)^-3*(3+5x)^5//2, x) == :(715//9604*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+65*(1+-2x)^(1/2)*(3+5x)^(1/2)*(2744+4116x)^-1+4//231*(1+-2x)^-3//2*(2+3x)^-2*(3+5x)^7//2+26//231*(1+-2x)^-1//2*(2+3x)^-2*(3+5x)^5//2+65//3234*(1+-2x)^(1/2)*(2+3x)^-2*(3+5x)^3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^-4*(3+5x)^5//2, x) == :(-2585//134456*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+15755//86436*(1+-2x)^-1//2*(3+5x)^(1/2)+-2365//8232*(1+-2x)^-1//2*(2+3x)^-1*(3+5x)^(1/2)+-187//588*(1+-2x)^-1//2*(2+3x)^-2*(3+5x)^(1/2)+11//21*(1+-2x)^-3//2*(2+3x)^-3*(3+5x)^3//2+32//441*(1+-2x)^-1//2*(2+3x)^-3*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^-5*(3+5x)^5//2, x) == :(-547745//7529536*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+139745//1613472*(1+-2x)^-1//2*(3+5x)^(1/2)+-14135//153664*(1+-2x)^-1//2*(2+3x)^-1*(3+5x)^(1/2)+-2717//8232*(1+-2x)^-1//2*(2+3x)^-3*(3+5x)^(1/2)+-2013//10976*(1+-2x)^-1//2*(2+3x)^-2*(3+5x)^(1/2)+11//21*(1+-2x)^-3//2*(2+3x)^-4*(3+5x)^3//2+43//588*(1+-2x)^-1//2*(2+3x)^-4*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^5*(3+5x)^-1//2, x) == :(8261577//64000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-23909//4840*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^(1/2)+-2051//726*(1+-2x)^-1//2*(2+3x)^3*(3+5x)^(1/2)+-1//774400*(1+-2x)^(1/2)*(3+5x)^(1/2)*(120791143+50124540x)+7//33*(1+-2x)^-3//2*(2+3x)^4*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^4*(3+5x)^-1//2, x) == :(392283//16000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-1589//726*(1+-2x)^-1//2*(2+3x)^2*(3+5x)^(1/2)+-1//193600*(1+-2x)^(1/2)*(3+5x)^(1/2)*(5735477+2380020x)+7//33*(1+-2x)^-3//2*(2+3x)^3*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^3*(3+5x)^-1//2, x) == :(1593//400*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-1//14520*(1+-2x)^-1//2*(3+5x)^(1/2)*(95621+-33462x)+7//33*(1+-2x)^-3//2*(2+3x)^2*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^2*(3+5x)^-1//2, x) == :(-448//363*(1+-2x)^-1//2*(3+5x)^(1/2)+9//20*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+49//66*(1+-2x)^-3//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(3+5x)^-1//2*(2+3x), x) == :(-29//363*(1+-2x)^-1//2*(3+5x)^(1/2)+7//33*(1+-2x)^-3//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(3+5x)^-1//2, x) == :(2//33*(1+-2x)^-3//2*(3+5x)^(1/2)+20//363*(1+-2x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^-1*(3+5x)^-1//2, x) == :(-18//343*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+4//231*(1+-2x)^-3//2*(3+5x)^(1/2)+676//17787*(1+-2x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^-2*(3+5x)^-1//2, x) == :(-4390//124509*(1+-2x)^-1//2*(3+5x)^(1/2)+-405//2401*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-190//1617*(1+-2x)^-3//2*(3+5x)^(1/2)+3//7*(1+-2x)^-3//2*(2+3x)^-1*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^-3*(3+5x)^-1//2, x) == :(-57595//249018*(1+-2x)^-1//2*(3+5x)^(1/2)+-5805//9604*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-1735//3234*(1+-2x)^-3//2*(3+5x)^(1/2)+3//14*(1+-2x)^-3//2*(2+3x)^-2*(3+5x)^(1/2)+51//28*(1+-2x)^-3//2*(2+3x)^-1*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^-4*(3+5x)^-1//2, x) == :(-3471145//3486252*(1+-2x)^-1//2*(3+5x)^(1/2)+-330255//134456*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-101485//45276*(1+-2x)^-3//2*(3+5x)^(1/2)+1//7*(1+-2x)^-3//2*(2+3x)^-3*(3+5x)^(1/2)+193//196*(1+-2x)^-3//2*(2+3x)^-2*(3+5x)^(1/2)+423//56*(1+-2x)^-3//2*(2+3x)^-1*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^5*(3+5x)^-3//2, x) == :(243189//16000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-1561//726*(1+-2x)^-1//2*(2+3x)^3*(3+5x)^-1//2+-1//2129600*(1+-2x)^(1/2)*(3+5x)^(1/2)*(39109961+16227780x)+7//33*(1+-2x)^-3//2*(2+3x)^4*(3+5x)^-1//2+7723//39930*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^-1//2)
@test integrate((1+-2x)^-5//2*(2+3x)^4*(3+5x)^-3//2, x) == :(4887//2000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-1099//726*(1+-2x)^-1//2*(2+3x)^2*(3+5x)^-1//2+-1//798600*(1+-2x)^(1/2)*(3+5x)^-1//2*(4898747+8200665x)+7//33*(1+-2x)^-3//2*(2+3x)^3*(3+5x)^-1//2)
@test integrate((1+-2x)^-5//2*(2+3x)^3*(3+5x)^-3//2, x) == :(27//100*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-1//39930*(1+-2x)^-1//2*(3+5x)^-1//2*(66967+111311x)+7//33*(1+-2x)^-3//2*(2+3x)^2*(3+5x)^-1//2)
@test integrate((1+-2x)^-5//2*(2+3x)^2*(3+5x)^-3//2, x) == :(-1237//3630*(1+-2x)^-1//2*(3+5x)^-1//2+-793//19965*(1+-2x)^-1//2*(3+5x)^(1/2)+49//66*(1+-2x)^-3//2*(3+5x)^-1//2)
@test integrate((1+-2x)^-5//2*(3+5x)^-3//2*(2+3x), x) == :(-2//55*(1+-2x)^-3//2*(3+5x)^-1//2+82//1815*(1+-2x)^-3//2*(3+5x)^(1/2)+164//3993*(1+-2x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(3+5x)^-3//2, x) == :(-400//3993*(1+-2x)^(1/2)*(3+5x)^-1//2+2//33*(1+-2x)^-3//2*(3+5x)^-1//2+40//363*(1+-2x)^-1//2*(3+5x)^-1//2)
@test integrate((1+-2x)^-5//2*(2+3x)^-1*(3+5x)^-3//2, x) == :(-42230//195657*(1+-2x)^(1/2)*(3+5x)^-1//2+4//231*(1+-2x)^-3//2*(3+5x)^-1//2+54//343*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+956//17787*(1+-2x)^-1//2*(3+5x)^-1//2)
@test integrate((1+-2x)^-5//2*(2+3x)^-2*(3+5x)^-3//2, x) == :(-1840225//1369599*(1+-2x)^(1/2)*(3+5x)^-1//2+-3830//124509*(1+-2x)^-1//2*(3+5x)^-1//2+-190//1617*(1+-2x)^-3//2*(3+5x)^-1//2+3105//2401*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+3//7*(1+-2x)^-3//2*(2+3x)^-1*(3+5x)^-1//2)
@test integrate((1+-2x)^-5//2*(2+3x)^-3*(3+5x)^-3//2, x) == :(-46307675//5478396*(1+-2x)^(1/2)*(3+5x)^-1//2+-89945//249018*(1+-2x)^-1//2*(3+5x)^-1//2+-2725//3234*(1+-2x)^-3//2*(3+5x)^-1//2+79515//9604*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+3//14*(1+-2x)^-3//2*(2+3x)^-2*(3+5x)^-1//2+81//28*(1+-2x)^-3//2*(2+3x)^-1*(3+5x)^-1//2)
@test integrate((1+-2x)^-5//2*(2+3x)^6*(3+5x)^-5//2, x) == :(753543//80000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-511//242*(1+-2x)^-1//2*(2+3x)^4*(3+5x)^-3//2+-7//117128000*(1+-2x)^(1/2)*(3+5x)^(1/2)*(190406711+78981180x)+7//33*(1+-2x)^-3//2*(2+3x)^5*(3+5x)^-3//2+7591//39930*(1+-2x)^(1/2)*(2+3x)^3*(3+5x)^-3//2+261331//2196150*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^-1//2)
@test integrate((1+-2x)^-5//2*(2+3x)^5*(3+5x)^-5//2, x) == :(2997//2000*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-357//242*(1+-2x)^-1//2*(2+3x)^3*(3+5x)^-3//2+-1//8784600*(1+-2x)^(1/2)*(3+5x)^-1//2*(33035947+55300905x)+7//33*(1+-2x)^-3//2*(2+3x)^4*(3+5x)^-3//2+5281//39930*(1+-2x)^(1/2)*(2+3x)^2*(3+5x)^-3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^4*(3+5x)^-5//2, x) == :(81//500*10^(1/2)*arcsin(1//11*22^(1/2)*(3+5x)^(1/2))+-203//242*(1+-2x)^-1//2*(2+3x)^2*(3+5x)^-3//2+1//2196150*(1+-2x)^(1/2)*(3+5x)^-3//2*(627287+991010x)+7//33*(1+-2x)^-3//2*(2+3x)^3*(3+5x)^-3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^3*(3+5x)^-5//2, x) == :(-8182//219615*(1+-2x)^(1/2)*(3+5x)^-1//2+-3679//19965*(1+-2x)^(1/2)*(3+5x)^-3//2+49//121*(1+-2x)^-1//2*(3+5x)^-3//2+2//33*(1+-2x)^-3//2*(2+3x)^3*(3+5x)^-3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^2*(3+5x)^-5//2, x) == :(-3298//43923*(1+-2x)^(1/2)*(3+5x)^-1//2+-1649//7986*(1+-2x)^(1/2)*(3+5x)^-3//2+14//121*(1+-2x)^-1//2*(3+5x)^-3//2+49//66*(1+-2x)^-3//2*(3+5x)^-3//2)
@test integrate((1+-2x)^-5//2*(3+5x)^-5//2*(2+3x), x) == :(-2960//43923*(1+-2x)^(1/2)*(3+5x)^-1//2+-2//165*(1+-2x)^-3//2*(3+5x)^-3//2+74//1815*(1+-2x)^-3//2*(3+5x)^-1//2+296//3993*(1+-2x)^-1//2*(3+5x)^-1//2)
@test integrate((1+-2x)^-5//2*(3+5x)^-5//2, x) == :(-1600//43923*(1+-2x)^(1/2)*(3+5x)^-1//2+-400//3993*(1+-2x)^(1/2)*(3+5x)^-3//2+2//33*(1+-2x)^-3//2*(3+5x)^-3//2+20//121*(1+-2x)^-1//2*(3+5x)^-3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^-1*(3+5x)^-5//2, x) == :(-19130//195657*(1+-2x)^(1/2)*(3+5x)^-3//2+-162//343*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+4//231*(1+-2x)^-3//2*(3+5x)^-3//2+412//5929*(1+-2x)^-1//2*(3+5x)^-3//2+1001590//2152227*(1+-2x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^-5//2*(2+3x)^-2*(3+5x)^-5//2, x) == :(-985525//1369599*(1+-2x)^(1/2)*(3+5x)^-3//2+-14985//2401*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-1090//41503*(1+-2x)^-1//2*(3+5x)^-3//2+-190//1617*(1+-2x)^-3//2*(3+5x)^-3//2+95783075//15065589*(1+-2x)^(1/2)*(3+5x)^-1//2+3//7*(1+-2x)^-3//2*(2+3x)^-1*(3+5x)^-3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^-3*(3+5x)^-5//2, x) == :(-34551425//5478396*(1+-2x)^(1/2)*(3+5x)^-3//2+-538245//9604*7^(1/2)*arctan(1//7*7^(1/2)*(1+-2x)^(1/2)*(3+5x)^-1//2)+-40765//83006*(1+-2x)^-1//2*(3+5x)^-3//2+-3715//3234*(1+-2x)^-3//2*(3+5x)^-3//2+3443814775//60262356*(1+-2x)^(1/2)*(3+5x)^-1//2+3//14*(1+-2x)^-3//2*(2+3x)^-2*(3+5x)^-3//2+111//28*(1+-2x)^-3//2*(2+3x)^-1*(3+5x)^-3//2)
@test integrate((a+b*x)^-1//2*(c+b*x*a^-1*(-1+c))^-1//2*(e+b*x*a^-1*(-1+e))^-1//2, x) == :(2*a^(1/2)*b^-1*(1+-1c)^-1//2*Elliptic.F(arcsin(a^-1//2*(1+-1c)^(1/2)*(a+b*x)^(1/2)),(1+-1c)^-1*(1+-1*e)))
@test integrate((a+b*x)^-1//2*(c+d*x)^-1//2*(e+b*x*a^-1*(-1+e))^-1//2, x) == :(2*a^(1/2)*b^-1*(b*(b*c+-1*a*d)^-1*(c+d*x))^(1/2)*(1+-1*e)^-1//2*(c+d*x)^-1//2*Elliptic.F(arcsin(a^-1//2*(1+-1*e)^(1/2)*(a+b*x)^(1/2)),-1*a*d*(1+-1*e)^-1*(b*c+-1*a*d)^-1))
@test integrate((a+b*x)^-1//2*(c+d*x)^-1//2*(e+f*x)^-1//2, x) == :(2*b^-1*d^-1//2*(b*(b*c+-1*a*d)^-1*(c+d*x))^(1/2)*(b*(b*e+-1*a*f)^-1*(e+f*x))^(1/2)*(c+d*x)^-1//2*(e+f*x)^-1//2*(a*d+-1*b*c)^(1/2)*Elliptic.F(arcsin(d^(1/2)*(a+b*x)^(1/2)*(a*d+-1*b*c)^-1//2),f*d^-1*(b*e+-1*a*f)^-1*(b*c+-1*a*d)))
@test integrate((a+b*x)^-1//2*(c+b*x*a^-1*(-1+c))^-1//2*(e+b*x*a^-1*(-1+e))^(1/2), x) == :(2*a^(1/2)*b^-1*(1+-1c)^-1//2*Elliptic.E(arcsin(a^-1//2*(1+-1c)^(1/2)*(a+b*x)^(1/2)),(1+-1c)^-1*(1+-1*e)))
@test integrate((a+b*x)^-1//2*(c+d*x)^(1/2)*(e+b*x*a^-1*(-1+e))^-1//2, x) == :(2*a^(1/2)*b^-1*(b*(b*c+-1*a*d)^-1*(c+d*x))^-1//2*(1+-1*e)^-1//2*(c+d*x)^(1/2)*Elliptic.E(arcsin(a^-1//2*(1+-1*e)^(1/2)*(a+b*x)^(1/2)),-1*a*d*(1+-1*e)^-1*(b*c+-1*a*d)^-1))
@test integrate((a+b*x)^(1/2)*(c+b*x*a^-1*(-1+c))^-1//2*(e+b*x*a^-1*(-1+e))^-1//2, x) == :(-2*a*b^-1*(a^-1*(1+-1c)*(a+b*x))^-1//2*(-1*a^-1*(c+-1*e)^-1*(1+-1c)*(a*e+-1*b*x*(1+-1*e)))^(1/2)*(1+-1c)^-1*(1+-1*e)^-1//2*(a+b*x)^(1/2)*(c+-1*e)^(1/2)*(e+-1*b*x*a^-1*(1+-1*e))^-1//2*Elliptic.E(arcsin((1+-1*e)^(1/2)*(c+-1*e)^-1//2*(c+-1*b*x*a^-1*(1+-1c))^(1/2)),(1+-1*e)^-1*(c+-1*e)))
@test integrate((a+b*x)^-1//2*(c+d*x)^-1//2*(e+f*x)^(1/2), x) == :(2*b^-1*d^-1//2*(b*(b*c+-1*a*d)^-1*(c+d*x))^(1/2)*(b*(b*e+-1*a*f)^-1*(e+f*x))^-1//2*(c+d*x)^-1//2*(e+f*x)^(1/2)*(a*d+-1*b*c)^(1/2)*Elliptic.E(arcsin(d^(1/2)*(a+b*x)^(1/2)*(a*d+-1*b*c)^-1//2),f*d^-1*(b*e+-1*a*f)^-1*(b*c+-1*a*d)))
@test integrate((c+d*x)^-1//2*(e+f*x)^-1//2*(-1c+d*x)^-1//2, x) == :(2*c^(1/2)*d^-1*(c^-1*(c+-1*d*x))^(1/2)*(d*(d*e+-1*c*f)^-1*(e+f*x))^(1/2)*(e+f*x)^-1//2*(-1c+d*x)^-1//2*Elliptic.F(arcsin((1/2)*2^(1/2)*c^-1//2*(c+d*x)^(1/2)),-2*c*f*(d*e+-1*c*f)^-1))
@test integrate((1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^(1/2), x) == :(-2911577//1771875*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-175111//3543750*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-175111//236250*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-1244//13125*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+-23//1575*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^3//2+2//45*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^3//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2), x) == :(-55019//78750*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-823//39375*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-823//2625*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-27//875*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+2//35*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^3//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2), x) == :(-1159//3375*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-31//3375*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-31//225*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+2//25*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2), x) == :(-37//135*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+2//135*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+2//9*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2), x) == :(-2//9*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+4//9*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2//3*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2), x) == :(-74//189*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+4//189*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2//9*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+74//63*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^(1/2), x) == :(-4636//6615*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-124//6615*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2//15*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+74//315*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+4636//2205*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^-9//2*(3+5x)^(1/2), x) == :(-220076//108045*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-6584//108045*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2//21*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^(1/2)+74//735*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+3184//5145*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+220076//36015*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^3//2, x) == :(-1508889271//233887500*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-11346991//58471875*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-11346991//3898125*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-342971//866250*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+-543//9625*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2+-23//2475*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^5//2+2//55*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^5//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^3//2, x) == :(-5327983//2126250*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-160297//2126250*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-160297//141750*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-1208//7875*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+-3//175*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2+2//45*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^5//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2, x) == :(-148831//141750*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2252//70875*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2252//4725*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-31//525*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+2//35*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^3//2, x) == :(-974//2025*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-41//2025*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-41//135*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+2//15*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^3//2, x) == :(-49//81*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+8//81*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2//3*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^3//2+40//27*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^3//2, x) == :(-214//567*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+494//567*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-214//189*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2)+-2//9*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^3//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^3//2, x) == :(-8314//19845*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+824//19845*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-214//945*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+-2//15*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^3//2+8314//6615*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^-9//2*(3+5x)^3//2, x) == :(-475592//972405*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-10628//972405*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-214//2205*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+-2//21*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^3//2+8578//46305*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+475592//324135*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^-11//2*(3+5x)^3//2, x) == :(-22738708//20420505*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-673072//20420505*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-214//3969*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^(1/2)+-2//27*(1+-2x)^(1/2)*(2+3x)^-9//2*(3+5x)^3//2+8842//138915*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+332372//972405*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+22738708//6806835*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^5//2, x) == :(-16416987253//608107500*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-493825477//608107500*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-493825477//40540500*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-1865989//1126125*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+-564731//2252250*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2+-2014//53625*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^7//2+-23//3575*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^7//2+2//65*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^7//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^5//2, x) == :(-30926081//3118500*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-465127//1559250*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-465127//103950*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-7031//11550*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+-177//1925*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2+-3//275*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^7//2+2//55*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^7//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2, x) == :(-488149//127575*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-29357//255150*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-29357//17010*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-223//945*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+-31//945*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2+2//45*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^7//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^5//2, x) == :(-9013//5670*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-131//2835*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-131//189*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-1//7*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+2//21*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^5//2, x) == :(-3//5*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1//15*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-2//3*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^5//2+4//3*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^5//2, x) == :(-2209//1701*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+494//1701*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-118//63*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^3//2+-2//9*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^5//2+2470//567*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^5//2, x) == :(-12758//19845*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+31588//19845*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-12758//6615*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2)+-118//315*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^3//2+-2//15*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^5//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-9//2*(3+5x)^5//2, x) == :(-173482//324135*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+23612//324135*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-4282//15435*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+-118//735*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^3//2+-2//21*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^5//2+173482//108045*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^-11//2*(3+5x)^5//2, x) == :(-27198452//61261515*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-442868//61261515*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-12934//138915*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+-118//1323*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^3//2+-2//27*(1+-2x)^(1/2)*(2+3x)^-9//2*(3+5x)^5//2+568318//2917215*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+27198452//20420505*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^-13//2*(3+5x)^5//2, x) == :(-1305025844//1572378885*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-37904696//1572378885*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-13022//305613*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^(1/2)+-118//2079*(1+-2x)^(1/2)*(2+3x)^-9//2*(3+5x)^3//2+-2//33*(1+-2x)^(1/2)*(2+3x)^-11//2*(3+5x)^5//2+627806//10696455*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+19417096//74875185*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+1305025844//524126295*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((a+b*x)^-1//2*(c+d*x)^-1//2*(e+f*x)^(1/2), x) == :(2*b^-1*d^-1//2*(b*(b*c+-1*a*d)^-1*(c+d*x))^(1/2)*(b*(b*e+-1*a*f)^-1*(e+f*x))^-1//2*(c+d*x)^-1//2*(e+f*x)^(1/2)*(a*d+-1*b*c)^(1/2)*Elliptic.E(arcsin(d^(1/2)*(a+b*x)^(1/2)*(a*d+-1*b*c)^-1//2),f*d^-1*(b*e+-1*a*f)^-1*(b*c+-1*a*d)))
@test integrate((a+b*x)^-3//2*(c+d*x)^-1//2*(e+f*x)^(1/2), x) == :(-2*(a+b*x)^-1//2*(c+d*x)^(1/2)*(e+f*x)^(1/2)*(b*c+-1*a*d)^-1+2*b^-1*f^(1/2)*(b*(b*c+-1*a*d)^-1*(c+d*x))^-1//2*(b*(b*e+-1*a*f)^-1*(e+f*x))^(1/2)*(c+d*x)^(1/2)*(e+f*x)^-1//2*(a*f+-1*b*e)^(1/2)*(b*c+-1*a*d)^-1*Elliptic.E(arcsin(f^(1/2)*(a+b*x)^(1/2)*(a*f+-1*b*e)^-1//2),d*f^-1*(b*c+-1*a*d)^-1*(b*e+-1*a*f)))
@test integrate((1+-2x)^(1/2)*(-3+-5x)^-1//2*(2+3x)^-1//2, x) == :(2//15*35^(1/2)*Elliptic.E(arcsin(5^(1/2)*(2+3x)^(1/2)),2//35))
@test integrate((1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^-1//2, x) == :(-61151//131250*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-314//21875*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-859//4375*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-23//875*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2)+2//35*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^-1//2, x) == :(-146//625*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-17//1875*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-9//125*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+2//25*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2, x) == :(-31//225*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-4//225*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+2//15*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-1//2, x) == :(2//15*35^(1/2)*(-3+-5x)^(1/2)*(3+5x)^-1//2*Elliptic.E(arcsin(5^(1/2)*(2+3x)^(1/2)),2//35))
@test integrate((1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^-1//2, x) == :(-2//3*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+2*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^-1//2, x) == :(-136//63*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-4//63*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+2//3*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+136//21*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^-1//2, x) == :(-6388//735*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-64//245*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+2//5*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+92//35*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+6388//245*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^7//2*(3+5x)^-3//2, x) == :(-203179//656250*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-38723//3609375*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2486//21875*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-2//5*(1+-2x)^(1/2)*(2+3x)^7//2*(3+5x)^-1//2+48//175*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^(1/2)+183//4375*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^-3//2, x) == :(-1409//9375*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1091//103125*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2//5*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^-1//2+13//625*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+36//125*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^-3//2, x) == :(-106//4125*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-19//375*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2//5*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^-1//2+8//25*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2, x) == :(-62//825*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+4//25*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2//5*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-3//2, x) == :(2//5*35^(1/2)*Elliptic.E(arcsin(1//11*55^(1/2)*(1+-2x)^(1/2)),33//35)+-2*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^-3//2, x) == :(4*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+4//33*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-20*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+2*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-1//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^-3//2, x) == :(184//231*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+556//21*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2780//21*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+2//3*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^-1//2+92//7*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-1//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^-3//2, x) == :(38536//8085*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+116464//735*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-116464//147*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+2//5*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^-1//2+416//105*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^-1//2+19268//245*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-1//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^9//2*(3+5x)^-5//2, x) == :(-1473539//7218750*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-31288//3609375*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-12601//240625*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-118//165*(1+-2x)^(1/2)*(2+3x)^7//2*(3+5x)^-1//2+-2//15*(1+-2x)^(1/2)*(2+3x)^9//2*(3+5x)^-3//2+958//1925*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^(1/2)+5153//48125*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^7//2*(3+5x)^-5//2, x) == :(-47342//515625*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-523//46875*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-458//825*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^-1//2+-2//15*(1+-2x)^(1/2)*(2+3x)^7//2*(3+5x)^-3//2+2719//34375*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+2818//6875*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^-5//2, x) == :(-496//20625*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-169//20625*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-326//825*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^-1//2+-2//15*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^-3//2+458//1375*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^-5//2, x) == :(-178//4125*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+458//4125*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-194//825*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+-2//15*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^-3//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-5//2, x) == :(8//825*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+62//825*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-62//165*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+-2//15*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-5//2, x) == :(-136//165*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-4//165*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2//3*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+136//33*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^-5//2, x) == :(-532//33*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-16//33*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+2*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-3//2+-40//3*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+2660//33*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^-5//2, x) == :(-36968//231*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1112//231*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2780//21*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+2//3*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^-3//2+416//21*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-3//2+184840//231*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^-5//2, x) == :(-10312712//8085*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-310208//8085*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-155104//147*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+2//5*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^-3//2+556//105*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^-3//2+116044//735*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-3//2+10312712//1617*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^3//2*(2+3x)^5//2*(3+5x)^(1/2), x) == :(-604915631//584718750*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-18177329//584718750*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-18177329//38981250*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-124891//2165625*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+2//55*(1+-2x)^3//2*(2+3x)^5//2*(3+5x)^3//2+178//7425*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^3//2+1103//259875*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^3//2)
@test integrate((1+-2x)^3//2*(2+3x)^3//2*(3+5x)^(1/2), x) == :(-5684677//10631250*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-84134//5315625*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-84134//354375*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-347//39375*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+2//45*(1+-2x)^3//2*(2+3x)^3//2*(3+5x)^3//2+62//1575*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^3//2)
@test integrate((1+-2x)^3//2*(2+3x)^(1/2)*(3+5x)^(1/2), x) == :(-118898//354375*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2657//354375*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2657//23625*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+2//35*(1+-2x)^3//2*(2+3x)^(1/2)*(3+5x)^3//2+194//2625*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2)
@test integrate((1+-2x)^3//2*(2+3x)^-1//2*(3+5x)^(1/2), x) == :(-4157//10125*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+412//10125*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+2//15*(1+-2x)^3//2*(2+3x)^(1/2)*(3+5x)^(1/2)+214//675*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^-3//2*(3+5x)^(1/2), x) == :(-214//405*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+494//405*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-16//27*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-2//3*(1+-2x)^3//2*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^-5//2*(3+5x)^(1/2), x) == :(-98//81*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+16//81*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2//9*(1+-2x)^3//2*(2+3x)^-3//2*(3+5x)^(1/2)+82//27*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^-7//2*(3+5x)^(1/2), x) == :(-3896//2835*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-164//2835*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2//15*(1+-2x)^3//2*(2+3x)^-5//2*(3+5x)^(1/2)+82//135*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+3896//945*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^-9//2*(3+5x)^(1/2), x) == :(-595324//138915*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-18016//138915*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2//21*(1+-2x)^3//2*(2+3x)^-7//2*(3+5x)^(1/2)+82//315*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+8516//6615*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+595324//46305*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^-11//2*(3+5x)^(1/2), x) == :(-42623864//2917215*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1282376//2917215*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2//27*(1+-2x)^3//2*(2+3x)^-9//2*(3+5x)^(1/2)+82//567*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^(1/2)+13136//19845*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+613276//138915*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+42623864//972405*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^5//2*(3+5x)^3//2, x) == :(-51601293223//15202687500*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-776112041//7601343750*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-776112041//506756250*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-11725073//56306250*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+-18034//625625*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2+2//65*(1+-2x)^3//2*(2+3x)^5//2*(3+5x)^5//2+178//10725*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^5//2+601//160875*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^5//2)
@test integrate((1+-2x)^3//2*(2+3x)^3//2*(3+5x)^3//2, x) == :(-90397364//58471875*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-5442127//116943750*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-5442127//7796250*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-40703//433125*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+-23//9625*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2+2//55*(1+-2x)^3//2*(2+3x)^3//2*(3+5x)^5//2+62//2475*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^5//2)
@test integrate((1+-2x)^3//2*(2+3x)^(1/2)*(3+5x)^3//2, x) == :(-4971289//6378750*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-76163//3189375*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-76163//212625*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-839//23625*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+2//45*(1+-2x)^3//2*(2+3x)^(1/2)*(3+5x)^5//2+194//4725*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2)
@test integrate((1+-2x)^3//2*(2+3x)^-1//2*(3+5x)^3//2, x) == :(-29933//70875*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1847//70875*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1847//4725*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+2//21*(1+-2x)^3//2*(2+3x)^(1/2)*(3+5x)^3//2+74//525*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2)
@test integrate((1+-2x)^3//2*(2+3x)^-3//2*(3+5x)^3//2, x) == :(-2209//2025*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+494//2025*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-8//15*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+-2//3*(1+-2x)^3//2*(2+3x)^-1//2*(3+5x)^3//2+494//135*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^-5//2*(3+5x)^3//2, x) == :(-230//243*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+592//243*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1150//81*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-2//9*(1+-2x)^3//2*(2+3x)^-3//2*(3+5x)^3//2+74//9*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^3//2)
@test integrate((1+-2x)^3//2*(2+3x)^-7//2*(3+5x)^3//2, x) == :(-4418//2835*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+988//2835*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2//15*(1+-2x)^3//2*(2+3x)^-5//2*(3+5x)^3//2+74//45*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^3//2+988//945*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^-9//2*(3+5x)^3//2, x) == :(-119732//138915*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-7388//138915*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-3632//6615*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+-2//21*(1+-2x)^3//2*(2+3x)^-7//2*(3+5x)^3//2+74//105*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^3//2+119732//46305*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^-11//2*(3+5x)^3//2, x) == :(-19885156//8751645*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-609304//8751645*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-8252//19845*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+-2//27*(1+-2x)^3//2*(2+3x)^-9//2*(3+5x)^3//2+74//189*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^3//2+280904//416745*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+19885156//2917215*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^-13//2*(3+5x)^3//2, x) == :(-1446357824//224625555*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-43537016//224625555*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-12872//43659*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^(1/2)+-2//33*(1+-2x)^3//2*(2+3x)^-11//2*(3+5x)^3//2+74//297*(1+-2x)^(1/2)*(2+3x)^-9//2*(3+5x)^3//2+442076//1528065*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+20799916//10696455*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+1446357824//74875185*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^5//2*(3+5x)^5//2, x) == :(-836091184171//68412093750*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-50299451003//136824187500*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-50299451003//9121612500*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-380132617//506756250*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+-57509209//506756250*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2+-199721//12065625*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^7//2+2//75*(1+-2x)^3//2*(2+3x)^5//2*(3+5x)^7//2+178//14625*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^7//2+2503//804375*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^7//2)
@test integrate((1+-2x)^3//2*(2+3x)^3//2*(3+5x)^5//2, x) == :(-9380126059//1824322500*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-70536439//456080625*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-70536439//30405375*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-2133359//6756750*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+-160084//3378375*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2+-67//160875*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^7//2+2//65*(1+-2x)^3//2*(2+3x)^3//2*(3+5x)^7//2+62//3575*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^7//2)
@test integrate((1+-2x)^3//2*(2+3x)^(1/2)*(3+5x)^5//2, x) == :(-97540001//42099750*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2930159//42099750*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2930159//2806650*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-22576//155925*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+-2377//155925*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2+2//55*(1+-2x)^3//2*(2+3x)^(1/2)*(3+5x)^7//2+194//7425*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^7//2)
@test integrate((1+-2x)^3//2*(2+3x)^-1//2*(3+5x)^5//2, x) == :(-886499//765450*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-11908//382725*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-11908//25515*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-499//2835*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+2//27*(1+-2x)^3//2*(2+3x)^(1/2)*(3+5x)^5//2+46//567*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2)
@test integrate((1+-2x)^3//2*(2+3x)^-3//2*(3+5x)^5//2, x) == :(-2894//8505*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1061//8505*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1061//567*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-32//63*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2+-2//3*(1+-2x)^3//2*(2+3x)^-1//2*(3+5x)^5//2+202//63*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2)
@test integrate((1+-2x)^3//2*(2+3x)^-5//2*(3+5x)^5//2, x) == :(-9587//3645*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+2632//3645*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-614//27*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+-2//9*(1+-2x)^3//2*(2+3x)^-3//2*(3+5x)^5//2+362//27*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^5//2+2632//243*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^-7//2*(3+5x)^5//2, x) == :(-43214//25515*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+116854//25515*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-43214//1701*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-2//15*(1+-2x)^3//2*(2+3x)^-5//2*(3+5x)^5//2+362//135*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^5//2+9808//945*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^3//2)
@test integrate((1+-2x)^3//2*(2+3x)^-9//2*(3+5x)^5//2, x) == :(-962678//416745*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+249448//416745*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2//21*(1+-2x)^3//2*(2+3x)^-7//2*(3+5x)^5//2+362//315*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^5//2+2108//6615*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^3//2+249448//138915*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^-11//2*(3+5x)^5//2, x) == :(-17830424//26254935*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1717916//26254935*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-558524//1250235*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+-1864//6615*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^3//2+-2//27*(1+-2x)^3//2*(2+3x)^-9//2*(3+5x)^5//2+362//567*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^5//2+17830424//8751645*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^-13//2*(3+5x)^5//2, x) == :(-3316711588//2021629995*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-103970992//2021629995*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1366496//4584195*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+-13292//43659*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^3//2+-2//33*(1+-2x)^3//2*(2+3x)^-11//2*(3+5x)^5//2+362//891*(1+-2x)^(1/2)*(2+3x)^-9//2*(3+5x)^5//2+45748292//96268095*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+3316711588//673876665*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^-15//2*(3+5x)^5//2, x) == :(-245282464136//61322776515*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-7391549624//61322776515*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2174468//11918907*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^(1/2)+-20992//81081*(1+-2x)^(1/2)*(2+3x)^-9//2*(3+5x)^3//2+-2//39*(1+-2x)^3//2*(2+3x)^-13//2*(3+5x)^5//2+362//1287*(1+-2x)^(1/2)*(2+3x)^-11//2*(3+5x)^5//2+73596464//417161745*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+3523482724//2920132215*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+245282464136//20440925505*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^5//2*(3+5x)^-1//2, x) == :(-6515539//17718750*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-104663//8859375*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-87476//590625*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+2//45*(1+-2x)^3//2*(2+3x)^5//2*(3+5x)^(1/2)+178//4725*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^(1/2)+403//118125*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^3//2*(3+5x)^-1//2, x) == :(-46159//196875*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2281//196875*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-487//13125*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+2//35*(1+-2x)^3//2*(2+3x)^3//2*(3+5x)^(1/2)+62//875*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^(1/2)*(3+5x)^-1//2, x) == :(-2797//16875*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-598//16875*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+2//25*(1+-2x)^3//2*(2+3x)^(1/2)*(3+5x)^(1/2)+194//1125*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^-1//2*(3+5x)^-1//2, x) == :(-202//675*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+272//675*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-4//45*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^-3//2*(3+5x)^-1//2, x) == :(-74//45*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+4//45*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+14//3*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^-5//2*(3+5x)^-1//2, x) == :(-124//27*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-4//27*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+14//9*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+124//9*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^-7//2*(3+5x)^-1//2, x) == :(-17804//945*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-536//945*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+14//15*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+256//45*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+17804//315*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^-9//2*(3+5x)^-1//2, x) == :(-1255552//15435*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-37768//15435*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+2//3*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^(1/2)+388//105*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+18068//735*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+1255552//5145*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^7//2*(3+5x)^-3//2, x) == :(-1473539//5906250*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-31288//2953125*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-12601//196875*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-8//45*(1+-2x)^(1/2)*(2+3x)^7//2*(3+5x)^(1/2)+-2//5*(1+-2x)^3//2*(2+3x)^7//2*(3+5x)^-1//2+958//1575*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^(1/2)+5153//39375*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^5//2*(3+5x)^-3//2, x) == :(-47342//328125*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-5753//328125*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-32//175*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^(1/2)+-2//5*(1+-2x)^3//2*(2+3x)^5//2*(3+5x)^-1//2+2719//21875*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+2818//4375*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^3//2*(3+5x)^-3//2, x) == :(-496//9375*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-169//9375*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-24//125*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2)+-2//5*(1+-2x)^3//2*(2+3x)^3//2*(3+5x)^-1//2+458//625*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^(1/2)*(3+5x)^-3//2, x) == :(-178//1125*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+458//1125*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-16//75*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-2//5*(1+-2x)^3//2*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^3//2*(2+3x)^-1//2*(3+5x)^-3//2, x) == :(8//75*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+62//75*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-22//5*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^3//2*(2+3x)^-3//2*(3+5x)^-3//2, x) == :(4//15*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+136//15*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-136//3*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+14//3*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-1//2)
@test integrate((1+-2x)^3//2*(2+3x)^-5//2*(3+5x)^-3//2, x) == :(16//9*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+532//9*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2660//9*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+14//9*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^-1//2+88//3*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-1//2)
@test integrate((1+-2x)^3//2*(2+3x)^-7//2*(3+5x)^-3//2, x) == :(1112//105*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+36968//105*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-36968//21*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+14//15*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^-1//2+44//5*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^-1//2+6116//35*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-1//2)
@test integrate((1+-2x)^3//2*(2+3x)^-9//2*(3+5x)^-3//2, x) == :(310208//5145*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+10312712//5145*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-10312712//1029*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+2//3*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^-1//2+176//35*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^-1//2+12276//245*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^-1//2+1706144//1715*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-1//2)
@test integrate((1+-2x)^3//2*(2+3x)^7//2*(3+5x)^-5//2, x) == :(-25643//328125*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-24369//1203125*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-6*(1+-2x)^(1/2)*(2+3x)^7//2*(3+5x)^-1//2+-2//15*(1+-2x)^3//2*(2+3x)^7//2*(3+5x)^-3//2+622//175*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^(1/2)+3872//4375*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2)+4801//21875*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^5//2*(3+5x)^-5//2, x) == :(-8366//171875*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+1973//46875*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-106//25*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^-1//2+-2//15*(1+-2x)^3//2*(2+3x)^5//2*(3+5x)^-3//2+1558//625*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2)+2264//3125*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^3//2*(3+5x)^-5//2, x) == :(-582//6875*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+496//1875*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-62//25*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^-1//2+-2//15*(1+-2x)^3//2*(2+3x)^3//2*(3+5x)^-3//2+178//125*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^3//2*(2+3x)^(1/2)*(3+5x)^-5//2, x) == :(38//375*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+212//4125*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-18//25*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+-2//15*(1+-2x)^3//2*(2+3x)^(1/2)*(3+5x)^-3//2)
@test integrate((1+-2x)^3//2*(2+3x)^-1//2*(3+5x)^-5//2, x) == :(-148//75*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-52//825*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-22//15*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+148//15*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^3//2*(2+3x)^-3//2*(3+5x)^-5//2, x) == :(-556//15*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-184//165*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-92//3*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+14//3*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-3//2+556//3*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^3//2*(2+3x)^-5//2*(3+5x)^-5//2, x) == :(-1088//3*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-120//11*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-300*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+14//9*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^-3//2+404//9*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-3//2+5440//3*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^3//2*(2+3x)^-7//2*(3+5x)^-5//2, x) == :(-301304//105*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-33232//385*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-16616//7*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+14//15*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^-3//2+536//45*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^-3//2+111884//315*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-3//2+301304//21*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^5//2*(2+3x)^5//2*(3+5x)^(1/2), x) == :(-1163388067//1266890625*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-69808931//2533781250*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-69808931//168918750*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-445024//9384375*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+2//65*(1+-2x)^5//2*(2+3x)^5//2*(3+5x)^3//2+34//2475*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^3//2+62//2145*(1+-2x)^3//2*(2+3x)^5//2*(3+5x)^3//2+32717//1126125*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^3//2)
@test integrate((1+-2x)^5//2*(2+3x)^3//2*(3+5x)^(1/2), x) == :(-326256461//584718750*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-4738087//292359375*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-4738087//19490625*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+2//55*(1+-2x)^5//2*(2+3x)^3//2*(3+5x)^3//2+106//2475*(1+-2x)^3//2*(2+3x)^3//2*(3+5x)^3//2+2866//86625*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^3//2+38729//2165625*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2)
@test integrate((1+-2x)^5//2*(2+3x)^(1/2)*(3+5x)^(1/2), x) == :(-6799613//15946875*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-110717//15946875*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-110717//1063125*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+2//45*(1+-2x)^5//2*(2+3x)^(1/2)*(3+5x)^3//2+326//4725*(1+-2x)^3//2*(2+3x)^(1/2)*(3+5x)^3//2+10214//118125*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2)
@test integrate((1+-2x)^5//2*(2+3x)^-1//2*(3+5x)^(1/2), x) == :(-86741//118125*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+11806//118125*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+2//21*(1+-2x)^5//2*(2+3x)^(1/2)*(3+5x)^(1/2)+118//525*(1+-2x)^3//2*(2+3x)^(1/2)*(3+5x)^(1/2)+4282//7875*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^-3//2*(3+5x)^(1/2), x) == :(-12758//10125*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+31588//10125*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1076//675*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-8//15*(1+-2x)^3//2*(2+3x)^(1/2)*(3+5x)^(1/2)+-2//3*(1+-2x)^5//2*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^-5//2*(3+5x)^(1/2), x) == :(-4418//1215*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+988//1215*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2//9*(1+-2x)^5//2*(2+3x)^-3//2*(3+5x)^(1/2)+10//3*(1+-2x)^3//2*(2+3x)^-1//2*(3+5x)^(1/2)+196//81*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^-7//2*(3+5x)^(1/2), x) == :(-12//5*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-4//15*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+8*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2)+-2//15*(1+-2x)^5//2*(2+3x)^-5//2*(3+5x)^(1/2)+2//3*(1+-2x)^3//2*(2+3x)^-3//2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^-9//2*(3+5x)^(1/2), x) == :(-36052//3969*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1048//3969*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2//21*(1+-2x)^5//2*(2+3x)^-7//2*(3+5x)^(1/2)+2//7*(1+-2x)^3//2*(2+3x)^-5//2*(3+5x)^(1/2)+524//189*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+36052//1323*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^-11//2*(3+5x)^(1/2), x) == :(-7810384//250047*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-234856//250047*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2//27*(1+-2x)^5//2*(2+3x)^-9//2*(3+5x)^(1/2)+10//63*(1+-2x)^3//2*(2+3x)^-7//2*(3+5x)^(1/2)+832//567*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+112436//11907*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+7810384//83349*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^-13//2*(3+5x)^(1/2), x) == :(-247408648//2139291*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-7442032//2139291*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2//33*(1+-2x)^5//2*(2+3x)^-11//2*(3+5x)^(1/2)+10//99*(1+-2x)^3//2*(2+3x)^-9//2*(3+5x)^(1/2)+1900//2079*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^(1/2)+76492//14553*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+3560432//101871*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+247408648//713097*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^5//2*(3+5x)^3//2, x) == :(-1764163292393//684120937500*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-13267820528//171030234375*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-13267820528//11402015625*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-400516993//2533781250*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+-569519//28153125*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2+2//75*(1+-2x)^5//2*(2+3x)^5//2*(3+5x)^5//2+62//2925*(1+-2x)^3//2*(2+3x)^5//2*(3+5x)^5//2+3698//482625*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^5//2+142391//7239375*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^5//2)
@test integrate((1+-2x)^5//2*(2+3x)^3//2*(3+5x)^3//2, x) == :(-30660308017//22804031250*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-923943703//22804031250*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-923943703//1520268750*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-6794792//84459375*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+2//65*(1+-2x)^5//2*(2+3x)^3//2*(3+5x)^5//2+106//3575*(1+-2x)^3//2*(2+3x)^3//2*(3+5x)^5//2+8318//482625*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^5//2+25603//1876875*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2)
@test integrate((1+-2x)^5//2*(2+3x)^(1/2)*(3+5x)^3//2, x) == :(-829177897//1052493750*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-12996374//526246875*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-12996374//35083125*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-78797//3898125*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+2//55*(1+-2x)^5//2*(2+3x)^(1/2)*(3+5x)^5//2+326//7425*(1+-2x)^3//2*(2+3x)^(1/2)*(3+5x)^5//2+30362//779625*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2)
@test integrate((1+-2x)^5//2*(2+3x)^-1//2*(3+5x)^3//2, x) == :(-4457606//9568125*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-429479//9568125*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-429479//637875*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+2//27*(1+-2x)^5//2*(2+3x)^(1/2)*(3+5x)^3//2+362//2835*(1+-2x)^3//2*(2+3x)^(1/2)*(3+5x)^3//2+14318//70875*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2)
@test integrate((1+-2x)^5//2*(2+3x)^-3//2*(3+5x)^3//2, x) == :(-481339//212625*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+124724//212625*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2108//1575*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+-32//63*(1+-2x)^3//2*(2+3x)^(1/2)*(3+5x)^3//2+-2//3*(1+-2x)^5//2*(2+3x)^-1//2*(3+5x)^3//2+124724//14175*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^-5//2*(3+5x)^3//2, x) == :(-43214//18225*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+116854//18225*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-43214//1215*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-2//9*(1+-2x)^5//2*(2+3x)^-3//2*(3+5x)^3//2+230//27*(1+-2x)^3//2*(2+3x)^-1//2*(3+5x)^3//2+788//135*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2)
@test integrate((1+-2x)^5//2*(2+3x)^-7//2*(3+5x)^3//2, x) == :(-19174//3645*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+5264//3645*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-316//27*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^3//2+-2//15*(1+-2x)^5//2*(2+3x)^-5//2*(3+5x)^3//2+46//27*(1+-2x)^3//2*(2+3x)^-3//2*(3+5x)^3//2+5264//243*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^-9//2*(3+5x)^3//2, x) == :(-11576//11907*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-4244//11907*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-4244//3969*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2)+-2//21*(1+-2x)^5//2*(2+3x)^-7//2*(3+5x)^3//2+46//63*(1+-2x)^3//2*(2+3x)^-5//2*(3+5x)^3//2+608//189*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^3//2)
@test integrate((1+-2x)^5//2*(2+3x)^-11//2*(3+5x)^3//2, x) == :(-3545996//750141*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-95264//750141*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-104036//35721*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+-2//27*(1+-2x)^5//2*(2+3x)^-9//2*(3+5x)^3//2+230//567*(1+-2x)^3//2*(2+3x)^-7//2*(3+5x)^3//2+1532//567*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^3//2+3545996//250047*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^-13//2*(3+5x)^3//2, x) == :(-780320008//57760857*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-23441272//57760857*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-325796//130977*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+-2//33*(1+-2x)^5//2*(2+3x)^-11//2*(3+5x)^3//2+230//891*(1+-2x)^3//2*(2+3x)^-9//2*(3+5x)^3//2+12280//6237*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^3//2+11243972//2750517*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+780320008//19253619*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^-15//2*(3+5x)^3//2, x) == :(-75041008472//1752079329*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2257166048//1752079329*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-3347620//1702701*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^(1/2)+-2//39*(1+-2x)^5//2*(2+3x)^-13//2*(3+5x)^3//2+230//1287*(1+-2x)^3//2*(2+3x)^-11//2*(3+5x)^3//2+1300//891*(1+-2x)^(1/2)*(2+3x)^-9//2*(3+5x)^3//2+23210828//11918907*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+1079936248//83432349*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+75041008472//584026443*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^3//2*(3+5x)^5//2, x) == :(-1580201444291//410472562500*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-23763809947//205236281250*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-23763809947//13682418750*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-359748241//1520268750*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+-26534891//760134375*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2+2//75*(1+-2x)^5//2*(2+3x)^3//2*(3+5x)^7//2+106//4875*(1+-2x)^3//2*(2+3x)^3//2*(3+5x)^7//2+8038//804375*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^7//2+364267//36196875*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^7//2)
@test integrate((1+-2x)^5//2*(2+3x)^(1/2)*(3+5x)^5//2, x) == :(-8120161139//4104725625*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-486785077//8209451250*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-486785077//547296750*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-3872003//30405375*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+-121031//30405375*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2+2//65*(1+-2x)^5//2*(2+3x)^(1/2)*(3+5x)^7//2+326//10725*(1+-2x)^3//2*(2+3x)^(1/2)*(3+5x)^7//2+2314//111375*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^7//2)
@test integrate((1+-2x)^5//2*(2+3x)^-1//2*(3+5x)^5//2, x) == :(-146222113//126299250*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1654421//63149625*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1654421//4209975*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-146963//467775*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+2//33*(1+-2x)^5//2*(2+3x)^(1/2)*(3+5x)^5//2+74//891*(1+-2x)^3//2*(2+3x)^(1/2)*(3+5x)^5//2+9698//93555*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2)
@test integrate((1+-2x)^5//2*(2+3x)^-3//2*(3+5x)^5//2, x) == :(-310399//1148175*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-25111//1148175*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-310399//76545*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-2108//1701*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2+-40//81*(1+-2x)^3//2*(2+3x)^(1/2)*(3+5x)^5//2+-2//3*(1+-2x)^5//2*(2+3x)^-1//2*(3+5x)^5//2+64628//8505*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2)
@test integrate((1+-2x)^5//2*(2+3x)^-5//2*(3+5x)^5//2, x) == :(-452399//76545*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+135334//76545*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-31298//567*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+-2//9*(1+-2x)^5//2*(2+3x)^-3//2*(3+5x)^5//2+370//27*(1+-2x)^3//2*(2+3x)^-1//2*(3+5x)^5//2+5260//567*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2+135334//5103*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^-7//2*(3+5x)^5//2, x) == :(-48478//10935*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+136028//10935*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-48478//729*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-6464//81*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^5//2+-2//15*(1+-2x)^5//2*(2+3x)^-5//2*(3+5x)^5//2+74//27*(1+-2x)^3//2*(2+3x)^-3//2*(3+5x)^5//2+11036//81*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2)
@test integrate((1+-2x)^5//2*(2+3x)^-9//2*(3+5x)^5//2, x) == :(-904798//107163*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+270668//107163*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-62596//3969*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^3//2+-1844//567*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^5//2+-2//21*(1+-2x)^5//2*(2+3x)^-7//2*(3+5x)^5//2+74//63*(1+-2x)^3//2*(2+3x)^-5//2*(3+5x)^5//2+1353340//35721*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^-11//2*(3+5x)^5//2, x) == :(-1241596//2250423*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-100444//2250423*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1241596//750141*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2)+-13316//35721*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^3//2+-2//27*(1+-2x)^5//2*(2+3x)^-9//2*(3+5x)^5//2+370//567*(1+-2x)^3//2*(2+3x)^-7//2*(3+5x)^5//2+2776//1701*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^5//2)
@test integrate((1+-2x)^5//2*(2+3x)^-13//2*(3+5x)^5//2, x) == :(-584888452//173282571*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-13235368//173282571*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-17089252//8251551*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+-55772//43659*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^3//2+-2//33*(1+-2x)^5//2*(2+3x)^-11//2*(3+5x)^5//2+370//891*(1+-2x)^3//2*(2+3x)^-9//2*(3+5x)^5//2+36980//18711*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^5//2+584888452//57760857*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^-15//2*(3+5x)^5//2, x) == :(-129922578224//15768713961*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-3894280616//15768713961*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-54281308//35756721*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+-2622980//1702701*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^3//2+-2//39*(1+-2x)^5//2*(2+3x)^-13//2*(3+5x)^5//2+370//1287*(1+-2x)^3//2*(2+3x)^-11//2*(3+5x)^5//2+60080//34749*(1+-2x)^(1/2)*(2+3x)^-9//2*(3+5x)^5//2+1876198516//750891141*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+129922578224//5256237987*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^-17//2*(3+5x)^5//2, x) == :(-12641611554328//551904988635*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-380220959152//551904988635*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-112817764//107270163*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^(1/2)+-1085156//729729*(1+-2x)^(1/2)*(2+3x)^-9//2*(3+5x)^3//2+-2//45*(1+-2x)^5//2*(2+3x)^-15//2*(3+5x)^5//2+74//351*(1+-2x)^3//2*(2+3x)^-13//2*(3+5x)^5//2+16636//11583*(1+-2x)^(1/2)*(2+3x)^-11//2*(3+5x)^5//2+3914701972//3754455705*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+181941877952//26281189935*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+12641611554328//183968329545*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^5//2*(3+5x)^-1//2, x) == :(-231061879//584718750*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-3963068//292359375*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2865161//19490625*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+2//55*(1+-2x)^5//2*(2+3x)^5//2*(3+5x)^(1/2)+62//1485*(1+-2x)^3//2*(2+3x)^5//2*(3+5x)^(1/2)+4258//155925*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^(1/2)+181333//3898125*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^3//2*(3+5x)^-1//2, x) == :(-8024546//26578125*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-509189//26578125*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+2//45*(1+-2x)^5//2*(2+3x)^3//2*(3+5x)^(1/2)+106//1575*(1+-2x)^3//2*(2+3x)^3//2*(3+5x)^(1/2)+8878//118125*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2)+21547//1771875*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^(1/2)*(3+5x)^-1//2, x) == :(-408311//1771875*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-132824//1771875*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+2//35*(1+-2x)^5//2*(2+3x)^(1/2)*(3+5x)^(1/2)+326//2625*(1+-2x)^3//2*(2+3x)^(1/2)*(3+5x)^(1/2)+30922//118125*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^-1//2*(3+5x)^-1//2, x) == :(-34154//50625*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+53194//50625*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1088//3375*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-4//75*(1+-2x)^3//2*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^-3//2*(3+5x)^-1//2, x) == :(-8314//2025*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+824//2025*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+14//3*(1+-2x)^3//2*(2+3x)^-1//2*(3+5x)^(1/2)+428//135*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^-5//2*(3+5x)^-1//2, x) == :(-3896//405*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-164//405*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+14//9*(1+-2x)^3//2*(2+3x)^-3//2*(3+5x)^(1/2)+812//27*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^-7//2*(3+5x)^-1//2, x) == :(-16564//405*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-496//405*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+14//15*(1+-2x)^3//2*(2+3x)^-5//2*(3+5x)^(1/2)+1736//135*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+16564//135*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^-9//2*(3+5x)^-1//2, x) == :(-703480//3969*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-21160//3969*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+2//3*(1+-2x)^3//2*(2+3x)^-7//2*(3+5x)^(1/2)+76//9*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+10124//189*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+703480//1323*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^-11//2*(3+5x)^-1//2, x) == :(-66055016//83349*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1986944//83349*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+14//27*(1+-2x)^3//2*(2+3x)^-9//2*(3+5x)^(1/2)+512//81*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^(1/2)+20420//567*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+950584//3969*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+66055016//27783*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^-13//2*(3+5x)^-1//2, x) == :(-23204503328//6417873*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-697995152//6417873*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+14//33*(1+-2x)^3//2*(2+3x)^-11//2*(3+5x)^(1/2)+4508//891*(1+-2x)^(1/2)*(2+3x)^-9//2*(3+5x)^(1/2)+171004//6237*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^(1/2)+7173272//43659*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+333930952//305613*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+23204503328//2139291*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^7//2*(3+5x)^-3//2, x) == :(-264260033//974531250*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-7261561//487265625*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-703672//32484375*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-2972//7425*(1+-2x)^(1/2)*(2+3x)^7//2*(3+5x)^(1/2)+-48//275*(1+-2x)^3//2*(2+3x)^7//2*(3+5x)^(1/2)+-2//5*(1+-2x)^5//2*(2+3x)^7//2*(3+5x)^-1//2+346636//259875*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^(1/2)+2020841//6496875*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^5//2*(3+5x)^-3//2, x) == :(-1509007//8859375*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-299863//8859375*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1972//4725*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^(1/2)+-8//45*(1+-2x)^3//2*(2+3x)^5//2*(3+5x)^(1/2)+-2//5*(1+-2x)^5//2*(2+3x)^5//2*(3+5x)^-1//2+167228//118125*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2)+196499//590625*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^3//2*(3+5x)^-3//2, x) == :(-110014//984375*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+53279//984375*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1972//4375*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2)+-32//175*(1+-2x)^3//2*(2+3x)^3//2*(3+5x)^(1/2)+-2//5*(1+-2x)^5//2*(2+3x)^3//2*(3+5x)^-1//2+106772//65625*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^(1/2)*(3+5x)^-3//2, x) == :(-28174//84375*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+81164//84375*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-3028//5625*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-24//125*(1+-2x)^3//2*(2+3x)^(1/2)*(3+5x)^(1/2)+-2//5*(1+-2x)^5//2*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^5//2*(2+3x)^-1//2*(3+5x)^-3//2, x) == :(1196//3375*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+5594//3375*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-388//225*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-22//5*(1+-2x)^3//2*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^5//2*(2+3x)^-3//2*(3+5x)^-3//2, x) == :(124//225*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+4636//225*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1496//15*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+14//3*(1+-2x)^3//2*(2+3x)^-1//2*(3+5x)^-1//2)
@test integrate((1+-2x)^5//2*(2+3x)^-5//2*(3+5x)^-3//2, x) == :(536//135*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+17804//135*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-17804//27*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+14//9*(1+-2x)^3//2*(2+3x)^-3//2*(3+5x)^-1//2+1792//27*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-1//2)
@test integrate((1+-2x)^5//2*(2+3x)^-7//2*(3+5x)^-3//2, x) == :(3176//135*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+105584//135*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-105584//27*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+14//15*(1+-2x)^3//2*(2+3x)^-5//2*(3+5x)^-1//2+2716//135*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^-1//2+17468//45*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-1//2)
@test integrate((1+-2x)^5//2*(2+3x)^-9//2*(3+5x)^-3//2, x) == :(58928//441*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+1959032//441*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-9795160//441*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+2//3*(1+-2x)^3//2*(2+3x)^-7//2*(3+5x)^-1//2+104//9*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^-1//2+2332//21*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^-1//2+324104//147*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-1//2)
@test integrate((1+-2x)^5//2*(2+3x)^-11//2*(3+5x)^-3//2, x) == :(20549264//27783*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+683150096//27783*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-3415750480//27783*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+14//27*(1+-2x)^3//2*(2+3x)^-9//2*(3+5x)^-1//2+652//81*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^-1//2+11660//189*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^-1//2+813208//1323*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^-1//2+113020952//9261*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-1//2)
@test integrate((1+-2x)^5//2*(2+3x)^7//2*(3+5x)^-5//2, x) == :(-1065118//14765625*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-595387//14765625*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-524//225*(1+-2x)^(1/2)*(2+3x)^7//2*(3+5x)^(1/2)+-442//75*(1+-2x)^3//2*(2+3x)^7//2*(3+5x)^-1//2+-2//15*(1+-2x)^5//2*(2+3x)^7//2*(3+5x)^-3//2+59662//7875*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^(1/2)+373022//196875*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2)+500501//984375*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^5//2*(3+5x)^-5//2, x) == :(-32836//328125*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+49321//328125*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-284//175*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^(1/2)+-62//15*(1+-2x)^3//2*(2+3x)^5//2*(3+5x)^-1//2+-2//15*(1+-2x)^5//2*(2+3x)^5//2*(3+5x)^-3//2+22866//4375*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2)+33778//21875*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^3//2*(3+5x)^-5//2, x) == :(-7738//46875*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+9206//15625*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-572//625*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2)+-178//75*(1+-2x)^3//2*(2+3x)^3//2*(3+5x)^-1//2+-2//15*(1+-2x)^5//2*(2+3x)^3//2*(3+5x)^-3//2+8874//3125*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^5//2*(2+3x)^(1/2)*(3+5x)^-5//2, x) == :(338//5625*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+992//5625*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-76//375*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-46//75*(1+-2x)^3//2*(2+3x)^(1/2)*(3+5x)^-1//2+-2//15*(1+-2x)^5//2*(2+3x)^(1/2)*(3+5x)^-3//2)
@test integrate((1+-2x)^5//2*(2+3x)^-1//2*(3+5x)^-5//2, x) == :(-584//125*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-68//375*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-22//15*(1+-2x)^3//2*(2+3x)^(1/2)*(3+5x)^-3//2+572//25*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^5//2*(2+3x)^-3//2*(3+5x)^-5//2, x) == :(-6388//75*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-64//25*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1012//15*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+14//3*(1+-2x)^3//2*(2+3x)^-1//2*(3+5x)^-3//2+6388//15*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^5//2*(2+3x)^-5//2*(3+5x)^-5//2, x) == :(-36968//45*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1112//45*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-6116//9*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+14//9*(1+-2x)^3//2*(2+3x)^-3//2*(3+5x)^-3//2+308//3*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-3//2+36968//9*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^5//2*(2+3x)^-7//2*(3+5x)^-5//2, x) == :(-96808//15*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2912//15*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-16016//3*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+14//15*(1+-2x)^3//2*(2+3x)^-5//2*(3+5x)^-3//2+1232//45*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^-3//2+35948//45*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-3//2+96808//3*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^5//2*(2+3x)^-9//2*(3+5x)^-5//2, x) == :(-2234208//49*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-201616//147*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-5544440//147*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+2//3*(1+-2x)^3//2*(2+3x)^-7//2*(3+5x)^-3//2+44//3*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^-3//2+11924//63*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^-3//2+2488904//441*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-3//2+11171040//49*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^-1//2*(2+3x)^5//2*(3+5x)^(1/2), x) == :(-56041//8750*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-5057//26250*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-4839//1750*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-104//175*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2)+-1//7*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^3//2*(3+5x)^(1/2), x) == :(-1597//750*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-8//125*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-23//25*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-1//5*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^(1/2), x) == :(-34//45*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1//45*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1//3*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^-1//2*(3+5x)^(1/2), x) == :(-1//3*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33))
@test integrate((1+-2x)^-1//2*(2+3x)^-3//2*(3+5x)^(1/2), x) == :(-2//7*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2)+2//21*35^(1/2)*(-3+-5x)^(1/2)*(3+5x)^-1//2*Elliptic.E(arcsin(5^(1/2)*(2+3x)^(1/2)),2//35))
@test integrate((1+-2x)^-1//2*(2+3x)^-5//2*(3+5x)^(1/2), x) == :(-62//441*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-8//441*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2//21*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+62//147*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^-7//2*(3+5x)^(1/2), x) == :(-584//1715*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-68//5145*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2//35*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+18//245*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+1752//1715*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^5//2*(3+5x)^3//2, x) == :(-44109377//1417500*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-663409//708750*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-663409//47250*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-9547//5250*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+-137//315*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^3//2+-1//9*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^3//2)
@test integrate((1+-2x)^-1//2*(2+3x)^3//2*(3+5x)^3//2, x) == :(-78472//7875*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-4721//15750*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-4721//1050*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-102//175*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+-1//7*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^3//2)
@test integrate((1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^3//2, x) == :(-4451//1350*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-67//675*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-67//45*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-1//5*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2)
@test integrate((1+-2x)^-1//2*(2+3x)^-1//2*(3+5x)^3//2, x) == :(-31//27*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1//27*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-5//9*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^-3//2*(3+5x)^3//2, x) == :(-37//63*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+2//63*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+2//21*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^-5//2*(3+5x)^3//2, x) == :(-202//1323*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+272//1323*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-272//441*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2)+2//63*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^-7//2*(3+5x)^3//2, x) == :(-5594//46305*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1196//46305*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-404//2205*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+2//105*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+5594//15435*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^-9//2*(3+5x)^3//2, x) == :(-184636//756315*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-9124//756315*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-536//5145*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+2//147*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^(1/2)+974//36015*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+184636//252105*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^7//2*(3+5x)^5//2, x) == :(-610627101631//1216215000*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2295970088//152026875*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2295970088//10135125*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-138809831//4504500*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+-221673//50050*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2+-14303//12870*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^5//2+-41//143*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^5//2+-1//13*(1+-2x)^(1/2)*(2+3x)^7//2*(3+5x)^5//2)
@test integrate((1+-2x)^-1//2*(2+3x)^5//2*(3+5x)^5//2, x) == :(-725140729//4677750*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-43624697//9355500*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-43624697//623700*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-329683//34650*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+-1053//770*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2+-34//99*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^5//2+-1//11*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^5//2)
@test integrate((1+-2x)^-1//2*(2+3x)^3//2*(3+5x)^5//2, x) == :(-8256877//170100*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-62092//42525*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-62092//2835*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-1877//630*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+-3//7*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2+-1//9*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^5//2)
@test integrate((1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^5//2, x) == :(-17587//1134*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-529//1134*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2645//378*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-20//21*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+-1//7*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2)
@test integrate((1+-2x)^-1//2*(2+3x)^-1//2*(3+5x)^5//2, x) == :(-4141//810*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-62//405*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-62//27*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-1//3*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2)
@test integrate((1+-2x)^-1//2*(2+3x)^-3//2*(3+5x)^5//2, x) == :(-974//567*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-41//567*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-205//189*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+2//21*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^3//2)
@test integrate((1+-2x)^-1//2*(2+3x)^-5//2*(3+5x)^5//2, x) == :(-4157//3969*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+412//3969*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+2//63*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^3//2+412//1323*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^-7//2*(3+5x)^5//2, x) == :(-34154//138915*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+53194//138915*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-53194//46305*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2)+2//105*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^3//2+544//6615*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^-9//2*(3+5x)^5//2, x) == :(-816622//6806835*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-265648//6806835*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-101902//324135*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+2//147*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^3//2+676//15435*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+816622//2268945*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^-11//2*(3+5x)^5//2, x) == :(-32098184//142943535*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2036756//142943535*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-168034//972405*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+-43094//6806835*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+2//189*(1+-2x)^(1/2)*(2+3x)^-9//2*(3+5x)^3//2+808//27783*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^(1/2)+32098184//47647845*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^-13//2*(3+5x)^5//2, x) == :(-924247516//2201330439*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-31704544//2201330439*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-362666//14975037*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+-251590//2139291*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^(1/2)+2//231*(1+-2x)^(1/2)*(2+3x)^-11//2*(3+5x)^3//2+940//43659*(1+-2x)^(1/2)*(2+3x)^-9//2*(3+5x)^(1/2)+11460644//104825259*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+924247516//733776813*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+x)^-1//2*(2+x)^-1//2*(3+x)^-1//2, x) == :(-2*Elliptic.F(arcsin((3+x)^-1//2),2))
@test integrate((1+x)^-1//2*(2+x)^-1//2*(3+-1x)^-1//2, x) == :(2*Elliptic.F(arcsin((1/2)*(1+x)^(1/2)),-4))
@test integrate((1+x)^-1//2*(2+-1x)^-1//2*(3+x)^-1//2, x) == :(2^(1/2)*Elliptic.F(arcsin(1//3*3^(1/2)*(1+x)^(1/2)),-3//2))
@test integrate((1+x)^-1//2*(2+-1x)^-1//2*(3+-1x)^-1//2, x) == :(Elliptic.F(arcsin(1//3*3^(1/2)*(1+x)^(1/2)),3//4))
@test integrate((1+-1x)^-1//2*(2+x)^-1//2*(3+x)^-1//2, x) == :(2*Elliptic.F(arcsin(1//3*3^(1/2)*(2+x)^(1/2)),-3))
@test integrate((1+-1x)^-1//2*(2+x)^-1//2*(3+-1x)^-1//2, x) == :(2//5*5^(1/2)*Elliptic.F(arcsin(1//3*3^(1/2)*(2+x)^(1/2)),3//5))
@test integrate((1+-1x)^-1//2*(2+-1x)^-1//2*(3+x)^-1//2, x) == :(2//5*5^(1/2)*Elliptic.F(arcsin((1/2)*(3+x)^(1/2)),4//5))
@test integrate((1+-1x)^-1//2*(2+-1x)^-1//2*(3+-1x)^-1//2, x) == :(2*Elliptic.F(arcsin((3+-1x)^-1//2),2))
@test integrate((-1+x)^-1//2*(-3+x)^-1//2*(-2+x)^-1//2, x) == :(-2*Elliptic.F(arcsin((-1+x)^-1//2),2))
@test integrate((-1+x)^-1//2*(-3+x)^-1//2*(-2+-1x)^-1//2, x) == :(-2//3*3^(1/2)*(-2+-1x)^-1//2*(2+x)^(1/2)*Elliptic.F(arcsin((2//3+1//3*x)^-1//2),5//3))
@test integrate((-1+-1x)^-1//2*(-3+x)^-1//2*(-2+x)^-1//2, x) == :(-2//3*3^(1/2)*(1+x)^(1/2)*(-1+-1x)^-1//2*Elliptic.F(arcsin((1//3+1//3*x)^-1//2),4//3))
@test integrate((-1+-1x)^-1//2*(-3+-1x)^-1//2*(-2+x)^-1//2, x) == :(-2//5*5^(1/2)*(1+x)^(1/2)*(-1+-1x)^-1//2*(-3+-1x)^-1//2*(3+x)^(1/2)*Elliptic.F(arcsin((3//5+1//5*x)^-1//2),2//5))
@test integrate((-1+-1x)^-1//2*(-3+x)^-1//2*(-2+-1x)^-1//2, x) == :(-2//5*5^(1/2)*(1+x)^(1/2)*(-1+-1x)^-1//2*(-2+-1x)^-1//2*(2+x)^(1/2)*Elliptic.F(arcsin((2//5+1//5*x)^-1//2),1//5))
@test integrate((-1+-1x)^-1//2*(-3+-1x)^-1//2*(-2+-1x)^-1//2, x) == :(2*Elliptic.F(arcsin((-1+-1x)^-1//2),2))
@test integrate((a+b*x)^-3//2*(c+d*x)^-1//2*(e+f*x)^-1//2, x) == :(-2*b*(a+b*x)^-1//2*(c+d*x)^(1/2)*(e+f*x)^(1/2)*(b*c+-1*a*d)^-1*(b*e+-1*a*f)^-1+2*f^(1/2)*(d*(d*e+-1*c*f)^-1*(e+f*x))^(1/2)*(-1*d*(b*c+-1*a*d)^-1*(a+b*x))^-1//2*(a+b*x)^(1/2)*(e+f*x)^-1//2*(b*c+-1*a*d)^-1*(b*e+-1*a*f)^-1*(c*f+-1*d*e)^(1/2)*Elliptic.E(arcsin(f^(1/2)*(c+d*x)^(1/2)*(c*f+-1*d*e)^-1//2),-1*b*f^-1*(b*c+-1*a*d)^-1*(d*e+-1*c*f)))
@test integrate((a+b*x)^-5//2*(c+d*x)^-1//2*(e+f*x)^-1//2, x) == :(-2*b*(a+b*x)^-3//2*(c+d*x)^(1/2)*(e+f*x)^(1/2)*(b*e+-1*a*f)^-1*(-3*a*d+3*b*c)^-1+4//3*b*(a+b*x)^-1//2*(c+d*x)^(1/2)*(e+f*x)^(1/2)*(b*c+-1*a*d)^-2*(b*e+-1*a*f)^-2*(b*c*f+b*d*e+-2*a*d*f)+-4//3*d^(1/2)*(b*(b*c+-1*a*d)^-1*(c+d*x))^(1/2)*(b*(b*e+-1*a*f)^-1*(e+f*x))^-1//2*(c+d*x)^-1//2*(e+f*x)^(1/2)*(a*d+-1*b*c)^-3//2*(b*e+-1*a*f)^-2*(b*c*f+b*d*e+-2*a*d*f)*Elliptic.E(arcsin(d^(1/2)*(a+b*x)^(1/2)*(a*d+-1*b*c)^-1//2),f*d^-1*(b*e+-1*a*f)^-1*(b*c+-1*a*d))+2//3*b^-1*d^(1/2)*(b*(b*c+-1*a*d)^-1*(c+d*x))^(1/2)*(b*(b*e+-1*a*f)^-1*(e+f*x))^(1/2)*(c+d*x)^-1//2*(e+f*x)^-1//2*(a*d+-1*b*c)^-3//2*(b*e+-1*a*f)^-1*(b*c*f+-3*a*d*f+2*b*d*e)*Elliptic.F(arcsin(d^(1/2)*(a+b*x)^(1/2)*(a*d+-1*b*c)^-1//2),f*d^-1*(b*e+-1*a*f)^-1*(b*c+-1*a*d)))
@test integrate((1+-2x)^-1//2*(2+3x)^7//2*(3+5x)^-1//2, x) == :(-270248//65625*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-178879//1443750*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-15553//8750*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-333//875*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2)+-3//35*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^5//2*(3+5x)^-1//2, x) == :(-5161//3750*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-857//20625*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-74//125*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-3//25*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^3//2*(3+5x)^-1//2, x) == :(-37//75*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-13//825*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1//5*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^-1//2, x) == :(-1//5*35^(1/2)*Elliptic.E(arcsin(1//11*55^(1/2)*(1+-2x)^(1/2)),33//35))
@test integrate((1+-2x)^-1//2*(2+3x)^-1//2*(3+5x)^-1//2, x) == :(-2//33*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33))
@test integrate((1+-2x)^-1//2*(2+3x)^-3//2*(3+5x)^-1//2, x) == :(-2//7*35^(1/2)*Elliptic.E(arcsin(1//11*55^(1/2)*(1+-2x)^(1/2)),33//35)+6//7*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^-5//2*(3+5x)^-1//2, x) == :(-148//147*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-52//1617*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+2//7*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+148//49*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^-7//2*(3+5x)^-1//2, x) == :(-20644//5145*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-6856//56595*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+6//35*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+296//245*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+20644//1715*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^7//2*(3+5x)^-3//2, x) == :(-61151//68750*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-942//34375*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2577//6875*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-69//1375*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2)+-2//55*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^-1//2)
@test integrate((1+-2x)^-1//2*(2+3x)^5//2*(3+5x)^-3//2, x) == :(-438//1375*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-17//1375*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-27//275*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-2//55*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^-1//2)
@test integrate((1+-2x)^-1//2*(2+3x)^3//2*(3+5x)^-3//2, x) == :(-31//275*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-4//275*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2//55*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^-3//2, x) == :(-2//11*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+2//55*35^(1/2)*(-3+-5x)^(1/2)*(3+5x)^-1//2*Elliptic.E(arcsin(5^(1/2)*(2+3x)^(1/2)),2//35))
@test integrate((1+-2x)^-1//2*(2+3x)^-1//2*(3+5x)^-3//2, x) == :(2//11*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-10//11*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^-1//2*(2+3x)^-3//2*(3+5x)^-3//2, x) == :(4//77*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+136//77*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-680//77*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+6//7*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-1//2)
@test integrate((1+-2x)^-1//2*(2+3x)^-5//2*(3+5x)^-3//2, x) == :(192//539*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+6388//539*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-31940//539*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+2//7*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^-1//2+288//49*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-1//2)
@test integrate((1+-2x)^-1//2*(2+3x)^-7//2*(3+5x)^-3//2, x) == :(40456//18865*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+1344984//18865*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1344984//3773*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+6//35*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^-1//2+436//245*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^-1//2+60684//1715*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-1//2)
@test integrate((1+-2x)^-1//2*(2+3x)^9//2*(3+5x)^-5//2, x) == :(-6515539//11343750*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-104663//5671875*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-87476//378125*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-668//9075*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^-1//2+-2//165*(1+-2x)^(1/2)*(2+3x)^7//2*(3+5x)^-3//2+403//75625*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-1//2*(2+3x)^7//2*(3+5x)^-5//2, x) == :(-46159//226875*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2281//226875*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-536//9075*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^-1//2+-487//15125*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-2//165*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^-3//2)
@test integrate((1+-2x)^-1//2*(2+3x)^5//2*(3+5x)^-5//2, x) == :(-2797//45375*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-598//45375*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-404//9075*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+-2//165*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^-3//2)
@test integrate((1+-2x)^-1//2*(2+3x)^3//2*(3+5x)^-5//2, x) == :(-202//9075*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+272//9075*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-272//1815*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+-2//165*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2)
@test integrate((1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^-5//2, x) == :(-4//1815*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+74//1815*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-74//363*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+-2//33*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2)
@test integrate((1+-2x)^-1//2*(2+3x)^-1//2*(3+5x)^-5//2, x) == :(-124//363*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-4//363*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-10//33*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+620//363*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^-1//2*(2+3x)^-3//2*(3+5x)^-5//2, x) == :(-17804//2541*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-536//2541*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1340//231*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+6//7*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-3//2+89020//2541*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^-1//2*(2+3x)^-5//2*(3+5x)^-5//2, x) == :(-1255552//17787*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-37768//17787*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-94420//1617*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+2//7*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^-3//2+428//49*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-3//2+6277760//17787*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^-1//2*(2+3x)^-7//2*(3+5x)^-5//2, x) == :(-352875016//622545*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-10614544//622545*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-5307272//11319*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+6//35*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^-3//2+576//245*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^-3//2+120324//1715*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-3//2+352875016//124509*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate(x^(1/2)*(a+2x)^-1//2*(c+2x)^-1//2, x) == :((1/2)*2^(1/2)*x^(1/2)*(-1*x*a^-1)^-1//2*(-1*(a+-1c)^-1*(c+2x))^(1/2)*(a+-1c)^(1/2)*(c+2x)^-1//2*Elliptic.E(arcsin((a+-1c)^-1//2*(a+2x)^(1/2)),1+-1*c*a^-1))
@test integrate((-3+x)^-1//2*(4+-1x)^-1//2*(5+-1x)^-1//2, x) == :(2^(1/2)*Elliptic.F(arcsin((-3+x)^(1/2)),1/2))
@test integrate(((-3+x)*(5+-1x))^-1//2*(4+-1x)^-1//2, x) == :(-2*Elliptic.F(arcsin((4+-1x)^(1/2)),-1))
@test integrate((4+-1x)^-1//2*(-15+-1*x^2+8x)^-1//2, x) == :(-2*Elliptic.F(arcsin((4+-1x)^(1/2)),-1))
@test integrate((-1+x)^-1//2*(-2+x)^-1//2*(6+-1x)^-1//2, x) == :(2*Elliptic.F(arcsin((1/2)*(-2+x)^(1/2)),-4))
@test integrate(((-2+x)*(6+-1x))^-1//2*(-1+x)^-1//2, x) == :(-2//5*5^(1/2)*Elliptic.F(arcsin((1/2)*(6+-1x)^(1/2)),4//5))
@test integrate((-1+x)^-1//2*(-12+-1*x^2+8x)^-1//2, x) == :(-2//5*5^(1/2)*Elliptic.F(arcsin((1/2)*(6+-1x)^(1/2)),4//5))
@test integrate((1+-2x)^-3//2*(2+3x)^7//2*(3+5x)^(1/2), x) == :(673523//288750*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+4071079//52500*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+(1+-2x)^-1//2*(2+3x)^7//2*(3+5x)^(1/2)+12//7*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^(1/2)+2517//350*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2)+29293//875*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^5//2*(3+5x)^(1/2), x) == :(4817//8250*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+7279//375*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+(1+-2x)^-1//2*(2+3x)^5//2*(3+5x)^(1/2)+9//5*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2)+419//50*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^3//2*(3+5x)^(1/2), x) == :(23//165*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+139//30*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+(1+-2x)^-1//2*(2+3x)^3//2*(3+5x)^(1/2)+2*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^(1/2)*(3+5x)^(1/2), x) == :(33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+1//33*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-1//2*(3+5x)^(1/2), x) == :(1//7*35^(1/2)*Elliptic.E(arcsin(1//11*55^(1/2)*(1+-2x)^(1/2)),33//35)+2//7*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-3//2*(3+5x)^(1/2), x) == :(-62//1617*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+4//49*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-12//49*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2)+2//7*(1+-2x)^-1//2*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-5//2*(3+5x)^(1/2), x) == :(-212//11319*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-38//1029*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-8//49*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+2//7*(1+-2x)^-1//2*(2+3x)^-3//2*(3+5x)^(1/2)+38//343*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-7//2*(3+5x)^(1/2), x) == :(-5636//36015*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-4364//396165*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-36//245*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+-26//1715*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+2//7*(1+-2x)^-1//2*(2+3x)^-5//2*(3+5x)^(1/2)+5636//12005*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^7//2*(3+5x)^3//2, x) == :(6770629//472500*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+112543103//236250*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+(1+-2x)^-1//2*(2+3x)^7//2*(3+5x)^3//2+5//3*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^3//2+1397//210*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^3//2+24358//875*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+6770629//31500*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^5//2*(3+5x)^3//2, x) == :(9694//2625*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+1289089//10500*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+(1+-2x)^-1//2*(2+3x)^5//2*(3+5x)^3//2+12//7*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^3//2+2511//350*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+9694//175*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^3//2*(3+5x)^3//2, x) == :(139//150*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+4621//150*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+(1+-2x)^-1//2*(2+3x)^3//2*(3+5x)^3//2+9//5*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+139//10*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^(1/2)*(3+5x)^3//2, x) == :(2//9*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+133//18*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^3//2+10//3*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-1//2*(3+5x)^3//2, x) == :(1//21*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+34//21*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+11//7*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-3//2*(3+5x)^3//2, x) == :(4//147*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+31//147*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-31//49*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2)+11//7*(1+-2x)^-1//2*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-5//2*(3+5x)^3//2, x) == :(-178//3087*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+458//3087*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-458//1029*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2)+-97//147*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+11//7*(1+-2x)^-1//2*(2+3x)^-3//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-7//2*(3+5x)^3//2, x) == :(-992//36015*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-338//36015*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-458//1715*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+-163//245*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+11//7*(1+-2x)^-1//2*(2+3x)^-5//2*(3+5x)^(1/2)+338//12005*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-9//2*(3+5x)^3//2, x) == :(-189368//1764735*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-23012//1764735*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-5438//84035*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+-2818//12005*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+-229//343*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^(1/2)+11//7*(1+-2x)^-1//2*(2+3x)^-7//2*(3+5x)^(1/2)+189368//588245*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^7//2*(3+5x)^5//2, x) == :(269045681//3118500*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+17888580643//6237000*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+(1+-2x)^-1//2*(2+3x)^7//2*(3+5x)^5//2+18//11*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^5//2+419//66*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^5//2+9741//385*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2+4066493//23100*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+269045681//207900*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^5//2*(3+5x)^5//2, x) == :(1284329//56700*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+42696881//56700*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+(1+-2x)^-1//2*(2+3x)^5//2*(3+5x)^5//2+5//3*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^5//2+93//14*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2+4853//105*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+1284329//3780*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^3//2*(3+5x)^5//2, x) == :(3683//630*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+244879//1260*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+(1+-2x)^-1//2*(2+3x)^3//2*(3+5x)^5//2+12//7*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2+167//14*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+3683//42*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^(1/2)*(3+5x)^5//2, x) == :(397//270*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+6599//135*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^5//2+3*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+397//18*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-1//2*(3+5x)^5//2, x) == :(67//189*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+4451//378*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+11//7*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^3//2+335//63*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-3//2*(3+5x)^5//2, x) == :(31//441*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+1159//441*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+11//7*(1+-2x)^-1//2*(2+3x)^-1//2*(3+5x)^3//2+31//147*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-5//2*(3+5x)^5//2, x) == :(598//9261*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+2797//9261*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2797//3087*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2)+11//7*(1+-2x)^-1//2*(2+3x)^-3//2*(3+5x)^3//2+97//441*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-7//2*(3+5x)^5//2, x) == :(-28174//324135*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+81164//324135*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-81164//108045*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2)+-15601//15435*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+11//7*(1+-2x)^-1//2*(2+3x)^-5//2*(3+5x)^3//2+163//735*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-9//2*(3+5x)^5//2, x) == :(-220028//5294205*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+106558//5294205*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-106772//252105*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+-106558//1764735*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2)+-37117//36015*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+11//7*(1+-2x)^-1//2*(2+3x)^-7//2*(3+5x)^3//2+229//1029*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-11//2*(3+5x)^5//2, x) == :(-6036028//66706983*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1199452//66706983*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-392998//3176523*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+-167228//453789*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+-67345//64827*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^(1/2)+11//7*(1+-2x)^-1//2*(2+3x)^-9//2*(3+5x)^3//2+295//1323*(1+-2x)^(1/2)*(2+3x)^-9//2*(3+5x)^(1/2)+6036028//22235661*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^7//2*(3+5x)^-1//2, x) == :(5057//13750*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+168123//13750*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+7//11*(1+-2x)^-1//2*(2+3x)^5//2*(3+5x)^(1/2)+312//275*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2)+14517//2750*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^5//2*(3+5x)^-1//2, x) == :(24//275*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+1597//550*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+7//11*(1+-2x)^-1//2*(2+3x)^3//2*(3+5x)^(1/2)+69//55*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^3//2*(3+5x)^-1//2, x) == :(1//55*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+34//55*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+7//11*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^(1/2)*(3+5x)^-1//2, x) == :(1//11*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+2//11*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-1//2*(3+5x)^-1//2, x) == :(4//77*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^(1/2)+2//77*35^(1/2)*(-3+-5x)^(1/2)*(3+5x)^-1//2*Elliptic.E(arcsin(5^(1/2)*(2+3x)^(1/2)),2//35))
@test integrate((1+-2x)^-3//2*(2+3x)^-3//2*(3+5x)^-1//2, x) == :(-62//539*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-8//539*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+4//77*(1+-2x)^-1//2*(2+3x)^-1//2*(3+5x)^(1/2)+186//539*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-5//2*(3+5x)^-1//2, x) == :(-1752//3773*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-68//3773*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+4//77*(1+-2x)^-1//2*(2+3x)^-3//2*(3+5x)^(1/2)+54//539*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+5256//3773*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^-7//2*(3+5x)^-1//2, x) == :(-244604//132055*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-7536//132055*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+4//77*(1+-2x)^-1//2*(2+3x)^-5//2*(3+5x)^(1/2)+138//2695*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+10308//18865*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+733812//132055*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^9//2*(3+5x)^-3//2, x) == :(175111//756250*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+2911577//378125*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-37//605*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^-1//2+7//11*(1+-2x)^-1//2*(2+3x)^7//2*(3+5x)^-1//2+10851//15125*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2)+502941//151250*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^7//2*(3+5x)^-3//2, x) == :(823//15125*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+55019//30250*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-37//605*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^-1//2+7//11*(1+-2x)^-1//2*(2+3x)^5//2*(3+5x)^-1//2+2388//3025*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^5//2*(3+5x)^-3//2, x) == :(31//3025*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+1159//3025*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-37//605*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+7//11*(1+-2x)^-1//2*(2+3x)^3//2*(3+5x)^-1//2)
@test integrate((1+-2x)^-3//2*(2+3x)^3//2*(3+5x)^-3//2, x) == :(-2//605*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+37//605*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-37//121*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+7//11*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^-3//2*(2+3x)^(1/2)*(3+5x)^-3//2, x) == :(-2//121*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+4//121*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-20//121*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+2//11*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^-3//2*(2+3x)^-1//2*(3+5x)^-3//2, x) == :(-4//847*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+74//847*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-370//847*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+4//77*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^-3//2*(2+3x)^-3//2*(3+5x)^-3//2, x) == :(124//5929*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+4636//5929*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-23180//5929*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+4//77*(1+-2x)^-1//2*(2+3x)^-1//2*(3+5x)^-1//2+186//539*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-1//2)
@test integrate((1+-2x)^-3//2*(2+3x)^-5//2*(3+5x)^-3//2, x) == :(6584//41503*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+220076//41503*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1100380//41503*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+4//77*(1+-2x)^-1//2*(2+3x)^-3//2*(3+5x)^-1//2+54//539*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^-1//2+9876//3773*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-1//2)
@test integrate((1+-2x)^-3//2*(2+3x)^-7//2*(3+5x)^-3//2, x) == :(1400888//1452605*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+46585232//1452605*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-46585232//290521*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+4//77*(1+-2x)^-1//2*(2+3x)^-5//2*(3+5x)^-1//2+138//2695*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^-1//2+14928//18865*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^-1//2+2101332//132055*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-1//2)
@test integrate((1+-2x)^-3//2*(2+3x)^11//2*(3+5x)^-5//2, x) == :(18177329//124781250*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+604915631//124781250*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-4553//99825*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^-1//2+-107//1815*(1+-2x)^(1/2)*(2+3x)^7//2*(3+5x)^-3//2+7//11*(1+-2x)^-1//2*(2+3x)^9//2*(3+5x)^-3//2+380188//831875*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2)+17427983//8318750*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^9//2*(3+5x)^-5//2, x) == :(84134//2495625*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+5684677//4991250*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-4421//99825*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^-1//2+-107//1815*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^-3//2+7//11*(1+-2x)^-1//2*(2+3x)^7//2*(3+5x)^-3//2+83093//166375*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-3//2*(2+3x)^7//2*(3+5x)^-5//2, x) == :(2657//499125*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+118898//499125*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-4289//99825*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+-107//1815*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^-3//2+7//11*(1+-2x)^-1//2*(2+3x)^5//2*(3+5x)^-3//2)
@test integrate((1+-2x)^-3//2*(2+3x)^5//2*(3+5x)^-5//2, x) == :(-412//99825*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+4157//99825*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-4157//19965*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+-107//1815*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+7//11*(1+-2x)^-1//2*(2+3x)^3//2*(3+5x)^-3//2)
@test integrate((1+-2x)^-3//2*(2+3x)^3//2*(3+5x)^-5//2, x) == :(-214//19965*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+494//19965*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-494//3993*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+-107//363*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+7//11*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^-3//2)
@test integrate((1+-2x)^-3//2*(2+3x)^(1/2)*(3+5x)^-5//2, x) == :(-16//3993*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+98//3993*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-490//3993*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+-40//363*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+2//11*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^-3//2)
@test integrate((1+-2x)^-3//2*(2+3x)^-1//2*(3+5x)^-5//2, x) == :(-3896//27951*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-164//27951*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-410//2541*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+4//77*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^-3//2+19480//27951*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^-3//2*(2+3x)^-3//2*(3+5x)^-5//2, x) == :(-595324//195657*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-18016//195657*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-45040//17787*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+4//77*(1+-2x)^-1//2*(2+3x)^-1//2*(3+5x)^-3//2+186//539*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-3//2+2976620//195657*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^-3//2*(2+3x)^-5//2*(3+5x)^-5//2, x) == :(-42623864//1369599*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1282376//1369599*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-3205940//124509*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+4//77*(1+-2x)^-1//2*(2+3x)^-3//2*(3+5x)^-3//2+54//539*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^-3//2+14496//3773*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-3//2+213119320//1369599*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^-3//2*(2+3x)^-7//2*(3+5x)^-5//2, x) == :(-12071114168//47935965*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-363103712//47935965*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-181551856//871563*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+4//77*(1+-2x)^-1//2*(2+3x)^-5//2*(3+5x)^-3//2+138//2695*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^-3//2+19548//18865*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^-3//2+4115652//132055*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-3//2+12071114168//9587193*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^-5//2*(2+3x)^9//2*(3+5x)^(1/2), x) == :(-112543103//288750*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-6770629//577500*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-6478333//38500*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-139163//3850*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2)+-1327//154*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^(1/2)+-166//33*(1+-2x)^-1//2*(2+3x)^7//2*(3+5x)^(1/2)+1//3*(1+-2x)^-3//2*(2+3x)^9//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^7//2*(3+5x)^(1/2), x) == :(-1289089//16500*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-9694//4125*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-18551//550*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-797//110*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2)+-133//33*(1+-2x)^-1//2*(2+3x)^5//2*(3+5x)^(1/2)+1//3*(1+-2x)^-3//2*(2+3x)^7//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^5//2*(3+5x)^(1/2), x) == :(-4621//330*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-139//330*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-133//22*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-100//33*(1+-2x)^-1//2*(2+3x)^3//2*(3+5x)^(1/2)+1//3*(1+-2x)^-3//2*(2+3x)^5//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^3//2*(3+5x)^(1/2), x) == :(-133//66*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2//33*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-67//33*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^(1/2)+1//3*(1+-2x)^-3//2*(2+3x)^3//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^(1/2)*(3+5x)^(1/2), x) == :(-34//231*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1//231*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-68//231*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^(1/2)+1//3*(1+-2x)^-3//2*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^-1//2*(3+5x)^(1/2), x) == :(4//1617*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+31//1617*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+2//21*(1+-2x)^-3//2*(2+3x)^(1/2)*(3+5x)^(1/2)+62//1617*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^-3//2*(3+5x)^(1/2), x) == :(-178//11319*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+458//11319*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-458//3773*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2)+2//21*(1+-2x)^-3//2*(2+3x)^-1//2*(3+5x)^(1/2)+194//1617*(1+-2x)^-1//2*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^-5//2*(3+5x)^(1/2), x) == :(-992//79233*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-338//79233*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-458//3773*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+2//21*(1+-2x)^-3//2*(2+3x)^-3//2*(3+5x)^(1/2)+326//1617*(1+-2x)^-1//2*(2+3x)^-3//2*(3+5x)^(1/2)+338//26411*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^-7//2*(3+5x)^(1/2), x) == :(-189368//2773155*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2092//252105*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-5438//132055*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+-2818//18865*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+2//21*(1+-2x)^-3//2*(2+3x)^-5//2*(3+5x)^(1/2)+458//1617*(1+-2x)^-1//2*(2+3x)^-5//2*(3+5x)^(1/2)+189368//924385*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^7//2*(3+5x)^3//2, x) == :(-6547351//10500*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-722133//38500*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2166399//7700*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-140289//3850*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+-1341//154*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^3//2+-56//11*(1+-2x)^-1//2*(2+3x)^5//2*(3+5x)^3//2+1//3*(1+-2x)^-3//2*(2+3x)^7//2*(3+5x)^3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^5//2*(3+5x)^3//2, x) == :(-37663//300*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2077//550*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-6231//110*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-807//110*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+-45//11*(1+-2x)^-1//2*(2+3x)^3//2*(3+5x)^3//2+1//3*(1+-2x)^-3//2*(2+3x)^5//2*(3+5x)^3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^3//2*(3+5x)^3//2, x) == :(-68//3*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-15//22*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-225//22*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-34//11*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^3//2+1//3*(1+-2x)^-3//2*(2+3x)^3//2*(3+5x)^3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^(1/2)*(3+5x)^3//2, x) == :(-139//42*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-23//231*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-23//7*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^(1/2)+1//3*(1+-2x)^-3//2*(2+3x)^(1/2)*(3+5x)^3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^-1//2*(3+5x)^3//2, x) == :(-37//147*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-13//1617*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-74//147*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^(1/2)+11//21*(1+-2x)^-3//2*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^-3//2*(3+5x)^3//2, x) == :(19//1029*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+106//11319*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-19//343*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2)+-8//147*(1+-2x)^-1//2*(2+3x)^-1//2*(3+5x)^(1/2)+11//21*(1+-2x)^-3//2*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^-5//2*(3+5x)^3//2, x) == :(-582//26411*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+496//7203*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-496//2401*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2)+-89//343*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+11//21*(1+-2x)^-3//2*(2+3x)^-3//2*(3+5x)^(1/2)+58//147*(1+-2x)^-1//2*(2+3x)^-3//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^-7//2*(3+5x)^3//2, x) == :(-16732//924385*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+3946//252105*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-3946//84035*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2)+-2264//12005*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+-779//1715*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+11//21*(1+-2x)^-3//2*(2+3x)^-5//2*(3+5x)^(1/2)+124//147*(1+-2x)^-1//2*(2+3x)^-5//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^7//2*(3+5x)^5//2, x) == :(-174654791//37800*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1313411//9450*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1313411//630*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-1310203//4620*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+-6277//154*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2+-225//22*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^5//2+-203//33*(1+-2x)^-1//2*(2+3x)^5//2*(3+5x)^5//2+1//3*(1+-2x)^-3//2*(2+3x)^7//2*(3+5x)^5//2)
@test integrate((1+-2x)^-5//2*(2+3x)^5//2*(3+5x)^5//2, x) == :(-69819//70*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-12601//420*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-28283//462*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+-12601//28*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-1355//154*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^5//2+-170//33*(1+-2x)^-1//2*(2+3x)^3//2*(3+5x)^5//2+1//3*(1+-2x)^-3//2*(2+3x)^5//2*(3+5x)^5//2)
@test integrate((1+-2x)^-5//2*(2+3x)^3//2*(3+5x)^5//2, x) == :(-12101//60*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-91//15*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-91*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-817//66*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^3//2+-137//33*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^5//2+1//3*(1+-2x)^-3//2*(2+3x)^3//2*(3+5x)^5//2)
@test integrate((1+-2x)^-5//2*(2+3x)^(1/2)*(3+5x)^5//2, x) == :(-4621//126*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-139//126*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-695//42*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-104//21*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^3//2+1//3*(1+-2x)^-3//2*(2+3x)^(1/2)*(3+5x)^5//2)
@test integrate((1+-2x)^-5//2*(2+3x)^-1//2*(3+5x)^5//2, x) == :(-1597//294*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-8//49*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-264//49*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^(1/2)+11//21*(1+-2x)^-3//2*(2+3x)^(1/2)*(3+5x)^3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^-3//2*(3+5x)^5//2, x) == :(-146//343*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-17//1029*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-143//49*(1+-2x)^-1//2*(2+3x)^-1//2*(3+5x)^(1/2)+11//21*(1+-2x)^-3//2*(2+3x)^-1//2*(3+5x)^3//2+438//343*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^-5//2*(3+5x)^5//2, x) == :(169//21609*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+496//21609*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-169//7203*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2)+-22//49*(1+-2x)^-1//2*(2+3x)^-3//2*(3+5x)^(1/2)+11//21*(1+-2x)^-3//2*(2+3x)^-3//2*(3+5x)^3//2+229//1029*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^-7//2*(3+5x)^5//2, x) == :(-7738//252105*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+9206//84035*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-27618//84035*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2)+-4437//12005*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+-1432//1715*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+11//21*(1+-2x)^-3//2*(2+3x)^-5//2*(3+5x)^3//2+99//49*(1+-2x)^-1//2*(2+3x)^-5//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^-9//2*(3+5x)^5//2, x) == :(-65672//2470629*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+98642//2470629*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-98642//823543*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2)+-33778//117649*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+-11433//16807*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+-4545//2401*(1+-2x)^(1/2)*(2+3x)^-7//2*(3+5x)^(1/2)+11//21*(1+-2x)^-3//2*(2+3x)^-7//2*(3+5x)^3//2+220//49*(1+-2x)^-1//2*(2+3x)^-7//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^9//2*(3+5x)^-1//2, x) == :(-44109377//907500*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-663409//453750*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-317384//15125*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-27271//6050*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2)+-910//363*(1+-2x)^-1//2*(2+3x)^5//2*(3+5x)^(1/2)+7//33*(1+-2x)^-3//2*(2+3x)^7//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^7//2*(3+5x)^-1//2, x) == :(-78472//9075*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-4721//18150*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-4517//1210*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-679//363*(1+-2x)^-1//2*(2+3x)^3//2*(3+5x)^(1/2)+7//33*(1+-2x)^-3//2*(2+3x)^5//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^5//2*(3+5x)^-1//2, x) == :(-4451//3630*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-67//1815*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-448//363*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^(1/2)+7//33*(1+-2x)^-3//2*(2+3x)^3//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^3//2*(3+5x)^-1//2, x) == :(-31//363*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1//363*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-62//363*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^(1/2)+7//33*(1+-2x)^-3//2*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^(1/2)*(3+5x)^-1//2, x) == :(-2//2541*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+37//2541*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+2//33*(1+-2x)^-3//2*(2+3x)^(1/2)*(3+5x)^(1/2)+74//2541*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^-1//2*(3+5x)^-1//2, x) == :(-202//17787*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+272//17787*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+4//231*(1+-2x)^-3//2*(2+3x)^(1/2)*(3+5x)^(1/2)+544//17787*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^-3//2*(3+5x)^-1//2, x) == :(-5594//124509*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1196//124509*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+4//231*(1+-2x)^-3//2*(2+3x)^-1//2*(3+5x)^(1/2)+808//17787*(1+-2x)^-1//2*(2+3x)^-1//2*(3+5x)^(1/2)+5594//41503*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^-5//2*(3+5x)^-1//2, x) == :(-184636//871563*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-9124//871563*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+4//231*(1+-2x)^-3//2*(2+3x)^-3//2*(3+5x)^(1/2)+974//41503*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+1072//17787*(1+-2x)^-1//2*(2+3x)^-3//2*(3+5x)^(1/2)+184636//290521*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^-7//2*(3+5x)^-1//2, x) == :(-26062156//30504705*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-837304//30504705*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-806//207515*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^(1/2)+4//231*(1+-2x)^-3//2*(2+3x)^-5//2*(3+5x)^(1/2)+1336//17787*(1+-2x)^-1//2*(2+3x)^-5//2*(3+5x)^(1/2)+349904//1452605*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^(1/2)+26062156//10168235*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^(1/2))
@test integrate((1+-2x)^-5//2*(2+3x)^11//2*(3+5x)^-3//2, x) == :(-1508889271//49912500*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-11346991//12478125*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-21713939//1663750*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-932783//332750*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2)+-896//363*(1+-2x)^-1//2*(2+3x)^7//2*(3+5x)^-1//2+7//33*(1+-2x)^-3//2*(2+3x)^9//2*(3+5x)^-1//2+4439//19965*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^-1//2)
@test integrate((1+-2x)^-5//2*(2+3x)^9//2*(3+5x)^-3//2, x) == :(-5327983//998250*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-160297//998250*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-153319//66550*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-665//363*(1+-2x)^-1//2*(2+3x)^5//2*(3+5x)^-1//2+7//33*(1+-2x)^-3//2*(2+3x)^7//2*(3+5x)^-1//2+3284//19965*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^-1//2)
@test integrate((1+-2x)^-5//2*(2+3x)^7//2*(3+5x)^-3//2, x) == :(-148831//199650*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2252//99825*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-434//363*(1+-2x)^-1//2*(2+3x)^3//2*(3+5x)^-1//2+7//33*(1+-2x)^-3//2*(2+3x)^5//2*(3+5x)^-1//2+2129//19965*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^-5//2*(2+3x)^5//2*(3+5x)^-3//2, x) == :(-974//19965*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-41//19965*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-203//363*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^-1//2+7//33*(1+-2x)^-3//2*(2+3x)^3//2*(3+5x)^-1//2+974//3993*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^-5//2*(2+3x)^3//2*(3+5x)^-3//2, x) == :(-8//3993*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+49//3993*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-245//3993*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+7//33*(1+-2x)^-3//2*(2+3x)^(1/2)*(3+5x)^-1//2+8//363*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^-5//2*(2+3x)^(1/2)*(3+5x)^-3//2, x) == :(-214//27951*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+494//27951*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2470//27951*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+2//33*(1+-2x)^-3//2*(2+3x)^(1/2)*(3+5x)^-1//2+214//2541*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^-5//2*(2+3x)^-1//2*(3+5x)^-3//2, x) == :(-824//195657*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+8314//195657*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-41570//195657*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+4//231*(1+-2x)^-3//2*(2+3x)^(1/2)*(3+5x)^-1//2+824//17787*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^-5//2*(2+3x)^-3//2*(3+5x)^-3//2, x) == :(10628//1369599*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+475592//1369599*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2377960//1369599*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+4//231*(1+-2x)^-3//2*(2+3x)^-1//2*(3+5x)^-1//2+1088//17787*(1+-2x)^-1//2*(2+3x)^-1//2*(3+5x)^-1//2+5314//41503*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-1//2)
@test integrate((1+-2x)^-5//2*(2+3x)^-5//2*(3+5x)^-3//2, x) == :(673072//9587193*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+22738708//9587193*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-113693540//9587193*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+4//231*(1+-2x)^-3//2*(2+3x)^-3//2*(3+5x)^-1//2+694//41503*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^-1//2+1352//17787*(1+-2x)^-1//2*(2+3x)^-3//2*(3+5x)^-1//2+336536//290521*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-1//2)
@test integrate((1+-2x)^-5//2*(2+3x)^-7//2*(3+5x)^-3//2, x) == :(145418632//335551755*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+4839325048//335551755*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-4839325048//67110351*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+-2206//207515*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^-1//2+4//231*(1+-2x)^-3//2*(2+3x)^-5//2*(3+5x)^-1//2+1616//17787*(1+-2x)^-1//2*(2+3x)^-5//2*(3+5x)^-1//2+499564//1452605*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^-1//2+72709316//10168235*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-1//2)
@test integrate((1+-2x)^-5//2*(2+3x)^13//2*(3+5x)^-5//2, x) == :(-51601293223//2745187500*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-776112041//1372593750*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-371279941//45753125*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-31887029//18301250*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^(1/2)+-294//121*(1+-2x)^-1//2*(2+3x)^9//2*(3+5x)^-3//2+7//33*(1+-2x)^-3//2*(2+3x)^11//2*(3+5x)^-3//2+4373//19965*(1+-2x)^(1/2)*(2+3x)^7//2*(3+5x)^-3//2+150812//1098075*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^-1//2)
@test integrate((1+-2x)^-5//2*(2+3x)^11//2*(3+5x)^-5//2, x) == :(-90397364//27451875*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-5442127//54903750*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-5199979//3660250*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^(1/2)+-217//121*(1+-2x)^-1//2*(2+3x)^7//2*(3+5x)^-3//2+7//33*(1+-2x)^-3//2*(2+3x)^9//2*(3+5x)^-3//2+3218//19965*(1+-2x)^(1/2)*(2+3x)^5//2*(3+5x)^-3//2+110519//1098075*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^-1//2)
@test integrate((1+-2x)^-5//2*(2+3x)^9//2*(3+5x)^-5//2, x) == :(-4971289//10980750*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-76163//5490375*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-140//121*(1+-2x)^-1//2*(2+3x)^5//2*(3+5x)^-3//2+7//33*(1+-2x)^-3//2*(2+3x)^7//2*(3+5x)^-3//2+2063//19965*(1+-2x)^(1/2)*(2+3x)^3//2*(3+5x)^-3//2+70226//1098075*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^-5//2*(2+3x)^7//2*(3+5x)^-5//2, x) == :(-29933//1098075*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1847//1098075*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-63//121*(1+-2x)^-1//2*(2+3x)^3//2*(3+5x)^-3//2+7//33*(1+-2x)^-3//2*(2+3x)^5//2*(3+5x)^-3//2+908//19965*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+29933//219615*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^-5//2*(2+3x)^5//2*(3+5x)^-5//2, x) == :(-494//219615*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+2209//219615*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2209//43923*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+-247//3993*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+7//33*(1+-2x)^-3//2*(2+3x)^3//2*(3+5x)^-3//2+14//121*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^-3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^3//2*(3+5x)^-5//2, x) == :(-230//43923*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+592//43923*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-2960//43923*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+-575//3993*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+7//33*(1+-2x)^-3//2*(2+3x)^(1/2)*(3+5x)^-3//2+26//121*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^-3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^(1/2)*(3+5x)^-5//2, x) == :(-988//307461*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+4418//307461*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-22090//307461*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2+-2470//27951*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+2//33*(1+-2x)^-3//2*(2+3x)^(1/2)*(3+5x)^-3//2+118//847*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^-3//2)
@test integrate((1+-2x)^-5//2*(2+3x)^-1//2*(3+5x)^-5//2, x) == :(-119732//2152227*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-7388//2152227*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-18470//195657*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+4//231*(1+-2x)^-3//2*(2+3x)^(1/2)*(3+5x)^-3//2+368//5929*(1+-2x)^-1//2*(2+3x)^(1/2)*(3+5x)^-3//2+598660//2152227*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^-5//2*(2+3x)^-3//2*(3+5x)^-5//2, x) == :(-19885156//15065589*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-609304//15065589*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-1523260//1369599*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+4//231*(1+-2x)^-3//2*(2+3x)^-1//2*(3+5x)^-3//2+456//5929*(1+-2x)^-1//2*(2+3x)^-1//2*(3+5x)^-3//2+5034//41503*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-3//2+99425780//15065589*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^-5//2*(2+3x)^-5//2*(3+5x)^-5//2, x) == :(-1446357824//105459123*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-43537016//105459123*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-108842540//9587193*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+4//231*(1+-2x)^-3//2*(2+3x)^-3//2*(3+5x)^-3//2+414//41503*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^-3//2+544//5929*(1+-2x)^-1//2*(2+3x)^-3//2*(3+5x)^-3//2+488436//290521*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-3//2+7231789120//105459123*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((1+-2x)^-5//2*(2+3x)^-7//2*(3+5x)^-5//2, x) == :(-412810345784//3691069305*33^(1/2)*Elliptic.E(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-12417792656//3691069305*33^(1/2)*Elliptic.F(arcsin(1//7*21^(1/2)*(1+-2x)^(1/2)),35//33)+-6208896328//67110351*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-3//2+-3606//207515*(1+-2x)^(1/2)*(2+3x)^-5//2*(3+5x)^-3//2+4//231*(1+-2x)^-3//2*(2+3x)^-5//2*(3+5x)^-3//2+632//5929*(1+-2x)^-1//2*(2+3x)^-5//2*(3+5x)^-3//2+649224//1452605*(1+-2x)^(1/2)*(2+3x)^-3//2*(3+5x)^-3//2+140700876//10168235*(1+-2x)^(1/2)*(2+3x)^-1//2*(3+5x)^-3//2+412810345784//738213861*(1+-2x)^(1/2)*(2+3x)^(1/2)*(3+5x)^-1//2)
@test integrate((a+b*x)^1//3*(c+d*x)^2//3*(e+f*x)^2, x) == :(1//54*b^-3*d^-2*(a+b*x)^4//3*(c+d*x)^2//3*(b^2*(7*c^2*f^2+27*d^2*e^2+-24*c*d*e*f)+10*a^2*d^2*f^2+-10*a*b*d*f*(-1*c*f+3*d*e))+1//162*b^-11//3*d^-10//3*(b*c+-1*a*d)^2*(b^2*(7*c^2*f^2+27*d^2*e^2+-24*c*d*e*f)+10*a^2*d^2*f^2+-10*a*b*d*f*(-1*c*f+3*d*e))*log(-1+b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3)+1//486*b^-11//3*d^-10//3*(b*c+-1*a*d)^2*(b^2*(7*c^2*f^2+27*d^2*e^2+-24*c*d*e*f)+10*a^2*d^2*f^2+-10*a*b*d*f*(-1*c*f+3*d*e))*log(a+b*x)+1//4*f*b^-1*d^-1*(a+b*x)^4//3*(c+d*x)^5//3*(e+f*x)+1//36*f*b^-2*d^-2*(a+b*x)^4//3*(c+d*x)^5//3*(-8*a*d*f+-7*b*c*f+15*b*d*e)+1//81*b^-3*d^-3*(a+b*x)^1//3*(c+d*x)^2//3*(b*c+-1*a*d)*(b^2*(7*c^2*f^2+27*d^2*e^2+-24*c*d*e*f)+10*a^2*d^2*f^2+-10*a*b*d*f*(-1*c*f+3*d*e))+1//243*3^(1/2)*b^-11//3*d^-10//3*(b*c+-1*a*d)^2*(b^2*(7*c^2*f^2+27*d^2*e^2+-24*c*d*e*f)+10*a^2*d^2*f^2+-10*a*b*d*f*(-1*c*f+3*d*e))*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3))
@test integrate((a+b*x)^1//3*(c+d*x)^2//3*(e+f*x), x) == :(1//3*f*b^-1*d^-1*(a+b*x)^4//3*(c+d*x)^5//3+1//18*b^-2*d^-1*(a+b*x)^4//3*(c+d*x)^2//3*(-5*a*d*f+-4*b*c*f+9*b*d*e)+1//54*b^-8//3*d^-7//3*(b*c+-1*a*d)^2*(-5*a*d*f+-4*b*c*f+9*b*d*e)*log(-1+b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3)+1//162*b^-8//3*d^-7//3*(b*c+-1*a*d)^2*(-5*a*d*f+-4*b*c*f+9*b*d*e)*log(a+b*x)+1//27*b^-2*d^-2*(a+b*x)^1//3*(c+d*x)^2//3*(b*c+-1*a*d)*(-5*a*d*f+-4*b*c*f+9*b*d*e)+1//81*3^(1/2)*b^-8//3*d^-7//3*(b*c+-1*a*d)^2*(-5*a*d*f+-4*b*c*f+9*b*d*e)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3))
@test integrate((a+b*x)^1//3*(c+d*x)^2//3, x) == :((1/2)*b^-1*(a+b*x)^4//3*(c+d*x)^2//3+1//6*b^-5//3*d^-4//3*(b*c+-1*a*d)^2*log(-1+b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3)+1//18*b^-5//3*d^-4//3*(b*c+-1*a*d)^2*log(a+b*x)+1//3*b^-1*d^-1*(a+b*x)^1//3*(c+d*x)^2//3*(b*c+-1*a*d)+1//9*3^(1/2)*b^-5//3*d^-4//3*(b*c+-1*a*d)^2*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3))
@test integrate((a+b*x)^1//3*(c+d*x)^2//3*(e+f*x)^-1, x) == :(f^-1*(a+b*x)^1//3*(c+d*x)^2//3+(1/2)*f^-2*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^2//3*log(e+f*x)+-3//2*f^-2*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^2//3*log(-1*(a+b*x)^1//3+(c+d*x)^1//3*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^-1//3)+(1/2)*b^-2//3*d^-1//3*f^-2*(-1*a*d*f+-2*b*c*f+3*b*d*e)*log(-1+b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3)+-1*3^(1/2)*f^-2*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^2//3*arctan(1//3*3^(1/2)+2//3*3^(1/2)*(a+b*x)^-1//3*(c+d*x)^1//3*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^-1//3)+1//6*b^-2//3*d^-1//3*f^-2*(-1*a*d*f+-2*b*c*f+3*b*d*e)*log(a+b*x)+1//3*3^(1/2)*b^-2//3*d^-1//3*f^-2*(-1*a*d*f+-2*b*c*f+3*b*d*e)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3))
@test integrate((a+b*x)^1//3*(c+d*x)^2//3*(e+f*x)^-2, x) == :(-1*f^-1*(a+b*x)^1//3*(c+d*x)^2//3*(e+f*x)^-1+-3//2*b^1//3*d^2//3*f^-2*log(-1+b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3)+-1//2*b^1//3*d^2//3*f^-2*log(a+b*x)+(1/2)*f^-2*(b*e+-1*a*f)^-2//3*(d*e+-1*c*f)^-1//3*(-1*b*c*f+-2*a*d*f+3*b*d*e)*log(-1*(a+b*x)^1//3+(c+d*x)^1//3*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^-1//3)+-1*3^(1/2)*b^1//3*d^2//3*f^-2*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3)+-1//6*f^-2*(b*e+-1*a*f)^-2//3*(d*e+-1*c*f)^-1//3*(-1*b*c*f+-2*a*d*f+3*b*d*e)*log(e+f*x)+1//3*3^(1/2)*f^-2*(b*e+-1*a*f)^-2//3*(d*e+-1*c*f)^-1//3*(-1*b*c*f+-2*a*d*f+3*b*d*e)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*(a+b*x)^-1//3*(c+d*x)^1//3*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^-1//3))
@test integrate((a+b*x)^1//3*(c+d*x)^2//3*(e+f*x)^-3, x) == :((a+b*x)^1//3*(c+d*x)^5//3*(e+f*x)^-2*(-2*c*f+2*d*e)^-1+-1//18*(b*c+-1*a*d)^2*(b*e+-1*a*f)^-5//3*(d*e+-1*c*f)^-4//3*log(e+f*x)+1//6*(b*c+-1*a*d)^2*(b*e+-1*a*f)^-5//3*(d*e+-1*c*f)^-4//3*log(-1*(a+b*x)^1//3+(c+d*x)^1//3*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^-1//3)+1//9*3^(1/2)*(b*c+-1*a*d)^2*(b*e+-1*a*f)^-5//3*(d*e+-1*c*f)^-4//3*arctan(1//3*3^(1/2)+2//3*3^(1/2)*(a+b*x)^-1//3*(c+d*x)^1//3*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^-1//3)+-1*(a+b*x)^1//3*(c+d*x)^2//3*(e+f*x)^-1*(d*e+-1*c*f)^-1*(-6*a*f+6*b*e)^-1*(b*c+-1*a*d))
@test integrate((a+b*x)^1//3*(c+d*x)^2//3*(e+f*x)^-4, x) == :(-1//162*(b*c+-1*a*d)^2*(b*e+-1*a*f)^-8//3*(d*e+-1*c*f)^-7//3*(-5*b*c*f+-4*a*d*f+9*b*d*e)*log(e+f*x)+1//54*(b*c+-1*a*d)^2*(b*e+-1*a*f)^-8//3*(d*e+-1*c*f)^-7//3*(-5*b*c*f+-4*a*d*f+9*b*d*e)*log(-1*(a+b*x)^1//3+(c+d*x)^1//3*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^-1//3)+(a+b*x)^1//3*(c+d*x)^5//3*(e+f*x)^-2*(d*e+-1*c*f)^-2*(-18*a*f+18*b*e)^-1*(-5*b*c*f+-4*a*d*f+9*b*d*e)+-1*f*(a+b*x)^4//3*(c+d*x)^5//3*(e+f*x)^-3*(d*e+-1*c*f)^-1*(-3*a*f+3*b*e)^-1+1//81*3^(1/2)*(b*c+-1*a*d)^2*(b*e+-1*a*f)^-8//3*(d*e+-1*c*f)^-7//3*(-5*b*c*f+-4*a*d*f+9*b*d*e)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*(a+b*x)^-1//3*(c+d*x)^1//3*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^-1//3)+-1//54*(a+b*x)^1//3*(c+d*x)^2//3*(e+f*x)^-1*(b*e+-1*a*f)^-2*(d*e+-1*c*f)^-2*(b*c+-1*a*d)*(-5*b*c*f+-4*a*d*f+9*b*d*e))
@test integrate((a+b*x)^1//3*(c+d*x)^-1//3*(e+f*x)^2, x) == :(1//27*b^-2*d^-3*(a+b*x)^1//3*(c+d*x)^2//3*(b^2*(14*c^2*f^2+27*d^2*e^2+-36*c*d*e*f)+5*a^2*d^2*f^2+-2*a*b*d*f*(-4*c*f+9*d*e))+1//54*b^-8//3*d^-10//3*(b*c+-1*a*d)*(b^2*(14*c^2*f^2+27*d^2*e^2+-36*c*d*e*f)+5*a^2*d^2*f^2+-2*a*b*d*f*(-4*c*f+9*d*e))*log(-1+b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3)+1//162*b^-8//3*d^-10//3*(b*c+-1*a*d)*(b^2*(14*c^2*f^2+27*d^2*e^2+-36*c*d*e*f)+5*a^2*d^2*f^2+-2*a*b*d*f*(-4*c*f+9*d*e))*log(a+b*x)+1//3*f*b^-1*d^-1*(a+b*x)^4//3*(c+d*x)^2//3*(e+f*x)+1//18*f*b^-2*d^-2*(a+b*x)^4//3*(c+d*x)^2//3*(-7*b*c*f+-5*a*d*f+12*b*d*e)+1//81*3^(1/2)*b^-8//3*d^-10//3*(b*c+-1*a*d)*(b^2*(14*c^2*f^2+27*d^2*e^2+-36*c*d*e*f)+5*a^2*d^2*f^2+-2*a*b*d*f*(-4*c*f+9*d*e))*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3))
@test integrate((a+b*x)^1//3*(c+d*x)^-1//3*(e+f*x), x) == :((1/2)*f*b^-1*d^-1*(a+b*x)^4//3*(c+d*x)^2//3+1//3*b^-1*d^-2*(a+b*x)^1//3*(c+d*x)^2//3*(-1*a*d*f+-2*b*c*f+3*b*d*e)+1//6*b^-5//3*d^-7//3*(b*c+-1*a*d)*(-1*a*d*f+-2*b*c*f+3*b*d*e)*log(-1+b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3)+1//18*b^-5//3*d^-7//3*(b*c+-1*a*d)*(-1*a*d*f+-2*b*c*f+3*b*d*e)*log(a+b*x)+1//9*3^(1/2)*b^-5//3*d^-7//3*(b*c+-1*a*d)*(-1*a*d*f+-2*b*c*f+3*b*d*e)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3))
@test integrate((a+b*x)^1//3*(c+d*x)^-1//3, x) == :(d^-1*(a+b*x)^1//3*(c+d*x)^2//3+(1/2)*b^-2//3*d^-4//3*(b*c+-1*a*d)*log(-1+b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3)+1//6*b^-2//3*d^-4//3*(b*c+-1*a*d)*log(a+b*x)+1//3*3^(1/2)*b^-2//3*d^-4//3*(b*c+-1*a*d)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3))
@test integrate((a+b*x)^1//3*(c+d*x)^-1//3*(e+f*x)^-1, x) == :(-3//2*b^1//3*d^-1//3*f^-1*log(-1+b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3)+-1//2*b^1//3*d^-1//3*f^-1*log(a+b*x)+-1//2*f^-1*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^-1//3*log(e+f*x)+3//2*f^-1*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^-1//3*log(-1*(a+b*x)^1//3+(c+d*x)^1//3*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^-1//3)+3^(1/2)*f^-1*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^-1//3*arctan(1//3*3^(1/2)+2//3*3^(1/2)*(a+b*x)^-1//3*(c+d*x)^1//3*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^-1//3)+-1*3^(1/2)*b^1//3*d^-1//3*f^-1*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3))
@test integrate((a+b*x)^1//3*(c+d*x)^-1//3*(e+f*x)^-2, x) == :((a+b*x)^1//3*(c+d*x)^2//3*(e+f*x)^-1*(d*e+-1*c*f)^-1+(1/2)*(b*e+-1*a*f)^-2//3*(d*e+-1*c*f)^-4//3*(b*c+-1*a*d)*log(-1*(a+b*x)^1//3+(c+d*x)^1//3*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^-1//3)+-1//6*(b*e+-1*a*f)^-2//3*(d*e+-1*c*f)^-4//3*(b*c+-1*a*d)*log(e+f*x)+1//3*3^(1/2)*(b*e+-1*a*f)^-2//3*(d*e+-1*c*f)^-4//3*(b*c+-1*a*d)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*(a+b*x)^-1//3*(c+d*x)^1//3*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^-1//3))
@test integrate((a+b*x)^1//3*(c+d*x)^-1//3*(e+f*x)^-3, x) == :(-1//18*(b*e+-1*a*f)^-5//3*(d*e+-1*c*f)^-7//3*(b*c+-1*a*d)*(-1*b*c*f+-2*a*d*f+3*b*d*e)*log(e+f*x)+1//6*(b*e+-1*a*f)^-5//3*(d*e+-1*c*f)^-7//3*(b*c+-1*a*d)*(-1*b*c*f+-2*a*d*f+3*b*d*e)*log(-1*(a+b*x)^1//3+(c+d*x)^1//3*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^-1//3)+(a+b*x)^1//3*(c+d*x)^2//3*(e+f*x)^-1*(d*e+-1*c*f)^-2*(-3*a*f+3*b*e)^-1*(-1*b*c*f+-2*a*d*f+3*b*d*e)+-1*f*(a+b*x)^4//3*(c+d*x)^2//3*(e+f*x)^-2*(d*e+-1*c*f)^-1*(-2*a*f+2*b*e)^-1+1//9*3^(1/2)*(b*e+-1*a*f)^-5//3*(d*e+-1*c*f)^-7//3*(b*c+-1*a*d)*(-1*b*c*f+-2*a*d*f+3*b*d*e)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*(a+b*x)^-1//3*(c+d*x)^1//3*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^-1//3))
@test integrate((a+b*x)^1//3*(c+d*x)^-1//3*(e+f*x)^-4, x) == :((a+b*x)^1//3*(c+d*x)^2//3*(e+f*x)^-3*(-3*c*f+3*d*e)^-1+-1//162*(b*e+-1*a*f)^-8//3*(d*e+-1*c*f)^-10//3*(b*c+-1*a*d)*(b^2*(5*c^2*f^2+27*d^2*e^2+-18*c*d*e*f)+14*a^2*d^2*f^2+-4*a*b*d*f*(-2*c*f+9*d*e))*log(e+f*x)+1//54*(b*e+-1*a*f)^-8//3*(d*e+-1*c*f)^-10//3*(b*c+-1*a*d)*(b^2*(5*c^2*f^2+27*d^2*e^2+-18*c*d*e*f)+14*a^2*d^2*f^2+-4*a*b*d*f*(-2*c*f+9*d*e))*log(-1*(a+b*x)^1//3+(c+d*x)^1//3*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^-1//3)+(a+b*x)^1//3*(c+d*x)^2//3*(e+f*x)^-2*(d*e+-1*c*f)^-2*(-18*a*f+18*b*e)^-1*(b*c*f+-7*a*d*f+6*b*d*e)+1//54*(a+b*x)^1//3*(c+d*x)^2//3*(e+f*x)^-1*(b*e+-1*a*f)^-2*(d*e+-1*c*f)^-3*(b^2*(-5*c^2*f^2+18*d^2*e^2+15*c*d*e*f)+28*a^2*d^2*f^2+-1*a*b*d*f*(5*c*f+51*d*e))+1//81*3^(1/2)*(b*e+-1*a*f)^-8//3*(d*e+-1*c*f)^-10//3*(b*c+-1*a*d)*(b^2*(5*c^2*f^2+27*d^2*e^2+-18*c*d*e*f)+14*a^2*d^2*f^2+-4*a*b*d*f*(-2*c*f+9*d*e))*arctan(1//3*3^(1/2)+2//3*3^(1/2)*(a+b*x)^-1//3*(c+d*x)^1//3*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^-1//3))
@test integrate((a+b*x)^-1//3*(c+d*x)^-2//3*(e+f*x)^3, x) == :(1//54*b^-10//3*d^-11//3*(-1*b^3*(-40*c^3*f^3+81*d^3*e^3+-162*c*f*d^2*e^2+135*d*e*c^2*f^2)+14*a^3*d^3*f^3+-6*b*a^2*d^2*f^2*(-2*c*f+9*d*e)+3*a*d*f*b^2*(5*c^2*f^2+27*d^2*e^2+-18*c*d*e*f))*log(-1+b^-1//3*d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3)+1//162*b^-10//3*d^-11//3*(-1*b^3*(-40*c^3*f^3+81*d^3*e^3+-162*c*f*d^2*e^2+135*d*e*c^2*f^2)+14*a^3*d^3*f^3+-6*b*a^2*d^2*f^2*(-2*c*f+9*d*e)+3*a*d*f*b^2*(5*c^2*f^2+27*d^2*e^2+-18*c*d*e*f))*log(c+d*x)+1//81*3^(1/2)*b^-10//3*d^-11//3*(-1*b^3*(-40*c^3*f^3+81*d^3*e^3+-162*c*f*d^2*e^2+135*d*e*c^2*f^2)+14*a^3*d^3*f^3+-6*b*a^2*d^2*f^2*(-2*c*f+9*d*e)+3*a*d*f*b^2*(5*c^2*f^2+27*d^2*e^2+-18*c*d*e*f))*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^-1//3*d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3)+1//3*f*b^-1*d^-1*(a+b*x)^2//3*(c+d*x)^1//3*(e+f*x)^2+1//54*f*b^-3*d^-3*(a+b*x)^2//3*(c+d*x)^1//3*(b^2*(40*c^2*f^2+144*d^2*e^2+-135*c*d*e*f)+28*a^2*d^2*f^2+-1*a*b*d*f*(-31*c*f+108*d*e)+3*b*d*f*x*(-8*b*c*f+-7*a*d*f+15*b*d*e)))
@test integrate((a+b*x)^-1//3*(c+d*x)^-2//3*(e+f*x)^2, x) == :(-1//6*b^-7//3*d^-8//3*(b^2*(5*c^2*f^2+9*d^2*e^2+-12*c*d*e*f)+2*a^2*d^2*f^2+-2*a*b*d*f*(-1*c*f+3*d*e))*log(-1+b^-1//3*d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3)+-1//18*b^-7//3*d^-8//3*(b^2*(5*c^2*f^2+9*d^2*e^2+-12*c*d*e*f)+2*a^2*d^2*f^2+-2*a*b*d*f*(-1*c*f+3*d*e))*log(c+d*x)+-1//9*3^(1/2)*b^-7//3*d^-8//3*(b^2*(5*c^2*f^2+9*d^2*e^2+-12*c*d*e*f)+2*a^2*d^2*f^2+-2*a*b*d*f*(-1*c*f+3*d*e))*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^-1//3*d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3)+(1/2)*f*b^-1*d^-1*(a+b*x)^2//3*(c+d*x)^1//3*(e+f*x)+1//6*f*b^-2*d^-2*(a+b*x)^2//3*(c+d*x)^1//3*(-5*b*c*f+-4*a*d*f+9*b*d*e))
@test integrate((a+b*x)^-1//3*(c+d*x)^-2//3*(e+f*x), x) == :(-1//2*b^-4//3*d^-5//3*(-1*a*d*f+-2*b*c*f+3*b*d*e)*log(-1+b^-1//3*d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3)+-1//6*b^-4//3*d^-5//3*(-1*a*d*f+-2*b*c*f+3*b*d*e)*log(c+d*x)+f*b^-1*d^-1*(a+b*x)^2//3*(c+d*x)^1//3+-1//3*3^(1/2)*b^-4//3*d^-5//3*(-1*a*d*f+-2*b*c*f+3*b*d*e)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^-1//3*d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3))
@test integrate((a+b*x)^-1//3*(c+d*x)^-2//3, x) == :(-3//2*b^-1//3*d^-2//3*log(-1+b^-1//3*d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3)+-1//2*b^-1//3*d^-2//3*log(c+d*x)+-1*3^(1/2)*b^-1//3*d^-2//3*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^-1//3*d^1//3*(a+b*x)^1//3*(c+d*x)^-1//3))
@test integrate((a+b*x)^-1//3*(c+d*x)^-2//3*(e+f*x)^-1, x) == :((1/2)*(b*e+-1*a*f)^-1//3*(d*e+-1*c*f)^-2//3*log(e+f*x)+-3//2*(b*e+-1*a*f)^-1//3*(d*e+-1*c*f)^-2//3*log(-1*(c+d*x)^1//3+(a+b*x)^1//3*(b*e+-1*a*f)^-1//3*(d*e+-1*c*f)^1//3)+-1*3^(1/2)*(b*e+-1*a*f)^-1//3*(d*e+-1*c*f)^-2//3*arctan(1//3*3^(1/2)+2//3*3^(1/2)*(a+b*x)^1//3*(c+d*x)^-1//3*(b*e+-1*a*f)^-1//3*(d*e+-1*c*f)^1//3))
@test integrate((a+b*x)^-1//3*(c+d*x)^-2//3*(e+f*x)^-2, x) == :(-1//2*(b*e+-1*a*f)^-4//3*(d*e+-1*c*f)^-5//3*(-1*b*c*f+-2*a*d*f+3*b*d*e)*log(-1*(c+d*x)^1//3+(a+b*x)^1//3*(b*e+-1*a*f)^-1//3*(d*e+-1*c*f)^1//3)+1//6*(b*e+-1*a*f)^-4//3*(d*e+-1*c*f)^-5//3*(-1*b*c*f+-2*a*d*f+3*b*d*e)*log(e+f*x)+-1//3*3^(1/2)*(b*e+-1*a*f)^-4//3*(d*e+-1*c*f)^-5//3*(-1*b*c*f+-2*a*d*f+3*b*d*e)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*(a+b*x)^1//3*(c+d*x)^-1//3*(b*e+-1*a*f)^-1//3*(d*e+-1*c*f)^1//3)+-1*f*(a+b*x)^2//3*(c+d*x)^1//3*(e+f*x)^-1*(b*e+-1*a*f)^-1*(d*e+-1*c*f)^-1)
@test integrate((a+b*x)^-1//3*(c+d*x)^-2//3*(e+f*x)^-3, x) == :(-1//6*(b*e+-1*a*f)^-7//3*(d*e+-1*c*f)^-8//3*(b^2*(2*c^2*f^2+9*d^2*e^2+-6*c*d*e*f)+5*a^2*d^2*f^2+-2*a*b*d*f*(-1*c*f+6*d*e))*log(-1*(c+d*x)^1//3+(a+b*x)^1//3*(b*e+-1*a*f)^-1//3*(d*e+-1*c*f)^1//3)+1//18*(b*e+-1*a*f)^-7//3*(d*e+-1*c*f)^-8//3*(b^2*(2*c^2*f^2+9*d^2*e^2+-6*c*d*e*f)+5*a^2*d^2*f^2+-2*a*b*d*f*(-1*c*f+6*d*e))*log(e+f*x)+-1//9*3^(1/2)*(b*e+-1*a*f)^-7//3*(d*e+-1*c*f)^-8//3*(b^2*(2*c^2*f^2+9*d^2*e^2+-6*c*d*e*f)+5*a^2*d^2*f^2+-2*a*b*d*f*(-1*c*f+6*d*e))*arctan(1//3*3^(1/2)+2//3*3^(1/2)*(a+b*x)^1//3*(c+d*x)^-1//3*(b*e+-1*a*f)^-1//3*(d*e+-1*c*f)^1//3)+-1*f*(a+b*x)^2//3*(c+d*x)^1//3*(e+f*x)^-2*(d*e+-1*c*f)^-1*(-2*a*f+2*b*e)^-1+-1//6*f*(a+b*x)^2//3*(c+d*x)^1//3*(e+f*x)^-1*(b*e+-1*a*f)^-2*(d*e+-1*c*f)^-2*(-5*a*d*f+-4*b*c*f+9*b*d*e))
@test integrate((a+b*x)^3*(c+d*x)^-1//3*(a*d+b*c+2*b*d*x)^-1//3, x) == :(3//20*d^-2*(a+b*x)^2*(c+d*x)^2//3*(a*d+b*c+2*b*d*x)^2//3+1//560*d^-4*(c+d*x)^2//3*(a*d+b*c+2*b*d*x)^2//3*(-9*a*d+9*b*c)*(-39*a*d+23*b*c+-16*b*d*x)+-81//112*b^-2//3*d^-6*((d*(a*d+3*b*c)+4*b*x*d^2)^2)^(1/2)*(d^2*(a*d+3*b*c+4*b*d*x)^2)^(1/2)*((c+d*x)*(a*d+b*c+2*b*d*x))^1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-1*(a*d+b*c+2*b*d*x)^-1//3*(a*d+3*b*c+4*b*d*x)^-1+-27//112*2^(1/2)*3^3//4*b^-2//3*d^-4*((d*(a*d+3*b*c)+4*b*x*d^2)^2)^(1/2)*(d^2*(a*d+3*b*c+4*b*d*x)^2)^-1//2*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^4//3+4*b^2//3*((c+d*x)*(a*d+b*(c+2*d*x)))^2//3+-2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((c+d*x)*(a*d+b*c+2*b*d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3))^-1//2*(c+d*x)^-1//3*(b*c+-1*a*d)^11//3*(a*d+b*c+2*b*d*x)^-1//3*(a*d+3*b*c+4*b*d*x)^-1*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)),-7+-4*3^(1/2))+81//224*3^1//4*b^-2//3*d^-4*((d*(a*d+3*b*c)+4*b*x*d^2)^2)^(1/2)*(d^2*(a*d+3*b*c+4*b*d*x)^2)^-1//2*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^4//3+4*b^2//3*((c+d*x)*(a*d+b*(c+2*d*x)))^2//3+-2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((c+d*x)*(a*d+b*c+2*b*d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x)^-1//3*(b*c+-1*a*d)^11//3*(a*d+b*c+2*b*d*x)^-1//3*(a*d+3*b*c+4*b*d*x)^-1*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)*Elliptic.E(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)),-7+-4*3^(1/2)))
@test integrate((a+b*x)^2*(c+d*x)^-1//3*(a*d+b*c+2*b*d*x)^-1//3, x) == :(-1//112*d^-3*(c+d*x)^2//3*(a*d+b*c+2*b*d*x)^2//3*(-45*a*d+45*b*c)+1//14*d^-2*(c+d*x)^2//3*(a*d+b*c+2*b*d*x)^2//3*(3a+3*b*x)+99//112*b^-2//3*d^-5*((d*(a*d+3*b*c)+4*b*x*d^2)^2)^(1/2)*(d^2*(a*d+3*b*c+4*b*d*x)^2)^(1/2)*((c+d*x)*(a*d+b*c+2*b*d*x))^1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^2*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-1*(a*d+b*c+2*b*d*x)^-1//3*(a*d+3*b*c+4*b*d*x)^-1+-99//224*3^1//4*b^-2//3*d^-3*((d*(a*d+3*b*c)+4*b*x*d^2)^2)^(1/2)*(d^2*(a*d+3*b*c+4*b*d*x)^2)^-1//2*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^4//3+4*b^2//3*((c+d*x)*(a*d+b*(c+2*d*x)))^2//3+-2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((c+d*x)*(a*d+b*c+2*b*d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x)^-1//3*(b*c+-1*a*d)^8//3*(a*d+b*c+2*b*d*x)^-1//3*(a*d+3*b*c+4*b*d*x)^-1*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)*Elliptic.E(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)),-7+-4*3^(1/2))+33//112*2^(1/2)*3^3//4*b^-2//3*d^-3*((d*(a*d+3*b*c)+4*b*x*d^2)^2)^(1/2)*(d^2*(a*d+3*b*c+4*b*d*x)^2)^-1//2*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^4//3+4*b^2//3*((c+d*x)*(a*d+b*(c+2*d*x)))^2//3+-2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((c+d*x)*(a*d+b*c+2*b*d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3))^-1//2*(c+d*x)^-1//3*(b*c+-1*a*d)^8//3*(a*d+b*c+2*b*d*x)^-1//3*(a*d+3*b*c+4*b*d*x)^-1*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)),-7+-4*3^(1/2)))
@test integrate((c+d*x)^-1//3*(a*d+b*c+2*b*d*x)^-1//3*(a+b*x), x) == :(3//8*d^-2*(c+d*x)^2//3*(a*d+b*c+2*b*d*x)^2//3+-1//8*b^-2//3*d^-4*((d*(a*d+3*b*c)+4*b*x*d^2)^2)^(1/2)*(d^2*(a*d+3*b*c+4*b*d*x)^2)^(1/2)*((c+d*x)*(a*d+b*c+2*b*d*x))^1//3*(c+d*x)^-1//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-1*(a*d+b*c+2*b*d*x)^-1//3*(a*d+3*b*c+4*b*d*x)^-1*(-9*a*d+9*b*c)+-3//8*2^(1/2)*3^3//4*b^-2//3*d^-2*((d*(a*d+3*b*c)+4*b*x*d^2)^2)^(1/2)*(d^2*(a*d+3*b*c+4*b*d*x)^2)^-1//2*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^4//3+4*b^2//3*((c+d*x)*(a*d+b*(c+2*d*x)))^2//3+-2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((c+d*x)*(a*d+b*c+2*b*d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3))^-1//2*(c+d*x)^-1//3*(b*c+-1*a*d)^5//3*(a*d+b*c+2*b*d*x)^-1//3*(a*d+3*b*c+4*b*d*x)^-1*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)),-7+-4*3^(1/2))+9//16*3^1//4*b^-2//3*d^-2*((d*(a*d+3*b*c)+4*b*x*d^2)^2)^(1/2)*(d^2*(a*d+3*b*c+4*b*d*x)^2)^-1//2*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^4//3+4*b^2//3*((c+d*x)*(a*d+b*(c+2*d*x)))^2//3+-2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((c+d*x)*(a*d+b*c+2*b*d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x)^-1//3*(b*c+-1*a*d)^5//3*(a*d+b*c+2*b*d*x)^-1//3*(a*d+3*b*c+4*b*d*x)^-1*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)*Elliptic.E(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)),-7+-4*3^(1/2)))
@test integrate((c+d*x)^-1//3*(a*d+b*c+2*b*d*x)^-1//3, x) == :(3//2*b^-2//3*d^-3*((d*(a*d+3*b*c)+4*b*x*d^2)^2)^(1/2)*(d^2*(a*d+3*b*c+4*b*d*x)^2)^(1/2)*((c+d*x)*(a*d+b*c+2*b*d*x))^1//3*(c+d*x)^-1//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-1*(a*d+b*c+2*b*d*x)^-1//3*(a*d+3*b*c+4*b*d*x)^-1+(1/2)*2^(1/2)*3^3//4*b^-2//3*d^-1*((d*(a*d+3*b*c)+4*b*x*d^2)^2)^(1/2)*(d^2*(a*d+3*b*c+4*b*d*x)^2)^-1//2*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^4//3+4*b^2//3*((c+d*x)*(a*d+b*(c+2*d*x)))^2//3+-2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((c+d*x)*(a*d+b*c+2*b*d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3))^-1//2*(c+d*x)^-1//3*(b*c+-1*a*d)^2//3*(a*d+b*c+2*b*d*x)^-1//3*(a*d+3*b*c+4*b*d*x)^-1*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)),-7+-4*3^(1/2))+-3//4*3^1//4*b^-2//3*d^-1*((d*(a*d+3*b*c)+4*b*x*d^2)^2)^(1/2)*(d^2*(a*d+3*b*c+4*b*d*x)^2)^-1//2*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^4//3+4*b^2//3*((c+d*x)*(a*d+b*(c+2*d*x)))^2//3+-2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((c+d*x)*(a*d+b*c+2*b*d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x)^-1//3*(b*c+-1*a*d)^2//3*(a*d+b*c+2*b*d*x)^-1//3*(a*d+3*b*c+4*b*d*x)^-1*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)*Elliptic.E(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)),-7+-4*3^(1/2)))
@test integrate((a+b*x)^-1*(c+d*x)^-1//3*(a*d+b*c+2*b*d*x)^-1//3, x) == :(-1//2*b^-2//3*(b*c+-1*a*d)^-2//3*log(a+b*x)+3//4*b^-2//3*(b*c+-1*a*d)^-2//3*log(-1*(a*d+b*c+2*b*d*x)^1//3+b^2//3*(c+d*x)^2//3*(b*c+-1*a*d)^-1//3)+-1//2*3^(1/2)*b^-2//3*(b*c+-1*a*d)^-2//3*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^2//3*(c+d*x)^2//3*(b*c+-1*a*d)^-1//3*(a*d+b*c+2*b*d*x)^-1//3))
@test integrate((a+b*x)^-2*(c+d*x)^-1//3*(a*d+b*c+2*b*d*x)^-1//3, x) == :((1/2)*d*b^-2//3*(b*c+-1*a*d)^-5//3*log(a+b*x)+-1*(a+b*x)^-1*(c+d*x)^2//3*(b*c+-1*a*d)^-2*(a*d+b*c+2*b*d*x)^2//3+-3//4*d*b^-2//3*(b*c+-1*a*d)^-5//3*log(-1*(a*d+b*c+2*b*d*x)^1//3+b^2//3*(c+d*x)^2//3*(b*c+-1*a*d)^-1//3)+(1/2)*d*3^(1/2)*b^-2//3*(b*c+-1*a*d)^-5//3*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^2//3*(c+d*x)^2//3*(b*c+-1*a*d)^-1//3*(a*d+b*c+2*b*d*x)^-1//3)+b^-2//3*d^-1*((d*(a*d+3*b*c)+4*b*x*d^2)^2)^(1/2)*(d^2*(a*d+3*b*c+4*b*d*x)^2)^(1/2)*((c+d*x)*(a*d+b*c+2*b*d*x))^1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-2*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-1*(a*d+b*c+2*b*d*x)^-1//3*(a*d+3*b*c+4*b*d*x)^-1+-1//2*d*3^1//4*b^-2//3*((d*(a*d+3*b*c)+4*b*x*d^2)^2)^(1/2)*(d^2*(a*d+3*b*c+4*b*d*x)^2)^-1//2*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^4//3+4*b^2//3*((c+d*x)*(a*d+b*(c+2*d*x)))^2//3+-2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((c+d*x)*(a*d+b*c+2*b*d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x)^-1//3*(b*c+-1*a*d)^-4//3*(a*d+b*c+2*b*d*x)^-1//3*(a*d+3*b*c+4*b*d*x)^-1*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)*Elliptic.E(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)),-7+-4*3^(1/2))+1//3*d*2^(1/2)*3^3//4*b^-2//3*((d*(a*d+3*b*c)+4*b*x*d^2)^2)^(1/2)*(d^2*(a*d+3*b*c+4*b*d*x)^2)^-1//2*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^4//3+4*b^2//3*((c+d*x)*(a*d+b*(c+2*d*x)))^2//3+-2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((c+d*x)*(a*d+b*c+2*b*d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3))^-1//2*(c+d*x)^-1//3*(b*c+-1*a*d)^-4//3*(a*d+b*c+2*b*d*x)^-1//3*(a*d+3*b*c+4*b*d*x)^-1*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)),-7+-4*3^(1/2)))
@test integrate((a+b*x)^-3*(c+d*x)^-1//3*(a*d+b*c+2*b*d*x)^-1//3, x) == :(b^-2//3*d^2*(b*c+-1*a*d)^-8//3*log(-1*(a*d+b*c+2*b*d*x)^1//3+b^2//3*(c+d*x)^2//3*(b*c+-1*a*d)^-1//3)+-2//3*b^-2//3*d^2*(b*c+-1*a*d)^-8//3*log(a+b*x)+-1//2*(a+b*x)^-2*(c+d*x)^2//3*(b*c+-1*a*d)^-2*(a*d+b*c+2*b*d*x)^2//3+2*d*(a+b*x)^-1*(c+d*x)^2//3*(b*c+-1*a*d)^-3*(a*d+b*c+2*b*d*x)^2//3+-2//3*3^(1/2)*b^-2//3*d^2*(b*c+-1*a*d)^-8//3*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^2//3*(c+d*x)^2//3*(b*c+-1*a*d)^-1//3*(a*d+b*c+2*b*d*x)^-1//3)+-2*b^-2//3*((d*(a*d+3*b*c)+4*b*x*d^2)^2)^(1/2)*(d^2*(a*d+3*b*c+4*b*d*x)^2)^(1/2)*((c+d*x)*(a*d+b*c+2*b*d*x))^1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-1*(a*d+b*c+2*b*d*x)^-1//3*(a*d+3*b*c+4*b*d*x)^-1+3^1//4*b^-2//3*d^2*((d*(a*d+3*b*c)+4*b*x*d^2)^2)^(1/2)*(d^2*(a*d+3*b*c+4*b*d*x)^2)^-1//2*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^4//3+4*b^2//3*((c+d*x)*(a*d+b*(c+2*d*x)))^2//3+-2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((c+d*x)*(a*d+b*c+2*b*d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x)^-1//3*(b*c+-1*a*d)^-7//3*(a*d+b*c+2*b*d*x)^-1//3*(a*d+3*b*c+4*b*d*x)^-1*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)*Elliptic.E(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)),-7+-4*3^(1/2))+-2//3*2^(1/2)*3^3//4*b^-2//3*d^2*((d*(a*d+3*b*c)+4*b*x*d^2)^2)^(1/2)*(d^2*(a*d+3*b*c+4*b*d*x)^2)^-1//2*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^4//3+4*b^2//3*((c+d*x)*(a*d+b*(c+2*d*x)))^2//3+-2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((c+d*x)*(a*d+b*c+2*b*d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3))^-1//2*(c+d*x)^-1//3*(b*c+-1*a*d)^-7//3*(a*d+b*c+2*b*d*x)^-1//3*(a*d+3*b*c+4*b*d*x)^-1*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)),-7+-4*3^(1/2)))
@test integrate((a+b*x)^3*(c+d*x)^-1//3*(a*d+b*c+2*b*d*x)^-4//3, x) == :(3//14*d^-2*(a+b*x)^2*(c+d*x)^2//3*(a*d+b*c+2*b*d*x)^-1//3+1//112*d^-4*(c+d*x)^2//3*(a*d+b*c+2*b*d*x)^-1//3*(-9*a*d+9*b*c)*(b*c+-7*a*d+-6*b*d*x)+81//112*b^-2//3*d^-6*((d*(a*d+3*b*c)+4*b*x*d^2)^2)^(1/2)*(d^2*(a*d+3*b*c+4*b*d*x)^2)^(1/2)*((c+d*x)*(a*d+b*c+2*b*d*x))^1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^2*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-1*(a*d+b*c+2*b*d*x)^-1//3*(a*d+3*b*c+4*b*d*x)^-1+-81//224*3^1//4*b^-2//3*d^-4*((d*(a*d+3*b*c)+4*b*x*d^2)^2)^(1/2)*(d^2*(a*d+3*b*c+4*b*d*x)^2)^-1//2*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^4//3+4*b^2//3*((c+d*x)*(a*d+b*(c+2*d*x)))^2//3+-2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((c+d*x)*(a*d+b*c+2*b*d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x)^-1//3*(b*c+-1*a*d)^8//3*(a*d+b*c+2*b*d*x)^-1//3*(a*d+3*b*c+4*b*d*x)^-1*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)*Elliptic.E(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)),-7+-4*3^(1/2))+27//112*2^(1/2)*3^3//4*b^-2//3*d^-4*((d*(a*d+3*b*c)+4*b*x*d^2)^2)^(1/2)*(d^2*(a*d+3*b*c+4*b*d*x)^2)^-1//2*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^4//3+4*b^2//3*((c+d*x)*(a*d+b*(c+2*d*x)))^2//3+-2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((c+d*x)*(a*d+b*c+2*b*d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3))^-1//2*(c+d*x)^-1//3*(b*c+-1*a*d)^8//3*(a*d+b*c+2*b*d*x)^-1//3*(a*d+3*b*c+4*b*d*x)^-1*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)),-7+-4*3^(1/2)))
@test integrate((a+b*x)^2*(c+d*x)^-1//3*(a*d+b*c+2*b*d*x)^-4//3, x) == :(3//16*d^-3*(c+d*x)^2//3*(a*d+b*c+2*b*d*x)^2//3+-1//4*d^-3*(c+d*x)^2//3*(a*d+b*c+2*b*d*x)^-1//3*(-3*a*d+3*b*c)+-1//16*b^-2//3*d^-5*((d*(a*d+3*b*c)+4*b*x*d^2)^2)^(1/2)*(d^2*(a*d+3*b*c+4*b*d*x)^2)^(1/2)*((c+d*x)*(a*d+b*c+2*b*d*x))^1//3*(c+d*x)^-1//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-1*(a*d+b*c+2*b*d*x)^-1//3*(a*d+3*b*c+4*b*d*x)^-1*(-9*a*d+9*b*c)+-3//16*2^(1/2)*3^3//4*b^-2//3*d^-3*((d*(a*d+3*b*c)+4*b*x*d^2)^2)^(1/2)*(d^2*(a*d+3*b*c+4*b*d*x)^2)^-1//2*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^4//3+4*b^2//3*((c+d*x)*(a*d+b*(c+2*d*x)))^2//3+-2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((c+d*x)*(a*d+b*c+2*b*d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3))^-1//2*(c+d*x)^-1//3*(b*c+-1*a*d)^5//3*(a*d+b*c+2*b*d*x)^-1//3*(a*d+3*b*c+4*b*d*x)^-1*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)),-7+-4*3^(1/2))+9//32*3^1//4*b^-2//3*d^-3*((d*(a*d+3*b*c)+4*b*x*d^2)^2)^(1/2)*(d^2*(a*d+3*b*c+4*b*d*x)^2)^-1//2*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^4//3+4*b^2//3*((c+d*x)*(a*d+b*(c+2*d*x)))^2//3+-2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((c+d*x)*(a*d+b*c+2*b*d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x)^-1//3*(b*c+-1*a*d)^5//3*(a*d+b*c+2*b*d*x)^-1//3*(a*d+3*b*c+4*b*d*x)^-1*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)*Elliptic.E(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)),-7+-4*3^(1/2)))
@test integrate((c+d*x)^-1//3*(a*d+b*c+2*b*d*x)^-4//3*(a+b*x), x) == :(3//2*d^-2*(c+d*x)^2//3*(a*d+b*c+2*b*d*x)^-1//3)
@test integrate((c+d*x)^-1//3*(a*d+b*c+2*b*d*x)^-4//3, x) == :(-3*d^-1*(c+d*x)^2//3*(b*c+-1*a*d)^-1*(a*d+b*c+2*b*d*x)^-1//3+3//2*b^-2//3*d^-3*((d*(a*d+3*b*c)+4*b*x*d^2)^2)^(1/2)*(d^2*(a*d+3*b*c+4*b*d*x)^2)^(1/2)*((c+d*x)*(a*d+b*c+2*b*d*x))^1//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-1*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-1*(a*d+b*c+2*b*d*x)^-1//3*(a*d+3*b*c+4*b*d*x)^-1+(1/2)*2^(1/2)*3^3//4*b^-2//3*d^-1*((d*(a*d+3*b*c)+4*b*x*d^2)^2)^(1/2)*(d^2*(a*d+3*b*c+4*b*d*x)^2)^-1//2*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^4//3+4*b^2//3*((c+d*x)*(a*d+b*(c+2*d*x)))^2//3+-2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((c+d*x)*(a*d+b*c+2*b*d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3))^-1//2*(c+d*x)^-1//3*(b*c+-1*a*d)^-1//3*(a*d+b*c+2*b*d*x)^-1//3*(a*d+3*b*c+4*b*d*x)^-1*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)*Elliptic.F(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)),-7+-4*3^(1/2))+-3//4*3^1//4*b^-2//3*d^-1*((d*(a*d+3*b*c)+4*b*x*d^2)^2)^(1/2)*(d^2*(a*d+3*b*c+4*b*d*x)^2)^-1//2*(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^4//3+4*b^2//3*((c+d*x)*(a*d+b*(c+2*d*x)))^2//3+-2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3*(b*c+-1*a*d)^2//3))^(1/2)*((c+d*x)*(a*d+b*c+2*b*d*x))^1//3*((b*c+-1*a*d)^2//3*((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-2*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x)^-1//3*(b*c+-1*a*d)^-1//3*(a*d+b*c+2*b*d*x)^-1//3*(a*d+3*b*c+4*b*d*x)^-1*((b*c+-1*a*d)^2//3+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)*Elliptic.E(arcsin(((b*c+-1*a*d)^2//3*(1+3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)^-1*((b*c+-1*a*d)^2//3*(1+-1*3^(1/2))+2*b^1//3*((c+d*x)*(a*d+b*(c+2*d*x)))^1//3)),-7+-4*3^(1/2)))
@test integrate((d+e*x)^-1*(d+-3*e*x)^-1//3*(d+3*e*x)^-1//3, x) == :(-3//8*d^-2//3*e^-1*log(-1*(d+3*e*x)^1//3+-1//2*d^-1//3*(d+-3*e*x)^2//3)+1//4*d^-2//3*e^-1*log(d+e*x)+1//4*3^(1/2)*d^-2//3*e^-1*arctan(1//3*3^(1/2)+-1//3*3^(1/2)*d^-1//3*(d+-3*e*x)^2//3*(d+3*e*x)^-1//3))
@test integrate((a+b*x)^4//3*(c+d*x)^-4//3*(e+f*x)^2, x) == :(3*d^-2*(a+b*x)^7//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-1*(d*e+-1*c*f)^2+-1//27*b^-1*d^-4*(a+b*x)^1//3*(c+d*x)^2//3*(-4*b^2*(27*d^2*e^2+35*c^2*f^2+-63*c*d*e*f)+4*a^2*d^2*f^2+-4*a*b*d*f*(-7*c*f+9*d*e))+-1//27*b^-5//3*d^-13//3*(-2*a*d+2*b*c)*(-1*b^2*(27*d^2*e^2+35*c^2*f^2+-63*c*d*e*f)+a^2*d^2*f^2+-1*a*b*d*f*(-7*c*f+9*d*e))*log(-1+b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3)+-1//81*b^-5//3*d^-13//3*(-2*a*d+2*b*c)*(-1*b^2*(27*d^2*e^2+35*c^2*f^2+-63*c*d*e*f)+a^2*d^2*f^2+-1*a*b*d*f*(-7*c*f+9*d*e))*log(a+b*x)+1//3*b^-1*d^-2*f^2*(a+b*x)^7//3*(c+d*x)^2//3+-1//81*3^(1/2)*b^-5//3*d^-13//3*(-4*a*d+4*b*c)*(-1*b^2*(27*d^2*e^2+35*c^2*f^2+-63*c*d*e*f)+a^2*d^2*f^2+-1*a*b*d*f*(-7*c*f+9*d*e))*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3)+1//9*b^-1*d^-3*(a+b*x)^4//3*(c+d*x)^2//3*(b*c+-1*a*d)^-1*(-1*b^2*(27*d^2*e^2+35*c^2*f^2+-63*c*d*e*f)+a^2*d^2*f^2+-1*a*b*d*f*(-7*c*f+9*d*e)))
@test integrate((a+b*x)^4//3*(c+d*x)^-4//3*(e+f*x), x) == :(1//3*d^-3*(a+b*x)^1//3*(c+d*x)^2//3*(-14*b*c*f+2*a*d*f+12*b*d*e)+d^-1*(a+b*x)^7//3*(c+d*x)^-1//3*(b*c+-1*a*d)^-1*(-3*c*f+3*d*e)+-1//2*d^-2*(a+b*x)^4//3*(c+d*x)^2//3*(b*c+-1*a*d)^-1*(a*d*f+-7*b*c*f+6*b*d*e)+1//3*b^-2//3*d^-10//3*(b*c+-1*a*d)*(a*d*f+-7*b*c*f+6*b*d*e)*log(-1+b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3)+1//9*b^-2//3*d^-10//3*(b*c+-1*a*d)*(a*d*f+-7*b*c*f+6*b*d*e)*log(a+b*x)+1//9*3^(1/2)*b^-2//3*d^-10//3*(-2*a*d+2*b*c)*(a*d*f+-7*b*c*f+6*b*d*e)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3))
@test integrate((a+b*x)^4//3*(c+d*x)^-4//3, x) == :(-3*d^-1*(a+b*x)^4//3*(c+d*x)^-1//3+2*b^1//3*d^-7//3*(b*c+-1*a*d)*log(-1+b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3)+4*b*d^-2*(a+b*x)^1//3*(c+d*x)^2//3+2//3*b^1//3*d^-7//3*(b*c+-1*a*d)*log(a+b*x)+4//3*3^(1/2)*b^1//3*d^-7//3*(b*c+-1*a*d)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3))
@test integrate((a+b*x)^4//3*(c+d*x)^-4//3*(e+f*x)^-1, x) == :(-3//2*b^4//3*d^-4//3*f^-1*log(-1+b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3)+-1//2*b^4//3*d^-4//3*f^-1*log(a+b*x)+-1//2*f^-1*(b*e+-1*a*f)^4//3*(d*e+-1*c*f)^-4//3*log(e+f*x)+3//2*f^-1*(b*e+-1*a*f)^4//3*(d*e+-1*c*f)^-4//3*log(-1*(a+b*x)^1//3+(c+d*x)^1//3*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^-1//3)+3^(1/2)*f^-1*(b*e+-1*a*f)^4//3*(d*e+-1*c*f)^-4//3*arctan(1//3*3^(1/2)+2//3*3^(1/2)*(a+b*x)^-1//3*(c+d*x)^1//3*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^-1//3)+d^-1*(a+b*x)^1//3*(c+d*x)^-1//3*(d*e+-1*c*f)^-1*(-3*a*d+3*b*c)+-1*3^(1/2)*b^4//3*d^-4//3*f^-1*arctan(1//3*3^(1/2)+2//3*3^(1/2)*b^1//3*d^-1//3*(a+b*x)^-1//3*(c+d*x)^1//3))
@test integrate((a+b*x)^4//3*(c+d*x)^-4//3*(e+f*x)^-2, x) == :((b*e+-1*a*f)^1//3*(d*e+-1*c*f)^-7//3*(-2*a*d+2*b*c)*log(-1*(a+b*x)^1//3+(c+d*x)^1//3*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^-1//3)+-3*(a+b*x)^4//3*(c+d*x)^-1//3*(e+f*x)^-1*(d*e+-1*c*f)^-1+-1//3*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^-7//3*(-2*a*d+2*b*c)*log(e+f*x)+(a+b*x)^1//3*(c+d*x)^2//3*(e+f*x)^-1*(d*e+-1*c*f)^-2*(-4*a*f+4*b*e)+1//3*3^(1/2)*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^-7//3*(-4*a*d+4*b*c)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*(a+b*x)^-1//3*(c+d*x)^1//3*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^-1//3))
@test integrate((a+b*x)^4//3*(c+d*x)^-4//3*(e+f*x)^-3, x) == :(-1//9*(b*e+-1*a*f)^-2//3*(d*e+-1*c*f)^-10//3*(b*c+-1*a*d)*(b*c*f+-7*a*d*f+6*b*d*e)*log(e+f*x)+1//3*(a+b*x)^1//3*(c+d*x)^2//3*(e+f*x)^-1*(d*e+-1*c*f)^-3*(-14*a*d*f+2*b*c*f+12*b*d*e)+1//3*(b*e+-1*a*f)^-2//3*(d*e+-1*c*f)^-10//3*(b*c+-1*a*d)*(b*c*f+-7*a*d*f+6*b*d*e)*log(-1*(a+b*x)^1//3+(c+d*x)^1//3*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^-1//3)+-1*(a+b*x)^4//3*(c+d*x)^2//3*(e+f*x)^-2*(d*e+-1*c*f)^-2*(-2*a*d+2*b*c)^-1*(b*c*f+-7*a*d*f+6*b*d*e)+3*d*(a+b*x)^7//3*(c+d*x)^-1//3*(e+f*x)^-2*(b*c+-1*a*d)^-1*(d*e+-1*c*f)^-1+1//9*3^(1/2)*(b*e+-1*a*f)^-2//3*(d*e+-1*c*f)^-10//3*(-2*a*d+2*b*c)*(b*c*f+-7*a*d*f+6*b*d*e)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*(a+b*x)^-1//3*(c+d*x)^1//3*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^-1//3))
@test integrate((a+b*x)^4//3*(c+d*x)^-4//3*(e+f*x)^-4, x) == :(-1//81*(b*e+-1*a*f)^-5//3*(d*e+-1*c*f)^-13//3*(-2*a*d+2*b*c)*(b^2*(-1*c^2*f^2+27*d^2*e^2+9*c*d*e*f)+35*a^2*d^2*f^2+-7*a*b*d*f*(c*f+9*d*e))*log(e+f*x)+1//9*(a+b*x)^1//3*(c+d*x)^2//3*(e+f*x)^-2*(d*e+-1*c*f)^-3*(-35*a*d*f+3*b*d*e+32*b*c*f)+1//27*(b*e+-1*a*f)^-5//3*(d*e+-1*c*f)^-13//3*(-2*a*d+2*b*c)*(b^2*(-1*c^2*f^2+27*d^2*e^2+9*c*d*e*f)+35*a^2*d^2*f^2+-7*a*b*d*f*(c*f+9*d*e))*log(-1*(a+b*x)^1//3+(c+d*x)^1//3*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^-1//3)+d^-1*(a+b*x)^1//3*(c+d*x)^-1//3*(e+f*x)^-3*(d*e+-1*c*f)^-1*(-3*a*d+3*b*c)+(a+b*x)^1//3*(c+d*x)^2//3*(e+f*x)^-1*(d*e+-1*c*f)^-4*(-27*a*f+27*b*e)^-1*(b^2*(2*c^2*f^2+9*d^2*e^2+129*c*d*e*f)+140*a^2*d^2*f^2+-7*a*b*d*f*(19*c*f+21*d*e))+1//3*d^-1*(a+b*x)^1//3*(c+d*x)^2//3*(e+f*x)^-3*(d*e+-1*c*f)^-2*(b*d*e+-10*a*d*f+9*b*c*f)+1//81*3^(1/2)*(b*e+-1*a*f)^-5//3*(d*e+-1*c*f)^-13//3*(-4*a*d+4*b*c)*(b^2*(-1*c^2*f^2+27*d^2*e^2+9*c*d*e*f)+35*a^2*d^2*f^2+-7*a*b*d*f*(c*f+9*d*e))*arctan(1//3*3^(1/2)+2//3*3^(1/2)*(a+b*x)^-1//3*(c+d*x)^1//3*(b*e+-1*a*f)^1//3*(d*e+-1*c*f)^-1//3))
@test integrate((c+d*x)^(-3+n)*(e+f*x)^(-1n)*(a+b*x), x) == :(d^-1*(2+-1n)^-1*(c+d*x)^(-2+n)*(e+f*x)^(1+-1n)*(d*e+-1*c*f)^-1*(b*c+-1*a*d)+d^-1*(1+-1n)^-1*(2+-1n)^-1*(c+d*x)^(-1+n)*(e+f*x)^(1+-1n)*(d*e+-1*c*f)^-2*(b*(c*f*(1+-1n)+-1*d*e*(2+-1n))+a*d*f))
@test integrate((c+d*x)^(-4+n)*(e+f*x)^(-1n)*(a+b*x), x) == :(d^-1*(3+-1n)^-1*(c+d*x)^(-3+n)*(e+f*x)^(1+-1n)*(d*e+-1*c*f)^-1*(b*c+-1*a*d)+d^-1*(2+-1n)^-1*(3+-1n)^-1*(c+d*x)^(-2+n)*(e+f*x)^(1+-1n)*(d*e+-1*c*f)^-2*(b*(c*f*(1+-1n)+-1*d*e*(3+-1n))+2*a*d*f)+-1*f*d^-1*(1+-1n)^-1*(2+-1n)^-1*(3+-1n)^-1*(c+d*x)^(-1+n)*(e+f*x)^(1+-1n)*(d*e+-1*c*f)^-3*(b*(c*f*(1+-1n)+-1*d*e*(3+-1n))+2*a*d*f))
@test integrate((c+d*x)^(-5+n)*(e+f*x)^(-1n)*(a+b*x), x) == :(d^-1*(4+-1n)^-1*(c+d*x)^(-4+n)*(e+f*x)^(1+-1n)*(d*e+-1*c*f)^-1*(b*c+-1*a*d)+d^-1*(3+-1n)^-1*(4+-1n)^-1*(c+d*x)^(-3+n)*(e+f*x)^(1+-1n)*(d*e+-1*c*f)^-2*(b*(c*f*(1+-1n)+-1*d*e*(4+-1n))+3*a*d*f)+-2*f*d^-1*(2+-1n)^-1*(3+-1n)^-1*(4+-1n)^-1*(c+d*x)^(-2+n)*(e+f*x)^(1+-1n)*(d*e+-1*c*f)^-3*(b*(c*f*(1+-1n)+-1*d*e*(4+-1n))+3*a*d*f)+2*d^-1*f^2*(1+-1n)^-1*(2+-1n)^-1*(3+-1n)^-1*(4+-1n)^-1*(c+d*x)^(-1+n)*(e+f*x)^(1+-1n)*(d*e+-1*c*f)^-4*(b*(c*f*(1+-1n)+-1*d*e*(4+-1n))+3*a*d*f))
@test integrate((a+b*x)^(-1n)*(e+f*x)^(-3+n)*(c+d*x), x) == :(-1*f^-1*(2+-1n)^-1*(a+b*x)^(1+-1n)*(e+f*x)^(-2+n)*(b*e+-1*a*f)^-1*(d*e+-1*c*f)+-1*f^-1*(1+-1n)^-1*(2+-1n)^-1*(a+b*x)^(1+-1n)*(e+f*x)^(-1+n)*(b*e+-1*a*f)^-2*(-1*b*(c*f+d*(e+-1*e*n))+a*d*f*(2+-1n)))
@test integrate((a+b*x)^(-1n)*(e+f*x)^(-4+n)*(c+d*x), x) == :(-1*f^-1*(3+-1n)^-1*(a+b*x)^(1+-1n)*(e+f*x)^(-3+n)*(b*e+-1*a*f)^-1*(d*e+-1*c*f)+f^-1*(2+-1n)^-1*(3+-1n)^-1*(a+b*x)^(1+-1n)*(e+f*x)^(-2+n)*(b*e+-1*a*f)^-2*(b*(2*c*f+d*e*(1+-1n))+-1*a*d*f*(3+-1n))+b*f^-1*(1+-1n)^-1*(2+-1n)^-1*(3+-1n)^-1*(a+b*x)^(1+-1n)*(e+f*x)^(-1+n)*(b*e+-1*a*f)^-3*(b*(2*c*f+d*e*(1+-1n))+-1*a*d*f*(3+-1n)))
@test integrate((a+b*x)^(-1n)*(e+f*x)^(-5+n)*(c+d*x), x) == :(-1*f^-1*(4+-1n)^-1*(a+b*x)^(1+-1n)*(e+f*x)^(-4+n)*(b*e+-1*a*f)^-1*(d*e+-1*c*f)+f^-1*(3+-1n)^-1*(4+-1n)^-1*(a+b*x)^(1+-1n)*(e+f*x)^(-3+n)*(b*e+-1*a*f)^-2*(b*(3*c*f+d*e*(1+-1n))+-1*a*d*f*(4+-1n))+2*b*f^-1*(2+-1n)^-1*(3+-1n)^-1*(4+-1n)^-1*(a+b*x)^(1+-1n)*(e+f*x)^(-2+n)*(b*e+-1*a*f)^-3*(b*(3*c*f+d*e*(1+-1n))+-1*a*d*f*(4+-1n))+2*b^2*f^-1*(1+-1n)^-1*(2+-1n)^-1*(3+-1n)^-1*(4+-1n)^-1*(a+b*x)^(1+-1n)*(e+f*x)^(-1+n)*(b*e+-1*a*f)^-4*(b*(3*c*f+d*e*(1+-1n))+-1*a*d*f*(4+-1n)))
@test integrate((a+b*x)^m*(c+d*x)^(-2+-1m), x) == :((1+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-1+-1m)*(b*c+-1*a*d)^-1)
@test integrate((a+b*x)^m*(c+d*x)^(-3+-1m)*(e+f*x), x) == :(d^-1*(2+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-2+-1m)*(b*c+-1*a*d)^-1*(d*e+-1*c*f)+-1*d^-1*(1+m)^-1*(2+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-1+-1m)*(b*c+-1*a*d)^-2*(-1*b*(d*e+c*f*(1+m))+a*d*f*(2+m)))
@test integrate((a+b*x)^m*(c+d*x)^(-3+-1m), x) == :((2+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-2+-1m)*(b*c+-1*a*d)^-1+b*(1+m)^-1*(2+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-1+-1m)*(b*c+-1*a*d)^-2)
@test integrate((a+b*x)^m*(c+d*x)^(-4+-1m)*(e+f*x)^2, x) == :(-1*f*b^-1*d^-1*(a+b*x)^(1+m)*(c+d*x)^(-3+-1m)*(e+f*x)+b^-1*d^-2*(2+m)^-1*(3+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-2+-1m)*(b*c+-1*a*d)^-2*(b^2*(2*d^2*e^2+c^2*f^2*(2+m^2+3m)+2*c*d*e*f*(1+m))+a^2*d^2*f^2*(6+m^2+5m)+-2*a*b*d*f*(3+m)*(d*e+c*f*(1+m)))+d^-2*(1+m)^-1*(2+m)^-1*(3+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-1+-1m)*(b*c+-1*a*d)^-3*(b^2*(2*d^2*e^2+c^2*f^2*(2+m^2+3m)+2*c*d*e*f*(1+m))+a^2*d^2*f^2*(6+m^2+5m)+-2*a*b*d*f*(3+m)*(d*e+c*f*(1+m)))+-1*b^-1*d^-2*(3+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-3+-1m)*(b*c+-1*a*d)^-1*(d*e+-1*c*f)*(-1*b*(d*e+c*f*(2+m))+a*d*f*(3+m)))
@test integrate((a+b*x)^m*(c+d*x)^(-4+-1m)*(e+f*x), x) == :(d^-1*(3+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-3+-1m)*(b*c+-1*a*d)^-1*(d*e+-1*c*f)+-1*d^-1*(2+m)^-1*(3+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-2+-1m)*(b*c+-1*a*d)^-2*(-1*b*(2*d*e+c*f*(1+m))+a*d*f*(3+m))+-1*b*d^-1*(1+m)^-1*(2+m)^-1*(3+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-1+-1m)*(b*c+-1*a*d)^-3*(-1*b*(2*d*e+c*f*(1+m))+a*d*f*(3+m)))
@test integrate((a+b*x)^m*(c+d*x)^(-4+-1m), x) == :((3+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-3+-1m)*(b*c+-1*a*d)^-1+2*b*(2+m)^-1*(3+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-2+-1m)*(b*c+-1*a*d)^-2+2*b^2*(1+m)^-1*(2+m)^-1*(3+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-1+-1m)*(b*c+-1*a*d)^-3)
@test integrate((a+b*x)^m*(c+d*x)^(-5+-1m)*(e+f*x)^3, x) == :((4+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-4+-1m)*(e+f*x)^3*(b*c+-1*a*d)^-1+-3*f*b^-1*d^-1*(4+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-3+-1m)*(b*c+-1*a*d)^-1*(e+f*x)*(b*e+-1*a*f)+b^-1*d^-2*(2+m)^-1*(3+m)^-1*(4+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-2+-1m)*(b*c+-1*a*d)^-3*(-3*a*f+3*b*e)*(b^2*(2*d^2*e^2+c^2*f^2*(2+m^2+3m)+2*c*d*e*f*(1+m))+a^2*d^2*f^2*(6+m^2+5m)+-2*a*b*d*f*(3+m)*(d*e+c*f*(1+m)))+d^-2*(1+m)^-1*(2+m)^-1*(3+m)^-1*(4+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-1+-1m)*(b*c+-1*a*d)^-4*(-3*a*f+3*b*e)*(b^2*(2*d^2*e^2+c^2*f^2*(2+m^2+3m)+2*c*d*e*f*(1+m))+a^2*d^2*f^2*(6+m^2+5m)+-2*a*b*d*f*(3+m)*(d*e+c*f*(1+m)))+-1*b^-1*d^-2*(3+m)^-1*(4+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-3+-1m)*(b*c+-1*a*d)^-2*(d*e+-1*c*f)*(-1*b*(d*e+c*f*(2+m))+a*d*f*(3+m))*(-3*a*f+3*b*e))
@test integrate((a+b*x)^m*(c+d*x)^(-5+-1m)*(e+f*x)^2, x) == :(-1//2*f*b^-1*d^-1*(a+b*x)^(1+m)*(c+d*x)^(-4+-1m)*(e+f*x)+d^-2*(2+m)^-1*(3+m)^-1*(4+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-2+-1m)*(b*c+-1*a*d)^-3*(b^2*(6*d^2*e^2+c^2*f^2*(2+m^2+3m)+4*c*d*e*f*(1+m))+a^2*d^2*f^2*(12+m^2+7m)+-2*a*b*d*f*(4+m)*(2*d*e+c*f*(1+m)))+(1/2)*b^-1*d^-2*(3+m)^-1*(4+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-3+-1m)*(b*c+-1*a*d)^-2*(b^2*(6*d^2*e^2+c^2*f^2*(2+m^2+3m)+4*c*d*e*f*(1+m))+a^2*d^2*f^2*(12+m^2+7m)+-2*a*b*d*f*(4+m)*(2*d*e+c*f*(1+m)))+-1//2*b^-1*d^-2*(4+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-4+-1m)*(b*c+-1*a*d)^-1*(d*e+-1*c*f)*(-1*b*(2*d*e+c*f*(2+m))+a*d*f*(4+m))+b*d^-2*(1+m)^-1*(2+m)^-1*(3+m)^-1*(4+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-1+-1m)*(b*c+-1*a*d)^-4*(b^2*(6*d^2*e^2+c^2*f^2*(2+m^2+3m)+4*c*d*e*f*(1+m))+a^2*d^2*f^2*(12+m^2+7m)+-2*a*b*d*f*(4+m)*(2*d*e+c*f*(1+m))))
@test integrate((a+b*x)^m*(c+d*x)^(-5+-1m)*(e+f*x), x) == :(d^-1*(4+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-4+-1m)*(b*c+-1*a*d)^-1*(d*e+-1*c*f)+-1*d^-1*(3+m)^-1*(4+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-3+-1m)*(b*c+-1*a*d)^-2*(-1*b*(3*d*e+c*f*(1+m))+a*d*f*(4+m))+-2*b*d^-1*(2+m)^-1*(3+m)^-1*(4+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-2+-1m)*(b*c+-1*a*d)^-3*(-1*b*(3*d*e+c*f*(1+m))+a*d*f*(4+m))+-2*b^2*d^-1*(1+m)^-1*(2+m)^-1*(3+m)^-1*(4+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-1+-1m)*(b*c+-1*a*d)^-4*(-1*b*(3*d*e+c*f*(1+m))+a*d*f*(4+m)))
@test integrate((a+b*x)^m*(c+d*x)^(-5+-1m), x) == :((4+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-4+-1m)*(b*c+-1*a*d)^-1+3*b*(3+m)^-1*(4+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-3+-1m)*(b*c+-1*a*d)^-2+6*b^2*(2+m)^-1*(3+m)^-1*(4+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-2+-1m)*(b*c+-1*a*d)^-3+6*b^3*(1+m)^-1*(2+m)^-1*(3+m)^-1*(4+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-1+-1m)*(b*c+-1*a*d)^-4)
@test integrate((a+b*x)^m*(c+d*x)^n*(f*x+b^-1*d^-1*(2+m+n)^-1*(a*d*f+b*c*f+a*d*f*m+b*c*f*n))^(-3+-1m+-1n), x) == :(b*d*f^-1*(1+m)^-1*(1+n)^-1*(a+b*x)^(1+m)*(c+d*x)^(1+n)*(b*c+-1*a*d)^-2*(f*x+f*b^-1*d^-1*(2+m+n)^-1*(a*d*(1+m)+b*c*(1+n)))^(-2+-1m+-1n)*(2+m+n))
@test integrate((a+b*x)^m*(c+d*x)^(-1+-1*d*b^-1*(d*e+-1*c*f)^-1*(1+m)*(b*e+-1*a*f))*(e+f*x)^(-1+f*b^-1*(d*e+-1*c*f)^-1*(1+m)*(b*c+-1*a*d)), x) == :(b*(1+m)^-1*(a+b*x)^(1+m)*(c+d*x)^(-1*d*b^-1*(d*e+-1*c*f)^-1*(1+m)*(b*e+-1*a*f))*(e+f*x)^(f*b^-1*(d*e+-1*c*f)^-1*(1+m)*(b*c+-1*a*d))*(b*c+-1*a*d)^-1*(b*e+-1*a*f)^-1)
@test integrate((a+b*x)^4*(d+e*x)^m*(A+B*x), x) == :(B*b^4*e^-6*(6+m)^-1*(d+e*x)^(6+m)+e^-6*(2+m)^-1*(d+e*x)^(2+m)*(b*d+-1*a*e)^3*(-1*B*a*e+-4*A*b*e+5*B*b*d)+-1*b^3*e^-6*(5+m)^-1*(d+e*x)^(5+m)*(-1*A*b*e+-4*B*a*e+5*B*b*d)+-1*e^-6*(1+m)^-1*(d+e*x)^(1+m)*(b*d+-1*a*e)^4*(B*d+-1*A*e)+-2*b*e^-6*(3+m)^-1*(d+e*x)^(3+m)*(b*d+-1*a*e)^2*(-3*A*b*e+-2*B*a*e+5*B*b*d)+2*b^2*e^-6*(4+m)^-1*(d+e*x)^(4+m)*(b*d+-1*a*e)*(-3*B*a*e+-2*A*b*e+5*B*b*d))
@test integrate((a+b*x)^3*(d+e*x)^m*(A+B*x), x) == :(B*b^3*e^-5*(5+m)^-1*(d+e*x)^(5+m)+e^-5*(1+m)^-1*(d+e*x)^(1+m)*(b*d+-1*a*e)^3*(B*d+-1*A*e)+-1*b^2*e^-5*(4+m)^-1*(d+e*x)^(4+m)*(-1*A*b*e+-3*B*a*e+4*B*b*d)+-1*e^-5*(2+m)^-1*(d+e*x)^(2+m)*(b*d+-1*a*e)^2*(-1*B*a*e+-3*A*b*e+4*B*b*d)+3*b*e^-5*(3+m)^-1*(d+e*x)^(3+m)*(b*d+-1*a*e)*(-1*A*b*e+-1*B*a*e+2*B*b*d))
@test integrate((a+b*x)^2*(d+e*x)^m*(A+B*x), x) == :(B*b^2*e^-4*(4+m)^-1*(d+e*x)^(4+m)+e^-4*(2+m)^-1*(d+e*x)^(2+m)*(b*d+-1*a*e)*(-1*B*a*e+-2*A*b*e+3*B*b*d)+-1*b*e^-4*(3+m)^-1*(d+e*x)^(3+m)*(-1*A*b*e+-2*B*a*e+3*B*b*d)+-1*e^-4*(1+m)^-1*(d+e*x)^(1+m)*(b*d+-1*a*e)^2*(B*d+-1*A*e))
@test integrate((d+e*x)^m*(A+B*x)*(a+b*x), x) == :(-1*e^-3*(2+m)^-1*(d+e*x)^(2+m)*(-1*A*b*e+-1*B*a*e+2*B*b*d)+B*b*e^-3*(3+m)^-1*(d+e*x)^(3+m)+e^-3*(1+m)^-1*(d+e*x)^(1+m)*(B*d+-1*A*e)*(b*d+-1*a*e))
@test integrate((d+e*x)^m*(A+B*x), x) == :(B*e^-2*(2+m)^-1*(d+e*x)^(2+m)+-1*e^-2*(1+m)^-1*(d+e*x)^(1+m)*(B*d+-1*A*e))
@test integrate((2+3x)^m*(3+5x)^3*(1+-2x), x) == :(-250*(2+3x)^(5+m)*(1215+243m)^-1+-185*(2+3x)^(3+m)*(243+81m)^-1+-7*(2+3x)^(1+m)*(243+243m)^-1+107*(2+3x)^(2+m)*(486+243m)^-1+1025*(2+3x)^(4+m)*(972+243m)^-1)
@test integrate((2+3x)^m*(3+5x)^2*(1+-2x), x) == :(-50*(2+3x)^(4+m)*(324+81m)^-1+-8*(2+3x)^(2+m)*(18+9m)^-1+7*(2+3x)^(1+m)*(81+81m)^-1+65*(2+3x)^(3+m)*(81+27m)^-1)
@test integrate((2+3x)^m*(1+-2x)*(3+5x), x) == :(-10*(2+3x)^(3+m)*(81+27m)^-1+-7*(2+3x)^(1+m)*(27+27m)^-1+37*(2+3x)^(2+m)*(54+27m)^-1)

max_stars_repo_path: test/1 Algebraic functions/1.1 Binomial products/1.1.1 Linear/1.1.1.3 (a+b x)^m (c+d x)^n (e+f x)^p.jl