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

@test integrate(x^2*(A+B*x^2)*(a+b*x^2), x) == :(1//5*x^5*(A*b+B*a)+1//3*A*a*x^3+1//7*B*b*x^7)
@test integrate(x*(A+B*x^2)*(a+b*x^2), x) == :(1//4*x^4*(A*b+B*a)+(1/2)*A*a*x^2+1//6*B*b*x^6)
@test integrate((A+B*x^2)*(a+b*x^2), x) == :(x^3*(1//3*A*b+1//3*B*a)+A*a*x+1//5*B*b*x^5)
@test integrate(x^-1*(A+B*x^2)*(a+b*x^2), x) == :((1/2)*x^2*(A*b+B*a)+A*a*log(x)+1//4*B*b*x^4)
@test integrate(x^-2*(A+B*x^2)*(a+b*x^2), x) == :(x*(A*b+B*a)+-1*A*a*x^-1+1//3*B*b*x^3)
@test integrate(x^-3*(A+B*x^2)*(a+b*x^2), x) == :((A*b+B*a)*log(x)+(1/2)*B*b*x^2+-1//2*A*a*x^-2)
@test integrate(x^-4*(A+B*x^2)*(a+b*x^2), x) == :(-1*x^-1*(A*b+B*a)+B*b*x+-1//3*A*a*x^-3)
@test integrate(x^-5*(A+B*x^2)*(a+b*x^2), x) == :(-1//2*x^-2*(A*b+B*a)+B*b*log(x)+-1//4*A*a*x^-4)
@test integrate(x^-6*(A+B*x^2)*(a+b*x^2), x) == :(-1//3*x^-3*(A*b+B*a)+-1*B*b*x^-1+-1//5*A*a*x^-5)
@test integrate(x^-7*(A+B*x^2)*(a+b*x^2), x) == :(-1//4*x^-4*(A*b+B*a)+-1//2*B*b*x^-2+-1//6*A*a*x^-6)
@test integrate(x^2*(a+b*x^2)^2*(A+B*x^2), x) == :(1//3*A*a^2*x^3+1//5*a*x^5*(B*a+2*A*b)+1//7*b*x^7*(A*b+2*B*a)+1//9*B*b^2*x^9)
@test integrate(x*(a+b*x^2)^2*(A+B*x^2), x) == :(1//6*b^-2*(a+b*x^2)^3*(A*b+-1*B*a)+1//8*B*b^-2*(a+b*x^2)^4)
@test integrate((a+b*x^2)^2*(A+B*x^2), x) == :(A*x*a^2+1//3*a*x^3*(B*a+2*A*b)+1//5*b*x^5*(A*b+2*B*a)+1//7*B*b^2*x^7)
@test integrate(x^-1*(a+b*x^2)^2*(A+B*x^2), x) == :(A*a^2*log(x)+1//4*A*b^2*x^4+1//6*B*b^-1*(a+b*x^2)^3+A*a*b*x^2)
@test integrate(x^-2*(a+b*x^2)^2*(A+B*x^2), x) == :(a*x*(B*a+2*A*b)+-1*A*a^2*x^-1+1//3*b*x^3*(A*b+2*B*a)+1//5*B*b^2*x^5)
@test integrate(x^-3*(a+b*x^2)^2*(A+B*x^2), x) == :(a*(B*a+2*A*b)*log(x)+(1/2)*b*x^2*(A*b+2*B*a)+-1//2*A*a^2*x^-2+1//4*B*b^2*x^4)
@test integrate(x^-4*(a+b*x^2)^2*(A+B*x^2), x) == :(b*x*(A*b+2*B*a)+-1*a*x^-1*(B*a+2*A*b)+-1//3*A*a^2*x^-3+1//3*B*b^2*x^3)
@test integrate(x^-5*(a+b*x^2)^2*(A+B*x^2), x) == :(b*(A*b+2*B*a)*log(x)+(1/2)*B*b^2*x^2+-1//2*a*x^-2*(B*a+2*A*b)+-1//4*A*a^2*x^-4)
@test integrate(x^-6*(a+b*x^2)^2*(A+B*x^2), x) == :(B*x*b^2+-1*b*x^-1*(A*b+2*B*a)+-1//3*a*x^-3*(B*a+2*A*b)+-1//5*A*a^2*x^-5)
@test integrate(x^-7*(a+b*x^2)^2*(A+B*x^2), x) == :(B*b^2*log(x)+-1//2*b*x^-2*(A*b+2*B*a)+-1//4*a*x^-4*(B*a+2*A*b)+-1//6*A*a^2*x^-6)
@test integrate(x^-8*(a+b*x^2)^2*(A+B*x^2), x) == :(-1*B*b^2*x^-1+-1//3*b*x^-3*(A*b+2*B*a)+-1//5*a*x^-5*(B*a+2*A*b)+-1//7*A*a^2*x^-7)
@test integrate(x^-9*(a+b*x^2)^2*(A+B*x^2), x) == :(-1//8*A*a^-1*x^-8*(a+b*x^2)^3+1//24*a^-2*x^-6*(a+b*x^2)^3*(A*b+-4*B*a))
@test integrate(x^9*(a+b*x^2)^5*(A+B*x^2), x) == :(1//10*A*a^5*x^10+1//12*a^4*x^12*(B*a+5*A*b)+1//20*b^4*x^20*(A*b+5*B*a)+1//22*B*b^5*x^22+5//8*a^2*b^2*x^16*(A*b+B*a)+5//14*b*a^3*x^14*(B*a+2*A*b)+5//18*a*b^3*x^18*(A*b+2*B*a))
@test integrate(x^8*(a+b*x^2)^5*(A+B*x^2), x) == :(1//9*A*a^5*x^9+1//11*a^4*x^11*(B*a+5*A*b)+1//19*b^4*x^19*(A*b+5*B*a)+1//21*B*b^5*x^21+2//3*a^2*b^2*x^15*(A*b+B*a)+5//13*b*a^3*x^13*(B*a+2*A*b)+5//17*a*b^3*x^17*(A*b+2*B*a))
@test integrate(x^7*(a+b*x^2)^5*(A+B*x^2), x) == :(1//18*b^-5*(a+b*x^2)^9*(A*b+-4*B*a)+1//20*B*b^-5*(a+b*x^2)^10+-3//16*a*b^-5*(a+b*x^2)^8*(A*b+-2*B*a)+-1//12*a^3*b^-5*(a+b*x^2)^6*(A*b+-1*B*a)+1//14*a^2*b^-5*(a+b*x^2)^7*(-4*B*a+3*A*b))
@test integrate(x^6*(a+b*x^2)^5*(A+B*x^2), x) == :(1//7*A*a^5*x^7+1//9*a^4*x^9*(B*a+5*A*b)+1//17*b^4*x^17*(A*b+5*B*a)+1//19*B*b^5*x^19+1//3*a*b^3*x^15*(A*b+2*B*a)+5//11*b*a^3*x^11*(B*a+2*A*b)+10//13*a^2*b^2*x^13*(A*b+B*a))
@test integrate(x^5*(a+b*x^2)^5*(A+B*x^2), x) == :(1//16*b^-4*(a+b*x^2)^8*(A*b+-3*B*a)+1//18*B*b^-4*(a+b*x^2)^9+-1//14*a*b^-4*(a+b*x^2)^7*(-3*B*a+2*A*b)+1//12*a^2*b^-4*(a+b*x^2)^6*(A*b+-1*B*a))
@test integrate(x^4*(a+b*x^2)^5*(A+B*x^2), x) == :(1//5*A*a^5*x^5+1//7*a^4*x^7*(B*a+5*A*b)+1//15*b^4*x^15*(A*b+5*B*a)+1//17*B*b^5*x^17+5//9*b*a^3*x^9*(B*a+2*A*b)+5//13*a*b^3*x^13*(A*b+2*B*a)+10//11*a^2*b^2*x^11*(A*b+B*a))
@test integrate(x^3*(a+b*x^2)^5*(A+B*x^2), x) == :(1//14*b^-3*(a+b*x^2)^7*(A*b+-2*B*a)+1//16*B*b^-3*(a+b*x^2)^8+-1//12*a*b^-3*(a+b*x^2)^6*(A*b+-1*B*a))
@test integrate(x^2*(a+b*x^2)^5*(A+B*x^2), x) == :(1//3*A*a^5*x^3+1//5*a^4*x^5*(B*a+5*A*b)+1//13*b^4*x^13*(A*b+5*B*a)+1//15*B*b^5*x^15+5//7*b*a^3*x^7*(B*a+2*A*b)+5//11*a*b^3*x^11*(A*b+2*B*a)+10//9*a^2*b^2*x^9*(A*b+B*a))
@test integrate(x*(a+b*x^2)^5*(A+B*x^2), x) == :(1//12*b^-2*(a+b*x^2)^6*(A*b+-1*B*a)+1//14*B*b^-2*(a+b*x^2)^7)
@test integrate((a+b*x^2)^5*(A+B*x^2), x) == :(A*x*a^5+1//3*a^4*x^3*(B*a+5*A*b)+1//11*b^4*x^11*(A*b+5*B*a)+1//13*B*b^5*x^13+b*a^3*x^5*(B*a+2*A*b)+5//9*a*b^3*x^9*(A*b+2*B*a)+10//7*a^2*b^2*x^7*(A*b+B*a))
@test integrate(x^-1*(a+b*x^2)^5*(A+B*x^2), x) == :(A*a^5*log(x)+1//10*A*b^5*x^10+1//12*B*b^-1*(a+b*x^2)^6+5//2*A*b*a^4*x^2+5//2*A*a^3*b^2*x^4+5//3*A*a^2*b^3*x^6+5//8*A*a*b^4*x^8)
@test integrate(x^-2*(a+b*x^2)^5*(A+B*x^2), x) == :(x*a^4*(B*a+5*A*b)+-1*A*a^5*x^-1+1//9*b^4*x^9*(A*b+5*B*a)+1//11*B*b^5*x^11+2*a^2*b^2*x^5*(A*b+B*a)+5//3*b*a^3*x^3*(B*a+2*A*b)+5//7*a*b^3*x^7*(A*b+2*B*a))
@test integrate(x^-3*(a+b*x^2)^5*(A+B*x^2), x) == :(a^4*(B*a+5*A*b)*log(x)+-1//2*A*a^5*x^-2+1//8*b^4*x^8*(A*b+5*B*a)+1//10*B*b^5*x^10+5//2*b*a^3*x^2*(B*a+2*A*b)+5//2*a^2*b^2*x^4*(A*b+B*a)+5//6*a*b^3*x^6*(A*b+2*B*a))
@test integrate(x^-4*(a+b*x^2)^5*(A+B*x^2), x) == :(-1*a^4*x^-1*(B*a+5*A*b)+-1//3*A*a^5*x^-3+1//7*b^4*x^7*(A*b+5*B*a)+1//9*B*b^5*x^9+a*b^3*x^5*(A*b+2*B*a)+5*b*x*a^3*(B*a+2*A*b)+10//3*a^2*b^2*x^3*(A*b+B*a))
@test integrate(x^-5*(a+b*x^2)^5*(A+B*x^2), x) == :(-1//2*a^4*x^-2*(B*a+5*A*b)+-1//4*A*a^5*x^-4+1//6*b^4*x^6*(A*b+5*B*a)+1//8*B*b^5*x^8+5*b*a^3*(B*a+2*A*b)*log(x)+5*a^2*b^2*x^2*(A*b+B*a)+5//4*a*b^3*x^4*(A*b+2*B*a))
@test integrate(x^-6*(a+b*x^2)^5*(A+B*x^2), x) == :(-1//3*a^4*x^-3*(B*a+5*A*b)+-1//5*A*a^5*x^-5+1//5*b^4*x^5*(A*b+5*B*a)+1//7*B*b^5*x^7+-5*b*a^3*x^-1*(B*a+2*A*b)+10*x*a^2*b^2*(A*b+B*a)+5//3*a*b^3*x^3*(A*b+2*B*a))
@test integrate(x^-7*(a+b*x^2)^5*(A+B*x^2), x) == :(-1//4*a^4*x^-4*(B*a+5*A*b)+-1//6*A*a^5*x^-6+1//4*b^4*x^4*(A*b+5*B*a)+1//6*B*b^5*x^6+10*a^2*b^2*(A*b+B*a)*log(x)+-5//2*b*a^3*x^-2*(B*a+2*A*b)+5//2*a*b^3*x^2*(A*b+2*B*a))
@test integrate(x^-8*(a+b*x^2)^5*(A+B*x^2), x) == :(-1//5*a^4*x^-5*(B*a+5*A*b)+-1//7*A*a^5*x^-7+1//3*b^4*x^3*(A*b+5*B*a)+1//5*B*b^5*x^5+-10*a^2*b^2*x^-1*(A*b+B*a)+5*a*x*b^3*(A*b+2*B*a)+-5//3*b*a^3*x^-3*(B*a+2*A*b))
@test integrate(x^-9*(a+b*x^2)^5*(A+B*x^2), x) == :((1/2)*b^4*x^2*(A*b+5*B*a)+-1//6*a^4*x^-6*(B*a+5*A*b)+-1//8*A*a^5*x^-8+1//4*B*b^5*x^4+-5*a^2*b^2*x^-2*(A*b+B*a)+5*a*b^3*(A*b+2*B*a)*log(x)+-5//4*b*a^3*x^-4*(B*a+2*A*b))
@test integrate(x^-10*(a+b*x^2)^5*(A+B*x^2), x) == :(x*b^4*(A*b+5*B*a)+-1//7*a^4*x^-7*(B*a+5*A*b)+-1//9*A*a^5*x^-9+1//3*B*b^5*x^3+-1*b*a^3*x^-5*(B*a+2*A*b)+-5*a*b^3*x^-1*(A*b+2*B*a)+-10//3*a^2*b^2*x^-3*(A*b+B*a))
@test integrate(x^-11*(a+b*x^2)^5*(A+B*x^2), x) == :(b^4*(A*b+5*B*a)*log(x)+(1/2)*B*b^5*x^2+-1//8*a^4*x^-8*(B*a+5*A*b)+-1//10*A*a^5*x^-10+-5//2*a*b^3*x^-2*(A*b+2*B*a)+-5//2*a^2*b^2*x^-4*(A*b+B*a)+-5//6*b*a^3*x^-6*(B*a+2*A*b))
@test integrate(x^-12*(a+b*x^2)^5*(A+B*x^2), x) == :(B*x*b^5+-1*b^4*x^-1*(A*b+5*B*a)+-1//9*a^4*x^-9*(B*a+5*A*b)+-1//11*A*a^5*x^-11+-2*a^2*b^2*x^-5*(A*b+B*a)+-5//3*a*b^3*x^-3*(A*b+2*B*a)+-5//7*b*a^3*x^-7*(B*a+2*A*b))
@test integrate(x^-13*(a+b*x^2)^5*(A+B*x^2), x) == :(B*b^5*log(x)+-1//10*B*a^5*x^-10+-5//2*B*a*b^4*x^-2+-5//2*B*a^2*b^3*x^-4+-5//3*B*a^3*b^2*x^-6+-5//8*B*b*a^4*x^-8+-1//12*A*a^-1*x^-12*(a+b*x^2)^6)
@test integrate(x^-14*(a+b*x^2)^5*(A+B*x^2), x) == :(-1*B*b^5*x^-1+-1//3*b^4*x^-3*(A*b+5*B*a)+-1//11*a^4*x^-11*(B*a+5*A*b)+-1//13*A*a^5*x^-13+-1*a*b^3*x^-5*(A*b+2*B*a)+-10//7*a^2*b^2*x^-7*(A*b+B*a)+-5//9*b*a^3*x^-9*(B*a+2*A*b))
@test integrate(x^-15*(a+b*x^2)^5*(A+B*x^2), x) == :(-1//14*A*a^-1*x^-14*(a+b*x^2)^6+1//84*a^-2*x^-12*(a+b*x^2)^6*(A*b+-7*B*a))
@test integrate(x^-16*(a+b*x^2)^5*(A+B*x^2), x) == :(-1//3*B*b^5*x^-3+-1//5*b^4*x^-5*(A*b+5*B*a)+-1//13*a^4*x^-13*(B*a+5*A*b)+-1//15*A*a^5*x^-15+-10//9*a^2*b^2*x^-9*(A*b+B*a)+-5//7*a*b^3*x^-7*(A*b+2*B*a)+-5//11*b*a^3*x^-11*(B*a+2*A*b))
@test integrate(x^-17*(a+b*x^2)^5*(A+B*x^2), x) == :(-1//16*A*a^-1*x^-16*(a+b*x^2)^6+1//56*a^-2*x^-14*(a+b*x^2)^6*(A*b+-4*B*a)+-1//336*b*a^-3*x^-12*(a+b*x^2)^6*(A*b+-4*B*a))
@test integrate(x^-18*(a+b*x^2)^5*(A+B*x^2), x) == :(-1//5*B*b^5*x^-5+-1//7*b^4*x^-7*(A*b+5*B*a)+-1//15*a^4*x^-15*(B*a+5*A*b)+-1//17*A*a^5*x^-17+-10//11*a^2*b^2*x^-11*(A*b+B*a)+-5//9*a*b^3*x^-9*(A*b+2*B*a)+-5//13*b*a^3*x^-13*(B*a+2*A*b))
@test integrate(x^-19*(a+b*x^2)^5*(A+B*x^2), x) == :(-1//6*B*b^5*x^-6+-1//8*b^4*x^-8*(A*b+5*B*a)+-1//16*a^4*x^-16*(B*a+5*A*b)+-1//18*A*a^5*x^-18+-5//6*a^2*b^2*x^-12*(A*b+B*a)+-5//14*b*a^3*x^-14*(B*a+2*A*b)+-1//2*a*b^3*x^-10*(A*b+2*B*a))
@test integrate(x^-20*(a+b*x^2)^5*(A+B*x^2), x) == :(-1//7*B*b^5*x^-7+-1//9*b^4*x^-9*(A*b+5*B*a)+-1//17*a^4*x^-17*(B*a+5*A*b)+-1//19*A*a^5*x^-19+-10//13*a^2*b^2*x^-13*(A*b+B*a)+-5//11*a*b^3*x^-11*(A*b+2*B*a)+-1//3*b*a^3*x^-15*(B*a+2*A*b))
@test integrate(x^-21*(a+b*x^2)^5*(A+B*x^2), x) == :(-1//8*B*b^5*x^-8+-1//10*b^4*x^-10*(A*b+5*B*a)+-1//18*a^4*x^-18*(B*a+5*A*b)+-1//20*A*a^5*x^-20+-5//7*a^2*b^2*x^-14*(A*b+B*a)+-5//12*a*b^3*x^-12*(A*b+2*B*a)+-5//16*b*a^3*x^-16*(B*a+2*A*b))
@test integrate(x^-22*(a+b*x^2)^5*(A+B*x^2), x) == :(-1//9*B*b^5*x^-9+-1//11*b^4*x^-11*(A*b+5*B*a)+-1//19*a^4*x^-19*(B*a+5*A*b)+-1//21*A*a^5*x^-21+-5//13*a*b^3*x^-13*(A*b+2*B*a)+-5//17*b*a^3*x^-17*(B*a+2*A*b)+-2//3*a^2*b^2*x^-15*(A*b+B*a))
@test integrate(x^-23*(a+b*x^2)^5*(A+B*x^2), x) == :(-1//10*B*b^5*x^-10+-1//12*b^4*x^-12*(A*b+5*B*a)+-1//20*a^4*x^-20*(B*a+5*A*b)+-1//22*A*a^5*x^-22+-5//8*a^2*b^2*x^-16*(A*b+B*a)+-5//14*a*b^3*x^-14*(A*b+2*B*a)+-5//18*b*a^3*x^-18*(B*a+2*A*b))
@test integrate(x^6*(a+b*x^2)^-1*(A+B*x^2), x) == :(1//5*b^-2*x^5*(A*b+-1*B*a)+1//7*B*b^-1*x^7+x*a^2*b^-4*(A*b+-1*B*a)+-1*a^5//2*b^-9//2*(A*b+-1*B*a)*arctan(x*a^-1//2*b^(1/2))+-1//3*a*b^-3*x^3*(A*b+-1*B*a))
@test integrate(x^5*(a+b*x^2)^-1*(A+B*x^2), x) == :(1//4*b^-2*x^4*(A*b+-1*B*a)+1//6*B*b^-1*x^6+(1/2)*a^2*b^-4*(A*b+-1*B*a)*log(a+b*x^2)+-1//2*a*b^-3*x^2*(A*b+-1*B*a))
@test integrate(x^4*(a+b*x^2)^-1*(A+B*x^2), x) == :(1//3*b^-2*x^3*(A*b+-1*B*a)+1//5*B*b^-1*x^5+a^3//2*b^-7//2*(A*b+-1*B*a)*arctan(x*a^-1//2*b^(1/2))+-1*a*x*b^-3*(A*b+-1*B*a))
@test integrate(x^3*(a+b*x^2)^-1*(A+B*x^2), x) == :((1/2)*b^-2*x^2*(A*b+-1*B*a)+1//4*B*b^-1*x^4+-1//2*a*b^-3*(A*b+-1*B*a)*log(a+b*x^2))
@test integrate(x^2*(a+b*x^2)^-1*(A+B*x^2), x) == :(x*b^-2*(A*b+-1*B*a)+1//3*B*b^-1*x^3+-1*a^(1/2)*b^-5//2*(A*b+-1*B*a)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x*(a+b*x^2)^-1*(A+B*x^2), x) == :((1/2)*B*b^-1*x^2+(1/2)*b^-2*(A*b+-1*B*a)*log(a+b*x^2))
@test integrate((a+b*x^2)^-1*(A+B*x^2), x) == :(B*x*b^-1+a^-1//2*b^-3//2*(A*b+-1*B*a)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-1*(a+b*x^2)^-1*(A+B*x^2), x) == :(A*a^-1*log(x)+-1//2*a^-1*b^-1*(A*b+-1*B*a)*log(a+b*x^2))
@test integrate(x^-2*(a+b*x^2)^-1*(A+B*x^2), x) == :(-1*A*a^-1*x^-1+-1*a^-3//2*b^-1//2*(A*b+-1*B*a)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-3*(a+b*x^2)^-1*(A+B*x^2), x) == :((1/2)*a^-2*(A*b+-1*B*a)*log(a+b*x^2)+-1*a^-2*(A*b+-1*B*a)*log(x)+-1//2*A*a^-1*x^-2)
@test integrate(x^-4*(a+b*x^2)^-1*(A+B*x^2), x) == :(a^-2*x^-1*(A*b+-1*B*a)+-1//3*A*a^-1*x^-3+a^-5//2*b^(1/2)*(A*b+-1*B*a)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-5*(a+b*x^2)^-1*(A+B*x^2), x) == :((1/2)*a^-2*x^-2*(A*b+-1*B*a)+-1//4*A*a^-1*x^-4+b*a^-3*(A*b+-1*B*a)*log(x)+-1//2*b*a^-3*(A*b+-1*B*a)*log(a+b*x^2))
@test integrate(x^-6*(a+b*x^2)^-1*(A+B*x^2), x) == :(-1//5*A*a^-1*x^-5+1//3*a^-2*x^-3*(A*b+-1*B*a)+-1*b*a^-3*x^-1*(A*b+-1*B*a)+-1*a^-7//2*b^3//2*(A*b+-1*B*a)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-7*(a+b*x^2)^-1*(A+B*x^2), x) == :(-1//6*A*a^-1*x^-6+1//4*a^-2*x^-4*(A*b+-1*B*a)+(1/2)*a^-4*b^2*(A*b+-1*B*a)*log(a+b*x^2)+-1*a^-4*b^2*(A*b+-1*B*a)*log(x)+-1//2*b*a^-3*x^-2*(A*b+-1*B*a))
@test integrate(x^-8*(a+b*x^2)^-1*(A+B*x^2), x) == :(-1//7*A*a^-1*x^-7+1//5*a^-2*x^-5*(A*b+-1*B*a)+a^-4*b^2*x^-1*(A*b+-1*B*a)+a^-9//2*b^5//2*(A*b+-1*B*a)*arctan(x*a^-1//2*b^(1/2))+-1//3*b*a^-3*x^-3*(A*b+-1*B*a))
@test integrate(x^9*(a+b*x^2)^-2*(A+B*x^2), x) == :(1//6*b^-3*x^6*(A*b+-2*B*a)+1//8*B*b^-2*x^8+(1/2)*a^2*b^-5*x^2*(-4*B*a+3*A*b)+-1//2*a^3*b^-6*(-5*B*a+4*A*b)*log(a+b*x^2)+-1//2*a^4*b^-6*(a+b*x^2)^-1*(A*b+-1*B*a)+-1//4*a*b^-4*x^4*(-3*B*a+2*A*b))
@test integrate(x^8*(a+b*x^2)^-2*(A+B*x^2), x) == :(1//5*b^-3*x^5*(A*b+-2*B*a)+1//7*B*b^-2*x^7+x*a^2*b^-5*(-4*B*a+3*A*b)+-1//2*a^5//2*b^-11//2*(-9*B*a+7*A*b)*arctan(x*a^-1//2*b^(1/2))+-1//3*a*b^-4*x^3*(-3*B*a+2*A*b)+(1/2)*x*a^3*b^-5*(a+b*x^2)^-1*(A*b+-1*B*a))
@test integrate(x^7*(a+b*x^2)^-2*(A+B*x^2), x) == :(1//4*b^-3*x^4*(A*b+-2*B*a)+1//6*B*b^-2*x^6+(1/2)*a^2*b^-5*(-4*B*a+3*A*b)*log(a+b*x^2)+(1/2)*a^3*b^-5*(a+b*x^2)^-1*(A*b+-1*B*a)+-1//2*a*b^-4*x^2*(-3*B*a+2*A*b))
@test integrate(x^6*(a+b*x^2)^-2*(A+B*x^2), x) == :(1//3*b^-3*x^3*(A*b+-2*B*a)+1//5*B*b^-2*x^5+(1/2)*a^3//2*b^-9//2*(-7*B*a+5*A*b)*arctan(x*a^-1//2*b^(1/2))+-1*a*x*b^-4*(-3*B*a+2*A*b)+-1//2*x*a^2*b^-4*(a+b*x^2)^-1*(A*b+-1*B*a))
@test integrate(x^5*(a+b*x^2)^-2*(A+B*x^2), x) == :((1/2)*b^-3*x^2*(A*b+-2*B*a)+1//4*B*b^-2*x^4+-1//2*a*b^-4*(-3*B*a+2*A*b)*log(a+b*x^2)+-1//2*a^2*b^-4*(a+b*x^2)^-1*(A*b+-1*B*a))
@test integrate(x^4*(a+b*x^2)^-2*(A+B*x^2), x) == :(x*b^-3*(A*b+-2*B*a)+1//3*B*b^-2*x^3+-1//2*a^(1/2)*b^-7//2*(-5*B*a+3*A*b)*arctan(x*a^-1//2*b^(1/2))+(1/2)*a*x*b^-3*(a+b*x^2)^-1*(A*b+-1*B*a))
@test integrate(x^3*(a+b*x^2)^-2*(A+B*x^2), x) == :((1/2)*B*b^-2*x^2+(1/2)*b^-3*(A*b+-2*B*a)*log(a+b*x^2)+(1/2)*a*b^-3*(a+b*x^2)^-1*(A*b+-1*B*a))
@test integrate(x^2*(a+b*x^2)^-2*(A+B*x^2), x) == :(B*x*b^-2+(1/2)*a^-1//2*b^-5//2*(A*b+-3*B*a)*arctan(x*a^-1//2*b^(1/2))+-1//2*x*b^-2*(a+b*x^2)^-1*(A*b+-1*B*a))
@test integrate(x*(a+b*x^2)^-2*(A+B*x^2), x) == :((1/2)*B*b^-2*log(a+b*x^2)+-1//2*b^-2*(a+b*x^2)^-1*(A*b+-1*B*a))
@test integrate((a+b*x^2)^-2*(A+B*x^2), x) == :((1/2)*a^-3//2*b^-3//2*(A*b+B*a)*arctan(x*a^-1//2*b^(1/2))+(1/2)*x*a^-1*b^-1*(a+b*x^2)^-1*(A*b+-1*B*a))
@test integrate(x^-1*(a+b*x^2)^-2*(A+B*x^2), x) == :(A*a^-2*log(x)+-1//2*A*a^-2*log(a+b*x^2)+(1/2)*a^-1*b^-1*(a+b*x^2)^-1*(A*b+-1*B*a))
@test integrate(x^-2*(a+b*x^2)^-2*(A+B*x^2), x) == :(-1*A*a^-2*x^-1+-1//2*x*a^-2*(a+b*x^2)^-1*(A*b+-1*B*a)+-1//2*a^-5//2*b^-1//2*(-1*B*a+3*A*b)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-3*(a+b*x^2)^-2*(A+B*x^2), x) == :((1/2)*a^-3*(-1*B*a+2*A*b)*log(a+b*x^2)+-1*a^-3*(-1*B*a+2*A*b)*log(x)+-1//2*A*a^-2*x^-2+-1//2*a^-2*(a+b*x^2)^-1*(A*b+-1*B*a))
@test integrate(x^-4*(a+b*x^2)^-2*(A+B*x^2), x) == :(a^-3*x^-1*(-1*B*a+2*A*b)+-1//3*A*a^-2*x^-3+(1/2)*a^-7//2*b^(1/2)*(-3*B*a+5*A*b)*arctan(x*a^-1//2*b^(1/2))+(1/2)*b*x*a^-3*(a+b*x^2)^-1*(A*b+-1*B*a))
@test integrate(x^-5*(a+b*x^2)^-2*(A+B*x^2), x) == :((1/2)*a^-3*x^-2*(-1*B*a+2*A*b)+-1//4*A*a^-2*x^-4+b*a^-4*(-2*B*a+3*A*b)*log(x)+(1/2)*b*a^-3*(a+b*x^2)^-1*(A*b+-1*B*a)+-1//2*b*a^-4*(-2*B*a+3*A*b)*log(a+b*x^2))
@test integrate(x^-6*(a+b*x^2)^-2*(A+B*x^2), x) == :(-1//5*A*a^-2*x^-5+1//3*a^-3*x^-3*(-1*B*a+2*A*b)+-1*b*a^-4*x^-1*(-2*B*a+3*A*b)+-1//2*a^-9//2*b^3//2*(-5*B*a+7*A*b)*arctan(x*a^-1//2*b^(1/2))+-1//2*x*a^-4*b^2*(a+b*x^2)^-1*(A*b+-1*B*a))
@test integrate(x^-7*(a+b*x^2)^-2*(A+B*x^2), x) == :(-1//6*A*a^-2*x^-6+1//4*a^-3*x^-4*(-1*B*a+2*A*b)+(1/2)*a^-5*b^2*(-3*B*a+4*A*b)*log(a+b*x^2)+-1*a^-5*b^2*(-3*B*a+4*A*b)*log(x)+-1//2*b*a^-4*x^-2*(-2*B*a+3*A*b)+-1//2*a^-4*b^2*(a+b*x^2)^-1*(A*b+-1*B*a))
@test integrate(x^11*(a+b*x^2)^-3*(A+B*x^2), x) == :(1//6*b^-4*x^6*(A*b+-3*B*a)+1//8*B*b^-3*x^8+a^2*b^-6*x^2*(-5*B*a+3*A*b)+-5//2*a^3*b^-7*(-3*B*a+2*A*b)*log(a+b*x^2)+-3//4*a*b^-5*x^4*(A*b+-2*B*a)+-1//2*a^4*b^-7*(a+b*x^2)^-1*(-6*B*a+5*A*b)+1//4*a^5*b^-7*(a+b*x^2)^-2*(A*b+-1*B*a))
@test integrate(x^9*(a+b*x^2)^-3*(A+B*x^2), x) == :(1//4*b^-4*x^4*(A*b+-3*B*a)+1//6*B*b^-3*x^6+a^2*b^-6*(-5*B*a+3*A*b)*log(a+b*x^2)+(1/2)*a^3*b^-6*(a+b*x^2)^-1*(-5*B*a+4*A*b)+-3//2*a*b^-5*x^2*(A*b+-2*B*a)+-1//4*a^4*b^-6*(a+b*x^2)^-2*(A*b+-1*B*a))
@test integrate(x^7*(a+b*x^2)^-3*(A+B*x^2), x) == :((1/2)*b^-4*x^2*(A*b+-3*B*a)+1//4*B*b^-3*x^4+-3//2*a*b^-5*(A*b+-2*B*a)*log(a+b*x^2)+-1//2*a^2*b^-5*(a+b*x^2)^-1*(-4*B*a+3*A*b)+1//4*a^3*b^-5*(a+b*x^2)^-2*(A*b+-1*B*a))
@test integrate(x^5*(a+b*x^2)^-3*(A+B*x^2), x) == :((1/2)*B*b^-3*x^2+(1/2)*b^-4*(A*b+-3*B*a)*log(a+b*x^2)+(1/2)*a*b^-4*(a+b*x^2)^-1*(-3*B*a+2*A*b)+-1//4*a^2*b^-4*(a+b*x^2)^-2*(A*b+-1*B*a))
@test integrate(x^3*(a+b*x^2)^-3*(A+B*x^2), x) == :((1/2)*B*b^-3*log(a+b*x^2)+-1//2*b^-3*(a+b*x^2)^-1*(A*b+-2*B*a)+1//4*a*b^-3*(a+b*x^2)^-2*(A*b+-1*B*a))
@test integrate(x*(a+b*x^2)^-3*(A+B*x^2), x) == :(-1*(A+B*x^2)^2*(a+b*x^2)^-2*(-4*B*a+4*A*b)^-1)
@test integrate(x^-1*(a+b*x^2)^-3*(A+B*x^2), x) == :(A*a^-3*log(x)+(1/2)*A*a^-2*(a+b*x^2)^-1+-1//2*A*a^-3*log(a+b*x^2)+1//4*a^-1*b^-1*(a+b*x^2)^-2*(A*b+-1*B*a))
@test integrate(x^-3*(a+b*x^2)^-3*(A+B*x^2), x) == :((1/2)*a^-4*(-1*B*a+3*A*b)*log(a+b*x^2)+-1*a^-4*(-1*B*a+3*A*b)*log(x)+-1//2*A*a^-3*x^-2+-1//2*a^-3*(a+b*x^2)^-1*(-1*B*a+2*A*b)+-1//4*a^-2*(a+b*x^2)^-2*(A*b+-1*B*a))
@test integrate(x^-5*(a+b*x^2)^-3*(A+B*x^2), x) == :((1/2)*a^-4*x^-2*(-1*B*a+3*A*b)+-1//4*A*a^-3*x^-4+(1/2)*b*a^-4*(a+b*x^2)^-1*(-2*B*a+3*A*b)+3*b*a^-5*(-1*B*a+2*A*b)*log(x)+-3//2*b*a^-5*(-1*B*a+2*A*b)*log(a+b*x^2)+1//4*b*a^-3*(a+b*x^2)^-2*(A*b+-1*B*a))
@test integrate(x^-7*(a+b*x^2)^-3*(A+B*x^2), x) == :(-1//6*A*a^-3*x^-6+1//4*a^-4*x^-4*(-1*B*a+3*A*b)+a^-6*b^2*(-3*B*a+5*A*b)*log(a+b*x^2)+-2*a^-6*b^2*(-3*B*a+5*A*b)*log(x)+-3//2*b*a^-5*x^-2*(-1*B*a+2*A*b)+-1//2*a^-5*b^2*(a+b*x^2)^-1*(-3*B*a+4*A*b)+-1//4*a^-4*b^2*(a+b*x^2)^-2*(A*b+-1*B*a))
@test integrate(x^10*(a+b*x^2)^-3*(A+B*x^2), x) == :(1//5*b^-4*x^5*(A*b+-3*B*a)+1//7*B*b^-3*x^7+-1*a*b^-5*x^3*(A*b+-2*B*a)+2*x*a^2*b^-6*(-5*B*a+3*A*b)+-9//8*a^5//2*b^-13//2*(-11*B*a+7*A*b)*arctan(x*a^-1//2*b^(1/2))+-1//4*x*a^4*b^-6*(a+b*x^2)^-2*(A*b+-1*B*a)+1//8*x*a^3*b^-6*(a+b*x^2)^-1*(-21*B*a+17*A*b))
@test integrate(x^8*(a+b*x^2)^-3*(A+B*x^2), x) == :(1//3*b^-4*x^3*(A*b+-3*B*a)+1//5*B*b^-3*x^5+-3*a*x*b^-5*(A*b+-2*B*a)+7//8*a^3//2*b^-11//2*(-9*B*a+5*A*b)*arctan(x*a^-1//2*b^(1/2))+-1//8*x*a^2*b^-5*(a+b*x^2)^-1*(-17*B*a+13*A*b)+1//4*x*a^3*b^-5*(a+b*x^2)^-2*(A*b+-1*B*a))
@test integrate(x^6*(a+b*x^2)^-3*(A+B*x^2), x) == :(x*b^-4*(A*b+-3*B*a)+1//3*B*b^-3*x^3+-5//8*a^(1/2)*b^-9//2*(-7*B*a+3*A*b)*arctan(x*a^-1//2*b^(1/2))+-1//4*x*a^2*b^-4*(a+b*x^2)^-2*(A*b+-1*B*a)+1//8*a*x*b^-4*(a+b*x^2)^-1*(-13*B*a+9*A*b))
@test integrate(x^4*(a+b*x^2)^-3*(A+B*x^2), x) == :(B*x*b^-3+-1//8*x*b^-3*(a+b*x^2)^-1*(-9*B*a+5*A*b)+1//8*a^-1//2*b^-7//2*(-15*B*a+3*A*b)*arctan(x*a^-1//2*b^(1/2))+1//4*a*x*b^-3*(a+b*x^2)^-2*(A*b+-1*B*a))
@test integrate(x^2*(a+b*x^2)^-3*(A+B*x^2), x) == :(-1//4*x*b^-2*(a+b*x^2)^-2*(A*b+-1*B*a)+1//8*a^-3//2*b^-5//2*(A*b+3*B*a)*arctan(x*a^-1//2*b^(1/2))+1//8*x*a^-1*b^-2*(a+b*x^2)^-1*(A*b+-5*B*a))
@test integrate((a+b*x^2)^-3*(A+B*x^2), x) == :(1//8*a^-5//2*b^-3//2*(B*a+3*A*b)*arctan(x*a^-1//2*b^(1/2))+1//4*x*a^-1*b^-1*(a+b*x^2)^-2*(A*b+-1*B*a)+1//8*x*a^-2*b^-1*(a+b*x^2)^-1*(B*a+3*A*b))
@test integrate(x^-2*(a+b*x^2)^-3*(A+B*x^2), x) == :(-1*A*a^-3*x^-1+-1//4*x*a^-2*(a+b*x^2)^-2*(A*b+-1*B*a)+-1//8*x*a^-3*(a+b*x^2)^-1*(-3*B*a+7*A*b)+-1//8*a^-7//2*b^-1//2*(-3*B*a+15*A*b)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-4*(a+b*x^2)^-3*(A+B*x^2), x) == :(a^-4*x^-1*(-1*B*a+3*A*b)+-1//3*A*a^-3*x^-3+5//8*a^-9//2*b^(1/2)*(-3*B*a+7*A*b)*arctan(x*a^-1//2*b^(1/2))+1//4*b*x*a^-3*(a+b*x^2)^-2*(A*b+-1*B*a)+1//8*b*x*a^-4*(a+b*x^2)^-1*(-7*B*a+11*A*b))
@test integrate(x^-6*(a+b*x^2)^-3*(A+B*x^2), x) == :(-1//5*A*a^-3*x^-5+1//3*a^-4*x^-3*(-1*B*a+3*A*b)+-3*b*a^-5*x^-1*(-1*B*a+2*A*b)+-7//8*a^-11//2*b^3//2*(-5*B*a+9*A*b)*arctan(x*a^-1//2*b^(1/2))+-1//4*x*a^-4*b^2*(a+b*x^2)^-2*(A*b+-1*B*a)+-1//8*x*a^-5*b^2*(a+b*x^2)^-1*(-11*B*a+15*A*b))
@test integrate((1+x^2)^-1*(a+b*x^2), x) == :(b*x+(a+-1b)*arctan(x))
@test integrate((1+-1*x^2)^-1*(a+b*x^2), x) == :((a+b)*arctanh(x)+-1*b*x)
@test integrate((-1+x^2)^-2*(1+x^2), x) == :(x*(1+-1*x^2)^-1)
@test integrate((1+x^2)^-2*(1+-1*x^2), x) == :(x*(1+x^2)^-1)
@test integrate((1+x^2)^-2*(3+2*x^2), x) == :(5//2*arctan(x)+x*(2+2*x^2)^-1)
@test integrate((1+x^2)^-2*(-2+x^2), x) == :(-1//2*arctan(x)+-3*x*(2+2*x^2)^-1)
@test integrate((1+x^2)^-2*(3+x^2), x) == :(2*arctan(x)+x*(1+x^2)^-1)
@test integrate((-1a+b*x^2)^-2*(a+b*x^2), x) == :(x*(a+-1*b*x^2)^-1)
@test integrate((a+-1*b*x^2)^-2*(a+b*x^2), x) == :(x*(a+-1*b*x^2)^-1)
@test integrate((a+-1*b*x^2)^-1*(A+B*x^2), x) == :(-1*B*x*b^-1+a^-1//2*b^-3//2*(A*b+B*a)*arctanh(x*a^-1//2*b^(1/2)))
@test integrate((16+x^2)^-3*(1+x^2), x) == :(19//8192*arctan(1//4*x)+19*x*(32768+2048*x^2)^-1+-15//64*x*(16+x^2)^-2)
@test integrate(x^-5*(1+x^2)^-3*(1+2*x^2), x) == :(-1//4*x^-4*(1+x^2)^-2)
@test integrate((1+-1*x^2)^2*(-1+x^2)^-2, x) == :(x)
@test integrate(x^3*(a+b*x^2)^-1*(a*c+b*c*x^2), x) == :(1//4*c*x^4)
@test integrate(x^2*(a+b*x^2)^-1*(a*c+b*c*x^2), x) == :(1//3*c*x^3)
@test integrate(x*(a+b*x^2)^-1*(a*c+b*c*x^2), x) == :((1/2)*c*x^2)
@test integrate((a+b*x^2)^-1*(a*c+b*c*x^2), x) == :(c*x)
@test integrate(x^-1*(a+b*x^2)^-1*(a*c+b*c*x^2), x) == :(c*log(x))
@test integrate(x^-2*(a+b*x^2)^-1*(a*c+b*c*x^2), x) == :(-1*c*x^-1)
@test integrate(x^-3*(a+b*x^2)^-1*(a*c+b*c*x^2), x) == :(-1//2*c*x^-2)
@test integrate(x^3*(a+b*x^2)^-2*(a*c+b*c*x^2), x) == :((1/2)*c*b^-1*x^2+-1//2*a*c*b^-2*log(a+b*x^2))
@test integrate(x^2*(a+b*x^2)^-2*(a*c+b*c*x^2), x) == :(c*x*b^-1+-1*c*a^(1/2)*b^-3//2*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x*(a+b*x^2)^-2*(a*c+b*c*x^2), x) == :((1/2)*c*b^-1*log(a+b*x^2))
@test integrate((a+b*x^2)^-2*(a*c+b*c*x^2), x) == :(c*a^-1//2*b^-1//2*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-1*(a+b*x^2)^-2*(a*c+b*c*x^2), x) == :(c*a^-1*log(x)+-1//2*c*a^-1*log(a+b*x^2))
@test integrate(x^-2*(a+b*x^2)^-2*(a*c+b*c*x^2), x) == :(-1*c*a^-1*x^-1+-1*c*a^-3//2*b^(1/2)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-3*(a+b*x^2)^-2*(a*c+b*c*x^2), x) == :(-1//2*c*a^-1*x^-2+(1/2)*b*c*a^-2*log(a+b*x^2)+-1*b*c*a^-2*log(x))
@test integrate(x^3*(a+b*x^2)^-3*(a*c+b*c*x^2), x) == :((1/2)*c*b^-2*log(a+b*x^2)+(1/2)*a*c*b^-2*(a+b*x^2)^-1)
@test integrate(x^2*(a+b*x^2)^-3*(a*c+b*c*x^2), x) == :((1/2)*c*a^-1//2*b^-3//2*arctan(x*a^-1//2*b^(1/2))+-1//2*c*x*b^-1*(a+b*x^2)^-1)
@test integrate(x*(a+b*x^2)^-3*(a*c+b*c*x^2), x) == :(-1//2*c*b^-1*(a+b*x^2)^-1)
@test integrate((a+b*x^2)^-3*(a*c+b*c*x^2), x) == :((1/2)*c*x*a^-1*(a+b*x^2)^-1+(1/2)*c*a^-3//2*b^-1//2*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-1*(a+b*x^2)^-3*(a*c+b*c*x^2), x) == :(c*a^-2*log(x)+(1/2)*c*a^-1*(a+b*x^2)^-1+-1//2*c*a^-2*log(a+b*x^2))
@test integrate(x^-2*(a+b*x^2)^-3*(a*c+b*c*x^2), x) == :(-3//2*c*a^-2*x^-1+(1/2)*c*a^-1*x^-1*(a+b*x^2)^-1+-3//2*c*a^-5//2*b^(1/2)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-3*(a+b*x^2)^-3*(a*c+b*c*x^2), x) == :(-1//2*c*a^-2*x^-2+b*c*a^-3*log(a+b*x^2)+-2*b*c*a^-3*log(x)+-1//2*b*c*a^-2*(a+b*x^2)^-1)
@test integrate(x^4*(a+b*x^2)^2*(c+d*x^2), x) == :(1//5*c*a^2*x^5+1//7*a*x^7*(a*d+2*b*c)+1//9*b*x^9*(b*c+2*a*d)+1//11*d*b^2*x^11)
@test integrate(x^3*(a+b*x^2)^2*(c+d*x^2), x) == :(1//4*c*a^2*x^4+1//6*a*x^6*(a*d+2*b*c)+1//8*b*x^8*(b*c+2*a*d)+1//10*d*b^2*x^10)
@test integrate(x^2*(a+b*x^2)^2*(c+d*x^2), x) == :(1//3*c*a^2*x^3+1//5*a*x^5*(a*d+2*b*c)+1//7*b*x^7*(b*c+2*a*d)+1//9*d*b^2*x^9)
@test integrate(x*(a+b*x^2)^2*(c+d*x^2), x) == :(1//6*b^-2*(a+b*x^2)^3*(b*c+-1*a*d)+1//8*d*b^-2*(a+b*x^2)^4)
@test integrate((a+b*x^2)^2*(c+d*x^2), x) == :(c*x*a^2+1//3*a*x^3*(a*d+2*b*c)+1//5*b*x^5*(b*c+2*a*d)+1//7*d*b^2*x^7)
@test integrate(x^-1*(a+b*x^2)^2*(c+d*x^2), x) == :(c*a^2*log(x)+1//4*c*b^2*x^4+1//6*d*b^-1*(a+b*x^2)^3+a*b*c*x^2)
@test integrate(x^-2*(a+b*x^2)^2*(c+d*x^2), x) == :(a*x*(a*d+2*b*c)+-1*c*a^2*x^-1+1//3*b*x^3*(b*c+2*a*d)+1//5*d*b^2*x^5)
@test integrate(x^-3*(a+b*x^2)^2*(c+d*x^2), x) == :(a*(a*d+2*b*c)*log(x)+(1/2)*b*x^2*(b*c+2*a*d)+-1//2*c*a^2*x^-2+1//4*d*b^2*x^4)
@test integrate(x^-4*(a+b*x^2)^2*(c+d*x^2), x) == :(b*x*(b*c+2*a*d)+-1*a*x^-1*(a*d+2*b*c)+-1//3*c*a^2*x^-3+1//3*d*b^2*x^3)
@test integrate(x^4*(a+b*x^2)^2*(c+d*x^2)^2, x) == :(x^9*(1//9*a^2*d^2+1//9*b^2*c^2+4//9*a*b*c*d)+1//5*a^2*c^2*x^5+1//13*b^2*d^2*x^13+2//7*a*c*x^7*(a*d+b*c)+2//11*b*d*x^11*(a*d+b*c))
@test integrate(x^3*(a+b*x^2)^2*(c+d*x^2)^2, x) == :(x^8*(1//8*a^2*d^2+1//8*b^2*c^2+(1/2)*a*b*c*d)+1//4*a^2*c^2*x^4+1//12*b^2*d^2*x^12+1//3*a*c*x^6*(a*d+b*c)+1//5*b*d*x^10*(a*d+b*c))
@test integrate(x^2*(a+b*x^2)^2*(c+d*x^2)^2, x) == :(x^7*(1//7*a^2*d^2+1//7*b^2*c^2+4//7*a*b*c*d)+1//3*a^2*c^2*x^3+1//11*b^2*d^2*x^11+2//5*a*c*x^5*(a*d+b*c)+2//9*b*d*x^9*(a*d+b*c))
@test integrate(x*(a+b*x^2)^2*(c+d*x^2)^2, x) == :(1//6*b^-3*(a+b*x^2)^3*(b*c+-1*a*d)^2+1//10*b^-3*d^2*(a+b*x^2)^5+1//4*d*b^-3*(a+b*x^2)^4*(b*c+-1*a*d))
@test integrate((a+b*x^2)^2*(c+d*x^2)^2, x) == :(1//5*x^5*(a^2*d^2+b^2*c^2+4*a*b*c*d)+x*a^2*c^2+1//9*b^2*d^2*x^9+2//3*a*c*x^3*(a*d+b*c)+2//7*b*d*x^7*(a*d+b*c))
@test integrate(x^-1*(a+b*x^2)^2*(c+d*x^2)^2, x) == :(x^4*(1//4*a^2*d^2+1//4*b^2*c^2+a*b*c*d)+a^2*c^2*log(x)+1//8*b^2*d^2*x^8+a*c*x^2*(a*d+b*c)+1//3*b*d*x^6*(a*d+b*c))
@test integrate(x^-2*(a+b*x^2)^2*(c+d*x^2)^2, x) == :(x^3*(1//3*a^2*d^2+1//3*b^2*c^2+4//3*a*b*c*d)+-1*a^2*c^2*x^-1+1//7*b^2*d^2*x^7+2*a*c*x*(a*d+b*c)+2//5*b*d*x^5*(a*d+b*c))
@test integrate(x^-3*(a+b*x^2)^2*(c+d*x^2)^2, x) == :(x^2*((1/2)*a^2*d^2+(1/2)*b^2*c^2+2*a*b*c*d)+-1//2*a^2*c^2*x^-2+1//6*b^2*d^2*x^6+(1/2)*b*d*x^4*(a*d+b*c)+2*a*c*(a*d+b*c)*log(x))
@test integrate(x^-4*(a+b*x^2)^2*(c+d*x^2)^2, x) == :(x*(a^2*d^2+b^2*c^2+4*a*b*c*d)+-1//3*a^2*c^2*x^-3+1//5*b^2*d^2*x^5+-2*a*c*x^-1*(a*d+b*c)+2//3*b*d*x^3*(a*d+b*c))
@test integrate(x^4*(a+b*x^2)^2*(c+d*x^2)^3, x) == :(1//5*a^2*c^3*x^5+1//9*c*x^9*(b^2*c^2+3*a^2*d^2+6*a*b*c*d)+1//11*d*x^11*(a^2*d^2+3*b^2*c^2+6*a*b*c*d)+1//15*b^2*d^3*x^15+1//7*a*c^2*x^7*(2*b*c+3*a*d)+1//13*b*d^2*x^13*(2*a*d+3*b*c))
@test integrate(x^3*(a+b*x^2)^2*(c+d*x^2)^3, x) == :(1//14*b^2*d^-4*(c+d*x^2)^7+-1//8*c*d^-4*(c+d*x^2)^4*(b*c+-1*a*d)^2+-1//12*b*d^-4*(c+d*x^2)^6*(-2*a*d+3*b*c)+1//10*d^-4*(c+d*x^2)^5*(b*c+-1*a*d)*(-1*a*d+3*b*c))
@test integrate(x^2*(a+b*x^2)^2*(c+d*x^2)^3, x) == :(1//3*a^2*c^3*x^3+1//7*c*x^7*(b^2*c^2+3*a^2*d^2+6*a*b*c*d)+1//9*d*x^9*(a^2*d^2+3*b^2*c^2+6*a*b*c*d)+1//13*b^2*d^3*x^13+1//5*a*c^2*x^5*(2*b*c+3*a*d)+1//11*b*d^2*x^11*(2*a*d+3*b*c))
@test integrate(x*(a+b*x^2)^2*(c+d*x^2)^3, x) == :(1//8*d^-3*(c+d*x^2)^4*(b*c+-1*a*d)^2+1//12*b^2*d^-3*(c+d*x^2)^6+-1//5*b*d^-3*(c+d*x^2)^5*(b*c+-1*a*d))
@test integrate((a+b*x^2)^2*(c+d*x^2)^3, x) == :(x*a^2*c^3+1//5*c*x^5*(b^2*c^2+3*a^2*d^2+6*a*b*c*d)+1//7*d*x^7*(a^2*d^2+3*b^2*c^2+6*a*b*c*d)+1//11*b^2*d^3*x^11+1//3*a*c^2*x^3*(2*b*c+3*a*d)+1//9*b*d^2*x^9*(2*a*d+3*b*c))
@test integrate(x^-1*(a+b*x^2)^2*(c+d*x^2)^3, x) == :(a^2*c^3*log(x)+1//4*c*x^4*(b^2*c^2+3*a^2*d^2+6*a*b*c*d)+1//6*d*x^6*(a^2*d^2+3*b^2*c^2+6*a*b*c*d)+1//10*b^2*d^3*x^10+(1/2)*a*c^2*x^2*(2*b*c+3*a*d)+1//8*b*d^2*x^8*(2*a*d+3*b*c))
@test integrate(x^-2*(a+b*x^2)^2*(c+d*x^2)^3, x) == :(-1*a^2*c^3*x^-1+1//3*c*x^3*(b^2*c^2+3*a^2*d^2+6*a*b*c*d)+1//5*d*x^5*(a^2*d^2+3*b^2*c^2+6*a*b*c*d)+1//9*b^2*d^3*x^9+a*x*c^2*(2*b*c+3*a*d)+1//7*b*d^2*x^7*(2*a*d+3*b*c))
@test integrate(x^-3*(a+b*x^2)^2*(c+d*x^2)^3, x) == :((1/2)*c*x^2*(b^2*c^2+3*a^2*d^2+6*a*b*c*d)+-1//2*a^2*c^3*x^-2+1//4*d*x^4*(a^2*d^2+3*b^2*c^2+6*a*b*c*d)+1//8*b^2*d^3*x^8+a*c^2*(2*b*c+3*a*d)*log(x)+1//6*b*d^2*x^6*(2*a*d+3*b*c))
@test integrate(x^-4*(a+b*x^2)^2*(c+d*x^2)^3, x) == :(c*x*(b^2*c^2+3*a^2*d^2+6*a*b*c*d)+-1//3*a^2*c^3*x^-3+1//3*d*x^3*(a^2*d^2+3*b^2*c^2+6*a*b*c*d)+1//7*b^2*d^3*x^7+-1*a*c^2*x^-1*(2*b*c+3*a*d)+1//5*b*d^2*x^5*(2*a*d+3*b*c))
@test integrate(x^4*(a+b*x^2)^2*(c+d*x^2)^-1, x) == :(1//3*d^-3*x^3*(b*c+-1*a*d)^2+1//7*b^2*d^-1*x^7+c^3//2*d^-9//2*(b*c+-1*a*d)^2*arctan(x*c^-1//2*d^(1/2))+-1*c*x*d^-4*(b*c+-1*a*d)^2+-1//5*b*d^-2*x^5*(b*c+-2*a*d))
@test integrate(x^3*(a+b*x^2)^2*(c+d*x^2)^-1, x) == :((1/2)*d^-3*x^2*(b*c+-1*a*d)^2+1//6*b^2*d^-1*x^6+-1//2*c*d^-4*(b*c+-1*a*d)^2*log(c+d*x^2)+-1//4*b*d^-2*x^4*(b*c+-2*a*d))
@test integrate(x^2*(a+b*x^2)^2*(c+d*x^2)^-1, x) == :(x*d^-3*(b*c+-1*a*d)^2+1//5*b^2*d^-1*x^5+-1*c^(1/2)*d^-7//2*(b*c+-1*a*d)^2*arctan(x*c^-1//2*d^(1/2))+-1//3*b*d^-2*x^3*(b*c+-2*a*d))
@test integrate(x*(a+b*x^2)^2*(c+d*x^2)^-1, x) == :(1//4*d^-1*(a+b*x^2)^2+(1/2)*d^-3*(b*c+-1*a*d)^2*log(c+d*x^2)+-1//2*b*d^-2*x^2*(b*c+-1*a*d))
@test integrate((a+b*x^2)^2*(c+d*x^2)^-1, x) == :(1//3*b^2*d^-1*x^3+c^-1//2*d^-5//2*(b*c+-1*a*d)^2*arctan(x*c^-1//2*d^(1/2))+-1*b*x*d^-2*(b*c+-2*a*d))
@test integrate(x^-1*(a+b*x^2)^2*(c+d*x^2)^-1, x) == :(a^2*c^-1*log(x)+(1/2)*b^2*d^-1*x^2+-1//2*c^-1*d^-2*(b*c+-1*a*d)^2*log(c+d*x^2))
@test integrate(x^-2*(a+b*x^2)^2*(c+d*x^2)^-1, x) == :(x*b^2*d^-1+-1*a^2*c^-1*x^-1+-1*c^-3//2*d^-3//2*(b*c+-1*a*d)^2*arctan(x*c^-1//2*d^(1/2)))
@test integrate(x^-3*(a+b*x^2)^2*(c+d*x^2)^-1, x) == :(-1//2*a^2*c^-1*x^-2+a*c^-2*(-1*a*d+2*b*c)*log(x)+(1/2)*c^-2*d^-1*(b*c+-1*a*d)^2*log(c+d*x^2))
@test integrate(x^-4*(a+b*x^2)^2*(c+d*x^2)^-1, x) == :(-1//3*a^2*c^-1*x^-3+c^-5//2*d^-1//2*(b*c+-1*a*d)^2*arctan(x*c^-1//2*d^(1/2))+-1*a*c^-2*x^-1*(-1*a*d+2*b*c))
@test integrate(x^-5*(a+b*x^2)^2*(c+d*x^2)^-1, x) == :(c^-3*(b*c+-1*a*d)^2*log(x)+-1//2*c^-3*(b*c+-1*a*d)^2*log(c+d*x^2)+-1//4*a^2*c^-1*x^-4+-1//2*a*c^-2*x^-2*(-1*a*d+2*b*c))
@test integrate(x^-6*(a+b*x^2)^2*(c+d*x^2)^-1, x) == :(-1*c^-3*x^-1*(b*c+-1*a*d)^2+-1//5*a^2*c^-1*x^-5+-1*c^-7//2*d^(1/2)*(b*c+-1*a*d)^2*arctan(x*c^-1//2*d^(1/2))+-1//3*a*c^-2*x^-3*(-1*a*d+2*b*c))
@test integrate(x^-7*(a+b*x^2)^2*(c+d*x^2)^-1, x) == :(-1//2*c^-3*x^-2*(b*c+-1*a*d)^2+-1//6*a^2*c^-1*x^-6+(1/2)*d*c^-4*(b*c+-1*a*d)^2*log(c+d*x^2)+-1*d*c^-4*(b*c+-1*a*d)^2*log(x)+-1//4*a*c^-2*x^-4*(-1*a*d+2*b*c))
@test integrate(x^4*(a+b*x^2)^2*(c+d*x^2)^-2, x) == :(1//5*b^2*d^-2*x^5+(1/2)*x*d^-4*(b*c+-1*a*d)*(-3*a*d+7*b*c)+(1/2)*c^-1*d^-2*x^5*(c+d*x^2)^-1*(b*c+-1*a*d)^2+-1//2*c^(1/2)*d^-9//2*(b*c+-1*a*d)*(-3*a*d+7*b*c)*arctan(x*c^-1//2*d^(1/2))+-1//6*c^-1*d^-3*x^3*(b*c+-1*a*d)*(-3*a*d+7*b*c))
@test integrate(x^3*(a+b*x^2)^2*(c+d*x^2)^-2, x) == :(1//4*b^2*d^-2*x^4+(1/2)*c*d^-4*(c+d*x^2)^-1*(b*c+-1*a*d)^2+(1/2)*d^-4*(b*c+-1*a*d)*(-1*a*d+3*b*c)*log(c+d*x^2)+-1*b*d^-3*x^2*(b*c+-1*a*d))
@test integrate(x^2*(a+b*x^2)^2*(c+d*x^2)^-2, x) == :(1//3*b^2*d^-2*x^3+(1/2)*c^-1*d^-2*x^3*(c+d*x^2)^-1*(b*c+-1*a*d)^2+(1/2)*c^-1//2*d^-7//2*(b*c+-1*a*d)*(-1*a*d+5*b*c)*arctan(x*c^-1//2*d^(1/2))+-1//2*x*c^-1*d^-3*(b*c+-1*a*d)*(-1*a*d+5*b*c))
@test integrate(x*(a+b*x^2)^2*(c+d*x^2)^-2, x) == :((1/2)*b^2*d^-2*x^2+-1//2*d^-3*(c+d*x^2)^-1*(b*c+-1*a*d)^2+-1*b*d^-3*(b*c+-1*a*d)*log(c+d*x^2))
@test integrate((a+b*x^2)^2*(c+d*x^2)^-2, x) == :(x*b^2*d^-2+(1/2)*x*c^-1*d^-2*(c+d*x^2)^-1*(b*c+-1*a*d)^2+-1//2*c^-3//2*d^-5//2*(a*d+3*b*c)*(b*c+-1*a*d)*arctan(x*c^-1//2*d^(1/2)))
@test integrate(x^-1*(a+b*x^2)^2*(c+d*x^2)^-2, x) == :(-1*((1/2)*a^2*c^-2+-1//2*b^2*d^-2)*log(c+d*x^2)+a^2*c^-2*log(x)+(1/2)*c^-1*d^-2*(c+d*x^2)^-1*(b*c+-1*a*d)^2)
@test integrate(x^-2*(a+b*x^2)^2*(c+d*x^2)^-2, x) == :(-1*a^2*c^-1*x^-1*(c+d*x^2)^-1+(1/2)*c^-5//2*d^-3//2*(b*c+-1*a*d)*(b*c+3*a*d)*arctan(x*c^-1//2*d^(1/2))+-1//2*x*c^-2*d^-1*(c+d*x^2)^-1*(b^2*c^2+3*a^2*d^2+-2*a*b*c*d))
@test integrate(x^-3*(a+b*x^2)^2*(c+d*x^2)^-2, x) == :(-1//2*a^2*c^-2*x^-2+-1*a*c^-3*(b*c+-1*a*d)*log(c+d*x^2)+2*a*c^-3*(b*c+-1*a*d)*log(x)+-1//2*c^-2*d^-1*(c+d*x^2)^-1*(b*c+-1*a*d)^2)
@test integrate(x^-4*(a+b*x^2)^2*(c+d*x^2)^-2, x) == :(-1//3*a*c^-3*x^-1*(-5*a*d+6*b*c)+-1//3*a^2*c^-1*x^-3*(c+d*x^2)^-1+1//6*x*c^-3*(c+d*x^2)^-1*(3*b^2*c^2+5*a^2*d^2+-6*a*b*c*d)+(1/2)*c^-7//2*d^-1//2*(b*c+-1*a*d)*(b*c+-5*a*d)*arctan(x*c^-1//2*d^(1/2)))
@test integrate(x^4*(a+b*x^2)^2*(c+d*x^2)^-3, x) == :(1//3*b^2*d^-3*x^3+-1//4*x*c^-1*d^-4*(a^2*d^2+13*b^2*c^2+-10*a*b*c*d)+1//8*c^-1//2*d^-9//2*(3*a^2*d^2+35*b^2*c^2+-30*a*b*c*d)*arctan(x*c^-1//2*d^(1/2))+-1//8*x*d^-4*(c+d*x^2)^-1*(b*c+-1*a*d)*(-1*a*d+9*b*c)+1//4*c^-1*d^-2*x^5*(c+d*x^2)^-2*(b*c+-1*a*d)^2)
@test integrate(x^3*(a+b*x^2)^2*(c+d*x^2)^-3, x) == :((1/2)*b^2*d^-3*x^2+-1//2*b*d^-4*(-2*a*d+3*b*c)*log(c+d*x^2)+-1//2*d^-4*(c+d*x^2)^-1*(b*c+-1*a*d)*(-1*a*d+3*b*c)+1//4*c*d^-4*(c+d*x^2)^-2*(b*c+-1*a*d)^2)
@test integrate(x^2*(a+b*x^2)^2*(c+d*x^2)^-3, x) == :(x*b^2*d^-3+-1//8*c^-3//2*d^-7//2*(-1*a^2*d^2+15*b^2*c^2+-6*a*b*c*d)*arctan(x*c^-1//2*d^(1/2))+1//4*c^-1*d^-2*x^3*(c+d*x^2)^-2*(b*c+-1*a*d)^2+1//8*x*c^-1*d^-3*(c+d*x^2)^-1*(a*d+7*b*c)*(b*c+-1*a*d))
@test integrate(x*(a+b*x^2)^2*(c+d*x^2)^-3, x) == :((1/2)*b^2*d^-3*log(c+d*x^2)+-1//4*d^-3*(c+d*x^2)^-2*(b*c+-1*a*d)^2+b*d^-3*(c+d*x^2)^-1*(b*c+-1*a*d))
@test integrate((a+b*x^2)^2*(c+d*x^2)^-3, x) == :(x*(8c+8*d*x^2)^-1*(-3*b^2*d^-2+3*a^2*c^-2)+1//8*c^-5//2*d^-5//2*(3*a^2*d^2+3*b^2*c^2+2*a*b*c*d)*arctan(x*c^-1//2*d^(1/2))+-1//4*x*c^-1*d^-1*(c+d*x^2)^-2*(a+b*x^2)*(b*c+-1*a*d))
@test integrate(x^-1*(a+b*x^2)^2*(c+d*x^2)^-3, x) == :((2c+2*d*x^2)^-1*(a^2*c^-2+-1*b^2*d^-2)+a^2*c^-3*log(x)+-1//2*a^2*c^-3*log(c+d*x^2)+1//4*c^-1*d^-2*(c+d*x^2)^-2*(b*c+-1*a*d)^2)
@test integrate(x^-2*(a+b*x^2)^2*(c+d*x^2)^-3, x) == :(-1*a^2*c^-1*x^-1*(c+d*x^2)^-2+1//8*c^-7//2*d^-3//2*(b^2*c^2+3*a*d*(-5*a*d+2*b*c))*arctan(x*c^-1//2*d^(1/2))+-1//4*x*c^-2*d^-1*(c+d*x^2)^-2*(b^2*c^2+5*a^2*d^2+-2*a*b*c*d)+1//8*x*c^-3*d^-1*(c+d*x^2)^-1*(b^2*c^2+3*a*d*(-5*a*d+2*b*c)))
@test integrate(x^-3*(a+b*x^2)^2*(c+d*x^2)^-3, x) == :(-1//2*a^2*c^-3*x^-2+a*c^-4*(-3*a*d+2*b*c)*log(x)+a*c^-3*(c+d*x^2)^-1*(b*c+-1*a*d)+-1//2*a*c^-4*(-3*a*d+2*b*c)*log(c+d*x^2)+-1//4*c^-2*d^-1*(c+d*x^2)^-2*(b*c+-1*a*d)^2)
@test integrate(x^-4*(a+b*x^2)^2*(c+d*x^2)^-3, x) == :(-1//3*a*c^-4*x^-1*(-7*a*d+6*b*c)+-1//3*a^2*c^-1*x^-3*(c+d*x^2)^-2+1//8*c^-9//2*d^-1//2*(3*b^2*c^2+35*a^2*d^2+-30*a*b*c*d)*arctan(x*c^-1//2*d^(1/2))+1//12*x*c^-3*(c+d*x^2)^-2*(3*b^2*c^2+7*a^2*d^2+-6*a*b*c*d)+1//24*x*c^-4*(c+d*x^2)^-1*(-7*a*d+3*b*c)^2)
@test integrate(x^5*(a+b*x^2)^-1*(c+d*x^2), x) == :(1//4*b^-2*x^4*(b*c+-1*a*d)+1//6*d*b^-1*x^6+(1/2)*a^2*b^-4*(b*c+-1*a*d)*log(a+b*x^2)+-1//2*a*b^-3*x^2*(b*c+-1*a*d))
@test integrate(x^4*(a+b*x^2)^-1*(c+d*x^2), x) == :(1//3*b^-2*x^3*(b*c+-1*a*d)+1//5*d*b^-1*x^5+a^3//2*b^-7//2*(b*c+-1*a*d)*arctan(x*a^-1//2*b^(1/2))+-1*a*x*b^-3*(b*c+-1*a*d))
@test integrate(x^3*(a+b*x^2)^-1*(c+d*x^2), x) == :((1/2)*b^-2*x^2*(b*c+-1*a*d)+1//4*d*b^-1*x^4+-1//2*a*b^-3*(b*c+-1*a*d)*log(a+b*x^2))
@test integrate(x^2*(a+b*x^2)^-1*(c+d*x^2), x) == :(x*b^-2*(b*c+-1*a*d)+1//3*d*b^-1*x^3+-1*a^(1/2)*b^-5//2*(b*c+-1*a*d)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x*(a+b*x^2)^-1*(c+d*x^2), x) == :((1/2)*d*b^-1*x^2+(1/2)*b^-2*(b*c+-1*a*d)*log(a+b*x^2))
@test integrate((a+b*x^2)^-1*(c+d*x^2), x) == :(d*x*b^-1+a^-1//2*b^-3//2*(b*c+-1*a*d)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-1*(a+b*x^2)^-1*(c+d*x^2), x) == :(c*a^-1*log(x)+-1//2*a^-1*b^-1*(b*c+-1*a*d)*log(a+b*x^2))
@test integrate(x^-2*(a+b*x^2)^-1*(c+d*x^2), x) == :(-1*c*a^-1*x^-1+-1*a^-3//2*b^-1//2*(b*c+-1*a*d)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-3*(a+b*x^2)^-1*(c+d*x^2), x) == :((1/2)*a^-2*(b*c+-1*a*d)*log(a+b*x^2)+-1*a^-2*(b*c+-1*a*d)*log(x)+-1//2*c*a^-1*x^-2)
@test integrate(x^-4*(a+b*x^2)^-1*(c+d*x^2), x) == :(a^-2*x^-1*(b*c+-1*a*d)+-1//3*c*a^-1*x^-3+a^-5//2*b^(1/2)*(b*c+-1*a*d)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^5*(a+b*x^2)^-1*(c+d*x^2)^2, x) == :(1//4*b^-3*x^4*(b*c+-1*a*d)^2+1//8*b^-1*d^2*x^8+(1/2)*a^2*b^-5*(b*c+-1*a*d)^2*log(a+b*x^2)+-1//2*a*b^-4*x^2*(b*c+-1*a*d)^2+1//6*d*b^-2*x^6*(-1*a*d+2*b*c))
@test integrate(x^4*(a+b*x^2)^-1*(c+d*x^2)^2, x) == :(1//3*b^-3*x^3*(b*c+-1*a*d)^2+1//7*b^-1*d^2*x^7+a^3//2*b^-9//2*(b*c+-1*a*d)^2*arctan(x*a^-1//2*b^(1/2))+-1*a*x*b^-4*(b*c+-1*a*d)^2+1//5*d*b^-2*x^5*(-1*a*d+2*b*c))
@test integrate(x^3*(a+b*x^2)^-1*(c+d*x^2)^2, x) == :((1/2)*b^-3*x^2*(b*c+-1*a*d)^2+1//6*b^-1*d^2*x^6+-1//2*a*b^-4*(b*c+-1*a*d)^2*log(a+b*x^2)+1//4*d*b^-2*x^4*(-1*a*d+2*b*c))
@test integrate(x^2*(a+b*x^2)^-1*(c+d*x^2)^2, x) == :(x*b^-3*(b*c+-1*a*d)^2+1//5*b^-1*d^2*x^5+-1*a^(1/2)*b^-7//2*(b*c+-1*a*d)^2*arctan(x*a^-1//2*b^(1/2))+1//3*d*b^-2*x^3*(-1*a*d+2*b*c))
@test integrate(x*(a+b*x^2)^-1*(c+d*x^2)^2, x) == :(1//4*b^-1*(c+d*x^2)^2+(1/2)*b^-3*(b*c+-1*a*d)^2*log(a+b*x^2)+(1/2)*d*b^-2*x^2*(b*c+-1*a*d))
@test integrate((a+b*x^2)^-1*(c+d*x^2)^2, x) == :(1//3*b^-1*d^2*x^3+d*x*b^-2*(-1*a*d+2*b*c)+a^-1//2*b^-5//2*(b*c+-1*a*d)^2*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-1*(a+b*x^2)^-1*(c+d*x^2)^2, x) == :(a^-1*c^2*log(x)+(1/2)*b^-1*d^2*x^2+-1//2*a^-1*b^-2*(b*c+-1*a*d)^2*log(a+b*x^2))
@test integrate(x^-2*(a+b*x^2)^-1*(c+d*x^2)^2, x) == :(x*b^-1*d^2+-1*a^-1*c^2*x^-1+-1*a^-3//2*b^-3//2*(b*c+-1*a*d)^2*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-3*(a+b*x^2)^-1*(c+d*x^2)^2, x) == :(-1//2*a^-1*c^2*x^-2+(1/2)*a^-2*b^-1*(b*c+-1*a*d)^2*log(a+b*x^2)+-1*c*a^-2*(b*c+-2*a*d)*log(x))
@test integrate(x^-4*(a+b*x^2)^-1*(c+d*x^2)^2, x) == :(-1//3*a^-1*c^2*x^-3+c*a^-2*x^-1*(b*c+-2*a*d)+a^-5//2*b^-1//2*(b*c+-1*a*d)^2*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^5*(a+b*x^2)^-1*(c+d*x^2)^3, x) == :(1//4*b^-4*x^4*(b*c+-1*a*d)^3+1//10*b^-1*d^3*x^10+(1/2)*a^2*b^-6*(b*c+-1*a*d)^3*log(a+b*x^2)+-1//2*a*b^-5*x^2*(b*c+-1*a*d)^3+1//6*d*b^-3*x^6*(a^2*d^2+3*b^2*c^2+-3*a*b*c*d)+1//8*b^-2*d^2*x^8*(-1*a*d+3*b*c))
@test integrate(x^4*(a+b*x^2)^-1*(c+d*x^2)^3, x) == :(1//3*b^-4*x^3*(b*c+-1*a*d)^3+1//9*b^-1*d^3*x^9+a^3//2*b^-11//2*(b*c+-1*a*d)^3*arctan(x*a^-1//2*b^(1/2))+-1*a*x*b^-5*(b*c+-1*a*d)^3+1//5*d*b^-3*x^5*(a^2*d^2+3*b^2*c^2+-3*a*b*c*d)+1//7*b^-2*d^2*x^7*(-1*a*d+3*b*c))
@test integrate(x^3*(a+b*x^2)^-1*(c+d*x^2)^3, x) == :((1/2)*b^-4*x^2*(b*c+-1*a*d)^3+1//8*b^-1*d^3*x^8+-1//2*a*b^-5*(b*c+-1*a*d)^3*log(a+b*x^2)+1//4*d*b^-3*x^4*(a^2*d^2+3*b^2*c^2+-3*a*b*c*d)+1//6*b^-2*d^2*x^6*(-1*a*d+3*b*c))
@test integrate(x^2*(a+b*x^2)^-1*(c+d*x^2)^3, x) == :(x*b^-4*(b*c+-1*a*d)^3+1//7*b^-1*d^3*x^7+-1*a^(1/2)*b^-9//2*(b*c+-1*a*d)^3*arctan(x*a^-1//2*b^(1/2))+1//3*d*b^-3*x^3*(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*(a+b*x^2)^-1*(c+d*x^2)^3, x) == :(1//6*b^-1*(c+d*x^2)^3+(1/2)*b^-4*(b*c+-1*a*d)^3*log(a+b*x^2)+1//4*b^-2*(c+d*x^2)^2*(b*c+-1*a*d)+(1/2)*d*b^-3*x^2*(b*c+-1*a*d)^2)
@test integrate((a+b*x^2)^-1*(c+d*x^2)^3, x) == :(1//5*b^-1*d^3*x^5+d*x*b^-3*(a^2*d^2+3*b^2*c^2+-3*a*b*c*d)+a^-1//2*b^-7//2*(b*c+-1*a*d)^3*arctan(x*a^-1//2*b^(1/2))+1//3*b^-2*d^2*x^3*(-1*a*d+3*b*c))
@test integrate(x^-1*(a+b*x^2)^-1*(c+d*x^2)^3, x) == :(a^-1*c^3*log(x)+1//4*b^-1*d^3*x^4+(1/2)*b^-2*d^2*x^2*(-1*a*d+3*b*c)+-1//2*a^-1*b^-3*(b*c+-1*a*d)^3*log(a+b*x^2))
@test integrate(x^-2*(a+b*x^2)^-1*(c+d*x^2)^3, x) == :(-1*a^-1*c^3*x^-1+1//3*b^-1*d^3*x^3+x*b^-2*d^2*(-1*a*d+3*b*c)+-1*a^-3//2*b^-5//2*(b*c+-1*a*d)^3*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-3*(a+b*x^2)^-1*(c+d*x^2)^3, x) == :((1/2)*b^-1*d^3*x^2+-1//2*a^-1*c^3*x^-2+(1/2)*a^-2*b^-2*(b*c+-1*a*d)^3*log(a+b*x^2)+-1*a^-2*c^2*(b*c+-3*a*d)*log(x))
@test integrate(x^-4*(a+b*x^2)^-1*(c+d*x^2)^3, x) == :(x*b^-1*d^3+-1//3*a^-1*c^3*x^-3+a^-2*c^2*x^-1*(b*c+-3*a*d)+a^-5//2*b^-3//2*(b*c+-1*a*d)^3*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^5*(a+b*x^2)^-1*(c+d*x^2)^-1, x) == :((1/2)*b^-1*d^-1*x^2+(1/2)*a^2*b^-2*(b*c+-1*a*d)^-1*log(a+b*x^2)+-1//2*c^2*d^-2*(b*c+-1*a*d)^-1*log(c+d*x^2))
@test integrate(x^4*(a+b*x^2)^-1*(c+d*x^2)^-1, x) == :(x*b^-1*d^-1+a^3//2*b^-3//2*(b*c+-1*a*d)^-1*arctan(x*a^-1//2*b^(1/2))+-1*c^3//2*d^-3//2*(b*c+-1*a*d)^-1*arctan(x*c^-1//2*d^(1/2)))
@test integrate(x^3*(a+b*x^2)^-1*(c+d*x^2)^-1, x) == :((1/2)*c*d^-1*(b*c+-1*a*d)^-1*log(c+d*x^2)+-1//2*a*b^-1*(b*c+-1*a*d)^-1*log(a+b*x^2))
@test integrate(x^2*(a+b*x^2)^-1*(c+d*x^2)^-1, x) == :(c^(1/2)*d^-1//2*(b*c+-1*a*d)^-1*arctan(x*c^-1//2*d^(1/2))+-1*a^(1/2)*b^-1//2*(b*c+-1*a*d)^-1*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x*(a+b*x^2)^-1*(c+d*x^2)^-1, x) == :((-2*a*d+2*b*c)^-1*log(a+b*x^2)+-1*(-2*a*d+2*b*c)^-1*log(c+d*x^2))
@test integrate((a+b*x^2)^-1*(c+d*x^2)^-1, x) == :(a^-1//2*b^(1/2)*(b*c+-1*a*d)^-1*arctan(x*a^-1//2*b^(1/2))+-1*c^-1//2*d^(1/2)*(b*c+-1*a*d)^-1*arctan(x*c^-1//2*d^(1/2)))
@test integrate(x^-1*(a+b*x^2)^-1*(c+d*x^2)^-1, x) == :(a^-1*c^-1*log(x)+(1/2)*d*c^-1*(b*c+-1*a*d)^-1*log(c+d*x^2)+-1//2*b*a^-1*(b*c+-1*a*d)^-1*log(a+b*x^2))
@test integrate(x^-2*(a+b*x^2)^-1*(c+d*x^2)^-1, x) == :(-1*a^-1*c^-1*x^-1+c^-3//2*d^3//2*(b*c+-1*a*d)^-1*arctan(x*c^-1//2*d^(1/2))+-1*a^-3//2*b^3//2*(b*c+-1*a*d)^-1*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-3*(a+b*x^2)^-1*(c+d*x^2)^-1, x) == :(-1//2*a^-1*c^-1*x^-2+(1/2)*a^-2*b^2*(b*c+-1*a*d)^-1*log(a+b*x^2)+-1*a^-2*c^-2*(a*d+b*c)*log(x)+-1//2*c^-2*d^2*(b*c+-1*a*d)^-1*log(c+d*x^2))
@test integrate(x^-4*(a+b*x^2)^-1*(c+d*x^2)^-1, x) == :(-1//3*a^-1*c^-1*x^-3+a^-2*c^-2*x^-1*(a*d+b*c)+a^-5//2*b^5//2*(b*c+-1*a*d)^-1*arctan(x*a^-1//2*b^(1/2))+-1*c^-5//2*d^5//2*(b*c+-1*a*d)^-1*arctan(x*c^-1//2*d^(1/2)))
@test integrate(x^-5*(a+b*x^2)^-1*(c+d*x^2)^-1, x) == :(-1//4*a^-1*c^-1*x^-4+a^-3*c^-3*(a^2*d^2+b^2*c^2+a*b*c*d)*log(x)+(1/2)*a^-2*c^-2*x^-2*(a*d+b*c)+(1/2)*c^-3*d^3*(b*c+-1*a*d)^-1*log(c+d*x^2)+-1//2*a^-3*b^3*(b*c+-1*a*d)^-1*log(a+b*x^2))
@test integrate(x^-6*(a+b*x^2)^-1*(c+d*x^2)^-1, x) == :(-1//5*a^-1*c^-1*x^-5+c^-7//2*d^7//2*(b*c+-1*a*d)^-1*arctan(x*c^-1//2*d^(1/2))+-1*a^-3*c^-3*x^-1*(a^2*d^2+b^2*c^2+a*b*c*d)+-1*a^-7//2*b^7//2*(b*c+-1*a*d)^-1*arctan(x*a^-1//2*b^(1/2))+1//3*a^-2*c^-2*x^-3*(a*d+b*c))
@test integrate(x^-7*(a+b*x^2)^-1*(c+d*x^2)^-1, x) == :(-1//6*a^-1*c^-1*x^-6+(1/2)*a^-4*b^4*(b*c+-1*a*d)^-1*log(a+b*x^2)+-1//2*a^-3*c^-3*x^-2*(a^2*d^2+b^2*c^2+a*b*c*d)+-1//2*c^-4*d^4*(b*c+-1*a*d)^-1*log(c+d*x^2)+1//4*a^-2*c^-2*x^-4*(a*d+b*c)+-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^2)^-2*(c+d*x^2)^-1, x) == :((1/2)*c^2*d^-1*(b*c+-1*a*d)^-2*log(c+d*x^2)+-1//2*a^2*b^-2*(a+b*x^2)^-1*(b*c+-1*a*d)^-1+-1//2*a*b^-2*(b*c+-1*a*d)^-2*(-1*a*d+2*b*c)*log(a+b*x^2))
@test integrate(x^4*(a+b*x^2)^-1*(c+d*x^2)^-2, x) == :(a^3//2*b^-1//2*(b*c+-1*a*d)^-2*arctan(x*a^-1//2*b^(1/2))+(1/2)*c^(1/2)*d^-3//2*(b*c+-1*a*d)^-2*(b*c+-3*a*d)*arctan(x*c^-1//2*d^(1/2))+-1//2*c*x*d^-1*(c+d*x^2)^-1*(b*c+-1*a*d)^-1)
@test integrate(x^3*(a+b*x^2)^-1*(c+d*x^2)^-2, x) == :((1/2)*a*(b*c+-1*a*d)^-2*log(c+d*x^2)+-1//2*a*(b*c+-1*a*d)^-2*log(a+b*x^2)+-1//2*c*d^-1*(c+d*x^2)^-1*(b*c+-1*a*d)^-1)
@test integrate(x^2*(a+b*x^2)^-1*(c+d*x^2)^-2, x) == :(x*(c+d*x^2)^-1*(-2*a*d+2*b*c)^-1+-1*a^(1/2)*b^(1/2)*(b*c+-1*a*d)^-2*arctan(x*a^-1//2*b^(1/2))+(1/2)*c^-1//2*d^-1//2*(b*c+-1*a*d)^-2*(a*d+b*c)*arctan(x*c^-1//2*d^(1/2)))
@test integrate(x*(a+b*x^2)^-1*(c+d*x^2)^-2, x) == :((c+d*x^2)^-1*(-2*a*d+2*b*c)^-1+(1/2)*b*(b*c+-1*a*d)^-2*log(a+b*x^2)+-1//2*b*(b*c+-1*a*d)^-2*log(c+d*x^2))
@test integrate((a+b*x^2)^-1*(c+d*x^2)^-2, x) == :(a^-1//2*b^3//2*(b*c+-1*a*d)^-2*arctan(x*a^-1//2*b^(1/2))+-1//2*d*x*c^-1*(c+d*x^2)^-1*(b*c+-1*a*d)^-1+-1//2*c^-3//2*d^(1/2)*(b*c+-1*a*d)^-2*(-1*a*d+3*b*c)*arctan(x*c^-1//2*d^(1/2)))
@test integrate(x^-1*(a+b*x^2)^-1*(c+d*x^2)^-2, x) == :(a^-1*c^-2*log(x)+-1//2*d*c^-1*(c+d*x^2)^-1*(b*c+-1*a*d)^-1+-1//2*a^-1*b^2*(b*c+-1*a*d)^-2*log(a+b*x^2)+(1/2)*d*c^-2*(b*c+-1*a*d)^-2*(-1*a*d+2*b*c)*log(c+d*x^2))
@test integrate(x^-2*(a+b*x^2)^-1*(c+d*x^2)^-2, x) == :(-1*a^-3//2*b^5//2*(b*c+-1*a*d)^-2*arctan(x*a^-1//2*b^(1/2))+(1/2)*c^-5//2*d^3//2*(b*c+-1*a*d)^-2*(-3*a*d+5*b*c)*arctan(x*c^-1//2*d^(1/2))+-1//2*d*c^-1*x^-1*(c+d*x^2)^-1*(b*c+-1*a*d)^-1+-1//2*a^-1*c^-2*x^-1*(b*c+-1*a*d)^-1*(-3*a*d+2*b*c))
@test integrate(x^-3*(a+b*x^2)^-1*(c+d*x^2)^-2, x) == :(-1//2*a^-1*c^-2*x^-2+(1/2)*a^-2*b^3*(b*c+-1*a*d)^-2*log(a+b*x^2)+(1/2)*c^-2*d^2*(c+d*x^2)^-1*(b*c+-1*a*d)^-1+-1*a^-2*c^-3*(b*c+2*a*d)*log(x)+-1//2*c^-3*d^2*(b*c+-1*a*d)^-2*(-2*a*d+3*b*c)*log(c+d*x^2))
@test integrate(x^-4*(a+b*x^2)^-1*(c+d*x^2)^-2, x) == :(a^-5//2*b^7//2*(b*c+-1*a*d)^-2*arctan(x*a^-1//2*b^(1/2))+(1/2)*a^-2*c^-3*x^-1*(b*c+-1*a*d)^-1*(-5*a^2*d^2+2*b^2*c^2+2*a*b*c*d)+-1//2*d*c^-1*x^-3*(c+d*x^2)^-1*(b*c+-1*a*d)^-1+-1//2*c^-7//2*d^5//2*(b*c+-1*a*d)^-2*(-5*a*d+7*b*c)*arctan(x*c^-1//2*d^(1/2))+-1//6*a^-1*c^-2*x^-3*(b*c+-1*a*d)^-1*(-5*a*d+2*b*c))
@test integrate(x^5*(a+b*x^2)^-3*(c+d*x^2)^-1, x) == :((1/2)*c^2*(b*c+-1*a*d)^-3*log(a+b*x^2)+-1//2*c^2*(b*c+-1*a*d)^-3*log(c+d*x^2)+-1//4*a^2*b^-2*(a+b*x^2)^-2*(b*c+-1*a*d)^-1+(1/2)*a*b^-2*(a+b*x^2)^-1*(b*c+-1*a*d)^-2*(-1*a*d+2*b*c))
@test integrate(x^4*(a+b*x^2)^-1*(c+d*x^2)^-3, x) == :(a^3//2*b^(1/2)*(b*c+-1*a*d)^-3*arctan(x*a^-1//2*b^(1/2))+-1//4*c*x*d^-1*(c+d*x^2)^-2*(b*c+-1*a*d)^-1+1//8*x*d^-1*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(b*c+-5*a*d)+1//8*c^-1//2*d^-3//2*(b*c+-1*a*d)^-3*(b^2*c^2+-3*a^2*d^2+-6*a*b*c*d)*arctan(x*c^-1//2*d^(1/2)))
@test integrate(x^3*(a+b*x^2)^-1*(c+d*x^2)^-3, x) == :(-1//2*a*(c+d*x^2)^-1*(b*c+-1*a*d)^-2+(1/2)*a*b*(b*c+-1*a*d)^-3*log(c+d*x^2)+-1//2*a*b*(b*c+-1*a*d)^-3*log(a+b*x^2)+-1//4*c*d^-1*(c+d*x^2)^-2*(b*c+-1*a*d)^-1)
@test integrate(x^2*(a+b*x^2)^-1*(c+d*x^2)^-3, x) == :(x*(c+d*x^2)^-2*(-4*a*d+4*b*c)^-1+-1*a^(1/2)*b^3//2*(b*c+-1*a*d)^-3*arctan(x*a^-1//2*b^(1/2))+1//8*x*c^-1*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(a*d+3*b*c)+1//8*c^-3//2*d^-1//2*(b*c+-1*a*d)^-3*(-1*a^2*d^2+3*b^2*c^2+6*a*b*c*d)*arctan(x*c^-1//2*d^(1/2)))
@test integrate(x*(a+b*x^2)^-1*(c+d*x^2)^-3, x) == :((c+d*x^2)^-2*(-4*a*d+4*b*c)^-1+(1/2)*b*(c+d*x^2)^-1*(b*c+-1*a*d)^-2+(1/2)*b^2*(b*c+-1*a*d)^-3*log(a+b*x^2)+-1//2*b^2*(b*c+-1*a*d)^-3*log(c+d*x^2))
@test integrate((a+b*x^2)^-1*(c+d*x^2)^-3, x) == :(a^-1//2*b^5//2*(b*c+-1*a*d)^-3*arctan(x*a^-1//2*b^(1/2))+-1//4*d*x*c^-1*(c+d*x^2)^-2*(b*c+-1*a*d)^-1+-1//8*c^-5//2*d^(1/2)*(b*c+-1*a*d)^-3*(3*a^2*d^2+15*b^2*c^2+-10*a*b*c*d)*arctan(x*c^-1//2*d^(1/2))+-1//8*d*x*c^-2*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(-3*a*d+7*b*c))
@test integrate(x^-1*(a+b*x^2)^-1*(c+d*x^2)^-3, x) == :(a^-1*c^-3*log(x)+-1//2*a^-1*b^3*(b*c+-1*a*d)^-3*log(a+b*x^2)+-1//4*d*c^-1*(c+d*x^2)^-2*(b*c+-1*a*d)^-1+(1/2)*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^2)+-1//2*d*c^-2*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(-1*a*d+2*b*c))
@test integrate(x^-2*(a+b*x^2)^-1*(c+d*x^2)^-3, x) == :(-1*a^-3//2*b^7//2*(b*c+-1*a*d)^-3*arctan(x*a^-1//2*b^(1/2))+-1//4*d*c^-1*x^-1*(c+d*x^2)^-2*(b*c+-1*a*d)^-1+-1//8*a^-1*c^-3*x^-1*(b*c+-1*a*d)^-2*(8*b^2*c^2+15*a^2*d^2+-27*a*b*c*d)+1//8*c^-7//2*d^3//2*(b*c+-1*a*d)^-3*(15*a^2*d^2+35*b^2*c^2+-42*a*b*c*d)*arctan(x*c^-1//2*d^(1/2))+-1//8*d*c^-2*x^-1*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(-5*a*d+9*b*c))
@test integrate(x^-3*(a+b*x^2)^-1*(c+d*x^2)^-3, x) == :(-1//2*a^-1*c^-3*x^-2+(1/2)*a^-2*b^4*(b*c+-1*a*d)^-3*log(a+b*x^2)+-1*a^-2*c^-4*(b*c+3*a*d)*log(x)+1//4*c^-2*d^2*(c+d*x^2)^-2*(b*c+-1*a*d)^-1+(1/2)*c^-3*d^2*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(-2*a*d+3*b*c)+-1//2*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^2))
@test integrate(x^-4*(a+b*x^2)^-1*(c+d*x^2)^-3, x) == :(a^-5//2*b^9//2*(b*c+-1*a*d)^-3*arctan(x*a^-1//2*b^(1/2))+-1//4*d*c^-1*x^-3*(c+d*x^2)^-2*(b*c+-1*a*d)^-1+-1//8*c^-9//2*d^5//2*(b*c+-1*a*d)^-3*(35*a^2*d^2+63*b^2*c^2+-90*a*b*c*d)*arctan(x*c^-1//2*d^(1/2))+-1//24*a^-1*c^-3*x^-3*(b*c+-1*a*d)^-2*(8*b^2*c^2+35*a^2*d^2+-55*a*b*c*d)+1//8*a^-2*c^-4*x^-1*(b*c+-1*a*d)^-2*(8*b^3*c^3+35*a^3*d^3+-55*b*c*a^2*d^2+8*a*d*b^2*c^2)+-1//8*d*c^-2*x^-3*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(-7*a*d+11*b*c))
@test integrate(x*(1+x^2)^-1*(4+x^2)^-1, x) == :(-1//6*log(4+x^2)+1//6*log(1+x^2))
@test integrate(x^4*(a+b*x^2)^-2*(c+d*x^2), x) == :(x*b^-3*(b*c+-2*a*d)+1//3*d*b^-2*x^3+-1//2*a^(1/2)*b^-7//2*(-5*a*d+3*b*c)*arctan(x*a^-1//2*b^(1/2))+(1/2)*a*x*b^-3*(a+b*x^2)^-1*(b*c+-1*a*d))
@test integrate(x^3*(a+b*x^2)^-2*(c+d*x^2), x) == :((1/2)*d*b^-2*x^2+(1/2)*b^-3*(b*c+-2*a*d)*log(a+b*x^2)+(1/2)*a*b^-3*(a+b*x^2)^-1*(b*c+-1*a*d))
@test integrate(x^2*(a+b*x^2)^-2*(c+d*x^2), x) == :(d*x*b^-2+(1/2)*a^-1//2*b^-5//2*(b*c+-3*a*d)*arctan(x*a^-1//2*b^(1/2))+-1//2*x*b^-2*(a+b*x^2)^-1*(b*c+-1*a*d))
@test integrate(x*(a+b*x^2)^-2*(c+d*x^2), x) == :((1/2)*d*b^-2*log(a+b*x^2)+(1/2)*b^-2*(a+b*x^2)^-1*(a*d+-1*b*c))
@test integrate((a+b*x^2)^-2*(c+d*x^2), x) == :((1/2)*a^-3//2*b^-3//2*(a*d+b*c)*arctan(x*a^-1//2*b^(1/2))+(1/2)*x*a^-1*b^-1*(a+b*x^2)^-1*(b*c+-1*a*d))
@test integrate(x^-1*(a+b*x^2)^-2*(c+d*x^2), x) == :(c*a^-2*log(x)+-1//2*c*a^-2*log(a+b*x^2)+(1/2)*a^-1*b^-1*(a+b*x^2)^-1*(b*c+-1*a*d))
@test integrate(x^-2*(a+b*x^2)^-2*(c+d*x^2), x) == :(-1*c*a^-2*x^-1+-1//2*x*a^-2*(a+b*x^2)^-1*(b*c+-1*a*d)+-1//2*a^-5//2*b^-1//2*(-1*a*d+3*b*c)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-3*(a+b*x^2)^-2*(c+d*x^2), x) == :((1/2)*a^-3*(-1*a*d+2*b*c)*log(a+b*x^2)+-1*a^-3*(-1*a*d+2*b*c)*log(x)+-1//2*c*a^-2*x^-2+-1//2*a^-2*(a+b*x^2)^-1*(b*c+-1*a*d))
@test integrate(x^-4*(a+b*x^2)^-2*(c+d*x^2), x) == :(a^-3*x^-1*(-1*a*d+2*b*c)+-1//3*c*a^-2*x^-3+(1/2)*a^-7//2*b^(1/2)*(-3*a*d+5*b*c)*arctan(x*a^-1//2*b^(1/2))+(1/2)*b*x*a^-3*(a+b*x^2)^-1*(b*c+-1*a*d))
@test integrate(x^4*(a+b*x^2)^-2*(c+d*x^2)^2, x) == :(1//5*b^-2*d^2*x^5+(1/2)*x*b^-4*(b*c+-1*a*d)*(-7*a*d+3*b*c)+(1/2)*a^-1*b^-2*x^5*(a+b*x^2)^-1*(b*c+-1*a*d)^2+-1//2*a^(1/2)*b^-9//2*(b*c+-1*a*d)*(-7*a*d+3*b*c)*arctan(x*a^-1//2*b^(1/2))+-1//6*a^-1*b^-3*x^3*(b*c+-1*a*d)*(-7*a*d+3*b*c))
@test integrate(x^3*(a+b*x^2)^-2*(c+d*x^2)^2, x) == :(1//4*b^-2*d^2*x^4+d*b^-3*x^2*(b*c+-1*a*d)+(1/2)*a*b^-4*(a+b*x^2)^-1*(b*c+-1*a*d)^2+(1/2)*b^-4*(b*c+-1*a*d)*(b*c+-3*a*d)*log(a+b*x^2))
@test integrate(x^2*(a+b*x^2)^-2*(c+d*x^2)^2, x) == :(1//3*b^-2*d^2*x^3+(1/2)*a^-1*b^-2*x^3*(a+b*x^2)^-1*(b*c+-1*a*d)^2+(1/2)*a^-1//2*b^-7//2*(b*c+-1*a*d)*(b*c+-5*a*d)*arctan(x*a^-1//2*b^(1/2))+-1//2*x*a^-1*b^-3*(b*c+-1*a*d)*(b*c+-5*a*d))
@test integrate(x*(a+b*x^2)^-2*(c+d*x^2)^2, x) == :((1/2)*b^-2*d^2*x^2+-1//2*b^-3*(a+b*x^2)^-1*(b*c+-1*a*d)^2+d*b^-3*(b*c+-1*a*d)*log(a+b*x^2))
@test integrate((a+b*x^2)^-2*(c+d*x^2)^2, x) == :(x*b^-2*d^2+(1/2)*x*a^-1*b^-2*(a+b*x^2)^-1*(b*c+-1*a*d)^2+(1/2)*a^-3//2*b^-5//2*(b*c+-1*a*d)*(b*c+3*a*d)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-1*(a+b*x^2)^-2*(c+d*x^2)^2, x) == :(-1*((1/2)*a^-2*c^2+-1//2*b^-2*d^2)*log(a+b*x^2)+a^-2*c^2*log(x)+(1/2)*a^-1*b^-2*(a+b*x^2)^-1*(b*c+-1*a*d)^2)
@test integrate(x^-2*(a+b*x^2)^-2*(c+d*x^2)^2, x) == :(-1*a^-1*c^2*x^-1*(a+b*x^2)^-1+-1//2*x*a^-1*(a+b*x^2)^-1*(-2*c*d+a*b^-1*d^2+3*b*a^-1*c^2)+-1//2*a^-5//2*b^-3//2*(a*d+3*b*c)*(b*c+-1*a*d)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-3*(a+b*x^2)^-2*(c+d*x^2)^2, x) == :(-1//2*a^-2*c^2*x^-2+c*a^-3*(b*c+-1*a*d)*log(a+b*x^2)+-2*c*a^-3*(b*c+-1*a*d)*log(x)+-1//2*a^-2*b^-1*(a+b*x^2)^-1*(b*c+-1*a*d)^2)
@test integrate(x^-4*(a+b*x^2)^-2*(c+d*x^2)^2, x) == :(-1//3*a^-1*c^2*x^-3*(a+b*x^2)^-1+1//3*c*a^-3*x^-1*(-6*a*d+5*b*c)+1//6*x*a^-3*(a+b*x^2)^-1*(3*a^2*d^2+5*b^2*c^2+-6*a*b*c*d)+(1/2)*a^-7//2*b^-1//2*(b*c+-1*a*d)*(-1*a*d+5*b*c)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^4*(a+b*x^2)^-2*(c+d*x^2)^3, x) == :(9//14*b^-2*d^3*x^7+(1/2)*d*b^-4*x^3*(3*a^2*d^2+5*b^2*c^2+-7*a*b*c*d)+(1/2)*x*b^-5*(b*c+-1*a*d)^2*(-9*a*d+3*b*c)+-1//2*b^-1*x^3*(a+b*x^2)^-1*(c+d*x^2)^3+3//10*b^-3*d^2*x^5*(-3*a*d+7*b*c)+-3//2*a^(1/2)*b^-11//2*(b*c+-1*a*d)^2*(b*c+-3*a*d)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^3*(a+b*x^2)^-2*(c+d*x^2)^3, x) == :(1//6*b^-2*d^3*x^6+(1/2)*a*b^-5*(a+b*x^2)^-1*(b*c+-1*a*d)^3+(1/2)*b^-5*(b*c+-1*a*d)^2*(b*c+-4*a*d)*log(a+b*x^2)+1//4*b^-3*d^2*x^4*(-2*a*d+3*b*c)+3//2*d*b^-4*x^2*(b*c+-1*a*d)^2)
@test integrate(x^2*(a+b*x^2)^-2*(c+d*x^2)^3, x) == :(-1//2*x*b^-1*(a+b*x^2)^-1*(c+d*x^2)^3+1//30*d*x*b^-4*(81*b^2*c^2+105*a^2*d^2+-190*a*b*c*d)+7//10*d*x*b^-2*(c+d*x^2)^2+(1/2)*a^-1//2*b^-9//2*(b*c+-1*a*d)^2*(b*c+-7*a*d)*arctan(x*a^-1//2*b^(1/2))+1//30*d*x*b^-3*(c+d*x^2)*(-35*a*d+33*b*c))
@test integrate(x*(a+b*x^2)^-2*(c+d*x^2)^3, x) == :(-1//2*b^-4*(a+b*x^2)^-1*(b*c+-1*a*d)^3+1//4*b^-2*d^3*x^4+(1/2)*b^-3*d^2*x^2*(-2*a*d+3*b*c)+3//2*d*b^-4*(b*c+-1*a*d)^2*log(a+b*x^2))
@test integrate((a+b*x^2)^-2*(c+d*x^2)^3, x) == :(1//3*b^-2*d^3*x^3+x*b^-3*d^2*(-2*a*d+3*b*c)+(1/2)*x*a^-1*b^-3*(a+b*x^2)^-1*(b*c+-1*a*d)^3+(1/2)*a^-3//2*b^-7//2*(b*c+-1*a*d)^2*(b*c+5*a*d)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-1*(a+b*x^2)^-2*(c+d*x^2)^3, x) == :(a^-2*c^3*log(x)+(1/2)*b^-2*d^3*x^2+(1/2)*a^-1*b^-3*(a+b*x^2)^-1*(b*c+-1*a*d)^3+-1//2*a^-2*b^-3*(b*c+-1*a*d)^2*(b*c+2*a*d)*log(a+b*x^2))
@test integrate(x^-2*(a+b*x^2)^-2*(c+d*x^2)^3, x) == :(-3//2*a^-5//2*b^-5//2*(b*c+-1*a*d)^2*(a*d+b*c)*arctan(x*a^-1//2*b^(1/2))+-1//2*x*a^-1*b^-2*d^2*(b*c+-3*a*d)+-1//2*a^-2*b^-1*c^2*x^-1*(-1*a*d+3*b*c)+(1/2)*a^-1*b^-1*x^-1*(a+b*x^2)^-1*(c+d*x^2)^2*(b*c+-1*a*d))
@test integrate(x^-3*(a+b*x^2)^-2*(c+d*x^2)^3, x) == :(-1//2*a^-2*c^3*x^-2+-1*a^-3*c^2*(-3*a*d+2*b*c)*log(x)+-1//2*a^-2*b^-2*(a+b*x^2)^-1*(b*c+-1*a*d)^3+(1/2)*a^-3*b^-2*(b*c+-1*a*d)^2*(a*d+2*b*c)*log(a+b*x^2))
@test integrate(x^-4*(a+b*x^2)^-2*(c+d*x^2)^3, x) == :((1/2)*c*a^-3*b^-1*x^-1*(2*a^2*d^2+5*b^2*c^2+-9*a*b*c*d)+(1/2)*a^-7//2*b^-3//2*(b*c+-1*a*d)^2*(a*d+5*b*c)*arctan(x*a^-1//2*b^(1/2))+-1//6*a^-2*b^-1*c^2*x^-3*(-3*a*d+5*b*c)+(1/2)*a^-1*b^-1*x^-3*(a+b*x^2)^-1*(c+d*x^2)^2*(b*c+-1*a*d))
@test integrate(x^4*(a+b*x^2)^-2*(c+d*x^2)^-1, x) == :(c^3//2*d^-1//2*(b*c+-1*a*d)^-2*arctan(x*c^-1//2*d^(1/2))+(1/2)*a*x*b^-1*(a+b*x^2)^-1*(b*c+-1*a*d)^-1+-1//2*a^(1/2)*b^-3//2*(b*c+-1*a*d)^-2*(-1*a*d+3*b*c)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^3*(a+b*x^2)^-2*(c+d*x^2)^-1, x) == :((1/2)*c*(b*c+-1*a*d)^-2*log(a+b*x^2)+-1//2*c*(b*c+-1*a*d)^-2*log(c+d*x^2)+(1/2)*a*b^-1*(a+b*x^2)^-1*(b*c+-1*a*d)^-1)
@test integrate(x^2*(a+b*x^2)^-2*(c+d*x^2)^-1, x) == :(-1*x*(a+b*x^2)^-1*(-2*a*d+2*b*c)^-1+-1*c^(1/2)*d^(1/2)*(b*c+-1*a*d)^-2*arctan(x*c^-1//2*d^(1/2))+(1/2)*a^-1//2*b^-1//2*(b*c+-1*a*d)^-2*(a*d+b*c)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x*(a+b*x^2)^-2*(c+d*x^2)^-1, x) == :(-1*(a+b*x^2)^-1*(-2*a*d+2*b*c)^-1+(1/2)*d*(b*c+-1*a*d)^-2*log(c+d*x^2)+-1//2*d*(b*c+-1*a*d)^-2*log(a+b*x^2))
@test integrate((a+b*x^2)^-2*(c+d*x^2)^-1, x) == :(c^-1//2*d^3//2*(b*c+-1*a*d)^-2*arctan(x*c^-1//2*d^(1/2))+(1/2)*b*x*a^-1*(a+b*x^2)^-1*(b*c+-1*a*d)^-1+(1/2)*a^-3//2*b^(1/2)*(b*c+-1*a*d)^-2*(b*c+-3*a*d)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-1*(a+b*x^2)^-2*(c+d*x^2)^-1, x) == :(a^-2*c^-1*log(x)+(1/2)*b*a^-1*(a+b*x^2)^-1*(b*c+-1*a*d)^-1+-1//2*c^-1*d^2*(b*c+-1*a*d)^-2*log(c+d*x^2)+-1//2*b*a^-2*(b*c+-1*a*d)^-2*(b*c+-2*a*d)*log(a+b*x^2))
@test integrate(x^-2*(a+b*x^2)^-2*(c+d*x^2)^-1, x) == :(-1*c^-3//2*d^5//2*(b*c+-1*a*d)^-2*arctan(x*c^-1//2*d^(1/2))+(1/2)*b*a^-1*x^-1*(a+b*x^2)^-1*(b*c+-1*a*d)^-1+-1//2*a^-2*c^-1*x^-1*(b*c+-1*a*d)^-1*(-2*a*d+3*b*c)+-1//2*a^-5//2*b^3//2*(b*c+-1*a*d)^-2*(-5*a*d+3*b*c)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-3*(a+b*x^2)^-2*(c+d*x^2)^-1, x) == :(-1//2*a^-2*c^-1*x^-2+(1/2)*c^-2*d^3*(b*c+-1*a*d)^-2*log(c+d*x^2)+-1*a^-3*c^-2*(a*d+2*b*c)*log(x)+-1//2*a^-2*b^2*(a+b*x^2)^-1*(b*c+-1*a*d)^-1+(1/2)*a^-3*b^2*(b*c+-1*a*d)^-2*(-3*a*d+2*b*c)*log(a+b*x^2))
@test integrate(x^-4*(a+b*x^2)^-2*(c+d*x^2)^-1, x) == :(c^-5//2*d^7//2*(b*c+-1*a*d)^-2*arctan(x*c^-1//2*d^(1/2))+(1/2)*b*a^-1*x^-3*(a+b*x^2)^-1*(b*c+-1*a*d)^-1+(1/2)*a^-3*c^-2*x^-1*(b*c+-1*a*d)^-1*(-2*a^2*d^2+5*b^2*c^2+-2*a*b*c*d)+(1/2)*a^-7//2*b^5//2*(b*c+-1*a*d)^-2*(-7*a*d+5*b*c)*arctan(x*a^-1//2*b^(1/2))+-1//6*a^-2*c^-1*x^-3*(b*c+-1*a*d)^-1*(-2*a*d+5*b*c))
@test integrate(x^-5*(a+b*x^2)^-2*(c+d*x^2)^-1, x) == :(-1//4*a^-2*c^-1*x^-4+a^-4*c^-3*(a^2*d^2+3*b^2*c^2+2*a*b*c*d)*log(x)+(1/2)*a^-3*b^3*(a+b*x^2)^-1*(b*c+-1*a*d)^-1+(1/2)*a^-3*c^-2*x^-2*(a*d+2*b*c)+-1//2*c^-3*d^4*(b*c+-1*a*d)^-2*log(c+d*x^2)+-1//2*a^-4*b^3*(b*c+-1*a*d)^-2*(-4*a*d+3*b*c)*log(a+b*x^2))
@test integrate(x^-6*(a+b*x^2)^-2*(c+d*x^2)^-1, x) == :(-1*c^-7//2*d^9//2*(b*c+-1*a*d)^-2*arctan(x*c^-1//2*d^(1/2))+(1/2)*b*a^-1*x^-5*(a+b*x^2)^-1*(b*c+-1*a*d)^-1+-1//2*a^-4*c^-3*x^-1*(b*c+-1*a*d)^-1*(-2*a^3*d^3+7*b^3*c^3+-2*a*d*b^2*c^2+-2*b*c*a^2*d^2)+-1//2*a^-9//2*b^7//2*(b*c+-1*a*d)^-2*(-9*a*d+7*b*c)*arctan(x*a^-1//2*b^(1/2))+-1//10*a^-2*c^-1*x^-5*(b*c+-1*a*d)^-1*(-2*a*d+7*b*c)+1//6*a^-3*c^-2*x^-3*(b*c+-1*a*d)^-1*(-2*a^2*d^2+7*b^2*c^2+-2*a*b*c*d))
@test integrate(x^-7*(a+b*x^2)^-2*(c+d*x^2)^-1, x) == :(-1//6*a^-2*c^-1*x^-6+(1/2)*c^-4*d^5*(b*c+-1*a*d)^-2*log(c+d*x^2)+-1*a^-5*c^-4*(a^3*d^3+4*b^3*c^3+2*b*c*a^2*d^2+3*a*d*b^2*c^2)*log(x)+-1//2*a^-4*b^4*(a+b*x^2)^-1*(b*c+-1*a*d)^-1+-1//2*a^-4*c^-3*x^-2*(a^2*d^2+3*b^2*c^2+2*a*b*c*d)+1//4*a^-3*c^-2*x^-4*(a*d+2*b*c)+(1/2)*a^-5*b^4*(b*c+-1*a*d)^-2*(-5*a*d+4*b*c)*log(a+b*x^2))
@test integrate(x^4*(a+b*x^2)^-2*(c+d*x^2)^-2, x) == :((1/2)*x*b^-1*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(a*d+b*c)+(1/2)*c^(1/2)*d^-1//2*(b*c+-1*a*d)^-3*(b*c+3*a*d)*arctan(x*c^-1//2*d^(1/2))+-1//2*a^(1/2)*b^-1//2*(b*c+-1*a*d)^-3*(a*d+3*b*c)*arctan(x*a^-1//2*b^(1/2))+(1/2)*a*x*b^-1*(a+b*x^2)^-1*(c+d*x^2)^-1*(b*c+-1*a*d)^-1)
@test integrate(x^3*(a+b*x^2)^-2*(c+d*x^2)^-2, x) == :((1/2)*a*(a+b*x^2)^-1*(b*c+-1*a*d)^-2+(1/2)*c*(c+d*x^2)^-1*(b*c+-1*a*d)^-2+(1/2)*(b*c+-1*a*d)^-3*(a*d+b*c)*log(a+b*x^2)+-1//2*(b*c+-1*a*d)^-3*(a*d+b*c)*log(c+d*x^2))
@test integrate(x^2*(a+b*x^2)^-2*(c+d*x^2)^-2, x) == :(-1*d*x*(c+d*x^2)^-1*(b*c+-1*a*d)^-2+-1*x*(a+b*x^2)^-1*(c+d*x^2)^-1*(-2*a*d+2*b*c)^-1+(1/2)*a^-1//2*b^(1/2)*(b*c+-1*a*d)^-3*(b*c+3*a*d)*arctan(x*a^-1//2*b^(1/2))+-1//2*c^-1//2*d^(1/2)*(b*c+-1*a*d)^-3*(a*d+3*b*c)*arctan(x*c^-1//2*d^(1/2)))
@test integrate(x*(a+b*x^2)^-2*(c+d*x^2)^-2, x) == :(-1//2*b*(a+b*x^2)^-1*(b*c+-1*a*d)^-2+-1//2*d*(c+d*x^2)^-1*(b*c+-1*a*d)^-2+b*d*(b*c+-1*a*d)^-3*log(c+d*x^2)+-1*b*d*(b*c+-1*a*d)^-3*log(a+b*x^2))
@test integrate((a+b*x^2)^-2*(c+d*x^2)^-2, x) == :((1/2)*a^-3//2*b^3//2*(b*c+-1*a*d)^-3*(b*c+-5*a*d)*arctan(x*a^-1//2*b^(1/2))+(1/2)*c^-3//2*d^3//2*(b*c+-1*a*d)^-3*(-1*a*d+5*b*c)*arctan(x*c^-1//2*d^(1/2))+(1/2)*b*x*a^-1*(a+b*x^2)^-1*(c+d*x^2)^-1*(b*c+-1*a*d)^-1+(1/2)*d*x*a^-1*c^-1*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(a*d+b*c))
@test integrate(x^-1*(a+b*x^2)^-2*(c+d*x^2)^-2, x) == :(a^-2*c^-2*log(x)+(1/2)*a^-1*b^2*(a+b*x^2)^-1*(b*c+-1*a*d)^-2+(1/2)*c^-1*d^2*(c+d*x^2)^-1*(b*c+-1*a*d)^-2+-1//2*a^-2*b^2*(b*c+-1*a*d)^-3*(b*c+-3*a*d)*log(a+b*x^2)+-1//2*c^-2*d^2*(b*c+-1*a*d)^-3*(-1*a*d+3*b*c)*log(c+d*x^2))
@test integrate(x^-2*(a+b*x^2)^-2*(c+d*x^2)^-2, x) == :(-1//2*a^-2*c^-2*x^-1*(b*c+-1*a*d)^-2*(3*a^2*d^2+3*b^2*c^2+-4*a*b*c*d)+-1//2*a^-5//2*b^5//2*(b*c+-1*a*d)^-3*(-7*a*d+3*b*c)*arctan(x*a^-1//2*b^(1/2))+-1//2*c^-5//2*d^5//2*(b*c+-1*a*d)^-3*(-3*a*d+7*b*c)*arctan(x*c^-1//2*d^(1/2))+(1/2)*b*a^-1*x^-1*(a+b*x^2)^-1*(c+d*x^2)^-1*(b*c+-1*a*d)^-1+(1/2)*d*a^-1*c^-1*x^-1*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(a*d+b*c))
@test integrate(x^-3*(a+b*x^2)^-2*(c+d*x^2)^-2, x) == :(-1//2*a^-2*c^-2*x^-2+-1*a^-3*c^-3*(2*a*d+2*b*c)*log(x)+-1//2*a^-2*b^3*(a+b*x^2)^-1*(b*c+-1*a*d)^-2+-1//2*c^-2*d^3*(c+d*x^2)^-1*(b*c+-1*a*d)^-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^2))
@test integrate(x^-4*(a+b*x^2)^-2*(c+d*x^2)^-2, x) == :((1/2)*a^-7//2*b^7//2*(b*c+-1*a*d)^-3*(-9*a*d+5*b*c)*arctan(x*a^-1//2*b^(1/2))+(1/2)*c^-7//2*d^7//2*(b*c+-1*a*d)^-3*(-5*a*d+9*b*c)*arctan(x*c^-1//2*d^(1/2))+-1//6*a^-2*c^-2*x^-3*(b*c+-1*a*d)^-2*(5*a^2*d^2+5*b^2*c^2+-4*a*b*c*d)+(1/2)*b*a^-1*x^-3*(a+b*x^2)^-1*(c+d*x^2)^-1*(b*c+-1*a*d)^-1+(1/2)*a^-3*c^-3*x^-1*(b*c+-1*a*d)^-2*(a*d+b*c)*(5*a^2*d^2+5*b^2*c^2+-9*a*b*c*d)+(1/2)*d*a^-1*c^-1*x^-3*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(a*d+b*c))
@test integrate(x^4*(a+b*x^2)^-2*(c+d*x^2)^-3, x) == :(1//8*x*(c+d*x^2)^-1*(b*c+-1*a*d)^-3*(3*b*c+9*a*d)+-3//2*a^(1/2)*b^(1/2)*(b*c+-1*a*d)^-4*(a*d+b*c)*arctan(x*a^-1//2*b^(1/2))+1//4*x*b^-1*(c+d*x^2)^-2*(b*c+-1*a*d)^-2*(b*c+2*a*d)+1//8*c^-1//2*d^-1//2*(b*c+-1*a*d)^-4*(3*a^2*d^2+3*b^2*c^2+18*a*b*c*d)*arctan(x*c^-1//2*d^(1/2))+(1/2)*a*x*b^-1*(a+b*x^2)^-1*(c+d*x^2)^-2*(b*c+-1*a*d)^-1)
@test integrate(x^3*(a+b*x^2)^-2*(c+d*x^2)^-3, x) == :((1/2)*(c+d*x^2)^-1*(b*c+-1*a*d)^-3*(a*d+b*c)+1//4*c*(c+d*x^2)^-2*(b*c+-1*a*d)^-2+(1/2)*a*b*(a+b*x^2)^-1*(b*c+-1*a*d)^-3+(1/2)*b*(b*c+-1*a*d)^-4*(b*c+2*a*d)*log(a+b*x^2)+-1//2*b*(b*c+-1*a*d)^-4*(b*c+2*a*d)*log(c+d*x^2))
@test integrate(x^2*(a+b*x^2)^-2*(c+d*x^2)^-3, x) == :(-1*x*(a+b*x^2)^-1*(c+d*x^2)^-2*(-2*a*d+2*b*c)^-1+-3//4*d*x*(c+d*x^2)^-2*(b*c+-1*a*d)^-2+(1/2)*a^-1//2*b^3//2*(b*c+-1*a*d)^-4*(b*c+5*a*d)*arctan(x*a^-1//2*b^(1/2))+-1//8*c^-3//2*d^(1/2)*(b*c+-1*a*d)^-4*(-1*a^2*d^2+15*b^2*c^2+10*a*b*c*d)*arctan(x*c^-1//2*d^(1/2))+-1//8*d*x*c^-1*(c+d*x^2)^-1*(b*c+-1*a*d)^-3*(a*d+11*b*c))
@test integrate(x*(a+b*x^2)^-2*(c+d*x^2)^-3, x) == :(-1//2*b^2*(a+b*x^2)^-1*(b*c+-1*a*d)^-3+-1//4*d*(c+d*x^2)^-2*(b*c+-1*a*d)^-2+-1*b*d*(c+d*x^2)^-1*(b*c+-1*a*d)^-3+-3//2*d*b^2*(b*c+-1*a*d)^-4*log(a+b*x^2)+3//2*d*b^2*(b*c+-1*a*d)^-4*log(c+d*x^2))
@test integrate((a+b*x^2)^-2*(c+d*x^2)^-3, x) == :((1/2)*a^-3//2*b^5//2*(b*c+-1*a*d)^-4*(b*c+-7*a*d)*arctan(x*a^-1//2*b^(1/2))+1//8*c^-5//2*d^3//2*(b*c+-1*a*d)^-4*(3*a^2*d^2+35*b^2*c^2+-14*a*b*c*d)*arctan(x*c^-1//2*d^(1/2))+(1/2)*b*x*a^-1*(a+b*x^2)^-1*(c+d*x^2)^-2*(b*c+-1*a*d)^-1+1//4*d*x*a^-1*c^-1*(c+d*x^2)^-2*(b*c+-1*a*d)^-2*(a*d+2*b*c)+1//8*d*x*a^-1*c^-2*(c+d*x^2)^-1*(b*c+-1*a*d)^-3*(b*c+3*a*d)*(-1*a*d+4*b*c))
@test integrate(x^-1*(a+b*x^2)^-2*(c+d*x^2)^-3, x) == :(a^-2*c^-3*log(x)+(1/2)*a^-1*b^3*(a+b*x^2)^-1*(b*c+-1*a*d)^-3+1//4*c^-1*d^2*(c+d*x^2)^-2*(b*c+-1*a*d)^-2+(1/2)*c^-2*d^2*(c+d*x^2)^-1*(b*c+-1*a*d)^-3*(-1*a*d+3*b*c)+-1//2*a^-2*b^3*(b*c+-1*a*d)^-4*(b*c+-4*a*d)*log(a+b*x^2)+-1//2*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^2))
@test integrate(x^-2*(a+b*x^2)^-2*(c+d*x^2)^-3, x) == :(-3//2*a^-5//2*b^7//2*(b*c+-1*a*d)^-4*(b*c+-3*a*d)*arctan(x*a^-1//2*b^(1/2))+-3//8*c^-7//2*d^5//2*(b*c+-1*a*d)^-4*(5*a^2*d^2+21*b^2*c^2+-18*a*b*c*d)*arctan(x*c^-1//2*d^(1/2))+(1/2)*b*a^-1*x^-1*(a+b*x^2)^-1*(c+d*x^2)^-2*(b*c+-1*a*d)^-1+-1//8*a^-2*c^-3*x^-1*(b*c+-1*a*d)^-3*(-3*a*d+6*b*c)*(2*b^2*c^2+5*a^2*d^2+-3*a*b*c*d)+1//4*d*a^-1*c^-1*x^-1*(c+d*x^2)^-2*(b*c+-1*a*d)^-2*(a*d+2*b*c)+1//8*d*a^-1*c^-2*x^-1*(c+d*x^2)^-1*(b*c+-1*a*d)^-3*(-5*a^2*d^2+4*b^2*c^2+13*a*b*c*d))
@test integrate(x^-3*(a+b*x^2)^-2*(c+d*x^2)^-3, x) == :(-1//2*a^-2*c^-3*x^-2+-1*a^-3*c^-4*(2*b*c+3*a*d)*log(x)+-1//2*a^-2*b^4*(a+b*x^2)^-1*(b*c+-1*a*d)^-3+-1//4*c^-2*d^3*(c+d*x^2)^-2*(b*c+-1*a*d)^-2+(1/2)*a^-3*b^4*(b*c+-1*a*d)^-4*(-5*a*d+2*b*c)*log(a+b*x^2)+(1/2)*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)+-1*c^-3*d^3*(c+d*x^2)^-1*(b*c+-1*a*d)^-3*(-1*a*d+2*b*c))
@test integrate(x^-4*(a+b*x^2)^-2*(c+d*x^2)^-3, x) == :((1/2)*a^-7//2*b^9//2*(b*c+-1*a*d)^-4*(-11*a*d+5*b*c)*arctan(x*a^-1//2*b^(1/2))+-1//24*a^-2*c^-3*x^-3*(b*c+-1*a*d)^-3*(-35*a^3*d^3+20*b^3*c^3+-24*a*d*b^2*c^2+75*b*c*a^2*d^2)+1//8*a^-3*c^-4*x^-1*(b*c+-1*a*d)^-3*(-35*a^4*d^4+20*b^4*c^4+-24*a*d*b^3*c^3+-24*a^2*b^2*c^2*d^2+75*b*c*a^3*d^3)+1//8*c^-9//2*d^7//2*(b*c+-1*a*d)^-4*(35*a^2*d^2+99*b^2*c^2+-110*a*b*c*d)*arctan(x*c^-1//2*d^(1/2))+(1/2)*b*a^-1*x^-3*(a+b*x^2)^-1*(c+d*x^2)^-2*(b*c+-1*a*d)^-1+1//4*d*a^-1*c^-1*x^-3*(c+d*x^2)^-2*(b*c+-1*a*d)^-2*(a*d+2*b*c)+1//8*d*a^-1*c^-2*x^-3*(c+d*x^2)^-1*(b*c+-1*a*d)^-3*(-7*a^2*d^2+4*b^2*c^2+15*a*b*c*d))
@test integrate(x^m*(a+b*x^2)^3*(A+B*x^2), x) == :(A*a^3*x^(1+m)*(1+m)^-1+B*b^3*x^(9+m)*(9+m)^-1+a^2*x^(3+m)*(3+m)^-1*(B*a+3*A*b)+b^2*x^(7+m)*(7+m)^-1*(A*b+3*B*a)+3*a*b*x^(5+m)*(5+m)^-1*(A*b+B*a))
@test integrate(x^m*(a+b*x^2)^2*(A+B*x^2), x) == :(A*a^2*x^(1+m)*(1+m)^-1+B*b^2*x^(7+m)*(7+m)^-1+a*x^(3+m)*(3+m)^-1*(B*a+2*A*b)+b*x^(5+m)*(5+m)^-1*(A*b+2*B*a))
@test integrate(x^m*(A+B*x^2)*(a+b*x^2), x) == :(x^(3+m)*(3+m)^-1*(A*b+B*a)+A*a*x^(1+m)*(1+m)^-1+B*b*x^(5+m)*(5+m)^-1)
@test integrate(x^m*(a+b*x^2)^2*(c+d*x^2)^3, x) == :(c*x^(5+m)*(5+m)^-1*(b^2*c^2+3*a^2*d^2+6*a*b*c*d)+d*x^(7+m)*(7+m)^-1*(a^2*d^2+3*b^2*c^2+6*a*b*c*d)+a^2*c^3*x^(1+m)*(1+m)^-1+b^2*d^3*x^(11+m)*(11+m)^-1+a*c^2*x^(3+m)*(3+m)^-1*(2*b*c+3*a*d)+b*d^2*x^(9+m)*(9+m)^-1*(2*a*d+3*b*c))
@test integrate(x^m*(a+b*x^2)^2*(c+d*x^2)^2, x) == :(x^(5+m)*(5+m)^-1*(a^2*d^2+b^2*c^2+4*a*b*c*d)+a^2*c^2*x^(1+m)*(1+m)^-1+b^2*d^2*x^(9+m)*(9+m)^-1+2*a*c*x^(3+m)*(3+m)^-1*(a*d+b*c)+2*b*d*x^(7+m)*(7+m)^-1*(a*d+b*c))
@test integrate(x^m*(a+b*x^2)^2*(c+d*x^2), x) == :(a*x^(3+m)*(3+m)^-1*(a*d+2*b*c)+b*x^(5+m)*(5+m)^-1*(b*c+2*a*d)+c*a^2*x^(1+m)*(1+m)^-1+d*b^2*x^(7+m)*(7+m)^-1)
@test integrate(x^7//2*(A+B*x^2)*(a+b*x^2), x) == :(1//13*x^13//2*(2*A*b+2*B*a)+2//9*A*a*x^9//2+2//17*B*b*x^17//2)
@test integrate(x^5//2*(A+B*x^2)*(a+b*x^2), x) == :(1//11*x^11//2*(2*A*b+2*B*a)+2//7*A*a*x^7//2+2//15*B*b*x^15//2)
@test integrate(x^3//2*(A+B*x^2)*(a+b*x^2), x) == :(1//9*x^9//2*(2*A*b+2*B*a)+2//5*A*a*x^5//2+2//13*B*b*x^13//2)
@test integrate(x^(1/2)*(A+B*x^2)*(a+b*x^2), x) == :(1//7*x^7//2*(2*A*b+2*B*a)+2//3*A*a*x^3//2+2//11*B*b*x^11//2)
@test integrate(x^-1//2*(A+B*x^2)*(a+b*x^2), x) == :(1//5*x^5//2*(2*A*b+2*B*a)+2*A*a*x^(1/2)+2//9*B*b*x^9//2)
@test integrate(x^-3//2*(A+B*x^2)*(a+b*x^2), x) == :(1//3*x^3//2*(2*A*b+2*B*a)+-2*A*a*x^-1//2+2//7*B*b*x^7//2)
@test integrate(x^-5//2*(A+B*x^2)*(a+b*x^2), x) == :(x^(1/2)*(2*A*b+2*B*a)+-2//3*A*a*x^-3//2+2//5*B*b*x^5//2)
@test integrate(x^-7//2*(A+B*x^2)*(a+b*x^2), x) == :(-1*x^-1//2*(2*A*b+2*B*a)+-2//5*A*a*x^-5//2+2//3*B*b*x^3//2)
@test integrate(x^7//2*(a+b*x^2)^2*(A+B*x^2), x) == :(2//9*A*a^2*x^9//2+2//13*a*x^13//2*(B*a+2*A*b)+2//17*b*x^17//2*(A*b+2*B*a)+2//21*B*b^2*x^21//2)
@test integrate(x^5//2*(a+b*x^2)^2*(A+B*x^2), x) == :(2//7*A*a^2*x^7//2+2//11*a*x^11//2*(B*a+2*A*b)+2//15*b*x^15//2*(A*b+2*B*a)+2//19*B*b^2*x^19//2)
@test integrate(x^3//2*(a+b*x^2)^2*(A+B*x^2), x) == :(2//5*A*a^2*x^5//2+2//9*a*x^9//2*(B*a+2*A*b)+2//13*b*x^13//2*(A*b+2*B*a)+2//17*B*b^2*x^17//2)
@test integrate(x^(1/2)*(a+b*x^2)^2*(A+B*x^2), x) == :(2//3*A*a^2*x^3//2+2//7*a*x^7//2*(B*a+2*A*b)+2//11*b*x^11//2*(A*b+2*B*a)+2//15*B*b^2*x^15//2)
@test integrate(x^-1//2*(a+b*x^2)^2*(A+B*x^2), x) == :(2*A*a^2*x^(1/2)+2//5*a*x^5//2*(B*a+2*A*b)+2//9*b*x^9//2*(A*b+2*B*a)+2//13*B*b^2*x^13//2)
@test integrate(x^-3//2*(a+b*x^2)^2*(A+B*x^2), x) == :(-2*A*a^2*x^-1//2+2//3*a*x^3//2*(B*a+2*A*b)+2//7*b*x^7//2*(A*b+2*B*a)+2//11*B*b^2*x^11//2)
@test integrate(x^-5//2*(a+b*x^2)^2*(A+B*x^2), x) == :(2*a*x^(1/2)*(B*a+2*A*b)+-2//3*A*a^2*x^-3//2+2//5*b*x^5//2*(A*b+2*B*a)+2//9*B*b^2*x^9//2)
@test integrate(x^-7//2*(a+b*x^2)^2*(A+B*x^2), x) == :(-2*a*x^-1//2*(B*a+2*A*b)+-2//5*A*a^2*x^-5//2+2//3*b*x^3//2*(A*b+2*B*a)+2//7*B*b^2*x^7//2)
@test integrate(x^7//2*(a+b*x^2)^3*(A+B*x^2), x) == :(2//9*A*a^3*x^9//2+2//13*a^2*x^13//2*(B*a+3*A*b)+2//21*b^2*x^21//2*(A*b+3*B*a)+2//25*B*b^3*x^25//2+6//17*a*b*x^17//2*(A*b+B*a))
@test integrate(x^5//2*(a+b*x^2)^3*(A+B*x^2), x) == :(2//7*A*a^3*x^7//2+2//11*a^2*x^11//2*(B*a+3*A*b)+2//19*b^2*x^19//2*(A*b+3*B*a)+2//23*B*b^3*x^23//2+2//5*a*b*x^15//2*(A*b+B*a))
@test integrate(x^3//2*(a+b*x^2)^3*(A+B*x^2), x) == :(2//5*A*a^3*x^5//2+2//9*a^2*x^9//2*(B*a+3*A*b)+2//17*b^2*x^17//2*(A*b+3*B*a)+2//21*B*b^3*x^21//2+6//13*a*b*x^13//2*(A*b+B*a))
@test integrate(x^(1/2)*(a+b*x^2)^3*(A+B*x^2), x) == :(2//3*A*a^3*x^3//2+2//7*a^2*x^7//2*(B*a+3*A*b)+2//15*b^2*x^15//2*(A*b+3*B*a)+2//19*B*b^3*x^19//2+6//11*a*b*x^11//2*(A*b+B*a))
@test integrate(x^-1//2*(a+b*x^2)^3*(A+B*x^2), x) == :(2*A*a^3*x^(1/2)+2//5*a^2*x^5//2*(B*a+3*A*b)+2//13*b^2*x^13//2*(A*b+3*B*a)+2//17*B*b^3*x^17//2+2//3*a*b*x^9//2*(A*b+B*a))
@test integrate(x^-3//2*(a+b*x^2)^3*(A+B*x^2), x) == :(-2*A*a^3*x^-1//2+2//3*a^2*x^3//2*(B*a+3*A*b)+2//11*b^2*x^11//2*(A*b+3*B*a)+2//15*B*b^3*x^15//2+6//7*a*b*x^7//2*(A*b+B*a))
@test integrate(x^-5//2*(a+b*x^2)^3*(A+B*x^2), x) == :(2*a^2*x^(1/2)*(B*a+3*A*b)+-2//3*A*a^3*x^-3//2+2//9*b^2*x^9//2*(A*b+3*B*a)+2//13*B*b^3*x^13//2+6//5*a*b*x^5//2*(A*b+B*a))
@test integrate(x^-7//2*(a+b*x^2)^3*(A+B*x^2), x) == :(-2*a^2*x^-1//2*(B*a+3*A*b)+-2//5*A*a^3*x^-5//2+2//7*b^2*x^7//2*(A*b+3*B*a)+2//11*B*b^3*x^11//2+2*a*b*x^3//2*(A*b+B*a))
@test integrate(x^7//2*(a+b*x^2)^-1*(A+B*x^2), x) == :(1//5*b^-2*x^5//2*(-2*B*a+2*A*b)+2//9*B*b^-1*x^9//2+-2*a*b^-3*x^(1/2)*(A*b+-1*B*a)+(1/2)*2^(1/2)*a^5//4*b^-13//4*(A*b+-1*B*a)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*a^5//4*b^-13//4*(A*b+-1*B*a)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^5//4*b^-13//4*(A*b+-1*B*a)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^5//4*b^-13//4*(A*b+-1*B*a)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^5//2*(a+b*x^2)^-1*(A+B*x^2), x) == :(1//3*b^-2*x^3//2*(-2*B*a+2*A*b)+2//7*B*b^-1*x^7//2+(1/2)*2^(1/2)*a^3//4*b^-11//4*(A*b+-1*B*a)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*a^3//4*b^-11//4*(A*b+-1*B*a)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^3//4*b^-11//4*(A*b+-1*B*a)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^3//4*b^-11//4*(A*b+-1*B*a)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^3//2*(a+b*x^2)^-1*(A+B*x^2), x) == :(b^-2*x^(1/2)*(-2*B*a+2*A*b)+2//5*B*b^-1*x^5//2+(1/2)*2^(1/2)*a^1//4*b^-9//4*(A*b+-1*B*a)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*a^1//4*b^-9//4*(A*b+-1*B*a)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^1//4*b^-9//4*(A*b+-1*B*a)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^1//4*b^-9//4*(A*b+-1*B*a)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^(1/2)*(a+b*x^2)^-1*(A+B*x^2), x) == :(2//3*B*b^-1*x^3//2+(1/2)*2^(1/2)*a^-1//4*b^-7//4*(A*b+-1*B*a)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*a^-1//4*b^-7//4*(A*b+-1*B*a)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^-1//4*b^-7//4*(A*b+-1*B*a)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^-1//4*b^-7//4*(A*b+-1*B*a)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^-1//2*(a+b*x^2)^-1*(A+B*x^2), x) == :(2*B*b^-1*x^(1/2)+(1/2)*2^(1/2)*a^-3//4*b^-5//4*(A*b+-1*B*a)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*a^-3//4*b^-5//4*(A*b+-1*B*a)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^-3//4*b^-5//4*(A*b+-1*B*a)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^-3//4*b^-5//4*(A*b+-1*B*a)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^-3//2*(a+b*x^2)^-1*(A+B*x^2), x) == :(-2*A*a^-1*x^-1//2+(1/2)*2^(1/2)*a^-5//4*b^-3//4*(A*b+-1*B*a)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*a^-5//4*b^-3//4*(A*b+-1*B*a)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^-5//4*b^-3//4*(A*b+-1*B*a)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^-5//4*b^-3//4*(A*b+-1*B*a)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^-5//2*(a+b*x^2)^-1*(A+B*x^2), x) == :(-2//3*A*a^-1*x^-3//2+(1/2)*2^(1/2)*a^-7//4*b^-1//4*(A*b+-1*B*a)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*a^-7//4*b^-1//4*(A*b+-1*B*a)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^-7//4*b^-1//4*(A*b+-1*B*a)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^-7//4*b^-1//4*(A*b+-1*B*a)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^-7//2*(a+b*x^2)^-1*(A+B*x^2), x) == :(a^-2*x^-1//2*(-2*B*a+2*A*b)+-2//5*A*a^-1*x^-5//2+(1/2)*2^(1/2)*a^-9//4*b^1//4*(A*b+-1*B*a)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*a^-9//4*b^1//4*(A*b+-1*B*a)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^-9//4*b^1//4*(A*b+-1*B*a)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^-9//4*b^1//4*(A*b+-1*B*a)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^7//2*(a+b*x^2)^-2*(A+B*x^2), x) == :((1/2)*b^-3*x^(1/2)*(-9*B*a+5*A*b)+-1//10*a^-1*b^-2*x^5//2*(-9*B*a+5*A*b)+(1/2)*a^-1*b^-1*x^9//2*(a+b*x^2)^-1*(A*b+-1*B*a)+-1//8*2^(1/2)*a^1//4*b^-13//4*(-9*B*a+5*A*b)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//16*2^(1/2)*a^1//4*b^-13//4*(-9*B*a+5*A*b)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//8*2^(1/2)*a^1//4*b^-13//4*(-9*B*a+5*A*b)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//16*2^(1/2)*a^1//4*b^-13//4*(-9*B*a+5*A*b)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^5//2*(a+b*x^2)^-2*(A+B*x^2), x) == :(-1//6*a^-1*b^-2*x^3//2*(-7*B*a+3*A*b)+(1/2)*a^-1*b^-1*x^7//2*(a+b*x^2)^-1*(A*b+-1*B*a)+-1//8*2^(1/2)*a^-1//4*b^-11//4*(-7*B*a+3*A*b)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//16*2^(1/2)*a^-1//4*b^-11//4*(-7*B*a+3*A*b)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//8*2^(1/2)*a^-1//4*b^-11//4*(-7*B*a+3*A*b)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//16*2^(1/2)*a^-1//4*b^-11//4*(-7*B*a+3*A*b)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^3//2*(a+b*x^2)^-2*(A+B*x^2), x) == :(-1//2*a^-1*b^-2*x^(1/2)*(A*b+-5*B*a)+(1/2)*a^-1*b^-1*x^5//2*(a+b*x^2)^-1*(A*b+-1*B*a)+-1//8*2^(1/2)*a^-3//4*b^-9//4*(A*b+-5*B*a)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//16*2^(1/2)*a^-3//4*b^-9//4*(A*b+-5*B*a)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//8*2^(1/2)*a^-3//4*b^-9//4*(A*b+-5*B*a)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//16*2^(1/2)*a^-3//4*b^-9//4*(A*b+-5*B*a)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^(1/2)*(a+b*x^2)^-2*(A+B*x^2), x) == :((1/2)*a^-1*b^-1*x^3//2*(a+b*x^2)^-1*(A*b+-1*B*a)+-1//8*2^(1/2)*a^-5//4*b^-7//4*(A*b+3*B*a)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//16*2^(1/2)*a^-5//4*b^-7//4*(A*b+3*B*a)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//8*2^(1/2)*a^-5//4*b^-7//4*(A*b+3*B*a)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//16*2^(1/2)*a^-5//4*b^-7//4*(A*b+3*B*a)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^-1//2*(a+b*x^2)^-2*(A+B*x^2), x) == :((1/2)*a^-1*b^-1*x^(1/2)*(a+b*x^2)^-1*(A*b+-1*B*a)+-1//8*2^(1/2)*a^-7//4*b^-5//4*(B*a+3*A*b)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//16*2^(1/2)*a^-7//4*b^-5//4*(B*a+3*A*b)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//8*2^(1/2)*a^-7//4*b^-5//4*(B*a+3*A*b)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//16*2^(1/2)*a^-7//4*b^-5//4*(B*a+3*A*b)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^-3//2*(a+b*x^2)^-2*(A+B*x^2), x) == :(-1//2*a^-2*b^-1*x^-1//2*(-1*B*a+5*A*b)+(1/2)*a^-1*b^-1*x^-1//2*(a+b*x^2)^-1*(A*b+-1*B*a)+-1//8*2^(1/2)*a^-9//4*b^-3//4*(-1*B*a+5*A*b)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//16*2^(1/2)*a^-9//4*b^-3//4*(-1*B*a+5*A*b)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//8*2^(1/2)*a^-9//4*b^-3//4*(-1*B*a+5*A*b)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//16*2^(1/2)*a^-9//4*b^-3//4*(-1*B*a+5*A*b)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^-5//2*(a+b*x^2)^-2*(A+B*x^2), x) == :(-1//6*a^-2*b^-1*x^-3//2*(-3*B*a+7*A*b)+(1/2)*a^-1*b^-1*x^-3//2*(a+b*x^2)^-1*(A*b+-1*B*a)+-1//8*2^(1/2)*a^-11//4*b^-1//4*(-3*B*a+7*A*b)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//16*2^(1/2)*a^-11//4*b^-1//4*(-3*B*a+7*A*b)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//8*2^(1/2)*a^-11//4*b^-1//4*(-3*B*a+7*A*b)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//16*2^(1/2)*a^-11//4*b^-1//4*(-3*B*a+7*A*b)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^-7//2*(a+b*x^2)^-2*(A+B*x^2), x) == :((1/2)*a^-3*x^-1//2*(-5*B*a+9*A*b)+-1//10*a^-2*b^-1*x^-5//2*(-5*B*a+9*A*b)+(1/2)*a^-1*b^-1*x^-5//2*(a+b*x^2)^-1*(A*b+-1*B*a)+-1//8*2^(1/2)*a^-13//4*b^1//4*(-5*B*a+9*A*b)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//16*2^(1/2)*a^-13//4*b^1//4*(-5*B*a+9*A*b)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//8*2^(1/2)*a^-13//4*b^1//4*(-5*B*a+9*A*b)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//16*2^(1/2)*a^-13//4*b^1//4*(-5*B*a+9*A*b)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^7//2*(a+b*x^2)^-3*(A+B*x^2), x) == :(-1//16*a^-1*b^-3*x^(1/2)*(-45*B*a+5*A*b)+-1//64*2^(1/2)*a^-3//4*b^-13//4*(-45*B*a+5*A*b)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//128*2^(1/2)*a^-3//4*b^-13//4*(-45*B*a+5*A*b)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*a^-1*b^-1*x^9//2*(a+b*x^2)^-2*(A*b+-1*B*a)+1//16*a^-1*b^-2*x^5//2*(a+b*x^2)^-1*(A*b+-9*B*a)+1//64*2^(1/2)*a^-3//4*b^-13//4*(-45*B*a+5*A*b)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//128*2^(1/2)*a^-3//4*b^-13//4*(-45*B*a+5*A*b)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^5//2*(a+b*x^2)^-3*(A+B*x^2), x) == :(-1//16*a^-1*b^-2*x^3//2*(a+b*x^2)^-1*(A*b+7*B*a)+-1//64*2^(1/2)*a^-5//4*b^-11//4*(3*A*b+21*B*a)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//128*2^(1/2)*a^-5//4*b^-11//4*(3*A*b+21*B*a)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*a^-1*b^-1*x^7//2*(a+b*x^2)^-2*(A*b+-1*B*a)+1//64*2^(1/2)*a^-5//4*b^-11//4*(3*A*b+21*B*a)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//128*2^(1/2)*a^-5//4*b^-11//4*(3*A*b+21*B*a)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^3//2*(a+b*x^2)^-3*(A+B*x^2), x) == :(-1//16*a^-1*b^-2*x^(1/2)*(a+b*x^2)^-1*(3*A*b+5*B*a)+-1//64*2^(1/2)*a^-7//4*b^-9//4*(3*A*b+5*B*a)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//128*2^(1/2)*a^-7//4*b^-9//4*(3*A*b+5*B*a)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*a^-1*b^-1*x^5//2*(a+b*x^2)^-2*(A*b+-1*B*a)+1//64*2^(1/2)*a^-7//4*b^-9//4*(3*A*b+5*B*a)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//128*2^(1/2)*a^-7//4*b^-9//4*(3*A*b+5*B*a)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^(1/2)*(a+b*x^2)^-3*(A+B*x^2), x) == :(-1//64*2^(1/2)*a^-9//4*b^-7//4*(3*B*a+5*A*b)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//128*2^(1/2)*a^-9//4*b^-7//4*(3*B*a+5*A*b)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*a^-1*b^-1*x^3//2*(a+b*x^2)^-2*(A*b+-1*B*a)+1//16*a^-2*b^-1*x^3//2*(a+b*x^2)^-1*(3*B*a+5*A*b)+1//64*2^(1/2)*a^-9//4*b^-7//4*(3*B*a+5*A*b)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//128*2^(1/2)*a^-9//4*b^-7//4*(3*B*a+5*A*b)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^-1//2*(a+b*x^2)^-3*(A+B*x^2), x) == :(-1//64*2^(1/2)*a^-11//4*b^-5//4*(3*B*a+21*A*b)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//128*2^(1/2)*a^-11//4*b^-5//4*(3*B*a+21*A*b)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*a^-1*b^-1*x^(1/2)*(a+b*x^2)^-2*(A*b+-1*B*a)+1//16*a^-2*b^-1*x^(1/2)*(a+b*x^2)^-1*(B*a+7*A*b)+1//64*2^(1/2)*a^-11//4*b^-5//4*(3*B*a+21*A*b)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//128*2^(1/2)*a^-11//4*b^-5//4*(3*B*a+21*A*b)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^-3//2*(a+b*x^2)^-3*(A+B*x^2), x) == :(-1//16*a^-3*b^-1*x^-1//2*(-5*B*a+45*A*b)+-1//64*2^(1/2)*a^-13//4*b^-3//4*(-5*B*a+45*A*b)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//128*2^(1/2)*a^-13//4*b^-3//4*(-5*B*a+45*A*b)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*a^-1*b^-1*x^-1//2*(a+b*x^2)^-2*(A*b+-1*B*a)+1//16*a^-2*b^-1*x^-1//2*(a+b*x^2)^-1*(-1*B*a+9*A*b)+1//64*2^(1/2)*a^-13//4*b^-3//4*(-5*B*a+45*A*b)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//128*2^(1/2)*a^-13//4*b^-3//4*(-5*B*a+45*A*b)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^-5//2*(a+b*x^2)^-3*(A+B*x^2), x) == :(-1//48*a^-3*b^-1*x^-3//2*(-21*B*a+77*A*b)+-1//64*2^(1/2)*a^-15//4*b^-1//4*(-21*B*a+77*A*b)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//128*2^(1/2)*a^-15//4*b^-1//4*(-21*B*a+77*A*b)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*a^-1*b^-1*x^-3//2*(a+b*x^2)^-2*(A*b+-1*B*a)+1//16*a^-2*b^-1*x^-3//2*(a+b*x^2)^-1*(-3*B*a+11*A*b)+1//64*2^(1/2)*a^-15//4*b^-1//4*(-21*B*a+77*A*b)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//128*2^(1/2)*a^-15//4*b^-1//4*(-21*B*a+77*A*b)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^-7//2*(a+b*x^2)^-3*(A+B*x^2), x) == :(1//16*a^-4*x^-1//2*(-45*B*a+117*A*b)+-1//80*a^-3*b^-1*x^-5//2*(-45*B*a+117*A*b)+-9//64*2^(1/2)*a^-17//4*b^1//4*(-5*B*a+13*A*b)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-9//128*2^(1/2)*a^-17//4*b^1//4*(-5*B*a+13*A*b)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*a^-1*b^-1*x^-5//2*(a+b*x^2)^-2*(A*b+-1*B*a)+1//16*a^-2*b^-1*x^-5//2*(a+b*x^2)^-1*(-5*B*a+13*A*b)+9//64*2^(1/2)*a^-17//4*b^1//4*(-5*B*a+13*A*b)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+9//128*2^(1/2)*a^-17//4*b^1//4*(-5*B*a+13*A*b)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^7//2*(a+b*x^2)^2*(c+d*x^2), x) == :(2//9*c*a^2*x^9//2+2//13*a*x^13//2*(a*d+2*b*c)+2//17*b*x^17//2*(b*c+2*a*d)+2//21*d*b^2*x^21//2)
@test integrate(x^5//2*(a+b*x^2)^2*(c+d*x^2), x) == :(2//7*c*a^2*x^7//2+2//11*a*x^11//2*(a*d+2*b*c)+2//15*b*x^15//2*(b*c+2*a*d)+2//19*d*b^2*x^19//2)
@test integrate(x^3//2*(a+b*x^2)^2*(c+d*x^2), x) == :(2//5*c*a^2*x^5//2+2//9*a*x^9//2*(a*d+2*b*c)+2//13*b*x^13//2*(b*c+2*a*d)+2//17*d*b^2*x^17//2)
@test integrate(x^(1/2)*(a+b*x^2)^2*(c+d*x^2), x) == :(2//3*c*a^2*x^3//2+2//7*a*x^7//2*(a*d+2*b*c)+2//11*b*x^11//2*(b*c+2*a*d)+2//15*d*b^2*x^15//2)
@test integrate(x^-1//2*(a+b*x^2)^2*(c+d*x^2), x) == :(2*c*a^2*x^(1/2)+2//5*a*x^5//2*(a*d+2*b*c)+2//9*b*x^9//2*(b*c+2*a*d)+2//13*d*b^2*x^13//2)
@test integrate(x^-3//2*(a+b*x^2)^2*(c+d*x^2), x) == :(-2*c*a^2*x^-1//2+2//3*a*x^3//2*(a*d+2*b*c)+2//7*b*x^7//2*(b*c+2*a*d)+2//11*d*b^2*x^11//2)
@test integrate(x^-5//2*(a+b*x^2)^2*(c+d*x^2), x) == :(2*a*x^(1/2)*(a*d+2*b*c)+-2//3*c*a^2*x^-3//2+2//5*b*x^5//2*(b*c+2*a*d)+2//9*d*b^2*x^9//2)
@test integrate(x^-7//2*(a+b*x^2)^2*(c+d*x^2), x) == :(-2*a*x^-1//2*(a*d+2*b*c)+-2//5*c*a^2*x^-5//2+2//3*b*x^3//2*(b*c+2*a*d)+2//7*d*b^2*x^7//2)
@test integrate(x^7//2*(a+b*x^2)^2*(c+d*x^2)^2, x) == :(x^17//2*(2//17*a^2*d^2+2//17*b^2*c^2+8//17*a*b*c*d)+2//9*a^2*c^2*x^9//2+2//25*b^2*d^2*x^25//2+4//13*a*c*x^13//2*(a*d+b*c)+4//21*b*d*x^21//2*(a*d+b*c))
@test integrate(x^5//2*(a+b*x^2)^2*(c+d*x^2)^2, x) == :(x^15//2*(2//15*a^2*d^2+2//15*b^2*c^2+8//15*a*b*c*d)+2//7*a^2*c^2*x^7//2+2//23*b^2*d^2*x^23//2+4//11*a*c*x^11//2*(a*d+b*c)+4//19*b*d*x^19//2*(a*d+b*c))
@test integrate(x^3//2*(a+b*x^2)^2*(c+d*x^2)^2, x) == :(x^13//2*(2//13*a^2*d^2+2//13*b^2*c^2+8//13*a*b*c*d)+2//5*a^2*c^2*x^5//2+2//21*b^2*d^2*x^21//2+4//9*a*c*x^9//2*(a*d+b*c)+4//17*b*d*x^17//2*(a*d+b*c))
@test integrate(x^(1/2)*(a+b*x^2)^2*(c+d*x^2)^2, x) == :(x^11//2*(2//11*a^2*d^2+2//11*b^2*c^2+8//11*a*b*c*d)+2//3*a^2*c^2*x^3//2+2//19*b^2*d^2*x^19//2+4//7*a*c*x^7//2*(a*d+b*c)+4//15*b*d*x^15//2*(a*d+b*c))
@test integrate(x^-1//2*(a+b*x^2)^2*(c+d*x^2)^2, x) == :(x^9//2*(2//9*a^2*d^2+2//9*b^2*c^2+8//9*a*b*c*d)+2*a^2*c^2*x^(1/2)+2//17*b^2*d^2*x^17//2+4//5*a*c*x^5//2*(a*d+b*c)+4//13*b*d*x^13//2*(a*d+b*c))
@test integrate(x^-3//2*(a+b*x^2)^2*(c+d*x^2)^2, x) == :(x^7//2*(2//7*a^2*d^2+2//7*b^2*c^2+8//7*a*b*c*d)+-2*a^2*c^2*x^-1//2+2//15*b^2*d^2*x^15//2+4//3*a*c*x^3//2*(a*d+b*c)+4//11*b*d*x^11//2*(a*d+b*c))
@test integrate(x^-5//2*(a+b*x^2)^2*(c+d*x^2)^2, x) == :(x^5//2*(2//5*a^2*d^2+2//5*b^2*c^2+8//5*a*b*c*d)+-2//3*a^2*c^2*x^-3//2+2//13*b^2*d^2*x^13//2+4*a*c*x^(1/2)*(a*d+b*c)+4//9*b*d*x^9//2*(a*d+b*c))
@test integrate(x^-7//2*(a+b*x^2)^2*(c+d*x^2)^2, x) == :(x^3//2*(2//3*a^2*d^2+2//3*b^2*c^2+8//3*a*b*c*d)+-2//5*a^2*c^2*x^-5//2+2//11*b^2*d^2*x^11//2+-4*a*c*x^-1//2*(a*d+b*c)+4//7*b*d*x^7//2*(a*d+b*c))
@test integrate(x^7//2*(a+b*x^2)^2*(c+d*x^2)^3, x) == :(2//9*a^2*c^3*x^9//2+2//17*c*x^17//2*(b^2*c^2+3*a^2*d^2+6*a*b*c*d)+2//21*d*x^21//2*(a^2*d^2+3*b^2*c^2+6*a*b*c*d)+2//29*b^2*d^3*x^29//2+2//13*a*c^2*x^13//2*(2*b*c+3*a*d)+2//25*b*d^2*x^25//2*(2*a*d+3*b*c))
@test integrate(x^5//2*(a+b*x^2)^2*(c+d*x^2)^3, x) == :(2//7*a^2*c^3*x^7//2+2//15*c*x^15//2*(b^2*c^2+3*a^2*d^2+6*a*b*c*d)+2//19*d*x^19//2*(a^2*d^2+3*b^2*c^2+6*a*b*c*d)+2//27*b^2*d^3*x^27//2+2//11*a*c^2*x^11//2*(2*b*c+3*a*d)+2//23*b*d^2*x^23//2*(2*a*d+3*b*c))
@test integrate(x^3//2*(a+b*x^2)^2*(c+d*x^2)^3, x) == :(2//5*a^2*c^3*x^5//2+2//13*c*x^13//2*(b^2*c^2+3*a^2*d^2+6*a*b*c*d)+2//17*d*x^17//2*(a^2*d^2+3*b^2*c^2+6*a*b*c*d)+2//25*b^2*d^3*x^25//2+2//9*a*c^2*x^9//2*(2*b*c+3*a*d)+2//21*b*d^2*x^21//2*(2*a*d+3*b*c))
@test integrate(x^(1/2)*(a+b*x^2)^2*(c+d*x^2)^3, x) == :(2//3*a^2*c^3*x^3//2+2//11*c*x^11//2*(b^2*c^2+3*a^2*d^2+6*a*b*c*d)+2//15*d*x^15//2*(a^2*d^2+3*b^2*c^2+6*a*b*c*d)+2//23*b^2*d^3*x^23//2+2//7*a*c^2*x^7//2*(2*b*c+3*a*d)+2//19*b*d^2*x^19//2*(2*a*d+3*b*c))
@test integrate(x^-1//2*(a+b*x^2)^2*(c+d*x^2)^3, x) == :(2*a^2*c^3*x^(1/2)+2//9*c*x^9//2*(b^2*c^2+3*a^2*d^2+6*a*b*c*d)+2//13*d*x^13//2*(a^2*d^2+3*b^2*c^2+6*a*b*c*d)+2//21*b^2*d^3*x^21//2+2//5*a*c^2*x^5//2*(2*b*c+3*a*d)+2//17*b*d^2*x^17//2*(2*a*d+3*b*c))
@test integrate(x^-3//2*(a+b*x^2)^2*(c+d*x^2)^3, x) == :(-2*a^2*c^3*x^-1//2+2//7*c*x^7//2*(b^2*c^2+3*a^2*d^2+6*a*b*c*d)+2//11*d*x^11//2*(a^2*d^2+3*b^2*c^2+6*a*b*c*d)+2//19*b^2*d^3*x^19//2+2//3*a*c^2*x^3//2*(2*b*c+3*a*d)+2//15*b*d^2*x^15//2*(2*a*d+3*b*c))
@test integrate(x^-5//2*(a+b*x^2)^2*(c+d*x^2)^3, x) == :(-2//3*a^2*c^3*x^-3//2+2//5*c*x^5//2*(b^2*c^2+3*a^2*d^2+6*a*b*c*d)+2//9*d*x^9//2*(a^2*d^2+3*b^2*c^2+6*a*b*c*d)+2//17*b^2*d^3*x^17//2+2*a*c^2*x^(1/2)*(2*b*c+3*a*d)+2//13*b*d^2*x^13//2*(2*a*d+3*b*c))
@test integrate(x^-7//2*(a+b*x^2)^2*(c+d*x^2)^3, x) == :(-2//5*a^2*c^3*x^-5//2+2//3*c*x^3//2*(b^2*c^2+3*a^2*d^2+6*a*b*c*d)+2//7*d*x^7//2*(a^2*d^2+3*b^2*c^2+6*a*b*c*d)+2//15*b^2*d^3*x^15//2+-2*a*c^2*x^-1//2*(2*b*c+3*a*d)+2//11*b*d^2*x^11//2*(2*a*d+3*b*c))
@test integrate(x^7//2*(a+b*x^2)^2*(c+d*x^2)^-1, x) == :(2//5*d^-3*x^5//2*(b*c+-1*a*d)^2+2//13*b^2*d^-1*x^13//2+-2*c*d^-4*x^(1/2)*(b*c+-1*a*d)^2+-2//9*b*d^-2*x^9//2*(b*c+-2*a*d)+(1/2)*2^(1/2)*c^5//4*d^-17//4*(b*c+-1*a*d)^2*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//2*2^(1/2)*c^5//4*d^-17//4*(b*c+-1*a*d)^2*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//4*2^(1/2)*c^5//4*d^-17//4*(b*c+-1*a*d)^2*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//4*2^(1/2)*c^5//4*d^-17//4*(b*c+-1*a*d)^2*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^5//2*(a+b*x^2)^2*(c+d*x^2)^-1, x) == :(2//3*d^-3*x^3//2*(b*c+-1*a*d)^2+2//11*b^2*d^-1*x^11//2+-2//7*b*d^-2*x^7//2*(b*c+-2*a*d)+(1/2)*2^(1/2)*c^3//4*d^-15//4*(b*c+-1*a*d)^2*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//2*2^(1/2)*c^3//4*d^-15//4*(b*c+-1*a*d)^2*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//4*2^(1/2)*c^3//4*d^-15//4*(b*c+-1*a*d)^2*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//4*2^(1/2)*c^3//4*d^-15//4*(b*c+-1*a*d)^2*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^3//2*(a+b*x^2)^2*(c+d*x^2)^-1, x) == :(2*d^-3*x^(1/2)*(b*c+-1*a*d)^2+2//9*b^2*d^-1*x^9//2+-2//5*b*d^-2*x^5//2*(b*c+-2*a*d)+(1/2)*2^(1/2)*c^1//4*d^-13//4*(b*c+-1*a*d)^2*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//2*2^(1/2)*c^1//4*d^-13//4*(b*c+-1*a*d)^2*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//4*2^(1/2)*c^1//4*d^-13//4*(b*c+-1*a*d)^2*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//4*2^(1/2)*c^1//4*d^-13//4*(b*c+-1*a*d)^2*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^(1/2)*(a+b*x^2)^2*(c+d*x^2)^-1, x) == :(2//7*b^2*d^-1*x^7//2+-2//3*b*d^-2*x^3//2*(b*c+-2*a*d)+(1/2)*2^(1/2)*c^-1//4*d^-11//4*(b*c+-1*a*d)^2*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//2*2^(1/2)*c^-1//4*d^-11//4*(b*c+-1*a*d)^2*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//4*2^(1/2)*c^-1//4*d^-11//4*(b*c+-1*a*d)^2*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//4*2^(1/2)*c^-1//4*d^-11//4*(b*c+-1*a*d)^2*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^-1//2*(a+b*x^2)^2*(c+d*x^2)^-1, x) == :(2//5*b^2*d^-1*x^5//2+-2*b*d^-2*x^(1/2)*(b*c+-2*a*d)+(1/2)*2^(1/2)*c^-3//4*d^-9//4*(b*c+-1*a*d)^2*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//2*2^(1/2)*c^-3//4*d^-9//4*(b*c+-1*a*d)^2*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//4*2^(1/2)*c^-3//4*d^-9//4*(b*c+-1*a*d)^2*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//4*2^(1/2)*c^-3//4*d^-9//4*(b*c+-1*a*d)^2*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^-3//2*(a+b*x^2)^2*(c+d*x^2)^-1, x) == :(-2*a^2*c^-1*x^-1//2+2//3*b^2*d^-1*x^3//2+(1/2)*2^(1/2)*c^-5//4*d^-7//4*(b*c+-1*a*d)^2*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//2*2^(1/2)*c^-5//4*d^-7//4*(b*c+-1*a*d)^2*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//4*2^(1/2)*c^-5//4*d^-7//4*(b*c+-1*a*d)^2*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//4*2^(1/2)*c^-5//4*d^-7//4*(b*c+-1*a*d)^2*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^-5//2*(a+b*x^2)^2*(c+d*x^2)^-1, x) == :(2*b^2*d^-1*x^(1/2)+-2//3*a^2*c^-1*x^-3//2+(1/2)*2^(1/2)*c^-7//4*d^-5//4*(b*c+-1*a*d)^2*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//2*2^(1/2)*c^-7//4*d^-5//4*(b*c+-1*a*d)^2*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//4*2^(1/2)*c^-7//4*d^-5//4*(b*c+-1*a*d)^2*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//4*2^(1/2)*c^-7//4*d^-5//4*(b*c+-1*a*d)^2*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^-7//2*(a+b*x^2)^2*(c+d*x^2)^-1, x) == :(-2//5*a^2*c^-1*x^-5//2+-2*a*c^-2*x^-1//2*(-1*a*d+2*b*c)+(1/2)*2^(1/2)*c^-9//4*d^-3//4*(b*c+-1*a*d)^2*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//2*2^(1/2)*c^-9//4*d^-3//4*(b*c+-1*a*d)^2*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//4*2^(1/2)*c^-9//4*d^-3//4*(b*c+-1*a*d)^2*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//4*2^(1/2)*c^-9//4*d^-3//4*(b*c+-1*a*d)^2*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^-9//2*(a+b*x^2)^2*(c+d*x^2)^-1, x) == :(-2//7*a^2*c^-1*x^-7//2+-2//3*a*c^-2*x^-3//2*(-1*a*d+2*b*c)+(1/2)*2^(1/2)*c^-11//4*d^-1//4*(b*c+-1*a*d)^2*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//2*2^(1/2)*c^-11//4*d^-1//4*(b*c+-1*a*d)^2*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//4*2^(1/2)*c^-11//4*d^-1//4*(b*c+-1*a*d)^2*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//4*2^(1/2)*c^-11//4*d^-1//4*(b*c+-1*a*d)^2*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^-11//2*(a+b*x^2)^-1*(c+d*x^2)^2, x) == :(-2*a^-3*x^-1//2*(b*c+-1*a*d)^2+-2//9*a^-1*c^2*x^-9//2+2//5*c*a^-2*x^-5//2*(b*c+-2*a*d)+(1/2)*2^(1/2)*a^-13//4*b^1//4*(b*c+-1*a*d)^2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*a^-13//4*b^1//4*(b*c+-1*a*d)^2*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^-13//4*b^1//4*(b*c+-1*a*d)^2*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^-13//4*b^1//4*(b*c+-1*a*d)^2*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^7//2*(a+b*x^2)^2*(c+d*x^2)^-2, x) == :(2//9*b^2*d^-2*x^9//2+(1/2)*d^-4*x^(1/2)*(b*c+-1*a*d)*(-5*a*d+13*b*c)+(1/2)*c^-1*d^-2*x^9//2*(c+d*x^2)^-1*(b*c+-1*a*d)^2+-1//10*c^-1*d^-3*x^5//2*(b*c+-1*a*d)*(-5*a*d+13*b*c)+-1//8*2^(1/2)*c^1//4*d^-17//4*(b*c+-1*a*d)*(-5*a*d+13*b*c)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//16*2^(1/2)*c^1//4*d^-17//4*(b*c+-1*a*d)*(-5*a*d+13*b*c)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*c^1//4*d^-17//4*(b*c+-1*a*d)*(-5*a*d+13*b*c)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//16*2^(1/2)*c^1//4*d^-17//4*(b*c+-1*a*d)*(-5*a*d+13*b*c)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^5//2*(a+b*x^2)^2*(c+d*x^2)^-2, x) == :(2//7*b^2*d^-2*x^7//2+(1/2)*c^-1*d^-2*x^7//2*(c+d*x^2)^-1*(b*c+-1*a*d)^2+-1//6*c^-1*d^-3*x^3//2*(b*c+-1*a*d)*(-3*a*d+11*b*c)+-1//8*2^(1/2)*c^-1//4*d^-15//4*(b*c+-1*a*d)*(-3*a*d+11*b*c)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//16*2^(1/2)*c^-1//4*d^-15//4*(b*c+-1*a*d)*(-3*a*d+11*b*c)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*c^-1//4*d^-15//4*(b*c+-1*a*d)*(-3*a*d+11*b*c)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//16*2^(1/2)*c^-1//4*d^-15//4*(b*c+-1*a*d)*(-3*a*d+11*b*c)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^3//2*(a+b*x^2)^2*(c+d*x^2)^-2, x) == :(2//5*b^2*d^-2*x^5//2+(1/2)*c^-1*d^-2*x^5//2*(c+d*x^2)^-1*(b*c+-1*a*d)^2+-1//2*c^-1*d^-3*x^(1/2)*(b*c+-1*a*d)*(-1*a*d+9*b*c)+-1//8*2^(1/2)*c^-3//4*d^-13//4*(b*c+-1*a*d)*(-1*a*d+9*b*c)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//16*2^(1/2)*c^-3//4*d^-13//4*(b*c+-1*a*d)*(-1*a*d+9*b*c)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*c^-3//4*d^-13//4*(b*c+-1*a*d)*(-1*a*d+9*b*c)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//16*2^(1/2)*c^-3//4*d^-13//4*(b*c+-1*a*d)*(-1*a*d+9*b*c)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^(1/2)*(a+b*x^2)^2*(c+d*x^2)^-2, x) == :(2//3*b^2*d^-2*x^3//2+(1/2)*c^-1*d^-2*x^3//2*(c+d*x^2)^-1*(b*c+-1*a*d)^2+-1//8*2^(1/2)*c^-5//4*d^-11//4*(a*d+7*b*c)*(b*c+-1*a*d)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//16*2^(1/2)*c^-5//4*d^-11//4*(a*d+7*b*c)*(b*c+-1*a*d)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*c^-5//4*d^-11//4*(a*d+7*b*c)*(b*c+-1*a*d)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//16*2^(1/2)*c^-5//4*d^-11//4*(a*d+7*b*c)*(b*c+-1*a*d)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^-1//2*(a+b*x^2)^2*(c+d*x^2)^-2, x) == :(2*b^2*d^-2*x^(1/2)+(1/2)*c^-1*d^-2*x^(1/2)*(c+d*x^2)^-1*(b*c+-1*a*d)^2+-1//8*2^(1/2)*c^-7//4*d^-9//4*(b*c+-1*a*d)*(3*a*d+5*b*c)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//16*2^(1/2)*c^-7//4*d^-9//4*(b*c+-1*a*d)*(3*a*d+5*b*c)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*c^-7//4*d^-9//4*(b*c+-1*a*d)*(3*a*d+5*b*c)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//16*2^(1/2)*c^-7//4*d^-9//4*(b*c+-1*a*d)*(3*a*d+5*b*c)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^-3//2*(a+b*x^2)^2*(c+d*x^2)^-2, x) == :(-2*a^2*c^-1*x^-1//2*(c+d*x^2)^-1+-1//2*c^-2*d^-1*x^3//2*(c+d*x^2)^-1*(b^2*c^2+5*a^2*d^2+-2*a*b*c*d)+-1//8*2^(1/2)*c^-9//4*d^-7//4*(b*c+-1*a*d)*(3*b*c+5*a*d)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//16*2^(1/2)*c^-9//4*d^-7//4*(b*c+-1*a*d)*(3*b*c+5*a*d)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*c^-9//4*d^-7//4*(b*c+-1*a*d)*(3*b*c+5*a*d)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//16*2^(1/2)*c^-9//4*d^-7//4*(b*c+-1*a*d)*(3*b*c+5*a*d)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^-5//2*(a+b*x^2)^2*(c+d*x^2)^-2, x) == :(-2//3*a^2*c^-1*x^-3//2*(c+d*x^2)^-1+-1//6*c^-2*d^-1*x^(1/2)*(c+d*x^2)^-1*(3*b^2*c^2+7*a^2*d^2+-6*a*b*c*d)+-1//8*2^(1/2)*c^-11//4*d^-5//4*(b*c+-1*a*d)*(b*c+7*a*d)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//16*2^(1/2)*c^-11//4*d^-5//4*(b*c+-1*a*d)*(b*c+7*a*d)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*c^-11//4*d^-5//4*(b*c+-1*a*d)*(b*c+7*a*d)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//16*2^(1/2)*c^-11//4*d^-5//4*(b*c+-1*a*d)*(b*c+7*a*d)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^-7//2*(a+b*x^2)^2*(c+d*x^2)^-2, x) == :(-2//5*a^2*c^-1*x^-5//2*(c+d*x^2)^-1+(1/2)*c^-3*d^-1*x^-1//2*(b*c+-1*a*d)*(b*c+-9*a*d)+-1//10*c^-2*d^-1*x^-1//2*(c+d*x^2)^-1*(5*b^2*c^2+9*a^2*d^2+-10*a*b*c*d)+-1//8*2^(1/2)*c^-13//4*d^-3//4*(b*c+-1*a*d)*(b*c+-9*a*d)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//16*2^(1/2)*c^-13//4*d^-3//4*(b*c+-1*a*d)*(b*c+-9*a*d)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*c^-13//4*d^-3//4*(b*c+-1*a*d)*(b*c+-9*a*d)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//16*2^(1/2)*c^-13//4*d^-3//4*(b*c+-1*a*d)*(b*c+-9*a*d)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^7//2*(a+b*x^2)^2*(c+d*x^2)^-3, x) == :(-1//16*c^-1*d^-4*x^(1/2)*(5*a^2*d^2+117*b^2*c^2+-90*a*b*c*d)+1//80*c^-2*d^-3*x^5//2*(5*a^2*d^2+117*b^2*c^2+-90*a*b*c*d)+-1//64*2^(1/2)*c^-3//4*d^-17//4*(5*a^2*d^2+117*b^2*c^2+-90*a*b*c*d)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//128*2^(1/2)*c^-3//4*d^-17//4*(5*a^2*d^2+117*b^2*c^2+-90*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//4*c^-1*d^-2*x^9//2*(c+d*x^2)^-2*(b*c+-1*a*d)^2+1//64*2^(1/2)*c^-3//4*d^-17//4*(5*a^2*d^2+117*b^2*c^2+-90*a*b*c*d)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//128*2^(1/2)*c^-3//4*d^-17//4*(5*a^2*d^2+117*b^2*c^2+-90*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+-1//16*c^-2*d^-2*x^9//2*(c+d*x^2)^-1*(b*c+-1*a*d)*(-1*a*d+17*b*c))
@test integrate(x^5//2*(a+b*x^2)^2*(c+d*x^2)^-3, x) == :(-1//48*c^-1*d^-2*x^3//2*(42*a*b+-77*c*b^2*d^-1+3*d*a^2*c^-1)+-1//64*2^(1/2)*c^-5//4*d^-15//4*(-3*a^2*d^2+77*b^2*c^2+-42*a*b*c*d)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//128*2^(1/2)*c^-5//4*d^-15//4*(-3*a^2*d^2+77*b^2*c^2+-42*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//4*c^-1*d^-2*x^7//2*(c+d*x^2)^-2*(b*c+-1*a*d)^2+1//64*2^(1/2)*c^-5//4*d^-15//4*(-3*a^2*d^2+77*b^2*c^2+-42*a*b*c*d)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//128*2^(1/2)*c^-5//4*d^-15//4*(-3*a^2*d^2+77*b^2*c^2+-42*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+-1//16*c^-2*d^-2*x^7//2*(c+d*x^2)^-1*(a*d+15*b*c)*(b*c+-1*a*d))
@test integrate(x^3//2*(a+b*x^2)^2*(c+d*x^2)^-3, x) == :(-1//16*c^-1*d^-2*x^(1/2)*(10*a*b+-45*c*b^2*d^-1+3*d*a^2*c^-1)+-1//64*2^(1/2)*c^-7//4*d^-13//4*(-3*a^2*d^2+45*b^2*c^2+-10*a*b*c*d)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//128*2^(1/2)*c^-7//4*d^-13//4*(-3*a^2*d^2+45*b^2*c^2+-10*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//4*c^-1*d^-2*x^5//2*(c+d*x^2)^-2*(b*c+-1*a*d)^2+1//64*2^(1/2)*c^-7//4*d^-13//4*(-3*a^2*d^2+45*b^2*c^2+-10*a*b*c*d)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//128*2^(1/2)*c^-7//4*d^-13//4*(-3*a^2*d^2+45*b^2*c^2+-10*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+-1//16*c^-2*d^-2*x^5//2*(c+d*x^2)^-1*(b*c+-1*a*d)*(3*a*d+13*b*c))
@test integrate(x^(1/2)*(a+b*x^2)^2*(c+d*x^2)^-3, x) == :(-1//64*2^(1/2)*c^-9//4*d^-11//4*(5*a^2*d^2+21*b^2*c^2+6*a*b*c*d)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//128*2^(1/2)*c^-9//4*d^-11//4*(5*a^2*d^2+21*b^2*c^2+6*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//4*c^-1*d^-2*x^3//2*(c+d*x^2)^-2*(b*c+-1*a*d)^2+1//64*2^(1/2)*c^-9//4*d^-11//4*(5*a^2*d^2+21*b^2*c^2+6*a*b*c*d)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//128*2^(1/2)*c^-9//4*d^-11//4*(5*a^2*d^2+21*b^2*c^2+6*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+-1//16*c^-2*d^-2*x^3//2*(c+d*x^2)^-1*(b*c+-1*a*d)*(5*a*d+11*b*c))
@test integrate(x^-1//2*(a+b*x^2)^2*(c+d*x^2)^-3, x) == :(-1//64*2^(1/2)*c^-11//4*d^-9//4*(5*b^2*c^2+21*a^2*d^2+6*a*b*c*d)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//128*2^(1/2)*c^-11//4*d^-9//4*(5*b^2*c^2+21*a^2*d^2+6*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//4*c^-1*d^-2*x^(1/2)*(c+d*x^2)^-2*(b*c+-1*a*d)^2+1//64*2^(1/2)*c^-11//4*d^-9//4*(5*b^2*c^2+21*a^2*d^2+6*a*b*c*d)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//128*2^(1/2)*c^-11//4*d^-9//4*(5*b^2*c^2+21*a^2*d^2+6*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+-1//16*c^-2*d^-2*x^(1/2)*(c+d*x^2)^-1*(b*c+-1*a*d)*(7*a*d+9*b*c))
@test integrate(x^-3//2*(a+b*x^2)^2*(c+d*x^2)^-3, x) == :(-2*a^2*c^-1*x^-1//2*(c+d*x^2)^-2+-1//4*c^-2*d^-1*x^3//2*(c+d*x^2)^-2*(b^2*c^2+9*a^2*d^2+-2*a*b*c*d)+-1//64*2^(1/2)*c^-13//4*d^-7//4*(3*b^2*c^2+5*a*d*(-9*a*d+2*b*c))*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//128*2^(1/2)*c^-13//4*d^-7//4*(3*b^2*c^2+5*a*d*(-9*a*d+2*b*c))*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//16*c^-3*d^-1*x^3//2*(c+d*x^2)^-1*(3*b^2*c^2+5*a*d*(-9*a*d+2*b*c))+1//64*2^(1/2)*c^-13//4*d^-7//4*(3*b^2*c^2+5*a*d*(-9*a*d+2*b*c))*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//128*2^(1/2)*c^-13//4*d^-7//4*(3*b^2*c^2+5*a*d*(-9*a*d+2*b*c))*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^-5//2*(a+b*x^2)^2*(c+d*x^2)^-3, x) == :(-2//3*a^2*c^-1*x^-3//2*(c+d*x^2)^-2+-1//12*c^-2*d^-1*x^(1/2)*(c+d*x^2)^-2*(3*b^2*c^2+11*a^2*d^2+-6*a*b*c*d)+-1//64*2^(1/2)*c^-15//4*d^-5//4*(3*b^2*c^2+7*a*d*(-11*a*d+6*b*c))*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//128*2^(1/2)*c^-15//4*d^-5//4*(3*b^2*c^2+7*a*d*(-11*a*d+6*b*c))*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//48*c^-3*d^-1*x^(1/2)*(c+d*x^2)^-1*(3*b^2*c^2+7*a*d*(-11*a*d+6*b*c))+1//64*2^(1/2)*c^-15//4*d^-5//4*(3*b^2*c^2+7*a*d*(-11*a*d+6*b*c))*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//128*2^(1/2)*c^-15//4*d^-5//4*(3*b^2*c^2+7*a*d*(-11*a*d+6*b*c))*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^-7//2*(a+b*x^2)^2*(c+d*x^2)^-3, x) == :(-2//5*a^2*c^-1*x^-5//2*(c+d*x^2)^-2+1//16*c^-4*d^-1*x^-1//2*(5*b^2*c^2+-9*a*d*(-13*a*d+10*b*c))+-1//20*c^-2*d^-1*x^-1//2*(c+d*x^2)^-2*(5*b^2*c^2+13*a^2*d^2+-10*a*b*c*d)+-1//64*2^(1/2)*c^-17//4*d^-3//4*(5*b^2*c^2+-9*a*d*(-13*a*d+10*b*c))*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//80*c^-3*d^-1*x^-1//2*(c+d*x^2)^-1*(5*b^2*c^2+-9*a*d*(-13*a*d+10*b*c))+-1//128*2^(1/2)*c^-17//4*d^-3//4*(5*b^2*c^2+-9*a*d*(-13*a*d+10*b*c))*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//64*2^(1/2)*c^-17//4*d^-3//4*(5*b^2*c^2+-9*a*d*(-13*a*d+10*b*c))*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//128*2^(1/2)*c^-17//4*d^-3//4*(5*b^2*c^2+-9*a*d*(-13*a*d+10*b*c))*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^5//2*(a+b*x^2)^-1*(c+d*x^2)^3, x) == :(2//3*b^-4*x^3//2*(b*c+-1*a*d)^3+2//15*b^-1*d^3*x^15//2+2//7*d*b^-3*x^7//2*(a^2*d^2+3*b^2*c^2+-3*a*b*c*d)+2//11*b^-2*d^2*x^11//2*(-1*a*d+3*b*c)+(1/2)*2^(1/2)*a^3//4*b^-19//4*(b*c+-1*a*d)^3*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*a^3//4*b^-19//4*(b*c+-1*a*d)^3*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^3//4*b^-19//4*(b*c+-1*a*d)^3*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^3//4*b^-19//4*(b*c+-1*a*d)^3*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^3//2*(a+b*x^2)^-1*(c+d*x^2)^3, x) == :(2*b^-4*x^(1/2)*(b*c+-1*a*d)^3+2//13*b^-1*d^3*x^13//2+2//5*d*b^-3*x^5//2*(a^2*d^2+3*b^2*c^2+-3*a*b*c*d)+2//9*b^-2*d^2*x^9//2*(-1*a*d+3*b*c)+(1/2)*2^(1/2)*a^1//4*b^-17//4*(b*c+-1*a*d)^3*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*a^1//4*b^-17//4*(b*c+-1*a*d)^3*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^1//4*b^-17//4*(b*c+-1*a*d)^3*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^1//4*b^-17//4*(b*c+-1*a*d)^3*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^(1/2)*(a+b*x^2)^-1*(c+d*x^2)^3, x) == :(2//11*b^-1*d^3*x^11//2+2//3*d*b^-3*x^3//2*(a^2*d^2+3*b^2*c^2+-3*a*b*c*d)+2//7*b^-2*d^2*x^7//2*(-1*a*d+3*b*c)+(1/2)*2^(1/2)*a^-1//4*b^-15//4*(b*c+-1*a*d)^3*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*a^-1//4*b^-15//4*(b*c+-1*a*d)^3*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^-1//4*b^-15//4*(b*c+-1*a*d)^3*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^-1//4*b^-15//4*(b*c+-1*a*d)^3*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^-1//2*(a+b*x^2)^-1*(c+d*x^2)^3, x) == :(2//9*b^-1*d^3*x^9//2+2*d*b^-3*x^(1/2)*(a^2*d^2+3*b^2*c^2+-3*a*b*c*d)+2//5*b^-2*d^2*x^5//2*(-1*a*d+3*b*c)+(1/2)*2^(1/2)*a^-3//4*b^-13//4*(b*c+-1*a*d)^3*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*a^-3//4*b^-13//4*(b*c+-1*a*d)^3*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^-3//4*b^-13//4*(b*c+-1*a*d)^3*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^-3//4*b^-13//4*(b*c+-1*a*d)^3*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^-3//2*(a+b*x^2)^-1*(c+d*x^2)^3, x) == :(-2*a^-1*c^3*x^-1//2+2//7*b^-1*d^3*x^7//2+2//3*b^-2*d^2*x^3//2*(-1*a*d+3*b*c)+(1/2)*2^(1/2)*a^-5//4*b^-11//4*(b*c+-1*a*d)^3*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*a^-5//4*b^-11//4*(b*c+-1*a*d)^3*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^-5//4*b^-11//4*(b*c+-1*a*d)^3*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^-5//4*b^-11//4*(b*c+-1*a*d)^3*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^-5//2*(a+b*x^2)^-1*(c+d*x^2)^3, x) == :(-2//3*a^-1*c^3*x^-3//2+2//5*b^-1*d^3*x^5//2+2*b^-2*d^2*x^(1/2)*(-1*a*d+3*b*c)+(1/2)*2^(1/2)*a^-7//4*b^-9//4*(b*c+-1*a*d)^3*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*a^-7//4*b^-9//4*(b*c+-1*a*d)^3*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^-7//4*b^-9//4*(b*c+-1*a*d)^3*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^-7//4*b^-9//4*(b*c+-1*a*d)^3*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^-7//2*(a+b*x^2)^-1*(c+d*x^2)^3, x) == :(-2//5*a^-1*c^3*x^-5//2+2//3*b^-1*d^3*x^3//2+2*a^-2*c^2*x^-1//2*(b*c+-3*a*d)+(1/2)*2^(1/2)*a^-9//4*b^-7//4*(b*c+-1*a*d)^3*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*a^-9//4*b^-7//4*(b*c+-1*a*d)^3*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^-9//4*b^-7//4*(b*c+-1*a*d)^3*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^-9//4*b^-7//4*(b*c+-1*a*d)^3*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^-9//2*(a+b*x^2)^-1*(c+d*x^2)^3, x) == :(2*b^-1*d^3*x^(1/2)+-2//7*a^-1*c^3*x^-7//2+2//3*a^-2*c^2*x^-3//2*(b*c+-3*a*d)+(1/2)*2^(1/2)*a^-11//4*b^-5//4*(b*c+-1*a*d)^3*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*a^-11//4*b^-5//4*(b*c+-1*a*d)^3*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^-11//4*b^-5//4*(b*c+-1*a*d)^3*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^-11//4*b^-5//4*(b*c+-1*a*d)^3*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^-11//2*(a+b*x^2)^-1*(c+d*x^2)^3, x) == :(-2//9*a^-1*c^3*x^-9//2+-2*c*a^-3*x^-1//2*(b^2*c^2+3*a^2*d^2+-3*a*b*c*d)+2//5*a^-2*c^2*x^-5//2*(b*c+-3*a*d)+(1/2)*2^(1/2)*a^-13//4*b^-3//4*(b*c+-1*a*d)^3*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*a^-13//4*b^-3//4*(b*c+-1*a*d)^3*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^-13//4*b^-3//4*(b*c+-1*a*d)^3*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^-13//4*b^-3//4*(b*c+-1*a*d)^3*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^-13//2*(a+b*x^2)^-1*(c+d*x^2)^3, x) == :(-2//11*a^-1*c^3*x^-11//2+-2//3*c*a^-3*x^-3//2*(b^2*c^2+3*a^2*d^2+-3*a*b*c*d)+2//7*a^-2*c^2*x^-7//2*(b*c+-3*a*d)+(1/2)*2^(1/2)*a^-15//4*b^-1//4*(b*c+-1*a*d)^3*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*a^-15//4*b^-1//4*(b*c+-1*a*d)^3*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^-15//4*b^-1//4*(b*c+-1*a*d)^3*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^-15//4*b^-1//4*(b*c+-1*a*d)^3*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^-15//2*(a+b*x^2)^-1*(c+d*x^2)^3, x) == :(2*a^-4*x^-1//2*(b*c+-1*a*d)^3+-2//13*a^-1*c^3*x^-13//2+-2//5*c*a^-3*x^-5//2*(b^2*c^2+3*a^2*d^2+-3*a*b*c*d)+2//9*a^-2*c^2*x^-9//2*(b*c+-3*a*d)+(1/2)*2^(1/2)*a^-17//4*b^1//4*(b*c+-1*a*d)^3*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*a^-17//4*b^1//4*(b*c+-1*a*d)^3*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^-17//4*b^1//4*(b*c+-1*a*d)^3*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^-17//4*b^1//4*(b*c+-1*a*d)^3*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^7//2*(a+b*x^2)^-2*(c+d*x^2)^3, x) == :(17//26*b^-2*d^3*x^13//2+(1/2)*b^-5*x^(1/2)*(b*c+-1*a*d)^2*(-17*a*d+5*b*c)+-1//2*b^-1*x^5//2*(a+b*x^2)^-1*(c+d*x^2)^3+1//10*d*b^-4*x^5//2*(17*a^2*d^2+27*b^2*c^2+-39*a*b*c*d)+1//18*b^-3*d^2*x^9//2*(-17*a*d+39*b*c)+-1//8*2^(1/2)*a^1//4*b^-21//4*(b*c+-1*a*d)^2*(-17*a*d+5*b*c)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//16*2^(1/2)*a^1//4*b^-21//4*(b*c+-1*a*d)^2*(-17*a*d+5*b*c)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//8*2^(1/2)*a^1//4*b^-21//4*(b*c+-1*a*d)^2*(-17*a*d+5*b*c)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//16*2^(1/2)*a^1//4*b^-21//4*(b*c+-1*a*d)^2*(-17*a*d+5*b*c)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^5//2*(a+b*x^2)^-2*(c+d*x^2)^3, x) == :(15//22*b^-2*d^3*x^11//2+(1/2)*d*b^-4*x^3//2*(5*a^2*d^2+7*b^2*c^2+-11*a*b*c*d)+-1//2*b^-1*x^3//2*(a+b*x^2)^-1*(c+d*x^2)^3+3//14*b^-3*d^2*x^7//2*(-5*a*d+11*b*c)+-1//8*2^(1/2)*a^-1//4*b^-19//4*(b*c+-1*a*d)^2*(-15*a*d+3*b*c)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//16*2^(1/2)*a^-1//4*b^-19//4*(b*c+-1*a*d)^2*(-15*a*d+3*b*c)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//8*2^(1/2)*a^-1//4*b^-19//4*(b*c+-1*a*d)^2*(-15*a*d+3*b*c)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//16*2^(1/2)*a^-1//4*b^-19//4*(b*c+-1*a*d)^2*(-15*a*d+3*b*c)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^3//2*(a+b*x^2)^-2*(c+d*x^2)^3, x) == :(-1//2*b^-1*x^(1/2)*(a+b*x^2)^-1*(c+d*x^2)^3+1//90*d*b^-4*x^(1/2)*(497*b^2*c^2+585*a^2*d^2+-1098*a*b*c*d)+13//18*d*b^-2*x^(1/2)*(c+d*x^2)^2+1//90*d*b^-3*x^(1/2)*(c+d*x^2)*(-117*a*d+113*b*c)+-1//8*2^(1/2)*a^-3//4*b^-17//4*(b*c+-1*a*d)^2*(b*c+-13*a*d)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//16*2^(1/2)*a^-3//4*b^-17//4*(b*c+-1*a*d)^2*(b*c+-13*a*d)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//8*2^(1/2)*a^-3//4*b^-17//4*(b*c+-1*a*d)^2*(b*c+-13*a*d)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//16*2^(1/2)*a^-3//4*b^-17//4*(b*c+-1*a*d)^2*(b*c+-13*a*d)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^(1/2)*(a+b*x^2)^-2*(c+d*x^2)^3, x) == :(-1//6*d*a^-1*b^-3*x^3//2*(6*b^2*c^2+11*a^2*d^2+-21*a*b*c*d)+-1//14*a^-1*b^-2*d^2*x^7//2*(-11*a*d+7*b*c)+(1/2)*a^-1*b^-1*x^3//2*(a+b*x^2)^-1*(c+d*x^2)^2*(b*c+-1*a*d)+-1//8*2^(1/2)*a^-5//4*b^-15//4*(b*c+-1*a*d)^2*(b*c+11*a*d)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//16*2^(1/2)*a^-5//4*b^-15//4*(b*c+-1*a*d)^2*(b*c+11*a*d)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//8*2^(1/2)*a^-5//4*b^-15//4*(b*c+-1*a*d)^2*(b*c+11*a*d)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//16*2^(1/2)*a^-5//4*b^-15//4*(b*c+-1*a*d)^2*(b*c+11*a*d)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^-1//2*(a+b*x^2)^-2*(c+d*x^2)^3, x) == :(2//5*b^-2*d^3*x^5//2+2*b^-3*d^2*x^(1/2)*(-2*a*d+3*b*c)+(1/2)*a^-1*b^-3*x^(1/2)*(a+b*x^2)^-1*(b*c+-1*a*d)^3+-3//8*2^(1/2)*a^-7//4*b^-13//4*(b*c+-1*a*d)^2*(b*c+3*a*d)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-3//16*2^(1/2)*a^-7//4*b^-13//4*(b*c+-1*a*d)^2*(b*c+3*a*d)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+3//8*2^(1/2)*a^-7//4*b^-13//4*(b*c+-1*a*d)^2*(b*c+3*a*d)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+3//16*2^(1/2)*a^-7//4*b^-13//4*(b*c+-1*a*d)^2*(b*c+3*a*d)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^-3//2*(a+b*x^2)^-2*(c+d*x^2)^3, x) == :(-1//2*a^-2*b^-1*c^2*x^-1//2*(-1*a*d+5*b*c)+-1//6*a^-1*b^-2*d^2*x^3//2*(-7*a*d+3*b*c)+(1/2)*a^-1*b^-1*x^-1//2*(a+b*x^2)^-1*(c+d*x^2)^2*(b*c+-1*a*d)+-1//8*2^(1/2)*a^-9//4*b^-11//4*(b*c+-1*a*d)^2*(5*b*c+7*a*d)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//16*2^(1/2)*a^-9//4*b^-11//4*(b*c+-1*a*d)^2*(5*b*c+7*a*d)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//8*2^(1/2)*a^-9//4*b^-11//4*(b*c+-1*a*d)^2*(5*b*c+7*a*d)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//16*2^(1/2)*a^-9//4*b^-11//4*(b*c+-1*a*d)^2*(5*b*c+7*a*d)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^-5//2*(a+b*x^2)^-2*(c+d*x^2)^3, x) == :(-1//2*a^-1*b^-2*d^2*x^(1/2)*(b*c+-5*a*d)+-1//6*a^-2*b^-1*c^2*x^-3//2*(-3*a*d+7*b*c)+(1/2)*a^-1*b^-1*x^-3//2*(a+b*x^2)^-1*(c+d*x^2)^2*(b*c+-1*a*d)+-1//8*2^(1/2)*a^-11//4*b^-9//4*(b*c+-1*a*d)^2*(5*a*d+7*b*c)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//16*2^(1/2)*a^-11//4*b^-9//4*(b*c+-1*a*d)^2*(5*a*d+7*b*c)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//8*2^(1/2)*a^-11//4*b^-9//4*(b*c+-1*a*d)^2*(5*a*d+7*b*c)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//16*2^(1/2)*a^-11//4*b^-9//4*(b*c+-1*a*d)^2*(5*a*d+7*b*c)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^-7//2*(a+b*x^2)^-2*(c+d*x^2)^3, x) == :((1/2)*c*a^-3*b^-1*x^-1//2*(2*a^2*d^2+9*b^2*c^2+-15*a*b*c*d)+-1//10*a^-2*b^-1*c^2*x^-5//2*(-5*a*d+9*b*c)+(1/2)*a^-1*b^-1*x^-5//2*(a+b*x^2)^-1*(c+d*x^2)^2*(b*c+-1*a*d)+-3//8*2^(1/2)*a^-13//4*b^-7//4*(b*c+-1*a*d)^2*(a*d+3*b*c)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-3//16*2^(1/2)*a^-13//4*b^-7//4*(b*c+-1*a*d)^2*(a*d+3*b*c)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+3//8*2^(1/2)*a^-13//4*b^-7//4*(b*c+-1*a*d)^2*(a*d+3*b*c)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+3//16*2^(1/2)*a^-13//4*b^-7//4*(b*c+-1*a*d)^2*(a*d+3*b*c)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^-9//2*(a+b*x^2)^-2*(c+d*x^2)^3, x) == :(-1//14*a^-2*b^-1*c^2*x^-7//2*(-7*a*d+11*b*c)+1//6*c*a^-3*b^-1*x^-3//2*(6*a^2*d^2+11*b^2*c^2+-21*a*b*c*d)+(1/2)*a^-1*b^-1*x^-7//2*(a+b*x^2)^-1*(c+d*x^2)^2*(b*c+-1*a*d)+-1//8*2^(1/2)*a^-15//4*b^-5//4*(b*c+-1*a*d)^2*(a*d+11*b*c)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//16*2^(1/2)*a^-15//4*b^-5//4*(b*c+-1*a*d)^2*(a*d+11*b*c)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//8*2^(1/2)*a^-15//4*b^-5//4*(b*c+-1*a*d)^2*(a*d+11*b*c)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//16*2^(1/2)*a^-15//4*b^-5//4*(b*c+-1*a*d)^2*(a*d+11*b*c)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2)))
@test integrate(x^9//2*(a+b*x^2)^-1*(c+d*x^2)^-1, x) == :(2//3*b^-1*d^-1*x^3//2+(1/2)*2^(1/2)*a^7//4*b^-7//4*(b*c+-1*a*d)^-1*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+(1/2)*2^(1/2)*c^7//4*d^-7//4*(b*c+-1*a*d)^-1*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//2*2^(1/2)*a^7//4*b^-7//4*(b*c+-1*a*d)^-1*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*c^7//4*d^-7//4*(b*c+-1*a*d)^-1*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//4*2^(1/2)*a^7//4*b^-7//4*(b*c+-1*a*d)^-1*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*c^7//4*d^-7//4*(b*c+-1*a*d)^-1*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//4*2^(1/2)*a^7//4*b^-7//4*(b*c+-1*a*d)^-1*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*c^7//4*d^-7//4*(b*c+-1*a*d)^-1*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^7//2*(a+b*x^2)^-1*(c+d*x^2)^-1, x) == :(2*b^-1*d^-1*x^(1/2)+(1/2)*2^(1/2)*a^5//4*b^-5//4*(b*c+-1*a*d)^-1*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+(1/2)*2^(1/2)*c^5//4*d^-5//4*(b*c+-1*a*d)^-1*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//2*2^(1/2)*a^5//4*b^-5//4*(b*c+-1*a*d)^-1*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*c^5//4*d^-5//4*(b*c+-1*a*d)^-1*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//4*2^(1/2)*a^5//4*b^-5//4*(b*c+-1*a*d)^-1*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*c^5//4*d^-5//4*(b*c+-1*a*d)^-1*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//4*2^(1/2)*a^5//4*b^-5//4*(b*c+-1*a*d)^-1*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*c^5//4*d^-5//4*(b*c+-1*a*d)^-1*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^5//2*(a+b*x^2)^-1*(c+d*x^2)^-1, x) == :((1/2)*2^(1/2)*a^3//4*b^-3//4*(b*c+-1*a*d)^-1*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+(1/2)*2^(1/2)*c^3//4*d^-3//4*(b*c+-1*a*d)^-1*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//2*2^(1/2)*a^3//4*b^-3//4*(b*c+-1*a*d)^-1*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*c^3//4*d^-3//4*(b*c+-1*a*d)^-1*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//4*2^(1/2)*a^3//4*b^-3//4*(b*c+-1*a*d)^-1*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*c^3//4*d^-3//4*(b*c+-1*a*d)^-1*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//4*2^(1/2)*a^3//4*b^-3//4*(b*c+-1*a*d)^-1*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*c^3//4*d^-3//4*(b*c+-1*a*d)^-1*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^3//2*(a+b*x^2)^-1*(c+d*x^2)^-1, x) == :((1/2)*2^(1/2)*a^1//4*b^-1//4*(b*c+-1*a*d)^-1*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+(1/2)*2^(1/2)*c^1//4*d^-1//4*(b*c+-1*a*d)^-1*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//2*2^(1/2)*a^1//4*b^-1//4*(b*c+-1*a*d)^-1*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*c^1//4*d^-1//4*(b*c+-1*a*d)^-1*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//4*2^(1/2)*a^1//4*b^-1//4*(b*c+-1*a*d)^-1*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*c^1//4*d^-1//4*(b*c+-1*a*d)^-1*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//4*2^(1/2)*a^1//4*b^-1//4*(b*c+-1*a*d)^-1*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*c^1//4*d^-1//4*(b*c+-1*a*d)^-1*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^(1/2)*(a+b*x^2)^-1*(c+d*x^2)^-1, x) == :((1/2)*2^(1/2)*a^-1//4*b^1//4*(b*c+-1*a*d)^-1*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+(1/2)*2^(1/2)*c^-1//4*d^1//4*(b*c+-1*a*d)^-1*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//2*2^(1/2)*a^-1//4*b^1//4*(b*c+-1*a*d)^-1*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*c^-1//4*d^1//4*(b*c+-1*a*d)^-1*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//4*2^(1/2)*a^-1//4*b^1//4*(b*c+-1*a*d)^-1*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*c^-1//4*d^1//4*(b*c+-1*a*d)^-1*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//4*2^(1/2)*a^-1//4*b^1//4*(b*c+-1*a*d)^-1*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*c^-1//4*d^1//4*(b*c+-1*a*d)^-1*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^-1//2*(a+b*x^2)^-1*(c+d*x^2)^-1, x) == :((1/2)*2^(1/2)*a^-3//4*b^3//4*(b*c+-1*a*d)^-1*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+(1/2)*2^(1/2)*c^-3//4*d^3//4*(b*c+-1*a*d)^-1*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//2*2^(1/2)*a^-3//4*b^3//4*(b*c+-1*a*d)^-1*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*c^-3//4*d^3//4*(b*c+-1*a*d)^-1*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//4*2^(1/2)*a^-3//4*b^3//4*(b*c+-1*a*d)^-1*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*c^-3//4*d^3//4*(b*c+-1*a*d)^-1*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//4*2^(1/2)*a^-3//4*b^3//4*(b*c+-1*a*d)^-1*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*c^-3//4*d^3//4*(b*c+-1*a*d)^-1*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^-3//2*(a+b*x^2)^-1*(c+d*x^2)^-1, x) == :(-2*a^-1*c^-1*x^-1//2+(1/2)*2^(1/2)*a^-5//4*b^5//4*(b*c+-1*a*d)^-1*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+(1/2)*2^(1/2)*c^-5//4*d^5//4*(b*c+-1*a*d)^-1*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//2*2^(1/2)*a^-5//4*b^5//4*(b*c+-1*a*d)^-1*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*c^-5//4*d^5//4*(b*c+-1*a*d)^-1*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//4*2^(1/2)*a^-5//4*b^5//4*(b*c+-1*a*d)^-1*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*c^-5//4*d^5//4*(b*c+-1*a*d)^-1*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//4*2^(1/2)*a^-5//4*b^5//4*(b*c+-1*a*d)^-1*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*c^-5//4*d^5//4*(b*c+-1*a*d)^-1*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^-5//2*(a+b*x^2)^-1*(c+d*x^2)^-1, x) == :(-2//3*a^-1*c^-1*x^-3//2+(1/2)*2^(1/2)*a^-7//4*b^7//4*(b*c+-1*a*d)^-1*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+(1/2)*2^(1/2)*c^-7//4*d^7//4*(b*c+-1*a*d)^-1*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//2*2^(1/2)*a^-7//4*b^7//4*(b*c+-1*a*d)^-1*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*c^-7//4*d^7//4*(b*c+-1*a*d)^-1*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//4*2^(1/2)*a^-7//4*b^7//4*(b*c+-1*a*d)^-1*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*c^-7//4*d^7//4*(b*c+-1*a*d)^-1*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//4*2^(1/2)*a^-7//4*b^7//4*(b*c+-1*a*d)^-1*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*c^-7//4*d^7//4*(b*c+-1*a*d)^-1*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^-7//2*(a+b*x^2)^-1*(c+d*x^2)^-1, x) == :(-2//5*a^-1*c^-1*x^-5//2+a^-2*c^-2*x^-1//2*(2*a*d+2*b*c)+(1/2)*2^(1/2)*a^-9//4*b^9//4*(b*c+-1*a*d)^-1*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+(1/2)*2^(1/2)*c^-9//4*d^9//4*(b*c+-1*a*d)^-1*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//2*2^(1/2)*a^-9//4*b^9//4*(b*c+-1*a*d)^-1*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*c^-9//4*d^9//4*(b*c+-1*a*d)^-1*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//4*2^(1/2)*a^-9//4*b^9//4*(b*c+-1*a*d)^-1*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*c^-9//4*d^9//4*(b*c+-1*a*d)^-1*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//4*2^(1/2)*a^-9//4*b^9//4*(b*c+-1*a*d)^-1*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*c^-9//4*d^9//4*(b*c+-1*a*d)^-1*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^11//2*(a+b*x^2)^-1*(c+d*x^2)^-2, x) == :((1/2)*2^(1/2)*a^9//4*b^-5//4*(b*c+-1*a*d)^-2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+(1/2)*b^-1*d^-2*x^(1/2)*(b*c+-1*a*d)^-1*(-4*a*d+5*b*c)+-1//2*c*d^-1*x^5//2*(c+d*x^2)^-1*(b*c+-1*a*d)^-1+-1//2*2^(1/2)*a^9//4*b^-5//4*(b*c+-1*a*d)^-2*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^9//4*b^-5//4*(b*c+-1*a*d)^-2*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^9//4*b^-5//4*(b*c+-1*a*d)^-2*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//8*2^(1/2)*c^5//4*d^-9//4*(b*c+-1*a*d)^-2*(-9*a*d+5*b*c)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//16*2^(1/2)*c^5//4*d^-9//4*(b*c+-1*a*d)^-2*(-9*a*d+5*b*c)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*c^5//4*d^-9//4*(b*c+-1*a*d)^-2*(-9*a*d+5*b*c)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//16*2^(1/2)*c^5//4*d^-9//4*(b*c+-1*a*d)^-2*(-9*a*d+5*b*c)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^9//2*(a+b*x^2)^-1*(c+d*x^2)^-2, x) == :((1/2)*2^(1/2)*a^7//4*b^-3//4*(b*c+-1*a*d)^-2*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*c*d^-1*x^3//2*(c+d*x^2)^-1*(b*c+-1*a*d)^-1+-1//2*2^(1/2)*a^7//4*b^-3//4*(b*c+-1*a*d)^-2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^7//4*b^-3//4*(b*c+-1*a*d)^-2*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^7//4*b^-3//4*(b*c+-1*a*d)^-2*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//8*2^(1/2)*c^3//4*d^-7//4*(b*c+-1*a*d)^-2*(-7*a*d+3*b*c)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//16*2^(1/2)*c^3//4*d^-7//4*(b*c+-1*a*d)^-2*(-7*a*d+3*b*c)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*c^3//4*d^-7//4*(b*c+-1*a*d)^-2*(-7*a*d+3*b*c)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//16*2^(1/2)*c^3//4*d^-7//4*(b*c+-1*a*d)^-2*(-7*a*d+3*b*c)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^7//2*(a+b*x^2)^-1*(c+d*x^2)^-2, x) == :((1/2)*2^(1/2)*a^5//4*b^-1//4*(b*c+-1*a*d)^-2*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*c*d^-1*x^(1/2)*(c+d*x^2)^-1*(b*c+-1*a*d)^-1+-1//2*2^(1/2)*a^5//4*b^-1//4*(b*c+-1*a*d)^-2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^5//4*b^-1//4*(b*c+-1*a*d)^-2*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^5//4*b^-1//4*(b*c+-1*a*d)^-2*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//8*2^(1/2)*c^1//4*d^-5//4*(b*c+-1*a*d)^-2*(b*c+-5*a*d)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//16*2^(1/2)*c^1//4*d^-5//4*(b*c+-1*a*d)^-2*(b*c+-5*a*d)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*c^1//4*d^-5//4*(b*c+-1*a*d)^-2*(b*c+-5*a*d)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//16*2^(1/2)*c^1//4*d^-5//4*(b*c+-1*a*d)^-2*(b*c+-5*a*d)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^5//2*(a+b*x^2)^-1*(c+d*x^2)^-2, x) == :(x^3//2*(c+d*x^2)^-1*(-2*a*d+2*b*c)^-1+(1/2)*2^(1/2)*a^3//4*b^1//4*(b*c+-1*a*d)^-2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*a^3//4*b^1//4*(b*c+-1*a*d)^-2*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^3//4*b^1//4*(b*c+-1*a*d)^-2*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^3//4*b^1//4*(b*c+-1*a*d)^-2*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//8*2^(1/2)*c^-1//4*d^-3//4*(b*c+-1*a*d)^-2*(b*c+3*a*d)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//16*2^(1/2)*c^-1//4*d^-3//4*(b*c+-1*a*d)^-2*(b*c+3*a*d)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*c^-1//4*d^-3//4*(b*c+-1*a*d)^-2*(b*c+3*a*d)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//16*2^(1/2)*c^-1//4*d^-3//4*(b*c+-1*a*d)^-2*(b*c+3*a*d)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^3//2*(a+b*x^2)^-1*(c+d*x^2)^-2, x) == :(x^(1/2)*(c+d*x^2)^-1*(-2*a*d+2*b*c)^-1+(1/2)*2^(1/2)*a^1//4*b^3//4*(b*c+-1*a*d)^-2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*a^1//4*b^3//4*(b*c+-1*a*d)^-2*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^1//4*b^3//4*(b*c+-1*a*d)^-2*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^1//4*b^3//4*(b*c+-1*a*d)^-2*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//8*2^(1/2)*c^-3//4*d^-1//4*(b*c+-1*a*d)^-2*(a*d+3*b*c)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//16*2^(1/2)*c^-3//4*d^-1//4*(b*c+-1*a*d)^-2*(a*d+3*b*c)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*c^-3//4*d^-1//4*(b*c+-1*a*d)^-2*(a*d+3*b*c)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//16*2^(1/2)*c^-3//4*d^-1//4*(b*c+-1*a*d)^-2*(a*d+3*b*c)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^(1/2)*(a+b*x^2)^-1*(c+d*x^2)^-2, x) == :((1/2)*2^(1/2)*a^-1//4*b^5//4*(b*c+-1*a*d)^-2*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*d*c^-1*x^3//2*(c+d*x^2)^-1*(b*c+-1*a*d)^-1+-1//2*2^(1/2)*a^-1//4*b^5//4*(b*c+-1*a*d)^-2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^-1//4*b^5//4*(b*c+-1*a*d)^-2*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^-1//4*b^5//4*(b*c+-1*a*d)^-2*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//8*2^(1/2)*c^-5//4*d^1//4*(b*c+-1*a*d)^-2*(-1*a*d+5*b*c)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//16*2^(1/2)*c^-5//4*d^1//4*(b*c+-1*a*d)^-2*(-1*a*d+5*b*c)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*c^-5//4*d^1//4*(b*c+-1*a*d)^-2*(-1*a*d+5*b*c)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//16*2^(1/2)*c^-5//4*d^1//4*(b*c+-1*a*d)^-2*(-1*a*d+5*b*c)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^-1//2*(a+b*x^2)^-1*(c+d*x^2)^-2, x) == :((1/2)*2^(1/2)*a^-3//4*b^7//4*(b*c+-1*a*d)^-2*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*d*c^-1*x^(1/2)*(c+d*x^2)^-1*(b*c+-1*a*d)^-1+-1//2*2^(1/2)*a^-3//4*b^7//4*(b*c+-1*a*d)^-2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^-3//4*b^7//4*(b*c+-1*a*d)^-2*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^-3//4*b^7//4*(b*c+-1*a*d)^-2*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//8*2^(1/2)*c^-7//4*d^3//4*(b*c+-1*a*d)^-2*(-3*a*d+7*b*c)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//16*2^(1/2)*c^-7//4*d^3//4*(b*c+-1*a*d)^-2*(-3*a*d+7*b*c)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*c^-7//4*d^3//4*(b*c+-1*a*d)^-2*(-3*a*d+7*b*c)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//16*2^(1/2)*c^-7//4*d^3//4*(b*c+-1*a*d)^-2*(-3*a*d+7*b*c)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^-3//2*(a+b*x^2)^-1*(c+d*x^2)^-2, x) == :((1/2)*2^(1/2)*a^-5//4*b^9//4*(b*c+-1*a*d)^-2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*d*c^-1*x^-1//2*(c+d*x^2)^-1*(b*c+-1*a*d)^-1+-1//2*2^(1/2)*a^-5//4*b^9//4*(b*c+-1*a*d)^-2*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*a^-1*c^-2*x^-1//2*(b*c+-1*a*d)^-1*(-5*a*d+4*b*c)+-1//4*2^(1/2)*a^-5//4*b^9//4*(b*c+-1*a*d)^-2*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^-5//4*b^9//4*(b*c+-1*a*d)^-2*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//8*2^(1/2)*c^-9//4*d^5//4*(b*c+-1*a*d)^-2*(-5*a*d+9*b*c)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//16*2^(1/2)*c^-9//4*d^5//4*(b*c+-1*a*d)^-2*(-5*a*d+9*b*c)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*c^-9//4*d^5//4*(b*c+-1*a*d)^-2*(-5*a*d+9*b*c)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//16*2^(1/2)*c^-9//4*d^5//4*(b*c+-1*a*d)^-2*(-5*a*d+9*b*c)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^-5//2*(a+b*x^2)^-1*(c+d*x^2)^-2, x) == :((1/2)*2^(1/2)*a^-7//4*b^11//4*(b*c+-1*a*d)^-2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*d*c^-1*x^-3//2*(c+d*x^2)^-1*(b*c+-1*a*d)^-1+-1//2*2^(1/2)*a^-7//4*b^11//4*(b*c+-1*a*d)^-2*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^-7//4*b^11//4*(b*c+-1*a*d)^-2*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//6*a^-1*c^-2*x^-3//2*(b*c+-1*a*d)^-1*(-7*a*d+4*b*c)+1//4*2^(1/2)*a^-7//4*b^11//4*(b*c+-1*a*d)^-2*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//8*2^(1/2)*c^-11//4*d^7//4*(b*c+-1*a*d)^-2*(-7*a*d+11*b*c)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//16*2^(1/2)*c^-11//4*d^7//4*(b*c+-1*a*d)^-2*(-7*a*d+11*b*c)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*c^-11//4*d^7//4*(b*c+-1*a*d)^-2*(-7*a*d+11*b*c)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//16*2^(1/2)*c^-11//4*d^7//4*(b*c+-1*a*d)^-2*(-7*a*d+11*b*c)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^-7//2*(a+b*x^2)^-1*(c+d*x^2)^-2, x) == :((1/2)*2^(1/2)*a^-9//4*b^13//4*(b*c+-1*a*d)^-2*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+(1/2)*a^-2*c^-3*x^-1//2*(b*c+-1*a*d)^-1*(-9*a^2*d^2+4*b^2*c^2+4*a*b*c*d)+-1//2*d*c^-1*x^-5//2*(c+d*x^2)^-1*(b*c+-1*a*d)^-1+-1//2*2^(1/2)*a^-9//4*b^13//4*(b*c+-1*a*d)^-2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^-9//4*b^13//4*(b*c+-1*a*d)^-2*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//10*a^-1*c^-2*x^-5//2*(b*c+-1*a*d)^-1*(-9*a*d+4*b*c)+1//4*2^(1/2)*a^-9//4*b^13//4*(b*c+-1*a*d)^-2*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//8*2^(1/2)*c^-13//4*d^9//4*(b*c+-1*a*d)^-2*(-9*a*d+13*b*c)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//16*2^(1/2)*c^-13//4*d^9//4*(b*c+-1*a*d)^-2*(-9*a*d+13*b*c)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*c^-13//4*d^9//4*(b*c+-1*a*d)^-2*(-9*a*d+13*b*c)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//16*2^(1/2)*c^-13//4*d^9//4*(b*c+-1*a*d)^-2*(-9*a*d+13*b*c)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^7//2*(a+b*x^2)^-1*(c+d*x^2)^-3, x) == :((1/2)*2^(1/2)*a^5//4*b^3//4*(b*c+-1*a*d)^-3*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*a^5//4*b^3//4*(b*c+-1*a*d)^-3*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*c*d^-1*x^(1/2)*(c+d*x^2)^-2*(b*c+-1*a*d)^-1+-1//4*2^(1/2)*a^5//4*b^3//4*(b*c+-1*a*d)^-3*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^5//4*b^3//4*(b*c+-1*a*d)^-3*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//16*d^-1*x^(1/2)*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(b*c+-9*a*d)+-1//64*2^(1/2)*c^-3//4*d^-5//4*(b*c+-1*a*d)^-3*(-5*a^2*d^2+3*b^2*c^2+-30*a*b*c*d)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//128*2^(1/2)*c^-3//4*d^-5//4*(b*c+-1*a*d)^-3*(-5*a^2*d^2+3*b^2*c^2+-30*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//64*2^(1/2)*c^-3//4*d^-5//4*(b*c+-1*a*d)^-3*(-5*a^2*d^2+3*b^2*c^2+-30*a*b*c*d)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//128*2^(1/2)*c^-3//4*d^-5//4*(b*c+-1*a*d)^-3*(-5*a^2*d^2+3*b^2*c^2+-30*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^5//2*(a+b*x^2)^-1*(c+d*x^2)^-3, x) == :(x^3//2*(c+d*x^2)^-2*(-4*a*d+4*b*c)^-1+(1/2)*2^(1/2)*a^3//4*b^5//4*(b*c+-1*a*d)^-3*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*a^3//4*b^5//4*(b*c+-1*a*d)^-3*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^3//4*b^5//4*(b*c+-1*a*d)^-3*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^3//4*b^5//4*(b*c+-1*a*d)^-3*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//16*c^-1*x^3//2*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(3*a*d+5*b*c)+-1//64*2^(1/2)*c^-5//4*d^-3//4*(b*c+-1*a*d)^-3*(-3*a^2*d^2+5*b^2*c^2+30*a*b*c*d)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//128*2^(1/2)*c^-5//4*d^-3//4*(b*c+-1*a*d)^-3*(-3*a^2*d^2+5*b^2*c^2+30*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//64*2^(1/2)*c^-5//4*d^-3//4*(b*c+-1*a*d)^-3*(-3*a^2*d^2+5*b^2*c^2+30*a*b*c*d)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//128*2^(1/2)*c^-5//4*d^-3//4*(b*c+-1*a*d)^-3*(-3*a^2*d^2+5*b^2*c^2+30*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^3//2*(a+b*x^2)^-1*(c+d*x^2)^-3, x) == :(x^(1/2)*(c+d*x^2)^-2*(-4*a*d+4*b*c)^-1+(1/2)*2^(1/2)*a^1//4*b^7//4*(b*c+-1*a*d)^-3*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*a^1//4*b^7//4*(b*c+-1*a*d)^-3*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*2^(1/2)*a^1//4*b^7//4*(b*c+-1*a*d)^-3*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^1//4*b^7//4*(b*c+-1*a*d)^-3*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//16*c^-1*x^(1/2)*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(a*d+7*b*c)+-1//64*2^(1/2)*c^-7//4*d^-1//4*(b*c+-1*a*d)^-3*(-3*a^2*d^2+21*b^2*c^2+14*a*b*c*d)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//128*2^(1/2)*c^-7//4*d^-1//4*(b*c+-1*a*d)^-3*(-3*a^2*d^2+21*b^2*c^2+14*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//64*2^(1/2)*c^-7//4*d^-1//4*(b*c+-1*a*d)^-3*(-3*a^2*d^2+21*b^2*c^2+14*a*b*c*d)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//128*2^(1/2)*c^-7//4*d^-1//4*(b*c+-1*a*d)^-3*(-3*a^2*d^2+21*b^2*c^2+14*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^(1/2)*(a+b*x^2)^-1*(c+d*x^2)^-3, x) == :((1/2)*2^(1/2)*a^-1//4*b^9//4*(b*c+-1*a*d)^-3*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*a^-1//4*b^9//4*(b*c+-1*a*d)^-3*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*d*c^-1*x^3//2*(c+d*x^2)^-2*(b*c+-1*a*d)^-1+-1//4*2^(1/2)*a^-1//4*b^9//4*(b*c+-1*a*d)^-3*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^-1//4*b^9//4*(b*c+-1*a*d)^-3*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//16*d*c^-2*x^3//2*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(-5*a*d+13*b*c)+-1//64*2^(1/2)*c^-9//4*d^1//4*(b*c+-1*a*d)^-3*(5*a^2*d^2+45*b^2*c^2+-18*a*b*c*d)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//128*2^(1/2)*c^-9//4*d^1//4*(b*c+-1*a*d)^-3*(5*a^2*d^2+45*b^2*c^2+-18*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//64*2^(1/2)*c^-9//4*d^1//4*(b*c+-1*a*d)^-3*(5*a^2*d^2+45*b^2*c^2+-18*a*b*c*d)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//128*2^(1/2)*c^-9//4*d^1//4*(b*c+-1*a*d)^-3*(5*a^2*d^2+45*b^2*c^2+-18*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^-1//2*(a+b*x^2)^-1*(c+d*x^2)^-3, x) == :((1/2)*2^(1/2)*a^-3//4*b^11//4*(b*c+-1*a*d)^-3*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*a^-3//4*b^11//4*(b*c+-1*a*d)^-3*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*d*c^-1*x^(1/2)*(c+d*x^2)^-2*(b*c+-1*a*d)^-1+-1//4*2^(1/2)*a^-3//4*b^11//4*(b*c+-1*a*d)^-3*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//4*2^(1/2)*a^-3//4*b^11//4*(b*c+-1*a*d)^-3*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//16*d*c^-2*x^(1/2)*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(-7*a*d+15*b*c)+-1//64*2^(1/2)*c^-11//4*d^3//4*(b*c+-1*a*d)^-3*(21*a^2*d^2+77*b^2*c^2+-66*a*b*c*d)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//128*2^(1/2)*c^-11//4*d^3//4*(b*c+-1*a*d)^-3*(21*a^2*d^2+77*b^2*c^2+-66*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//64*2^(1/2)*c^-11//4*d^3//4*(b*c+-1*a*d)^-3*(21*a^2*d^2+77*b^2*c^2+-66*a*b*c*d)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//128*2^(1/2)*c^-11//4*d^3//4*(b*c+-1*a*d)^-3*(21*a^2*d^2+77*b^2*c^2+-66*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^-3//2*(a+b*x^2)^-1*(c+d*x^2)^-3, x) == :((1/2)*2^(1/2)*a^-5//4*b^13//4*(b*c+-1*a*d)^-3*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*a^-5//4*b^13//4*(b*c+-1*a*d)^-3*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*d*c^-1*x^-1//2*(c+d*x^2)^-2*(b*c+-1*a*d)^-1+-1//4*2^(1/2)*a^-5//4*b^13//4*(b*c+-1*a*d)^-3*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//16*a^-1*c^-3*x^-1//2*(b*c+-1*a*d)^-2*(32*b^2*c^2+45*a^2*d^2+-85*a*b*c*d)+1//4*2^(1/2)*a^-5//4*b^13//4*(b*c+-1*a*d)^-3*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//16*d*c^-2*x^-1//2*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(-9*a*d+17*b*c)+-1//64*2^(1/2)*c^-13//4*d^5//4*(b*c+-1*a*d)^-3*(45*a^2*d^2+117*b^2*c^2+-130*a*b*c*d)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//128*2^(1/2)*c^-13//4*d^5//4*(b*c+-1*a*d)^-3*(45*a^2*d^2+117*b^2*c^2+-130*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//64*2^(1/2)*c^-13//4*d^5//4*(b*c+-1*a*d)^-3*(45*a^2*d^2+117*b^2*c^2+-130*a*b*c*d)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//128*2^(1/2)*c^-13//4*d^5//4*(b*c+-1*a*d)^-3*(45*a^2*d^2+117*b^2*c^2+-130*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^-5//2*(a+b*x^2)^-1*(c+d*x^2)^-3, x) == :((1/2)*2^(1/2)*a^-7//4*b^15//4*(b*c+-1*a*d)^-3*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*a^-7//4*b^15//4*(b*c+-1*a*d)^-3*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*d*c^-1*x^-3//2*(c+d*x^2)^-2*(b*c+-1*a*d)^-1+-1//4*2^(1/2)*a^-7//4*b^15//4*(b*c+-1*a*d)^-3*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//48*a^-1*c^-3*x^-3//2*(b*c+-1*a*d)^-2*(32*b^2*c^2+77*a^2*d^2+-133*a*b*c*d)+1//4*2^(1/2)*a^-7//4*b^15//4*(b*c+-1*a*d)^-3*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//16*d*c^-2*x^-3//2*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(-11*a*d+19*b*c)+-1//64*2^(1/2)*c^-15//4*d^7//4*(b*c+-1*a*d)^-3*(77*a^2*d^2+165*b^2*c^2+-210*a*b*c*d)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//128*2^(1/2)*c^-15//4*d^7//4*(b*c+-1*a*d)^-3*(77*a^2*d^2+165*b^2*c^2+-210*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//64*2^(1/2)*c^-15//4*d^7//4*(b*c+-1*a*d)^-3*(77*a^2*d^2+165*b^2*c^2+-210*a*b*c*d)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//128*2^(1/2)*c^-15//4*d^7//4*(b*c+-1*a*d)^-3*(77*a^2*d^2+165*b^2*c^2+-210*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^-7//2*(a+b*x^2)^-1*(c+d*x^2)^-3, x) == :((1/2)*2^(1/2)*a^-9//4*b^17//4*(b*c+-1*a*d)^-3*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//2*2^(1/2)*a^-9//4*b^17//4*(b*c+-1*a*d)^-3*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//4*d*c^-1*x^-5//2*(c+d*x^2)^-2*(b*c+-1*a*d)^-1+-1//4*2^(1/2)*a^-9//4*b^17//4*(b*c+-1*a*d)^-3*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//80*a^-1*c^-3*x^-5//2*(b*c+-1*a*d)^-2*(32*b^2*c^2+117*a^2*d^2+-189*a*b*c*d)+1//4*2^(1/2)*a^-9//4*b^17//4*(b*c+-1*a*d)^-3*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//16*a^-2*c^-4*x^-1//2*(b*c+-1*a*d)^-2*(32*b^3*c^3+117*a^3*d^3+-189*b*c*a^2*d^2+32*a*d*b^2*c^2)+-1//16*d*c^-2*x^-5//2*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(-13*a*d+21*b*c)+-1//64*2^(1/2)*c^-17//4*d^9//4*(b*c+-1*a*d)^-3*(117*a^2*d^2+221*b^2*c^2+-306*a*b*c*d)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//128*2^(1/2)*c^-17//4*d^9//4*(b*c+-1*a*d)^-3*(117*a^2*d^2+221*b^2*c^2+-306*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//64*2^(1/2)*c^-17//4*d^9//4*(b*c+-1*a*d)^-3*(117*a^2*d^2+221*b^2*c^2+-306*a*b*c*d)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//128*2^(1/2)*c^-17//4*d^9//4*(b*c+-1*a*d)^-3*(117*a^2*d^2+221*b^2*c^2+-306*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^7//2*(a+b*x^2)^-2*(c+d*x^2)^-2, x) == :((1/2)*b^-1*x^(1/2)*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(a*d+b*c)+(1/2)*a*b^-1*x^(1/2)*(a+b*x^2)^-1*(c+d*x^2)^-1*(b*c+-1*a*d)^-1+-1//8*2^(1/2)*a^1//4*b^-1//4*(b*c+-1*a*d)^-3*(3*a*d+5*b*c)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//8*2^(1/2)*c^1//4*d^-1//4*(b*c+-1*a*d)^-3*(3*b*c+5*a*d)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//16*2^(1/2)*a^1//4*b^-1//4*(b*c+-1*a*d)^-3*(3*a*d+5*b*c)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//16*2^(1/2)*c^1//4*d^-1//4*(b*c+-1*a*d)^-3*(3*b*c+5*a*d)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*a^1//4*b^-1//4*(b*c+-1*a*d)^-3*(3*a*d+5*b*c)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//8*2^(1/2)*c^1//4*d^-1//4*(b*c+-1*a*d)^-3*(3*b*c+5*a*d)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//16*2^(1/2)*a^1//4*b^-1//4*(b*c+-1*a*d)^-3*(3*a*d+5*b*c)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//16*2^(1/2)*c^1//4*d^-1//4*(b*c+-1*a*d)^-3*(3*b*c+5*a*d)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^5//2*(a+b*x^2)^-2*(c+d*x^2)^-2, x) == :(-1*d*x^3//2*(c+d*x^2)^-1*(b*c+-1*a*d)^-2+-1*x^3//2*(a+b*x^2)^-1*(c+d*x^2)^-1*(-2*a*d+2*b*c)^-1+-1//8*2^(1/2)*a^-1//4*b^1//4*(b*c+-1*a*d)^-3*(3*b*c+5*a*d)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//8*2^(1/2)*c^-1//4*d^1//4*(b*c+-1*a*d)^-3*(3*a*d+5*b*c)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//16*2^(1/2)*a^-1//4*b^1//4*(b*c+-1*a*d)^-3*(3*b*c+5*a*d)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//16*2^(1/2)*c^-1//4*d^1//4*(b*c+-1*a*d)^-3*(3*a*d+5*b*c)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*a^-1//4*b^1//4*(b*c+-1*a*d)^-3*(3*b*c+5*a*d)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//8*2^(1/2)*c^-1//4*d^1//4*(b*c+-1*a*d)^-3*(3*a*d+5*b*c)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//16*2^(1/2)*a^-1//4*b^1//4*(b*c+-1*a*d)^-3*(3*b*c+5*a*d)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//16*2^(1/2)*c^-1//4*d^1//4*(b*c+-1*a*d)^-3*(3*a*d+5*b*c)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^3//2*(a+b*x^2)^-2*(c+d*x^2)^-2, x) == :(-1*d*x^(1/2)*(c+d*x^2)^-1*(b*c+-1*a*d)^-2+-1*x^(1/2)*(a+b*x^2)^-1*(c+d*x^2)^-1*(-2*a*d+2*b*c)^-1+-1//8*2^(1/2)*a^-3//4*b^3//4*(b*c+-1*a*d)^-3*(b*c+7*a*d)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//8*2^(1/2)*c^-3//4*d^3//4*(b*c+-1*a*d)^-3*(a*d+7*b*c)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//16*2^(1/2)*a^-3//4*b^3//4*(b*c+-1*a*d)^-3*(b*c+7*a*d)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//16*2^(1/2)*c^-3//4*d^3//4*(b*c+-1*a*d)^-3*(a*d+7*b*c)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*a^-3//4*b^3//4*(b*c+-1*a*d)^-3*(b*c+7*a*d)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//8*2^(1/2)*c^-3//4*d^3//4*(b*c+-1*a*d)^-3*(a*d+7*b*c)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//16*2^(1/2)*a^-3//4*b^3//4*(b*c+-1*a*d)^-3*(b*c+7*a*d)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//16*2^(1/2)*c^-3//4*d^3//4*(b*c+-1*a*d)^-3*(a*d+7*b*c)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^(1/2)*(a+b*x^2)^-2*(c+d*x^2)^-2, x) == :((1/2)*b*a^-1*x^3//2*(a+b*x^2)^-1*(c+d*x^2)^-1*(b*c+-1*a*d)^-1+-1//8*2^(1/2)*a^-5//4*b^5//4*(b*c+-1*a*d)^-3*(b*c+-9*a*d)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//8*2^(1/2)*c^-5//4*d^5//4*(b*c+-1*a*d)^-3*(-1*a*d+9*b*c)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//16*2^(1/2)*a^-5//4*b^5//4*(b*c+-1*a*d)^-3*(b*c+-9*a*d)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//16*2^(1/2)*c^-5//4*d^5//4*(b*c+-1*a*d)^-3*(-1*a*d+9*b*c)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*a^-5//4*b^5//4*(b*c+-1*a*d)^-3*(b*c+-9*a*d)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//8*2^(1/2)*c^-5//4*d^5//4*(b*c+-1*a*d)^-3*(-1*a*d+9*b*c)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//16*2^(1/2)*a^-5//4*b^5//4*(b*c+-1*a*d)^-3*(b*c+-9*a*d)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//16*2^(1/2)*c^-5//4*d^5//4*(b*c+-1*a*d)^-3*(-1*a*d+9*b*c)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+(1/2)*d*a^-1*c^-1*x^3//2*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(a*d+b*c))
@test integrate(x^-1//2*(a+b*x^2)^-2*(c+d*x^2)^-2, x) == :((1/2)*b*a^-1*x^(1/2)*(a+b*x^2)^-1*(c+d*x^2)^-1*(b*c+-1*a*d)^-1+-1//8*2^(1/2)*a^-7//4*b^7//4*(b*c+-1*a*d)^-3*(-11*a*d+3*b*c)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//8*2^(1/2)*c^-7//4*d^7//4*(b*c+-1*a*d)^-3*(-3*a*d+11*b*c)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//16*2^(1/2)*a^-7//4*b^7//4*(b*c+-1*a*d)^-3*(-11*a*d+3*b*c)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//16*2^(1/2)*c^-7//4*d^7//4*(b*c+-1*a*d)^-3*(-3*a*d+11*b*c)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*a^-7//4*b^7//4*(b*c+-1*a*d)^-3*(-11*a*d+3*b*c)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//8*2^(1/2)*c^-7//4*d^7//4*(b*c+-1*a*d)^-3*(-3*a*d+11*b*c)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//16*2^(1/2)*a^-7//4*b^7//4*(b*c+-1*a*d)^-3*(-11*a*d+3*b*c)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//16*2^(1/2)*c^-7//4*d^7//4*(b*c+-1*a*d)^-3*(-3*a*d+11*b*c)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+(1/2)*d*a^-1*c^-1*x^(1/2)*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(a*d+b*c))
@test integrate(x^-3//2*(a+b*x^2)^-2*(c+d*x^2)^-2, x) == :((1/2)*a^-2*c^-2*x^-1//2*(b*c+-1*a*d)^-2*(-5*a^2*d^2+-5*b^2*c^2+8*a*b*c*d)+(1/2)*b*a^-1*x^-1//2*(a+b*x^2)^-1*(c+d*x^2)^-1*(b*c+-1*a*d)^-1+-1//8*2^(1/2)*a^-9//4*b^9//4*(b*c+-1*a*d)^-3*(-13*a*d+5*b*c)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//8*2^(1/2)*c^-9//4*d^9//4*(b*c+-1*a*d)^-3*(-5*a*d+13*b*c)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//16*2^(1/2)*a^-9//4*b^9//4*(b*c+-1*a*d)^-3*(-13*a*d+5*b*c)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//16*2^(1/2)*c^-9//4*d^9//4*(b*c+-1*a*d)^-3*(-5*a*d+13*b*c)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*a^-9//4*b^9//4*(b*c+-1*a*d)^-3*(-13*a*d+5*b*c)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//8*2^(1/2)*c^-9//4*d^9//4*(b*c+-1*a*d)^-3*(-5*a*d+13*b*c)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//16*2^(1/2)*a^-9//4*b^9//4*(b*c+-1*a*d)^-3*(-13*a*d+5*b*c)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//16*2^(1/2)*c^-9//4*d^9//4*(b*c+-1*a*d)^-3*(-5*a*d+13*b*c)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+(1/2)*d*a^-1*c^-1*x^-1//2*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(a*d+b*c))
@test integrate(x^-5//2*(a+b*x^2)^-2*(c+d*x^2)^-2, x) == :(1//6*a^-2*c^-2*x^-3//2*(b*c+-1*a*d)^-2*(-7*a^2*d^2+-7*b^2*c^2+8*a*b*c*d)+(1/2)*b*a^-1*x^-3//2*(a+b*x^2)^-1*(c+d*x^2)^-1*(b*c+-1*a*d)^-1+-1//8*2^(1/2)*a^-11//4*b^11//4*(b*c+-1*a*d)^-3*(-15*a*d+7*b*c)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//8*2^(1/2)*c^-11//4*d^11//4*(b*c+-1*a*d)^-3*(-7*a*d+15*b*c)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//16*2^(1/2)*a^-11//4*b^11//4*(b*c+-1*a*d)^-3*(-15*a*d+7*b*c)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//16*2^(1/2)*c^-11//4*d^11//4*(b*c+-1*a*d)^-3*(-7*a*d+15*b*c)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*a^-11//4*b^11//4*(b*c+-1*a*d)^-3*(-15*a*d+7*b*c)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//8*2^(1/2)*c^-11//4*d^11//4*(b*c+-1*a*d)^-3*(-7*a*d+15*b*c)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//16*2^(1/2)*a^-11//4*b^11//4*(b*c+-1*a*d)^-3*(-15*a*d+7*b*c)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//16*2^(1/2)*c^-11//4*d^11//4*(b*c+-1*a*d)^-3*(-7*a*d+15*b*c)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+(1/2)*d*a^-1*c^-1*x^-3//2*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(a*d+b*c))
@test integrate(x^-7//2*(a+b*x^2)^-2*(c+d*x^2)^-2, x) == :(1//10*a^-2*c^-2*x^-5//2*(b*c+-1*a*d)^-2*(-9*a^2*d^2+-9*b^2*c^2+8*a*b*c*d)+(1/2)*b*a^-1*x^-5//2*(a+b*x^2)^-1*(c+d*x^2)^-1*(b*c+-1*a*d)^-1+(1/2)*a^-3*c^-3*x^-1//2*(b*c+-1*a*d)^-2*(a*d+b*c)*(9*a^2*d^2+9*b^2*c^2+-17*a*b*c*d)+-1//8*2^(1/2)*a^-13//4*b^13//4*(b*c+-1*a*d)^-3*(-17*a*d+9*b*c)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//8*2^(1/2)*c^-13//4*d^13//4*(b*c+-1*a*d)^-3*(-9*a*d+17*b*c)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//16*2^(1/2)*a^-13//4*b^13//4*(b*c+-1*a*d)^-3*(-17*a*d+9*b*c)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//16*2^(1/2)*c^-13//4*d^13//4*(b*c+-1*a*d)^-3*(-9*a*d+17*b*c)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*a^-13//4*b^13//4*(b*c+-1*a*d)^-3*(-17*a*d+9*b*c)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//8*2^(1/2)*c^-13//4*d^13//4*(b*c+-1*a*d)^-3*(-9*a*d+17*b*c)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//16*2^(1/2)*a^-13//4*b^13//4*(b*c+-1*a*d)^-3*(-17*a*d+9*b*c)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//16*2^(1/2)*c^-13//4*d^13//4*(b*c+-1*a*d)^-3*(-9*a*d+17*b*c)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+(1/2)*d*a^-1*c^-1*x^-5//2*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(a*d+b*c))
@test integrate(x^7//2*(a+b*x^2)^-2*(c+d*x^2)^-3, x) == :(1//16*x^(1/2)*(c+d*x^2)^-1*(b*c+-1*a*d)^-3*(7*b*c+17*a*d)+1//4*b^-1*x^(1/2)*(c+d*x^2)^-2*(b*c+-1*a*d)^-2*(b*c+2*a*d)+(1/2)*a*b^-1*x^(1/2)*(a+b*x^2)^-1*(c+d*x^2)^-2*(b*c+-1*a*d)^-1+-1//8*2^(1/2)*a^1//4*b^3//4*(b*c+-1*a*d)^-4*(5*b*c+7*a*d)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//16*2^(1/2)*a^1//4*b^3//4*(b*c+-1*a*d)^-4*(5*b*c+7*a*d)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//64*2^(1/2)*c^-3//4*d^-1//4*(b*c+-1*a*d)^-4*(5*a^2*d^2+21*b^2*c^2+70*a*b*c*d)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//128*2^(1/2)*c^-3//4*d^-1//4*(b*c+-1*a*d)^-4*(5*a^2*d^2+21*b^2*c^2+70*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*a^1//4*b^3//4*(b*c+-1*a*d)^-4*(5*b*c+7*a*d)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//16*2^(1/2)*a^1//4*b^3//4*(b*c+-1*a*d)^-4*(5*b*c+7*a*d)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//64*2^(1/2)*c^-3//4*d^-1//4*(b*c+-1*a*d)^-4*(5*a^2*d^2+21*b^2*c^2+70*a*b*c*d)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//128*2^(1/2)*c^-3//4*d^-1//4*(b*c+-1*a*d)^-4*(5*a^2*d^2+21*b^2*c^2+70*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^5//2*(a+b*x^2)^-2*(c+d*x^2)^-3, x) == :(-1*x^3//2*(a+b*x^2)^-1*(c+d*x^2)^-2*(-2*a*d+2*b*c)^-1+-3//4*d*x^3//2*(c+d*x^2)^-2*(b*c+-1*a*d)^-2+-3//8*2^(1/2)*a^-1//4*b^5//4*(b*c+-1*a*d)^-4*(b*c+3*a*d)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-3//16*d*c^-1*x^3//2*(c+d*x^2)^-1*(b*c+-1*a*d)^-3*(a*d+7*b*c)+-3//16*2^(1/2)*a^-1//4*b^5//4*(b*c+-1*a*d)^-4*(b*c+3*a*d)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+-3//64*2^(1/2)*c^-5//4*d^1//4*(b*c+-1*a*d)^-4*(-1*a^2*d^2+15*b^2*c^2+18*a*b*c*d)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-3//128*2^(1/2)*c^-5//4*d^1//4*(b*c+-1*a*d)^-4*(-1*a^2*d^2+15*b^2*c^2+18*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+3//8*2^(1/2)*a^-1//4*b^5//4*(b*c+-1*a*d)^-4*(b*c+3*a*d)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+3//16*2^(1/2)*a^-1//4*b^5//4*(b*c+-1*a*d)^-4*(b*c+3*a*d)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+3//64*2^(1/2)*c^-5//4*d^1//4*(b*c+-1*a*d)^-4*(-1*a^2*d^2+15*b^2*c^2+18*a*b*c*d)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+3//128*2^(1/2)*c^-5//4*d^1//4*(b*c+-1*a*d)^-4*(-1*a^2*d^2+15*b^2*c^2+18*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^3//2*(a+b*x^2)^-2*(c+d*x^2)^-3, x) == :(-1*x^(1/2)*(a+b*x^2)^-1*(c+d*x^2)^-2*(-2*a*d+2*b*c)^-1+-3//4*d*x^(1/2)*(c+d*x^2)^-2*(b*c+-1*a*d)^-2+-1//8*2^(1/2)*a^-3//4*b^7//4*(b*c+-1*a*d)^-4*(b*c+11*a*d)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//16*d*c^-1*x^(1/2)*(c+d*x^2)^-1*(b*c+-1*a*d)^-3*(a*d+23*b*c)+-1//16*2^(1/2)*a^-3//4*b^7//4*(b*c+-1*a*d)^-4*(b*c+11*a*d)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//64*2^(1/2)*c^-7//4*d^3//4*(b*c+-1*a*d)^-4*(-3*a^2*d^2+77*b^2*c^2+22*a*b*c*d)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//128*2^(1/2)*c^-7//4*d^3//4*(b*c+-1*a*d)^-4*(-3*a^2*d^2+77*b^2*c^2+22*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*a^-3//4*b^7//4*(b*c+-1*a*d)^-4*(b*c+11*a*d)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//16*2^(1/2)*a^-3//4*b^7//4*(b*c+-1*a*d)^-4*(b*c+11*a*d)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//64*2^(1/2)*c^-7//4*d^3//4*(b*c+-1*a*d)^-4*(-3*a^2*d^2+77*b^2*c^2+22*a*b*c*d)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//128*2^(1/2)*c^-7//4*d^3//4*(b*c+-1*a*d)^-4*(-3*a^2*d^2+77*b^2*c^2+22*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2)))
@test integrate(x^(1/2)*(a+b*x^2)^-2*(c+d*x^2)^-3, x) == :((1/2)*b*a^-1*x^3//2*(a+b*x^2)^-1*(c+d*x^2)^-2*(b*c+-1*a*d)^-1+-1//8*2^(1/2)*a^-5//4*b^9//4*(b*c+-1*a*d)^-4*(b*c+-13*a*d)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//16*2^(1/2)*a^-5//4*b^9//4*(b*c+-1*a*d)^-4*(b*c+-13*a*d)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//64*2^(1/2)*c^-9//4*d^5//4*(b*c+-1*a*d)^-4*(5*a^2*d^2+117*b^2*c^2+-26*a*b*c*d)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//128*2^(1/2)*c^-9//4*d^5//4*(b*c+-1*a*d)^-4*(5*a^2*d^2+117*b^2*c^2+-26*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*a^-5//4*b^9//4*(b*c+-1*a*d)^-4*(b*c+-13*a*d)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//16*2^(1/2)*a^-5//4*b^9//4*(b*c+-1*a*d)^-4*(b*c+-13*a*d)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//64*2^(1/2)*c^-9//4*d^5//4*(b*c+-1*a*d)^-4*(5*a^2*d^2+117*b^2*c^2+-26*a*b*c*d)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//128*2^(1/2)*c^-9//4*d^5//4*(b*c+-1*a*d)^-4*(5*a^2*d^2+117*b^2*c^2+-26*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//4*d*a^-1*c^-1*x^3//2*(c+d*x^2)^-2*(b*c+-1*a*d)^-2*(a*d+2*b*c)+1//16*d*a^-1*c^-2*x^3//2*(c+d*x^2)^-1*(b*c+-1*a*d)^-3*(-5*a^2*d^2+8*b^2*c^2+21*a*b*c*d))
@test integrate(x^-1//2*(a+b*x^2)^-2*(c+d*x^2)^-3, x) == :((1/2)*b*a^-1*x^(1/2)*(a+b*x^2)^-1*(c+d*x^2)^-2*(b*c+-1*a*d)^-1+-3//8*2^(1/2)*a^-7//4*b^11//4*(b*c+-1*a*d)^-4*(b*c+-5*a*d)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-3//16*2^(1/2)*a^-7//4*b^11//4*(b*c+-1*a*d)^-4*(b*c+-5*a*d)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+-3//64*2^(1/2)*c^-11//4*d^7//4*(b*c+-1*a*d)^-4*(7*a^2*d^2+55*b^2*c^2+-30*a*b*c*d)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-3//128*2^(1/2)*c^-11//4*d^7//4*(b*c+-1*a*d)^-4*(7*a^2*d^2+55*b^2*c^2+-30*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+3//8*2^(1/2)*a^-7//4*b^11//4*(b*c+-1*a*d)^-4*(b*c+-5*a*d)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+3//16*2^(1/2)*a^-7//4*b^11//4*(b*c+-1*a*d)^-4*(b*c+-5*a*d)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+3//64*2^(1/2)*c^-11//4*d^7//4*(b*c+-1*a*d)^-4*(7*a^2*d^2+55*b^2*c^2+-30*a*b*c*d)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+3//128*2^(1/2)*c^-11//4*d^7//4*(b*c+-1*a*d)^-4*(7*a^2*d^2+55*b^2*c^2+-30*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//4*d*a^-1*c^-1*x^(1/2)*(c+d*x^2)^-2*(b*c+-1*a*d)^-2*(a*d+2*b*c)+1//16*d*a^-1*c^-2*x^(1/2)*(c+d*x^2)^-1*(b*c+-1*a*d)^-3*(-7*a^2*d^2+8*b^2*c^2+23*a*b*c*d))
@test integrate(x^-3//2*(a+b*x^2)^-2*(c+d*x^2)^-3, x) == :(1//16*a^-2*c^-3*x^-1//2*(b*c+-1*a*d)^-3*(-40*b^3*c^3+45*a^3*d^3+-125*b*c*a^2*d^2+96*a*d*b^2*c^2)+(1/2)*b*a^-1*x^-1//2*(a+b*x^2)^-1*(c+d*x^2)^-2*(b*c+-1*a*d)^-1+-1//8*2^(1/2)*a^-9//4*b^13//4*(b*c+-1*a*d)^-4*(-17*a*d+5*b*c)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//16*2^(1/2)*a^-9//4*b^13//4*(b*c+-1*a*d)^-4*(-17*a*d+5*b*c)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//64*2^(1/2)*c^-13//4*d^9//4*(b*c+-1*a*d)^-4*(45*a^2*d^2+221*b^2*c^2+-170*a*b*c*d)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//128*2^(1/2)*c^-13//4*d^9//4*(b*c+-1*a*d)^-4*(45*a^2*d^2+221*b^2*c^2+-170*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*a^-9//4*b^13//4*(b*c+-1*a*d)^-4*(-17*a*d+5*b*c)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//16*2^(1/2)*a^-9//4*b^13//4*(b*c+-1*a*d)^-4*(-17*a*d+5*b*c)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//64*2^(1/2)*c^-13//4*d^9//4*(b*c+-1*a*d)^-4*(45*a^2*d^2+221*b^2*c^2+-170*a*b*c*d)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//128*2^(1/2)*c^-13//4*d^9//4*(b*c+-1*a*d)^-4*(45*a^2*d^2+221*b^2*c^2+-170*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//4*d*a^-1*c^-1*x^-1//2*(c+d*x^2)^-2*(b*c+-1*a*d)^-2*(a*d+2*b*c)+1//16*d*a^-1*c^-2*x^-1//2*(c+d*x^2)^-1*(b*c+-1*a*d)^-3*(-9*a^2*d^2+8*b^2*c^2+25*a*b*c*d))
@test integrate(x^-5//2*(a+b*x^2)^-2*(c+d*x^2)^-3, x) == :(1//48*a^-2*c^-3*x^-3//2*(b*c+-1*a*d)^-3*(-56*b^3*c^3+77*a^3*d^3+-189*b*c*a^2*d^2+96*a*d*b^2*c^2)+(1/2)*b*a^-1*x^-3//2*(a+b*x^2)^-1*(c+d*x^2)^-2*(b*c+-1*a*d)^-1+-1//8*2^(1/2)*a^-11//4*b^15//4*(b*c+-1*a*d)^-4*(-19*a*d+7*b*c)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-1//16*2^(1/2)*a^-11//4*b^15//4*(b*c+-1*a*d)^-4*(-19*a*d+7*b*c)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+-1//64*2^(1/2)*c^-15//4*d^11//4*(b*c+-1*a*d)^-4*(77*a^2*d^2+285*b^2*c^2+-266*a*b*c*d)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-1//128*2^(1/2)*c^-15//4*d^11//4*(b*c+-1*a*d)^-4*(77*a^2*d^2+285*b^2*c^2+-266*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//8*2^(1/2)*a^-11//4*b^15//4*(b*c+-1*a*d)^-4*(-19*a*d+7*b*c)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+1//16*2^(1/2)*a^-11//4*b^15//4*(b*c+-1*a*d)^-4*(-19*a*d+7*b*c)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+1//64*2^(1/2)*c^-15//4*d^11//4*(b*c+-1*a*d)^-4*(77*a^2*d^2+285*b^2*c^2+-266*a*b*c*d)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+1//128*2^(1/2)*c^-15//4*d^11//4*(b*c+-1*a*d)^-4*(77*a^2*d^2+285*b^2*c^2+-266*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//4*d*a^-1*c^-1*x^-3//2*(c+d*x^2)^-2*(b*c+-1*a*d)^-2*(a*d+2*b*c)+1//16*d*a^-1*c^-2*x^-3//2*(c+d*x^2)^-1*(b*c+-1*a*d)^-3*(-11*a^2*d^2+8*b^2*c^2+27*a*b*c*d))
@test integrate(x^-7//2*(a+b*x^2)^-2*(c+d*x^2)^-3, x) == :(1//16*a^-3*c^-4*x^-1//2*(b*c+-1*a*d)^-3*(-117*a^4*d^4+72*b^4*c^4+-96*a*d*b^3*c^3+-96*a^2*b^2*c^2*d^2+261*b*c*a^3*d^3)+1//80*a^-2*c^-3*x^-5//2*(b*c+-1*a*d)^-3*(-72*b^3*c^3+117*a^3*d^3+-261*b*c*a^2*d^2+96*a*d*b^2*c^2)+(1/2)*b*a^-1*x^-5//2*(a+b*x^2)^-1*(c+d*x^2)^-2*(b*c+-1*a*d)^-1+-3//8*2^(1/2)*a^-13//4*b^17//4*(b*c+-1*a*d)^-4*(-7*a*d+3*b*c)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*x^(1/2))+-3//16*2^(1/2)*a^-13//4*b^17//4*(b*c+-1*a*d)^-4*(-7*a*d+3*b*c)*log(a^(1/2)+x*b^(1/2)+2^(1/2)*a^1//4*b^1//4*x^(1/2))+-3//64*2^(1/2)*c^-17//4*d^13//4*(b*c+-1*a*d)^-4*(39*a^2*d^2+119*b^2*c^2+-126*a*b*c*d)*arctan(1+-1*2^(1/2)*c^-1//4*d^1//4*x^(1/2))+-3//128*2^(1/2)*c^-17//4*d^13//4*(b*c+-1*a*d)^-4*(39*a^2*d^2+119*b^2*c^2+-126*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+2^(1/2)*c^1//4*d^1//4*x^(1/2))+3//8*2^(1/2)*a^-13//4*b^17//4*(b*c+-1*a*d)^-4*(-7*a*d+3*b*c)*arctan(1+2^(1/2)*a^-1//4*b^1//4*x^(1/2))+3//16*2^(1/2)*a^-13//4*b^17//4*(b*c+-1*a*d)^-4*(-7*a*d+3*b*c)*log(a^(1/2)+x*b^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*x^(1/2))+3//64*2^(1/2)*c^-17//4*d^13//4*(b*c+-1*a*d)^-4*(39*a^2*d^2+119*b^2*c^2+-126*a*b*c*d)*arctan(1+2^(1/2)*c^-1//4*d^1//4*x^(1/2))+3//128*2^(1/2)*c^-17//4*d^13//4*(b*c+-1*a*d)^-4*(39*a^2*d^2+119*b^2*c^2+-126*a*b*c*d)*log(c^(1/2)+x*d^(1/2)+-1*2^(1/2)*c^1//4*d^1//4*x^(1/2))+1//4*d*a^-1*c^-1*x^-5//2*(c+d*x^2)^-2*(b*c+-1*a*d)^-2*(a*d+2*b*c)+1//16*d*a^-1*c^-2*x^-5//2*(c+d*x^2)^-1*(b*c+-1*a*d)^-3*(-13*a^2*d^2+8*b^2*c^2+29*a*b*c*d))
@test integrate(x^5*(a+b*x^2)^(1/2)*(A+B*x^2), x) == :(1//7*b^-4*(a+b*x^2)^7//2*(A*b+-3*B*a)+1//9*B*b^-4*(a+b*x^2)^9//2+-1//5*a*b^-4*(a+b*x^2)^5//2*(-3*B*a+2*A*b)+1//3*a^2*b^-4*(a+b*x^2)^3//2*(A*b+-1*B*a))
@test integrate(x^4*(a+b*x^2)^(1/2)*(A+B*x^2), x) == :(1//8*B*b^-1*x^5*(a+b*x^2)^3//2+1//48*b^-1*x^5*(a+b*x^2)^(1/2)*(-5*B*a+8*A*b)+1//128*a^3*b^-7//2*(-5*B*a+8*A*b)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+-1//128*x*a^2*b^-3*(a+b*x^2)^(1/2)*(-5*B*a+8*A*b)+1//192*a*b^-2*x^3*(a+b*x^2)^(1/2)*(-5*B*a+8*A*b))
@test integrate(x^3*(a+b*x^2)^(1/2)*(A+B*x^2), x) == :(1//5*b^-3*(a+b*x^2)^5//2*(A*b+-2*B*a)+1//7*B*b^-3*(a+b*x^2)^7//2+-1//3*a*b^-3*(a+b*x^2)^3//2*(A*b+-1*B*a))
@test integrate(x^2*(a+b*x^2)^(1/2)*(A+B*x^2), x) == :(-1//16*a^2*b^-5//2*(-1*B*a+2*A*b)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+1//6*B*b^-1*x^3*(a+b*x^2)^3//2+1//8*b^-1*x^3*(a+b*x^2)^(1/2)*(-1*B*a+2*A*b)+1//16*a*x*b^-2*(a+b*x^2)^(1/2)*(-1*B*a+2*A*b))
@test integrate(x*(a+b*x^2)^(1/2)*(A+B*x^2), x) == :(1//3*b^-2*(a+b*x^2)^3//2*(A*b+-1*B*a)+1//5*B*b^-2*(a+b*x^2)^5//2)
@test integrate((a+b*x^2)^(1/2)*(A+B*x^2), x) == :(1//4*B*x*b^-1*(a+b*x^2)^3//2+1//8*a*b^-3//2*(-1*B*a+4*A*b)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+1//8*x*b^-1*(a+b*x^2)^(1/2)*(-1*B*a+4*A*b))
@test integrate(x^-1*(a+b*x^2)^(1/2)*(A+B*x^2), x) == :(A*(a+b*x^2)^(1/2)+-1*A*a^(1/2)*arctanh(a^-1//2*(a+b*x^2)^(1/2))+1//3*B*b^-1*(a+b*x^2)^3//2)
@test integrate(x^-2*(a+b*x^2)^(1/2)*(A+B*x^2), x) == :((1/2)*b^-1//2*(B*a+2*A*b)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+(1/2)*x*a^-1*(a+b*x^2)^(1/2)*(B*a+2*A*b)+-1*A*a^-1*x^-1*(a+b*x^2)^3//2)
@test integrate(x^-3*(a+b*x^2)^(1/2)*(A+B*x^2), x) == :((1/2)*a^-1*(a+b*x^2)^(1/2)*(A*b+2*B*a)+-1//2*a^-1//2*(A*b+2*B*a)*arctanh(a^-1//2*(a+b*x^2)^(1/2))+-1//2*A*a^-1*x^-2*(a+b*x^2)^3//2)
@test integrate(x^-4*(a+b*x^2)^(1/2)*(A+B*x^2), x) == :(B*b^(1/2)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+-1*B*x^-1*(a+b*x^2)^(1/2)+-1//3*A*a^-1*x^-3*(a+b*x^2)^3//2)
@test integrate(x^-5*(a+b*x^2)^(1/2)*(A+B*x^2), x) == :(-1//4*A*a^-1*x^-4*(a+b*x^2)^3//2+1//8*b*a^-3//2*(A*b+-4*B*a)*arctanh(a^-1//2*(a+b*x^2)^(1/2))+1//8*a^-1*x^-2*(a+b*x^2)^(1/2)*(A*b+-4*B*a))
@test integrate(x^-6*(a+b*x^2)^(1/2)*(A+B*x^2), x) == :(-1//5*A*a^-1*x^-5*(a+b*x^2)^3//2+1//15*a^-2*x^-3*(a+b*x^2)^3//2*(-5*B*a+2*A*b))
@test integrate(x^-7*(a+b*x^2)^(1/2)*(A+B*x^2), x) == :(-1//6*A*a^-1*x^-6*(a+b*x^2)^3//2+-1//16*a^-5//2*b^2*(A*b+-2*B*a)*arctanh(a^-1//2*(a+b*x^2)^(1/2))+1//8*a^-1*x^-4*(a+b*x^2)^(1/2)*(A*b+-2*B*a)+1//16*b*a^-2*x^-2*(a+b*x^2)^(1/2)*(A*b+-2*B*a))
@test integrate(x^-8*(a+b*x^2)^(1/2)*(A+B*x^2), x) == :(-1//7*A*a^-1*x^-7*(a+b*x^2)^3//2+1//35*a^-2*x^-5*(a+b*x^2)^3//2*(-7*B*a+4*A*b)+-2//105*b*a^-3*x^-3*(a+b*x^2)^3//2*(-7*B*a+4*A*b))
@test integrate(x^-9*(a+b*x^2)^(1/2)*(A+B*x^2), x) == :(-1//8*A*a^-1*x^-8*(a+b*x^2)^3//2+1//48*a^-1*x^-6*(a+b*x^2)^(1/2)*(-8*B*a+5*A*b)+1//128*a^-7//2*b^3*(-8*B*a+5*A*b)*arctanh(a^-1//2*(a+b*x^2)^(1/2))+-1//128*a^-3*b^2*x^-2*(a+b*x^2)^(1/2)*(-8*B*a+5*A*b)+1//192*b*a^-2*x^-4*(a+b*x^2)^(1/2)*(-8*B*a+5*A*b))
@test integrate(x^-10*(a+b*x^2)^(1/2)*(A+B*x^2), x) == :(-1//9*A*a^-1*x^-9*(a+b*x^2)^3//2+1//21*a^-2*x^-7*(a+b*x^2)^3//2*(-3*B*a+2*A*b)+-4//105*b*a^-3*x^-5*(a+b*x^2)^3//2*(-3*B*a+2*A*b)+8//315*a^-4*b^2*x^-3*(a+b*x^2)^3//2*(-3*B*a+2*A*b))
@test integrate(x^-11*(a+b*x^2)^(1/2)*(A+B*x^2), x) == :(-1//10*A*a^-1*x^-10*(a+b*x^2)^3//2+-1//256*a^-9//2*b^4*(-10*B*a+7*A*b)*arctanh(a^-1//2*(a+b*x^2)^(1/2))+1//80*a^-1*x^-8*(a+b*x^2)^(1/2)*(-10*B*a+7*A*b)+-1//384*a^-3*b^2*x^-4*(a+b*x^2)^(1/2)*(-10*B*a+7*A*b)+1//256*a^-4*b^3*x^-2*(a+b*x^2)^(1/2)*(-10*B*a+7*A*b)+1//480*b*a^-2*x^-6*(a+b*x^2)^(1/2)*(-10*B*a+7*A*b))
@test integrate(x^5*(a+b*x^2)^3//2*(A+B*x^2), x) == :(1//9*b^-4*(a+b*x^2)^9//2*(A*b+-3*B*a)+1//11*B*b^-4*(a+b*x^2)^11//2+-1//7*a*b^-4*(a+b*x^2)^7//2*(-3*B*a+2*A*b)+1//5*a^2*b^-4*(a+b*x^2)^5//2*(A*b+-1*B*a))
@test integrate(x^4*(a+b*x^2)^3//2*(A+B*x^2), x) == :(1//10*B*b^-1*x^5*(a+b*x^2)^5//2+1//16*b^-1*x^5*(a+b*x^2)^3//2*(-1*B*a+2*A*b)+3//256*a^4*b^-7//2*(-1*B*a+2*A*b)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+-3//256*x*a^3*b^-3*(a+b*x^2)^(1/2)*(-1*B*a+2*A*b)+1//32*a*b^-1*x^5*(a+b*x^2)^(1/2)*(-1*B*a+2*A*b)+1//128*a^2*b^-2*x^3*(a+b*x^2)^(1/2)*(-1*B*a+2*A*b))
@test integrate(x^3*(a+b*x^2)^3//2*(A+B*x^2), x) == :(1//7*b^-3*(a+b*x^2)^7//2*(A*b+-2*B*a)+1//9*B*b^-3*(a+b*x^2)^9//2+-1//5*a*b^-3*(a+b*x^2)^5//2*(A*b+-1*B*a))
@test integrate(x^2*(a+b*x^2)^3//2*(A+B*x^2), x) == :(-1//128*a^3*b^-5//2*(-3*B*a+8*A*b)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+1//8*B*b^-1*x^3*(a+b*x^2)^5//2+1//48*b^-1*x^3*(a+b*x^2)^3//2*(-3*B*a+8*A*b)+1//64*a*b^-1*x^3*(a+b*x^2)^(1/2)*(-3*B*a+8*A*b)+1//128*x*a^2*b^-2*(a+b*x^2)^(1/2)*(-3*B*a+8*A*b))
@test integrate(x*(a+b*x^2)^3//2*(A+B*x^2), x) == :(1//5*b^-2*(a+b*x^2)^5//2*(A*b+-1*B*a)+1//7*B*b^-2*(a+b*x^2)^7//2)
@test integrate((a+b*x^2)^3//2*(A+B*x^2), x) == :(1//6*B*x*b^-1*(a+b*x^2)^5//2+1//16*a^2*b^-3//2*(-1*B*a+6*A*b)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+1//24*x*b^-1*(a+b*x^2)^3//2*(-1*B*a+6*A*b)+1//16*a*x*b^-1*(a+b*x^2)^(1/2)*(-1*B*a+6*A*b))
@test integrate(x^-1*(a+b*x^2)^3//2*(A+B*x^2), x) == :(1//3*A*(a+b*x^2)^3//2+A*a*(a+b*x^2)^(1/2)+-1*A*a^3//2*arctanh(a^-1//2*(a+b*x^2)^(1/2))+1//5*B*b^-1*(a+b*x^2)^5//2)
@test integrate(x^-2*(a+b*x^2)^3//2*(A+B*x^2), x) == :(x*(a+b*x^2)^(1/2)*(3//2*A*b+3//8*B*a)+-1*A*a^-1*x^-1*(a+b*x^2)^5//2+1//4*x*a^-1*(a+b*x^2)^3//2*(B*a+4*A*b)+3//8*a*b^-1//2*(B*a+4*A*b)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2))
@test integrate(x^-3*(a+b*x^2)^3//2*(A+B*x^2), x) == :((a+b*x^2)^(1/2)*(B*a+3//2*A*b)+-1//2*a^(1/2)*(2*B*a+3*A*b)*arctanh(a^-1//2*(a+b*x^2)^(1/2))+1//6*a^-1*(a+b*x^2)^3//2*(2*B*a+3*A*b)+-1//2*A*a^-1*x^-2*(a+b*x^2)^5//2)
@test integrate(x^-4*(a+b*x^2)^3//2*(A+B*x^2), x) == :((1/2)*b^(1/2)*(2*A*b+3*B*a)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+-1//3*A*a^-1*x^-3*(a+b*x^2)^5//2+-1//3*a^-1*x^-1*(a+b*x^2)^3//2*(2*A*b+3*B*a)+(1/2)*b*x*a^-1*(a+b*x^2)^(1/2)*(2*A*b+3*B*a))
@test integrate(x^-5*(a+b*x^2)^3//2*(A+B*x^2), x) == :(-3//8*b*a^-1//2*(A*b+4*B*a)*arctanh(a^-1//2*(a+b*x^2)^(1/2))+-1//4*A*a^-1*x^-4*(a+b*x^2)^5//2+-1//8*a^-1*x^-2*(a+b*x^2)^3//2*(A*b+4*B*a)+3//8*b*a^-1*(a+b*x^2)^(1/2)*(A*b+4*B*a))
@test integrate(x^-6*(a+b*x^2)^3//2*(A+B*x^2), x) == :(B*b^3//2*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+-1//3*B*x^-3*(a+b*x^2)^3//2+-1*B*b*x^-1*(a+b*x^2)^(1/2)+-1//5*A*a^-1*x^-5*(a+b*x^2)^5//2)
@test integrate(x^-7*(a+b*x^2)^3//2*(A+B*x^2), x) == :(-1//6*A*a^-1*x^-6*(a+b*x^2)^5//2+1//16*a^-3//2*b^2*(A*b+-6*B*a)*arctanh(a^-1//2*(a+b*x^2)^(1/2))+1//24*a^-1*x^-4*(a+b*x^2)^3//2*(A*b+-6*B*a)+1//16*b*a^-1*x^-2*(a+b*x^2)^(1/2)*(A*b+-6*B*a))
@test integrate(x^-8*(a+b*x^2)^3//2*(A+B*x^2), x) == :(-1//7*A*a^-1*x^-7*(a+b*x^2)^5//2+1//35*a^-2*x^-5*(a+b*x^2)^5//2*(-7*B*a+2*A*b))
@test integrate(x^-9*(a+b*x^2)^3//2*(A+B*x^2), x) == :(-1//8*A*a^-1*x^-8*(a+b*x^2)^5//2+-1//128*a^-5//2*b^3*(-8*B*a+3*A*b)*arctanh(a^-1//2*(a+b*x^2)^(1/2))+1//48*a^-1*x^-6*(a+b*x^2)^3//2*(-8*B*a+3*A*b)+1//64*b*a^-1*x^-4*(a+b*x^2)^(1/2)*(-8*B*a+3*A*b)+1//128*a^-2*b^2*x^-2*(a+b*x^2)^(1/2)*(-8*B*a+3*A*b))
@test integrate(x^-10*(a+b*x^2)^3//2*(A+B*x^2), x) == :(-1//9*A*a^-1*x^-9*(a+b*x^2)^5//2+1//63*a^-2*x^-7*(a+b*x^2)^5//2*(-9*B*a+4*A*b)+-2//315*b*a^-3*x^-5*(a+b*x^2)^5//2*(-9*B*a+4*A*b))
@test integrate(x^-11*(a+b*x^2)^3//2*(A+B*x^2), x) == :(-1//10*A*a^-1*x^-10*(a+b*x^2)^5//2+1//16*a^-1*x^-8*(a+b*x^2)^3//2*(A*b+-2*B*a)+3//256*a^-7//2*b^4*(A*b+-2*B*a)*arctanh(a^-1//2*(a+b*x^2)^(1/2))+-3//256*a^-3*b^3*x^-2*(a+b*x^2)^(1/2)*(A*b+-2*B*a)+1//32*b*a^-1*x^-6*(a+b*x^2)^(1/2)*(A*b+-2*B*a)+1//128*a^-2*b^2*x^-4*(a+b*x^2)^(1/2)*(A*b+-2*B*a))
@test integrate(x^5*(a+b*x^2)^5//2*(A+B*x^2), x) == :(1//11*b^-4*(a+b*x^2)^11//2*(A*b+-3*B*a)+1//13*B*b^-4*(a+b*x^2)^13//2+-1//9*a*b^-4*(a+b*x^2)^9//2*(-3*B*a+2*A*b)+1//7*a^2*b^-4*(a+b*x^2)^7//2*(A*b+-1*B*a))
@test integrate(x^4*(a+b*x^2)^5//2*(A+B*x^2), x) == :(1//12*B*b^-1*x^5*(a+b*x^2)^7//2+1//120*b^-1*x^5*(a+b*x^2)^5//2*(-5*B*a+12*A*b)+1//1024*a^5*b^-7//2*(-5*B*a+12*A*b)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+-1//1024*x*a^4*b^-3*(a+b*x^2)^(1/2)*(-5*B*a+12*A*b)+1//192*a*b^-1*x^5*(a+b*x^2)^3//2*(-5*B*a+12*A*b)+1//384*a^2*b^-1*x^5*(a+b*x^2)^(1/2)*(-5*B*a+12*A*b)+1//1536*a^3*b^-2*x^3*(a+b*x^2)^(1/2)*(-5*B*a+12*A*b))
@test integrate(x^3*(a+b*x^2)^5//2*(A+B*x^2), x) == :(1//9*b^-3*(a+b*x^2)^9//2*(A*b+-2*B*a)+1//11*B*b^-3*(a+b*x^2)^11//2+-1//7*a*b^-3*(a+b*x^2)^7//2*(A*b+-1*B*a))
@test integrate(x^2*(a+b*x^2)^5//2*(A+B*x^2), x) == :(-1//256*a^4*b^-5//2*(-3*B*a+10*A*b)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+1//10*B*b^-1*x^3*(a+b*x^2)^7//2+1//80*b^-1*x^3*(a+b*x^2)^5//2*(-3*B*a+10*A*b)+1//96*a*b^-1*x^3*(a+b*x^2)^3//2*(-3*B*a+10*A*b)+1//128*a^2*b^-1*x^3*(a+b*x^2)^(1/2)*(-3*B*a+10*A*b)+1//256*x*a^3*b^-2*(a+b*x^2)^(1/2)*(-3*B*a+10*A*b))
@test integrate(x*(a+b*x^2)^5//2*(A+B*x^2), x) == :(1//7*b^-2*(a+b*x^2)^7//2*(A*b+-1*B*a)+1//9*B*b^-2*(a+b*x^2)^9//2)
@test integrate((a+b*x^2)^5//2*(A+B*x^2), x) == :(1//8*B*x*b^-1*(a+b*x^2)^7//2+1//48*x*b^-1*(a+b*x^2)^5//2*(-1*B*a+8*A*b)+5//128*a^3*b^-3//2*(-1*B*a+8*A*b)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+5//128*x*a^2*b^-1*(a+b*x^2)^(1/2)*(-1*B*a+8*A*b)+5//192*a*x*b^-1*(a+b*x^2)^3//2*(-1*B*a+8*A*b))
@test integrate(x^-1*(a+b*x^2)^5//2*(A+B*x^2), x) == :(1//5*A*(a+b*x^2)^5//2+A*a^2*(a+b*x^2)^(1/2)+-1*A*a^5//2*arctanh(a^-1//2*(a+b*x^2)^(1/2))+1//3*A*a*(a+b*x^2)^3//2+1//7*B*b^-1*(a+b*x^2)^7//2)
@test integrate(x^-2*(a+b*x^2)^5//2*(A+B*x^2), x) == :(1//24*x*(a+b*x^2)^3//2*(5*B*a+30*A*b)+-1*A*a^-1*x^-1*(a+b*x^2)^7//2+1//6*x*a^-1*(a+b*x^2)^5//2*(B*a+6*A*b)+5//16*a*x*(a+b*x^2)^(1/2)*(B*a+6*A*b)+5//16*a^2*b^-1//2*(B*a+6*A*b)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2))
@test integrate(x^-3*(a+b*x^2)^5//2*(A+B*x^2), x) == :(1//6*(a+b*x^2)^3//2*(2*B*a+5*A*b)+(1/2)*a*(a+b*x^2)^(1/2)*(2*B*a+5*A*b)+-1//2*a^3//2*(2*B*a+5*A*b)*arctanh(a^-1//2*(a+b*x^2)^(1/2))+1//10*a^-1*(a+b*x^2)^5//2*(2*B*a+5*A*b)+-1//2*A*a^-1*x^-2*(a+b*x^2)^7//2)
@test integrate(x^-4*(a+b*x^2)^5//2*(A+B*x^2), x) == :(-1//3*A*a^-1*x^-3*(a+b*x^2)^7//2+-1//3*a^-1*x^-1*(a+b*x^2)^5//2*(3*B*a+4*A*b)+5//8*a*b^(1/2)*(3*B*a+4*A*b)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+5//8*b*x*(a+b*x^2)^(1/2)*(3*B*a+4*A*b)+5//12*b*x*a^-1*(a+b*x^2)^3//2*(3*B*a+4*A*b))
@test integrate(x^-5*(a+b*x^2)^5//2*(A+B*x^2), x) == :(5//8*b*(a+b*x^2)^(1/2)*(3*A*b+4*B*a)+-5//8*b*a^(1/2)*(3*A*b+4*B*a)*arctanh(a^-1//2*(a+b*x^2)^(1/2))+-1//4*A*a^-1*x^-4*(a+b*x^2)^7//2+-1//8*a^-1*x^-2*(a+b*x^2)^5//2*(3*A*b+4*B*a)+5//24*b*a^-1*(a+b*x^2)^3//2*(3*A*b+4*B*a))
@test integrate(x^-6*(a+b*x^2)^5//2*(A+B*x^2), x) == :((1/2)*b^3//2*(2*A*b+5*B*a)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+-1//5*A*a^-1*x^-5*(a+b*x^2)^7//2+-1//15*a^-1*x^-3*(a+b*x^2)^5//2*(2*A*b+5*B*a)+(1/2)*x*a^-1*b^2*(a+b*x^2)^(1/2)*(2*A*b+5*B*a)+-1//3*b*a^-1*x^-1*(a+b*x^2)^3//2*(2*A*b+5*B*a))
@test integrate(x^-7*(a+b*x^2)^5//2*(A+B*x^2), x) == :(-5//16*a^-1//2*b^2*(A*b+6*B*a)*arctanh(a^-1//2*(a+b*x^2)^(1/2))+-1//6*A*a^-1*x^-6*(a+b*x^2)^7//2+-1//24*a^-1*x^-4*(a+b*x^2)^5//2*(A*b+6*B*a)+5//16*a^-1*b^2*(a+b*x^2)^(1/2)*(A*b+6*B*a)+-5//48*b*a^-1*x^-2*(a+b*x^2)^3//2*(A*b+6*B*a))
@test integrate(x^-8*(a+b*x^2)^5//2*(A+B*x^2), x) == :(B*b^5//2*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+-1//5*B*x^-5*(a+b*x^2)^5//2+-1*B*b^2*x^-1*(a+b*x^2)^(1/2)+-1//3*B*b*x^-3*(a+b*x^2)^3//2+-1//7*A*a^-1*x^-7*(a+b*x^2)^7//2)
@test integrate(x^-9*(a+b*x^2)^5//2*(A+B*x^2), x) == :(-1//8*A*a^-1*x^-8*(a+b*x^2)^7//2+1//48*a^-1*x^-6*(a+b*x^2)^5//2*(A*b+-8*B*a)+5//128*a^-3//2*b^3*(A*b+-8*B*a)*arctanh(a^-1//2*(a+b*x^2)^(1/2))+5//128*a^-1*b^2*x^-2*(a+b*x^2)^(1/2)*(A*b+-8*B*a)+5//192*b*a^-1*x^-4*(a+b*x^2)^3//2*(A*b+-8*B*a))
@test integrate(x^-10*(a+b*x^2)^5//2*(A+B*x^2), x) == :(-1//9*A*a^-1*x^-9*(a+b*x^2)^7//2+1//63*a^-2*x^-7*(a+b*x^2)^7//2*(-9*B*a+2*A*b))
@test integrate(x^-11*(a+b*x^2)^5//2*(A+B*x^2), x) == :(-1//10*A*a^-1*x^-10*(a+b*x^2)^7//2+-1//256*a^-5//2*b^4*(-10*B*a+3*A*b)*arctanh(a^-1//2*(a+b*x^2)^(1/2))+1//80*a^-1*x^-8*(a+b*x^2)^5//2*(-10*B*a+3*A*b)+1//96*b*a^-1*x^-6*(a+b*x^2)^3//2*(-10*B*a+3*A*b)+1//128*a^-1*b^2*x^-4*(a+b*x^2)^(1/2)*(-10*B*a+3*A*b)+1//256*a^-2*b^3*x^-2*(a+b*x^2)^(1/2)*(-10*B*a+3*A*b))
@test integrate(x^5*(a+b*x^2)^-1//2*(A+B*x^2), x) == :(1//5*b^-4*(a+b*x^2)^5//2*(A*b+-3*B*a)+1//7*B*b^-4*(a+b*x^2)^7//2+a^2*b^-4*(a+b*x^2)^(1/2)*(A*b+-1*B*a)+-1//3*a*b^-4*(a+b*x^2)^3//2*(-3*B*a+2*A*b))
@test integrate(x^4*(a+b*x^2)^-1//2*(A+B*x^2), x) == :(1//6*B*b^-1*x^5*(a+b*x^2)^(1/2)+1//16*a^2*b^-7//2*(-5*B*a+6*A*b)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+1//24*b^-2*x^3*(a+b*x^2)^(1/2)*(-5*B*a+6*A*b)+-1//16*a*x*b^-3*(a+b*x^2)^(1/2)*(-5*B*a+6*A*b))
@test integrate(x^3*(a+b*x^2)^-1//2*(A+B*x^2), x) == :(1//3*b^-3*(a+b*x^2)^3//2*(A*b+-2*B*a)+1//5*B*b^-3*(a+b*x^2)^5//2+-1*a*b^-3*(a+b*x^2)^(1/2)*(A*b+-1*B*a))
@test integrate(x^2*(a+b*x^2)^-1//2*(A+B*x^2), x) == :(-1//8*a*b^-5//2*(-3*B*a+4*A*b)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+1//4*B*b^-1*x^3*(a+b*x^2)^(1/2)+1//8*x*b^-2*(a+b*x^2)^(1/2)*(-3*B*a+4*A*b))
@test integrate(x*(a+b*x^2)^-1//2*(A+B*x^2), x) == :(b^-2*(a+b*x^2)^(1/2)*(A*b+-1*B*a)+1//3*B*b^-2*(a+b*x^2)^3//2)
@test integrate((a+b*x^2)^-1//2*(A+B*x^2), x) == :((1/2)*b^-3//2*(-1*B*a+2*A*b)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+(1/2)*B*x*b^-1*(a+b*x^2)^(1/2))
@test integrate(x^-1*(a+b*x^2)^-1//2*(A+B*x^2), x) == :(B*b^-1*(a+b*x^2)^(1/2)+-1*A*a^-1//2*arctanh(a^-1//2*(a+b*x^2)^(1/2)))
@test integrate(x^-2*(a+b*x^2)^-1//2*(A+B*x^2), x) == :(B*b^-1//2*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+-1*A*a^-1*x^-1*(a+b*x^2)^(1/2))
@test integrate(x^-3*(a+b*x^2)^-1//2*(A+B*x^2), x) == :((1/2)*a^-3//2*(A*b+-2*B*a)*arctanh(a^-1//2*(a+b*x^2)^(1/2))+-1//2*A*a^-1*x^-2*(a+b*x^2)^(1/2))
@test integrate(x^-4*(a+b*x^2)^-1//2*(A+B*x^2), x) == :(-1//3*A*a^-1*x^-3*(a+b*x^2)^(1/2)+1//3*a^-2*x^-1*(a+b*x^2)^(1/2)*(-3*B*a+2*A*b))
@test integrate(x^-5*(a+b*x^2)^-1//2*(A+B*x^2), x) == :(-1//4*A*a^-1*x^-4*(a+b*x^2)^(1/2)+-1//8*b*a^-5//2*(-4*B*a+3*A*b)*arctanh(a^-1//2*(a+b*x^2)^(1/2))+1//8*a^-2*x^-2*(a+b*x^2)^(1/2)*(-4*B*a+3*A*b))
@test integrate(x^-6*(a+b*x^2)^-1//2*(A+B*x^2), x) == :(-1//5*A*a^-1*x^-5*(a+b*x^2)^(1/2)+1//15*a^-2*x^-3*(a+b*x^2)^(1/2)*(-5*B*a+4*A*b)+-2//15*b*a^-3*x^-1*(a+b*x^2)^(1/2)*(-5*B*a+4*A*b))
@test integrate(x^-7*(a+b*x^2)^-1//2*(A+B*x^2), x) == :(-1//6*A*a^-1*x^-6*(a+b*x^2)^(1/2)+1//16*a^-7//2*b^2*(-6*B*a+5*A*b)*arctanh(a^-1//2*(a+b*x^2)^(1/2))+1//24*a^-2*x^-4*(a+b*x^2)^(1/2)*(-6*B*a+5*A*b)+-1//16*b*a^-3*x^-2*(a+b*x^2)^(1/2)*(-6*B*a+5*A*b))
@test integrate(x^-8*(a+b*x^2)^-1//2*(A+B*x^2), x) == :(-1//7*A*a^-1*x^-7*(a+b*x^2)^(1/2)+1//35*a^-2*x^-5*(a+b*x^2)^(1/2)*(-7*B*a+6*A*b)+-4//105*b*a^-3*x^-3*(a+b*x^2)^(1/2)*(-7*B*a+6*A*b)+8//105*a^-4*b^2*x^-1*(a+b*x^2)^(1/2)*(-7*B*a+6*A*b))
@test integrate(x^6*(a+b*x^2)^-3//2*(A+B*x^2), x) == :(-1//6*b^-2*x^5*(a+b*x^2)^-1//2*(-7*B*a+6*A*b)+1//6*B*b^-1*x^7*(a+b*x^2)^-1//2+1//24*b^-3*x^3*(a+b*x^2)^(1/2)*(-35*B*a+30*A*b)+5//16*a^2*b^-9//2*(-7*B*a+6*A*b)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+-5//16*a*x*b^-4*(a+b*x^2)^(1/2)*(-7*B*a+6*A*b))
@test integrate(x^5*(a+b*x^2)^-3//2*(A+B*x^2), x) == :(1//3*b^-4*(a+b*x^2)^3//2*(A*b+-3*B*a)+1//5*B*b^-4*(a+b*x^2)^5//2+-1*a*b^-4*(a+b*x^2)^(1/2)*(-3*B*a+2*A*b)+-1*a^2*b^-4*(a+b*x^2)^-1//2*(A*b+-1*B*a))
@test integrate(x^4*(a+b*x^2)^-3//2*(A+B*x^2), x) == :(-3//8*a*b^-7//2*(-5*B*a+4*A*b)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+-1//4*b^-2*x^3*(a+b*x^2)^-1//2*(-5*B*a+4*A*b)+1//4*B*b^-1*x^5*(a+b*x^2)^-1//2+1//8*x*b^-3*(a+b*x^2)^(1/2)*(-15*B*a+12*A*b))
@test integrate(x^3*(a+b*x^2)^-3//2*(A+B*x^2), x) == :(b^-3*(a+b*x^2)^(1/2)*(A*b+-2*B*a)+1//3*B*b^-3*(a+b*x^2)^3//2+a*b^-3*(a+b*x^2)^-1//2*(A*b+-1*B*a))
@test integrate(x^2*(a+b*x^2)^-3//2*(A+B*x^2), x) == :((1/2)*b^-5//2*(-3*B*a+2*A*b)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+(1/2)*B*x*b^-2*(a+b*x^2)^(1/2)+-1*x*b^-2*(a+b*x^2)^-1//2*(A*b+-1*B*a))
@test integrate(x*(a+b*x^2)^-3//2*(A+B*x^2), x) == :(B*b^-2*(a+b*x^2)^(1/2)+-1*b^-2*(a+b*x^2)^-1//2*(A*b+-1*B*a))
@test integrate((a+b*x^2)^-3//2*(A+B*x^2), x) == :(B*b^-3//2*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+x*a^-1*b^-1*(a+b*x^2)^-1//2*(A*b+-1*B*a))
@test integrate(x^-1*(a+b*x^2)^-3//2*(A+B*x^2), x) == :(-1*A*a^-3//2*arctanh(a^-1//2*(a+b*x^2)^(1/2))+a^-1*b^-1*(a+b*x^2)^-1//2*(A*b+-1*B*a))
@test integrate(x^-2*(a+b*x^2)^-3//2*(A+B*x^2), x) == :(-1*A*a^-1*x^-1*(a+b*x^2)^-1//2+-1*x*a^-2*(a+b*x^2)^-1//2*(-1*B*a+2*A*b))
@test integrate(x^-3*(a+b*x^2)^-3//2*(A+B*x^2), x) == :((1/2)*a^-5//2*(-2*B*a+3*A*b)*arctanh(a^-1//2*(a+b*x^2)^(1/2))+-1//2*a^-2*(a+b*x^2)^-1//2*(-2*B*a+3*A*b)+-1//2*A*a^-1*x^-2*(a+b*x^2)^-1//2)
@test integrate(x^-4*(a+b*x^2)^-3//2*(A+B*x^2), x) == :(-1//3*A*a^-1*x^-3*(a+b*x^2)^-1//2+1//3*a^-2*x^-1*(a+b*x^2)^-1//2*(-3*B*a+4*A*b)+2//3*b*x*a^-3*(a+b*x^2)^-1//2*(-3*B*a+4*A*b))
@test integrate(x^-5*(a+b*x^2)^-3//2*(A+B*x^2), x) == :(-3//8*b*a^-7//2*(-4*B*a+5*A*b)*arctanh(a^-1//2*(a+b*x^2)^(1/2))+-1//4*A*a^-1*x^-4*(a+b*x^2)^-1//2+1//8*a^-2*x^-2*(a+b*x^2)^-1//2*(-4*B*a+5*A*b)+3//8*b*a^-3*(a+b*x^2)^-1//2*(-4*B*a+5*A*b))
@test integrate(x^-6*(a+b*x^2)^-3//2*(A+B*x^2), x) == :(-1//5*A*a^-1*x^-5*(a+b*x^2)^-1//2+1//15*a^-2*x^-3*(a+b*x^2)^-1//2*(-5*B*a+6*A*b)+-8//15*x*a^-4*b^2*(a+b*x^2)^-1//2*(-5*B*a+6*A*b)+-4//15*b*a^-3*x^-1*(a+b*x^2)^-1//2*(-5*B*a+6*A*b))
@test integrate(x^-7*(a+b*x^2)^-3//2*(A+B*x^2), x) == :(-5//16*a^-4*b^2*(a+b*x^2)^-1//2*(-6*B*a+7*A*b)+-1//6*A*a^-1*x^-6*(a+b*x^2)^-1//2+1//24*a^-2*x^-4*(a+b*x^2)^-1//2*(-6*B*a+7*A*b)+5//16*a^-9//2*b^2*(-6*B*a+7*A*b)*arctanh(a^-1//2*(a+b*x^2)^(1/2))+-5//48*b*a^-3*x^-2*(a+b*x^2)^-1//2*(-6*B*a+7*A*b))
@test integrate(x^-8*(a+b*x^2)^-3//2*(A+B*x^2), x) == :(-1//7*A*a^-1*x^-7*(a+b*x^2)^-1//2+1//35*a^-2*x^-5*(a+b*x^2)^-1//2*(-7*B*a+8*A*b)+-2//35*b*a^-3*x^-3*(a+b*x^2)^-1//2*(-7*B*a+8*A*b)+8//35*a^-4*b^2*x^-1*(a+b*x^2)^-1//2*(-7*B*a+8*A*b)+16//35*x*a^-5*b^3*(a+b*x^2)^-1//2*(-7*B*a+8*A*b))
@test integrate(x^7*(a+b*x^2)^-5//2*(A+B*x^2), x) == :(1//3*b^-5*(a+b*x^2)^3//2*(A*b+-4*B*a)+1//5*B*b^-5*(a+b*x^2)^5//2+-1*a^2*b^-5*(a+b*x^2)^-1//2*(-4*B*a+3*A*b)+-3*a*b^-5*(a+b*x^2)^(1/2)*(A*b+-2*B*a)+1//3*a^3*b^-5*(a+b*x^2)^-3//2*(A*b+-1*B*a))
@test integrate(x^6*(a+b*x^2)^-5//2*(A+B*x^2), x) == :(-5//8*a*b^-9//2*(-7*B*a+4*A*b)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+-1//12*b^-3*x^3*(a+b*x^2)^-1//2*(-35*B*a+20*A*b)+-1//12*b^-2*x^5*(a+b*x^2)^-3//2*(-7*B*a+4*A*b)+1//4*B*b^-1*x^7*(a+b*x^2)^-3//2+1//8*x*b^-4*(a+b*x^2)^(1/2)*(-35*B*a+20*A*b))
@test integrate(x^5*(a+b*x^2)^-5//2*(A+B*x^2), x) == :(b^-4*(a+b*x^2)^(1/2)*(A*b+-3*B*a)+1//3*B*b^-4*(a+b*x^2)^3//2+a*b^-4*(a+b*x^2)^-1//2*(-3*B*a+2*A*b)+-1//3*a^2*b^-4*(a+b*x^2)^-3//2*(A*b+-1*B*a))
@test integrate(x^4*(a+b*x^2)^-5//2*(A+B*x^2), x) == :((1/2)*b^-7//2*(-5*B*a+2*A*b)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+(1/2)*B*x*b^-3*(a+b*x^2)^(1/2)+-1//3*x*b^-3*(a+b*x^2)^-1//2*(-7*B*a+4*A*b)+1//3*a*x*b^-3*(a+b*x^2)^-3//2*(A*b+-1*B*a))
@test integrate(x^3*(a+b*x^2)^-5//2*(A+B*x^2), x) == :(B*b^-3*(a+b*x^2)^(1/2)+-1*b^-3*(a+b*x^2)^-1//2*(A*b+-2*B*a)+1//3*a*b^-3*(a+b*x^2)^-3//2*(A*b+-1*B*a))
@test integrate(x^2*(a+b*x^2)^-5//2*(A+B*x^2), x) == :(B*b^-5//2*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+-1*B*x*b^-2*(a+b*x^2)^-1//2+1//3*a^-1*b^-1*x^3*(a+b*x^2)^-3//2*(A*b+-1*B*a))
@test integrate(x*(a+b*x^2)^-5//2*(A+B*x^2), x) == :(-1*B*b^-2*(a+b*x^2)^-1//2+1//3*b^-2*(a+b*x^2)^-3//2*(B*a+-1*A*b))
@test integrate((a+b*x^2)^-5//2*(A+B*x^2), x) == :(1//3*x*a^-1*(a+b*x^2)^-3//2*(A+B*x^2)+2//3*A*x*a^-2*(a+b*x^2)^-1//2)
@test integrate(x^-1*(a+b*x^2)^-5//2*(A+B*x^2), x) == :(A*a^-2*(a+b*x^2)^-1//2+-1*A*a^-5//2*arctanh(a^-1//2*(a+b*x^2)^(1/2))+1//3*a^-1*b^-1*(a+b*x^2)^-3//2*(A*b+-1*B*a))
@test integrate(x^-2*(a+b*x^2)^-5//2*(A+B*x^2), x) == :(-1*A*a^-1*x^-1*(a+b*x^2)^-3//2+-1//3*x*a^-3*(a+b*x^2)^-1//2*(-2*B*a+8*A*b)+-1//3*x*a^-2*(a+b*x^2)^-3//2*(-1*B*a+4*A*b))
@test integrate(x^-3*(a+b*x^2)^-5//2*(A+B*x^2), x) == :((1/2)*a^-7//2*(-2*B*a+5*A*b)*arctanh(a^-1//2*(a+b*x^2)^(1/2))+-1//2*a^-3*(a+b*x^2)^-1//2*(-2*B*a+5*A*b)+1//6*a^-2*(a+b*x^2)^-3//2*(-5*A*b+2*B*a)+-1//2*A*a^-1*x^-2*(a+b*x^2)^-3//2)
@test integrate(x^-4*(a+b*x^2)^-5//2*(A+B*x^2), x) == :(a^-2*x^-1*(a+b*x^2)^-3//2*(-1*B*a+2*A*b)+-1//3*A*a^-1*x^-3*(a+b*x^2)^-3//2+4//3*b*x*a^-3*(a+b*x^2)^-3//2*(-1*B*a+2*A*b)+8//3*b*x*a^-4*(a+b*x^2)^-1//2*(-1*B*a+2*A*b))
@test integrate(x^-5*(a+b*x^2)^-5//2*(A+B*x^2), x) == :(-5//8*b*a^-9//2*(-4*B*a+7*A*b)*arctanh(a^-1//2*(a+b*x^2)^(1/2))+-1//4*A*a^-1*x^-4*(a+b*x^2)^-3//2+1//8*a^-2*x^-2*(a+b*x^2)^-3//2*(-4*B*a+7*A*b)+5//8*b*a^-4*(a+b*x^2)^-1//2*(-4*B*a+7*A*b)+5//24*b*a^-3*(a+b*x^2)^-3//2*(-4*B*a+7*A*b))
@test integrate(x^-6*(a+b*x^2)^-5//2*(A+B*x^2), x) == :(-1//5*A*a^-1*x^-5*(a+b*x^2)^-3//2+1//15*a^-2*x^-3*(a+b*x^2)^-3//2*(-5*B*a+8*A*b)+-16//15*x*a^-5*b^2*(a+b*x^2)^-1//2*(-5*B*a+8*A*b)+-8//15*x*a^-4*b^2*(a+b*x^2)^-3//2*(-5*B*a+8*A*b)+-2//5*b*a^-3*x^-1*(a+b*x^2)^-3//2*(-5*B*a+8*A*b))
@test integrate(x^5*(a+b*x^2)^2*(c+d*x^2)^(1/2), x) == :(1//7*d^-5*(c+d*x^2)^7//2*(a^2*d^2+6*b^2*c^2+-6*a*b*c*d)+1//11*b^2*d^-5*(c+d*x^2)^11//2+-2//9*b*d^-5*(c+d*x^2)^9//2*(-1*a*d+2*b*c)+1//3*c^2*d^-5*(c+d*x^2)^3//2*(b*c+-1*a*d)^2+-2//5*c*d^-5*(c+d*x^2)^5//2*(b*c+-1*a*d)*(-1*a*d+2*b*c))
@test integrate(x^3*(a+b*x^2)^2*(c+d*x^2)^(1/2), x) == :(1//9*b^2*d^-4*(c+d*x^2)^9//2+-1//3*c*d^-4*(c+d*x^2)^3//2*(b*c+-1*a*d)^2+-1//7*b*d^-4*(c+d*x^2)^7//2*(-2*a*d+3*b*c)+1//5*d^-4*(c+d*x^2)^5//2*(b*c+-1*a*d)*(-1*a*d+3*b*c))
@test integrate(x*(a+b*x^2)^2*(c+d*x^2)^(1/2), x) == :(1//3*d^-3*(c+d*x^2)^3//2*(b*c+-1*a*d)^2+1//7*b^2*d^-3*(c+d*x^2)^7//2+-2//5*b*d^-3*(c+d*x^2)^5//2*(b*c+-1*a*d))
@test integrate(x^-1*(a+b*x^2)^2*(c+d*x^2)^(1/2), x) == :(a^2*(c+d*x^2)^(1/2)+-1*a^2*c^(1/2)*arctanh(c^-1//2*(c+d*x^2)^(1/2))+1//5*b^2*d^-2*(c+d*x^2)^5//2+-1//3*b*d^-2*(c+d*x^2)^3//2*(b*c+-2*a*d))
@test integrate(x^-3*(a+b*x^2)^2*(c+d*x^2)^(1/2), x) == :(1//3*b^2*d^-1*(c+d*x^2)^3//2+(1/2)*a*c^-1*(c+d*x^2)^(1/2)*(a*d+4*b*c)+-1//2*a*c^-1//2*(a*d+4*b*c)*arctanh(c^-1//2*(c+d*x^2)^(1/2))+-1//2*a^2*c^-1*x^-2*(c+d*x^2)^3//2)
@test integrate(x^-5*(a+b*x^2)^2*(c+d*x^2)^(1/2), x) == :(-1//8*c^-3//2*(8*b^2*c^2+a*d*(-1*a*d+8*b*c))*arctanh(c^-1//2*(c+d*x^2)^(1/2))+1//8*c^-2*(c+d*x^2)^(1/2)*(8*b^2*c^2+a*d*(-1*a*d+8*b*c))+-1//4*a^2*c^-1*x^-4*(c+d*x^2)^3//2+-1//8*a*c^-2*x^-2*(c+d*x^2)^3//2*(-1*a*d+8*b*c))
@test integrate(x^-7*(a+b*x^2)^2*(c+d*x^2)^(1/2), x) == :(-1//6*a^2*c^-1*x^-6*(c+d*x^2)^3//2+-1//16*d*c^-5//2*(a^2*d^2+8*b^2*c^2+-4*a*b*c*d)*arctanh(c^-1//2*(c+d*x^2)^(1/2))+-1//16*c^-2*x^-2*(c+d*x^2)^(1/2)*(a^2*d^2+8*b^2*c^2+-4*a*b*c*d)+-1//8*a*c^-2*x^-4*(c+d*x^2)^3//2*(-1*a*d+4*b*c))
@test integrate(x^2*(a+b*x^2)^2*(c+d*x^2)^(1/2), x) == :(-1//128*c^2*d^-7//2*(16*a^2*d^2+b*c*(-16*a*d+5*b*c))*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+1//8*b^2*d^-1*x^5*(c+d*x^2)^3//2+1//64*d^-2*x^3*(c+d*x^2)^(1/2)*(16*a^2*d^2+b*c*(-16*a*d+5*b*c))+-1//48*b*d^-2*x^3*(c+d*x^2)^3//2*(-16*a*d+5*b*c)+1//128*c*x*d^-3*(c+d*x^2)^(1/2)*(16*a^2*d^2+b*c*(-16*a*d+5*b*c)))
@test integrate((a+b*x^2)^2*(c+d*x^2)^(1/2), x) == :(1//16*c*d^-5//2*(b^2*c^2+8*a^2*d^2+-4*a*b*c*d)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+1//16*x*d^-2*(c+d*x^2)^(1/2)*(b^2*c^2+8*a^2*d^2+-4*a*b*c*d)+-1//24*b*x*d^-2*(c+d*x^2)^3//2*(-8*a*d+3*b*c)+1//6*b*x*d^-1*(c+d*x^2)^3//2*(a+b*x^2))
@test integrate(x^-2*(a+b*x^2)^2*(c+d*x^2)^(1/2), x) == :(-1//8*d^-3//2*(b^2*c^2+-8*a*d*(a*d+b*c))*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+-1*a^2*c^-1*x^-1*(c+d*x^2)^3//2+1//4*x*b^2*d^-1*(c+d*x^2)^3//2+-1//8*x*c^-1*d^-1*(c+d*x^2)^(1/2)*(b^2*c^2+-8*a*d*(a*d+b*c)))
@test integrate(x^-4*(a+b*x^2)^2*(c+d*x^2)^(1/2), x) == :((1/2)*b*d^-1//2*(b*c+4*a*d)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+-1//3*a^2*c^-1*x^-3*(c+d*x^2)^3//2+(1/2)*b*x*c^-1*(c+d*x^2)^(1/2)*(b*c+4*a*d)+-2*a*b*c^-1*x^-1*(c+d*x^2)^3//2)
@test integrate(x^-6*(a+b*x^2)^2*(c+d*x^2)^(1/2), x) == :(b^2*d^(1/2)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+-1*b^2*x^-1*(c+d*x^2)^(1/2)+-1//5*a^2*c^-1*x^-5*(c+d*x^2)^3//2+-2//15*a*c^-2*x^-3*(c+d*x^2)^3//2*(-1*a*d+5*b*c))
@test integrate(x^-8*(a+b*x^2)^2*(c+d*x^2)^(1/2), x) == :(-1//7*a^2*c^-1*x^-7*(c+d*x^2)^3//2+-1//105*c^-3*x^-3*(c+d*x^2)^3//2*(35*b^2*c^2+-4*a*d*(-2*a*d+7*b*c))+-2//35*a*c^-2*x^-5*(c+d*x^2)^3//2*(-2*a*d+7*b*c))
@test integrate(x^-10*(a+b*x^2)^2*(c+d*x^2)^(1/2), x) == :(-1//9*a^2*c^-1*x^-9*(c+d*x^2)^3//2+-1//105*c^-3*x^-5*(c+d*x^2)^3//2*(21*b^2*c^2+-8*a*d*(-1*a*d+3*b*c))+-2//21*a*c^-2*x^-7*(c+d*x^2)^3//2*(-1*a*d+3*b*c)+2//315*d*c^-4*x^-3*(c+d*x^2)^3//2*(21*b^2*c^2+-8*a*d*(-1*a*d+3*b*c)))
@test integrate(x^-12*(a+b*x^2)^2*(c+d*x^2)^(1/2), x) == :(-1//11*a^2*c^-1*x^-11*(c+d*x^2)^3//2+-1//231*c^-3*x^-7*(c+d*x^2)^3//2*(33*b^2*c^2+-4*a*d*(-4*a*d+11*b*c))+-8//3465*c^-5*d^2*x^-3*(c+d*x^2)^3//2*(33*b^2*c^2+-4*a*d*(-4*a*d+11*b*c))+-2//99*a*c^-2*x^-9*(c+d*x^2)^3//2*(-4*a*d+11*b*c)+4//1155*d*c^-4*x^-5*(c+d*x^2)^3//2*(33*b^2*c^2+-4*a*d*(-4*a*d+11*b*c)))
@test integrate(x^4*(a+b*x^2)^2*(c+d*x^2)^3//2, x) == :(1//12*b^2*d^-1*x^7*(c+d*x^2)^5//2+1//192*d^-2*x^5*(c+d*x^2)^3//2*(24*a^2*d^2+b*c*(-24*a*d+7*b*c))+1//1024*c^4*d^-9//2*(24*a^2*d^2+b*c*(-24*a*d+7*b*c))*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+-1//120*b*d^-2*x^5*(c+d*x^2)^5//2*(-24*a*d+7*b*c)+-1//1024*x*c^3*d^-4*(c+d*x^2)^(1/2)*(24*a^2*d^2+b*c*(-24*a*d+7*b*c))+1//384*c*d^-2*x^5*(c+d*x^2)^(1/2)*(24*a^2*d^2+b*c*(-24*a*d+7*b*c))+1//1536*c^2*d^-3*x^3*(c+d*x^2)^(1/2)*(24*a^2*d^2+b*c*(-24*a*d+7*b*c)))
@test integrate(x^3*(a+b*x^2)^2*(c+d*x^2)^3//2, x) == :(1//11*b^2*d^-4*(c+d*x^2)^11//2+-1//5*c*d^-4*(c+d*x^2)^5//2*(b*c+-1*a*d)^2+-1//9*b*d^-4*(c+d*x^2)^9//2*(-2*a*d+3*b*c)+1//7*d^-4*(c+d*x^2)^7//2*(b*c+-1*a*d)*(-1*a*d+3*b*c))
@test integrate(x^2*(a+b*x^2)^2*(c+d*x^2)^3//2, x) == :(-1//256*c^3*d^-7//2*(16*a^2*d^2+3*b*c*(b*c+-4*a*d))*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+1//10*b^2*d^-1*x^5*(c+d*x^2)^5//2+1//96*d^-2*x^3*(c+d*x^2)^3//2*(16*a^2*d^2+3*b*c*(b*c+-4*a*d))+-1//16*b*d^-2*x^3*(c+d*x^2)^5//2*(b*c+-4*a*d)+1//128*c*d^-2*x^3*(c+d*x^2)^(1/2)*(16*a^2*d^2+3*b*c*(b*c+-4*a*d))+1//256*x*c^2*d^-3*(c+d*x^2)^(1/2)*(16*a^2*d^2+3*b*c*(b*c+-4*a*d)))
@test integrate(x*(a+b*x^2)^2*(c+d*x^2)^3//2, x) == :(1//5*d^-3*(c+d*x^2)^5//2*(b*c+-1*a*d)^2+1//9*b^2*d^-3*(c+d*x^2)^9//2+-2//7*b*d^-3*(c+d*x^2)^7//2*(b*c+-1*a*d))
@test integrate((a+b*x^2)^2*(c+d*x^2)^3//2, x) == :(1//128*c^2*d^-5//2*(3*b^2*c^2+48*a^2*d^2+-16*a*b*c*d)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+1//192*x*d^-2*(c+d*x^2)^3//2*(3*b^2*c^2+48*a^2*d^2+-16*a*b*c*d)+-1//48*b*x*d^-2*(c+d*x^2)^5//2*(-10*a*d+3*b*c)+1//8*b*x*d^-1*(c+d*x^2)^5//2*(a+b*x^2)+1//128*c*x*d^-2*(c+d*x^2)^(1/2)*(3*b^2*c^2+48*a^2*d^2+-16*a*b*c*d))
@test integrate(x^-1*(a+b*x^2)^2*(c+d*x^2)^3//2, x) == :(1//3*a^2*(c+d*x^2)^3//2+c*a^2*(c+d*x^2)^(1/2)+-1*a^2*c^3//2*arctanh(c^-1//2*(c+d*x^2)^(1/2))+1//7*b^2*d^-2*(c+d*x^2)^7//2+-1//5*b*d^-2*(c+d*x^2)^5//2*(b*c+-2*a*d))
@test integrate(x^-2*(a+b*x^2)^2*(c+d*x^2)^3//2, x) == :(-1*a^2*c^-1*x^-1*(c+d*x^2)^5//2+-1//16*c*d^-3//2*(b^2*c^2+-12*a*d*(b*c+2*a*d))*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+-1//16*x*d^-1*(c+d*x^2)^(1/2)*(b^2*c^2+-12*a*d*(b*c+2*a*d))+1//6*x*b^2*d^-1*(c+d*x^2)^5//2+-1//24*x*c^-1*d^-1*(c+d*x^2)^3//2*(b^2*c^2+-12*a*d*(b*c+2*a*d)))
@test integrate(x^-3*(a+b*x^2)^2*(c+d*x^2)^3//2, x) == :((1/2)*a*(c+d*x^2)^(1/2)*(3*a*d+4*b*c)+1//5*b^2*d^-1*(c+d*x^2)^5//2+-1//2*a*c^(1/2)*(3*a*d+4*b*c)*arctanh(c^-1//2*(c+d*x^2)^(1/2))+-1//2*a^2*c^-1*x^-2*(c+d*x^2)^5//2+1//6*a*c^-1*(c+d*x^2)^3//2*(3*a*d+4*b*c))
@test integrate(x^-4*(a+b*x^2)^2*(c+d*x^2)^3//2, x) == :(1//8*d^-1//2*(3*b^2*c^2+8*a*d*(a*d+3*b*c))*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+-1//3*a^2*c^-1*x^-3*(c+d*x^2)^5//2+1//8*x*c^-1*(c+d*x^2)^(1/2)*(3*b^2*c^2+8*a*d*(a*d+3*b*c))+1//12*x*c^-2*(c+d*x^2)^3//2*(3*b^2*c^2+8*a*d*(a*d+3*b*c))+-2//3*a*c^-2*x^-1*(c+d*x^2)^5//2*(a*d+3*b*c))
@test integrate(x^-5*(a+b*x^2)^2*(c+d*x^2)^3//2, x) == :(-1//8*c^-1//2*(8*b^2*c^2+3*a*d*(a*d+8*b*c))*arctanh(c^-1//2*(c+d*x^2)^(1/2))+1//8*c^-1*(c+d*x^2)^(1/2)*(8*b^2*c^2+3*a*d*(a*d+8*b*c))+1//24*c^-2*(c+d*x^2)^3//2*(8*b^2*c^2+3*a*d*(a*d+8*b*c))+-1//4*a^2*c^-1*x^-4*(c+d*x^2)^5//2+-1//8*a*c^-2*x^-2*(c+d*x^2)^5//2*(a*d+8*b*c))
@test integrate(x^-6*(a+b*x^2)^2*(c+d*x^2)^3//2, x) == :((1/2)*b*d^(1/2)*(3*b*c+4*a*d)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+-1//5*a^2*c^-1*x^-5*(c+d*x^2)^5//2+-2//3*a*b*c^-1*x^-3*(c+d*x^2)^5//2+-1//3*b*c^-1*x^-1*(c+d*x^2)^3//2*(3*b*c+4*a*d)+(1/2)*b*d*x*c^-1*(c+d*x^2)^(1/2)*(3*b*c+4*a*d))
@test integrate(x^-7*(a+b*x^2)^2*(c+d*x^2)^3//2, x) == :(-1//6*a^2*c^-1*x^-6*(c+d*x^2)^5//2+-1//16*d*c^-3//2*(24*b^2*c^2+a*d*(-1*a*d+12*b*c))*arctanh(c^-1//2*(c+d*x^2)^(1/2))+-1//48*c^-2*x^-2*(c+d*x^2)^3//2*(24*b^2*c^2+a*d*(-1*a*d+12*b*c))+1//16*d*c^-2*(c+d*x^2)^(1/2)*(24*b^2*c^2+a*d*(-1*a*d+12*b*c))+-1//24*a*c^-2*x^-4*(c+d*x^2)^5//2*(-1*a*d+12*b*c))
@test integrate(x^3*(a+b*x^2)^2*(c+d*x^2)^5//2, x) == :(1//13*b^2*d^-4*(c+d*x^2)^13//2+-1//7*c*d^-4*(c+d*x^2)^7//2*(b*c+-1*a*d)^2+-1//11*b*d^-4*(c+d*x^2)^11//2*(-2*a*d+3*b*c)+1//9*d^-4*(c+d*x^2)^9//2*(b*c+-1*a*d)*(-1*a*d+3*b*c))
@test integrate(x^2*(a+b*x^2)^2*(c+d*x^2)^5//2, x) == :(-1//1024*c^4*d^-7//2*(40*a^2*d^2+b*c*(-24*a*d+5*b*c))*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+1//12*b^2*d^-1*x^5*(c+d*x^2)^7//2+1//320*d^-2*x^3*(c+d*x^2)^5//2*(40*a^2*d^2+b*c*(-24*a*d+5*b*c))+-1//120*b*d^-2*x^3*(c+d*x^2)^7//2*(-24*a*d+5*b*c)+1//384*c*d^-2*x^3*(c+d*x^2)^3//2*(40*a^2*d^2+b*c*(-24*a*d+5*b*c))+1//512*c^2*d^-2*x^3*(c+d*x^2)^(1/2)*(40*a^2*d^2+b*c*(-24*a*d+5*b*c))+1//1024*x*c^3*d^-3*(c+d*x^2)^(1/2)*(40*a^2*d^2+b*c*(-24*a*d+5*b*c)))
@test integrate(x*(a+b*x^2)^2*(c+d*x^2)^5//2, x) == :(1//7*d^-3*(c+d*x^2)^7//2*(b*c+-1*a*d)^2+1//11*b^2*d^-3*(c+d*x^2)^11//2+-2//9*b*d^-3*(c+d*x^2)^9//2*(b*c+-1*a*d))
@test integrate((a+b*x^2)^2*(c+d*x^2)^5//2, x) == :(1//256*c^3*d^-5//2*(3*b^2*c^2+80*a^2*d^2+-20*a*b*c*d)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+1//480*x*d^-2*(c+d*x^2)^5//2*(3*b^2*c^2+80*a^2*d^2+-20*a*b*c*d)+-3//80*b*x*d^-2*(c+d*x^2)^7//2*(b*c+-4*a*d)+1//10*b*x*d^-1*(c+d*x^2)^7//2*(a+b*x^2)+1//256*x*c^2*d^-2*(c+d*x^2)^(1/2)*(3*b^2*c^2+80*a^2*d^2+-20*a*b*c*d)+1//384*c*x*d^-2*(c+d*x^2)^3//2*(3*b^2*c^2+80*a^2*d^2+-20*a*b*c*d))
@test integrate(x^-1*(a+b*x^2)^2*(c+d*x^2)^5//2, x) == :(1//5*a^2*(c+d*x^2)^5//2+a^2*c^2*(c+d*x^2)^(1/2)+-1*a^2*c^5//2*arctanh(c^-1//2*(c+d*x^2)^(1/2))+1//3*c*a^2*(c+d*x^2)^3//2+1//9*b^2*d^-2*(c+d*x^2)^9//2+-1//7*b*d^-2*(c+d*x^2)^7//2*(b*c+-2*a*d))
@test integrate(x^-2*(a+b*x^2)^2*(c+d*x^2)^5//2, x) == :(-1*a^2*c^-1*x^-1*(c+d*x^2)^7//2+-5//128*c^2*d^-3//2*(b^2*c^2+-16*a*d*(b*c+3*a*d))*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+-1//192*x*d^-1*(c+d*x^2)^3//2*(5*b^2*c^2+-80*a*d*(b*c+3*a*d))+1//8*x*b^2*d^-1*(c+d*x^2)^7//2+-5//128*c*x*d^-1*(c+d*x^2)^(1/2)*(b^2*c^2+-16*a*d*(b*c+3*a*d))+-1//48*x*c^-1*d^-1*(c+d*x^2)^5//2*(b^2*c^2+-16*a*d*(b*c+3*a*d)))
@test integrate(x^-3*(a+b*x^2)^2*(c+d*x^2)^5//2, x) == :(1//6*a*(c+d*x^2)^3//2*(4*b*c+5*a*d)+1//7*b^2*d^-1*(c+d*x^2)^7//2+(1/2)*a*c*(c+d*x^2)^(1/2)*(4*b*c+5*a*d)+-1//2*a*c^3//2*(4*b*c+5*a*d)*arctanh(c^-1//2*(c+d*x^2)^(1/2))+-1//2*a^2*c^-1*x^-2*(c+d*x^2)^7//2+1//10*a*c^-1*(c+d*x^2)^5//2*(4*b*c+5*a*d))
@test integrate(x^-4*(a+b*x^2)^2*(c+d*x^2)^5//2, x) == :(x*(c+d*x^2)^(1/2)*(5//16*b^2*c^2+5//4*a*d*(2*a*d+3*b*c))+-1//3*a^2*c^-1*x^-3*(c+d*x^2)^7//2+1//6*x*c^-2*(c+d*x^2)^5//2*(b^2*c^2+4*a*d*(2*a*d+3*b*c))+1//24*x*c^-1*(c+d*x^2)^3//2*(5*b^2*c^2+20*a*d*(2*a*d+3*b*c))+5//16*c*d^-1//2*(b^2*c^2+4*a*d*(2*a*d+3*b*c))*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+-2//3*a*c^-2*x^-1*(c+d*x^2)^7//2*(2*a*d+3*b*c))
@test integrate(x^-5*(a+b*x^2)^2*(c+d*x^2)^5//2, x) == :((c+d*x^2)^(1/2)*(b^2*c^2+5//8*a*d*(3*a*d+8*b*c))+-1//8*c^(1/2)*(8*b^2*c^2+5*a*d*(3*a*d+8*b*c))*arctanh(c^-1//2*(c+d*x^2)^(1/2))+1//24*c^-1*(c+d*x^2)^3//2*(8*b^2*c^2+5*a*d*(3*a*d+8*b*c))+1//40*c^-2*(c+d*x^2)^5//2*(8*b^2*c^2+5*a*d*(3*a*d+8*b*c))+-1//4*a^2*c^-1*x^-4*(c+d*x^2)^7//2+-1//8*a*c^-2*x^-2*(c+d*x^2)^7//2*(3*a*d+8*b*c))
@test integrate(x^-6*(a+b*x^2)^2*(c+d*x^2)^5//2, x) == :(1//8*d^(1/2)*(15*b^2*c^2+8*a*d*(a*d+5*b*c))*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+-1//5*a^2*c^-1*x^-5*(c+d*x^2)^7//2+-1//15*c^-2*x^-1*(c+d*x^2)^5//2*(15*b^2*c^2+8*a*d*(a*d+5*b*c))+-2//15*a*c^-2*x^-3*(c+d*x^2)^7//2*(a*d+5*b*c)+1//8*d*x*c^-1*(c+d*x^2)^(1/2)*(15*b^2*c^2+8*a*d*(a*d+5*b*c))+1//12*d*x*c^-2*(c+d*x^2)^3//2*(15*b^2*c^2+8*a*d*(a*d+5*b*c)))
@test integrate(x^-7*(a+b*x^2)^2*(c+d*x^2)^5//2, x) == :(-5//16*d*c^-1//2*(8*b^2*c^2+a*d*(a*d+12*b*c))*arctanh(c^-1//2*(c+d*x^2)^(1/2))+-1//6*a^2*c^-1*x^-6*(c+d*x^2)^7//2+-1//16*c^-2*x^-2*(c+d*x^2)^5//2*(8*b^2*c^2+a*d*(a*d+12*b*c))+5//16*d*c^-1*(c+d*x^2)^(1/2)*(8*b^2*c^2+a*d*(a*d+12*b*c))+5//48*d*c^-2*(c+d*x^2)^3//2*(8*b^2*c^2+a*d*(a*d+12*b*c))+-1//24*a*c^-2*x^-4*(c+d*x^2)^7//2*(a*d+12*b*c))
@test integrate(x^4*(a+b*x^2)^2*(c+d*x^2)^-1//2, x) == :(1//8*b^2*d^-1*x^7*(c+d*x^2)^(1/2)+1//128*c^2*d^-9//2*(48*a^2*d^2+5*b*c*(-16*a*d+7*b*c))*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+1//192*d^-3*x^3*(c+d*x^2)^(1/2)*(48*a^2*d^2+5*b*c*(-16*a*d+7*b*c))+-1//48*b*d^-2*x^5*(c+d*x^2)^(1/2)*(-16*a*d+7*b*c)+-1//128*c*x*d^-4*(c+d*x^2)^(1/2)*(48*a^2*d^2+5*b*c*(-16*a*d+7*b*c)))
@test integrate(x^3*(a+b*x^2)^2*(c+d*x^2)^-1//2, x) == :(1//7*b^2*d^-4*(c+d*x^2)^7//2+-1*c*d^-4*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^2+-1//5*b*d^-4*(c+d*x^2)^5//2*(-2*a*d+3*b*c)+1//3*d^-4*(c+d*x^2)^3//2*(b*c+-1*a*d)*(-1*a*d+3*b*c))
@test integrate(x^2*(a+b*x^2)^2*(c+d*x^2)^-1//2, x) == :(-1//16*c*d^-7//2*(8*a^2*d^2+b*c*(-12*a*d+5*b*c))*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+1//6*b^2*d^-1*x^5*(c+d*x^2)^(1/2)+1//16*x*d^-3*(c+d*x^2)^(1/2)*(8*a^2*d^2+b*c*(-12*a*d+5*b*c))+-1//24*b*d^-2*x^3*(c+d*x^2)^(1/2)*(-12*a*d+5*b*c))
@test integrate(x*(a+b*x^2)^2*(c+d*x^2)^-1//2, x) == :(d^-3*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^2+1//5*b^2*d^-3*(c+d*x^2)^5//2+-2//3*b*d^-3*(c+d*x^2)^3//2*(b*c+-1*a*d))
@test integrate((a+b*x^2)^2*(c+d*x^2)^-1//2, x) == :(1//8*d^-5//2*(3*b^2*c^2+8*a^2*d^2+-8*a*b*c*d)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+-3//8*b*x*d^-2*(c+d*x^2)^(1/2)*(b*c+-2*a*d)+1//4*b*x*d^-1*(c+d*x^2)^(1/2)*(a+b*x^2))
@test integrate(x^-1*(a+b*x^2)^2*(c+d*x^2)^-1//2, x) == :(-1*a^2*c^-1//2*arctanh(c^-1//2*(c+d*x^2)^(1/2))+1//3*b^2*d^-2*(c+d*x^2)^3//2+-1*b*d^-2*(c+d*x^2)^(1/2)*(b*c+-2*a*d))
@test integrate(x^-2*(a+b*x^2)^2*(c+d*x^2)^-1//2, x) == :((1/2)*x*b^2*d^-1*(c+d*x^2)^(1/2)+-1*a^2*c^-1*x^-1*(c+d*x^2)^(1/2)+-1//2*b*d^-3//2*(b*c+-4*a*d)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2))
@test integrate(x^-3*(a+b*x^2)^2*(c+d*x^2)^-1//2, x) == :(b^2*d^-1*(c+d*x^2)^(1/2)+-1//2*a*c^-3//2*(-1*a*d+4*b*c)*arctanh(c^-1//2*(c+d*x^2)^(1/2))+-1//2*a^2*c^-1*x^-2*(c+d*x^2)^(1/2))
@test integrate(x^-4*(a+b*x^2)^2*(c+d*x^2)^-1//2, x) == :(b^2*d^-1//2*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+-1//3*a^2*c^-1*x^-3*(c+d*x^2)^(1/2)+-2//3*a*c^-2*x^-1*(c+d*x^2)^(1/2)*(-1*a*d+3*b*c))
@test integrate(x^-5*(a+b*x^2)^2*(c+d*x^2)^-1//2, x) == :(-1//8*c^-5//2*(3*a^2*d^2+8*b^2*c^2+-8*a*b*c*d)*arctanh(c^-1//2*(c+d*x^2)^(1/2))+-1//4*a^2*c^-1*x^-4*(c+d*x^2)^(1/2)+-1//8*a*c^-2*x^-2*(c+d*x^2)^(1/2)*(-3*a*d+8*b*c))
@test integrate(x^-6*(a+b*x^2)^2*(c+d*x^2)^-1//2, x) == :(-1//5*a^2*c^-1*x^-5*(c+d*x^2)^(1/2)+-1//15*c^-3*x^-1*(c+d*x^2)^(1/2)*(15*b^2*c^2+-4*a*d*(-2*a*d+5*b*c))+-2//15*a*c^-2*x^-3*(c+d*x^2)^(1/2)*(-2*a*d+5*b*c))
@test integrate(x^-7*(a+b*x^2)^2*(c+d*x^2)^-1//2, x) == :(-1//6*a^2*c^-1*x^-6*(c+d*x^2)^(1/2)+-1//16*c^-3*x^-2*(c+d*x^2)^(1/2)*(5*a^2*d^2+8*b^2*c^2+-12*a*b*c*d)+1//16*d*c^-7//2*(5*a^2*d^2+8*b^2*c^2+-12*a*b*c*d)*arctanh(c^-1//2*(c+d*x^2)^(1/2))+-1//24*a*c^-2*x^-4*(c+d*x^2)^(1/2)*(-5*a*d+12*b*c))
@test integrate(x^4*(a+b*x^2)^2*(c+d*x^2)^-3//2, x) == :(-1//16*c*d^-9//2*(24*a^2*d^2+35*b^2*c^2+-60*a*b*c*d)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+1//6*b^2*d^-2*x^5*(c+d*x^2)^(1/2)+1//16*x*d^-4*(c+d*x^2)^(1/2)*(24*a^2*d^2+35*b^2*c^2+-60*a*b*c*d)+c^-1*d^-2*x^5*(c+d*x^2)^-1//2*(b*c+-1*a*d)^2+-1//24*c^-1*d^-3*x^3*(c+d*x^2)^(1/2)*(24*a^2*d^2+35*b^2*c^2+-60*a*b*c*d))
@test integrate(x^3*(a+b*x^2)^2*(c+d*x^2)^-3//2, x) == :(1//5*b^2*d^-4*(c+d*x^2)^5//2+c*d^-4*(c+d*x^2)^-1//2*(b*c+-1*a*d)^2+d^-4*(c+d*x^2)^(1/2)*(b*c+-1*a*d)*(-1*a*d+3*b*c)+-1//3*b*d^-4*(c+d*x^2)^3//2*(-2*a*d+3*b*c))
@test integrate(x^2*(a+b*x^2)^2*(c+d*x^2)^-3//2, x) == :(1//8*d^-7//2*(8*a^2*d^2+15*b^2*c^2+-24*a*b*c*d)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+1//4*b^2*d^-2*x^3*(c+d*x^2)^(1/2)+c^-1*d^-2*x^3*(c+d*x^2)^-1//2*(b*c+-1*a*d)^2+-1//8*x*c^-1*d^-3*(c+d*x^2)^(1/2)*(8*a^2*d^2+15*b^2*c^2+-24*a*b*c*d))
@test integrate(x*(a+b*x^2)^2*(c+d*x^2)^-3//2, x) == :(-1*d^-3*(c+d*x^2)^-1//2*(b*c+-1*a*d)^2+1//3*b^2*d^-3*(c+d*x^2)^3//2+-2*b*d^-3*(c+d*x^2)^(1/2)*(b*c+-1*a*d))
@test integrate((a+b*x^2)^2*(c+d*x^2)^-3//2, x) == :(-1//2*b*d^-5//2*(-4*a*d+3*b*c)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+(1/2)*b*x*c^-1*d^-2*(c+d*x^2)^(1/2)*(-2*a*d+3*b*c)+-1*x*c^-1*d^-1*(c+d*x^2)^-1//2*(a+b*x^2)*(b*c+-1*a*d))
@test integrate(x^-1*(a+b*x^2)^2*(c+d*x^2)^-3//2, x) == :(b^2*d^-2*(c+d*x^2)^(1/2)+-1*a^2*c^-3//2*arctanh(c^-1//2*(c+d*x^2)^(1/2))+c^-1*d^-2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^2)
@test integrate(x^-2*(a+b*x^2)^2*(c+d*x^2)^-3//2, x) == :(b^2*d^-3//2*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+-1*a^2*c^-1*x^-1*(c+d*x^2)^-1//2+-1*x*c^-2*d^-1*(c+d*x^2)^-1//2*(b^2*c^2+-2*a*d*(b*c+-1*a*d)))
@test integrate(x^-3*(a+b*x^2)^2*(c+d*x^2)^-3//2, x) == :((1/2)*c^-1*(c+d*x^2)^-1//2*(4*a*b+-3*d*a^2*c^-1+-2*c*b^2*d^-1)+-1//2*a*c^-5//2*(-3*a*d+4*b*c)*arctanh(c^-1//2*(c+d*x^2)^(1/2))+-1//2*a^2*c^-1*x^-2*(c+d*x^2)^-1//2)
@test integrate(x^-4*(a+b*x^2)^2*(c+d*x^2)^-3//2, x) == :(-1//3*a^2*c^-1*x^-3*(c+d*x^2)^-1//2+1//3*x*c^-3*(c+d*x^2)^-1//2*(3*b^2*c^2+-4*a*d*(-2*a*d+3*b*c))+-2//3*a*c^-2*x^-1*(c+d*x^2)^-1//2*(-2*a*d+3*b*c))
@test integrate(x^-5*(a+b*x^2)^2*(c+d*x^2)^-3//2, x) == :(-1//8*c^-7//2*(8*b^2*c^2+-3*a*d*(-5*a*d+8*b*c))*arctanh(c^-1//2*(c+d*x^2)^(1/2))+1//8*c^-3*(c+d*x^2)^-1//2*(8*b^2*c^2+-3*a*d*(-5*a*d+8*b*c))+-1//4*a^2*c^-1*x^-4*(c+d*x^2)^-1//2+-1//8*a*c^-2*x^-2*(c+d*x^2)^-1//2*(-5*a*d+8*b*c))
@test integrate(x^-6*(a+b*x^2)^2*(c+d*x^2)^-3//2, x) == :(-1//5*a^2*c^-1*x^-5*(c+d*x^2)^-1//2+-1//15*c^-3*x^-1*(c+d*x^2)^-1//2*(15*b^2*c^2+-8*a*d*(-3*a*d+5*b*c))+-2//15*a*c^-2*x^-3*(c+d*x^2)^-1//2*(-3*a*d+5*b*c)+-2//15*d*x*c^-4*(c+d*x^2)^-1//2*(15*b^2*c^2+-8*a*d*(-3*a*d+5*b*c)))
@test integrate(x^-7*(a+b*x^2)^2*(c+d*x^2)^-3//2, x) == :(-1//6*a^2*c^-1*x^-6*(c+d*x^2)^-1//2+-1//16*d*c^-4*(c+d*x^2)^-1//2*(24*b^2*c^2+-5*a*d*(-7*a*d+12*b*c))+-1//48*c^-3*x^-2*(c+d*x^2)^-1//2*(24*b^2*c^2+-5*a*d*(-7*a*d+12*b*c))+1//16*d*c^-9//2*(24*b^2*c^2+-5*a*d*(-7*a*d+12*b*c))*arctanh(c^-1//2*(c+d*x^2)^(1/2))+-1//24*a*c^-2*x^-4*(c+d*x^2)^-1//2*(-7*a*d+12*b*c))
@test integrate(x^4*(a+b*x^2)^2*(c+d*x^2)^-5//2, x) == :(1//8*d^-9//2*(8*a^2*d^2+35*b^2*c^2+-40*a*b*c*d)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+1//4*b^2*d^-2*x^5*(c+d*x^2)^-1//2+-1//8*x*c^-1*d^-4*(c+d*x^2)^(1/2)*(8*a^2*d^2+35*b^2*c^2+-40*a*b*c*d)+1//3*c^-1*d^-2*x^5*(c+d*x^2)^-3//2*(b*c+-1*a*d)^2+1//12*c^-1*d^-3*x^3*(c+d*x^2)^-1//2*(8*a^2*d^2+35*b^2*c^2+-40*a*b*c*d))
@test integrate(x^3*(a+b*x^2)^2*(c+d*x^2)^-5//2, x) == :(1//3*b^2*d^-4*(c+d*x^2)^3//2+-1*b*d^-4*(c+d*x^2)^(1/2)*(-2*a*d+3*b*c)+-1*d^-4*(c+d*x^2)^-1//2*(b*c+-1*a*d)*(-1*a*d+3*b*c)+1//3*c*d^-4*(c+d*x^2)^-3//2*(b*c+-1*a*d)^2)
@test integrate(x^2*(a+b*x^2)^2*(c+d*x^2)^-5//2, x) == :((1/2)*x*b^2*d^-3*(c+d*x^2)^(1/2)+-1//2*b*d^-7//2*(-4*a*d+5*b*c)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+2*b*x*d^-3*(c+d*x^2)^-1//2*(b*c+-1*a*d)+1//3*c^-1*d^-2*x^3*(c+d*x^2)^-3//2*(b*c+-1*a*d)^2)
@test integrate(x*(a+b*x^2)^2*(c+d*x^2)^-5//2, x) == :(b^2*d^-3*(c+d*x^2)^(1/2)+-1//3*d^-3*(c+d*x^2)^-3//2*(b*c+-1*a*d)^2+2*b*d^-3*(c+d*x^2)^-1//2*(b*c+-1*a*d))
@test integrate((a+b*x^2)^2*(c+d*x^2)^-5//2, x) == :(b^2*d^-5//2*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+-1//3*x*c^-1*d^-1*(c+d*x^2)^-3//2*(a+b*x^2)*(b*c+-1*a*d)+-1//3*x*c^-2*d^-2*(c+d*x^2)^-1//2*(b*c+-1*a*d)*(2*a*d+3*b*c))
@test integrate(x^-1*(a+b*x^2)^2*(c+d*x^2)^-5//2, x) == :((c+d*x^2)^-1//2*(a^2*c^-2+-1*b^2*d^-2)+-1*a^2*c^-5//2*arctanh(c^-1//2*(c+d*x^2)^(1/2))+1//3*c^-1*d^-2*(c+d*x^2)^-3//2*(b*c+-1*a*d)^2)
@test integrate(x^-2*(a+b*x^2)^2*(c+d*x^2)^-5//2, x) == :(-1*a^2*c^-1*x^-1*(c+d*x^2)^-3//2+1//3*x*c^-2*(c+d*x^2)^-3//2*(2*a*(b*c+-2*a*d)+c*b^2*x^2)+4//3*a*x*c^-3*(c+d*x^2)^-1//2*(b*c+-2*a*d))
@test integrate(x^-3*(a+b*x^2)^2*(c+d*x^2)^-5//2, x) == :(1//6*c^-1*(c+d*x^2)^-3//2*(4*a*b+-5*d*a^2*c^-1+-2*c*b^2*d^-1)+(1/2)*a*c^-3*(c+d*x^2)^-1//2*(-5*a*d+4*b*c)+-1//2*a*c^-7//2*(-5*a*d+4*b*c)*arctanh(c^-1//2*(c+d*x^2)^(1/2))+-1//2*a^2*c^-1*x^-2*(c+d*x^2)^-3//2)
@test integrate(x^-4*(a+b*x^2)^2*(c+d*x^2)^-5//2, x) == :(-1//3*a^2*c^-1*x^-3*(c+d*x^2)^-3//2+1//3*x*c^-4*(c+d*x^2)^-1//2*(2*b^2*c^2+-16*a*d*(b*c+-1*a*d))+1//3*x*c^-3*(c+d*x^2)^-3//2*(b^2*c^2+-8*a*d*(b*c+-1*a*d))+-2*a*c^-2*x^-1*(c+d*x^2)^-3//2*(b*c+-1*a*d))
@test integrate(x^-5*(a+b*x^2)^2*(c+d*x^2)^-5//2, x) == :(-1//8*c^-9//2*(8*b^2*c^2+-5*a*d*(-7*a*d+8*b*c))*arctanh(c^-1//2*(c+d*x^2)^(1/2))+1//8*c^-4*(c+d*x^2)^-1//2*(8*b^2*c^2+-5*a*d*(-7*a*d+8*b*c))+1//24*c^-3*(c+d*x^2)^-3//2*(8*b^2*c^2+-5*a*d*(-7*a*d+8*b*c))+-1//4*a^2*c^-1*x^-4*(c+d*x^2)^-3//2+-1//8*a*c^-2*x^-2*(c+d*x^2)^-3//2*(-7*a*d+8*b*c))
@test integrate(x^-6*(a+b*x^2)^2*(c+d*x^2)^-5//2, x) == :(-1//5*a^2*c^-1*x^-5*(c+d*x^2)^-3//2+-1//5*c^-3*x^-1*(c+d*x^2)^-3//2*(5*b^2*c^2+-4*a*d*(-4*a*d+5*b*c))+-8//15*d*x*c^-5*(c+d*x^2)^-1//2*(5*b^2*c^2+-4*a*d*(-4*a*d+5*b*c))+-4//15*d*x*c^-4*(c+d*x^2)^-3//2*(5*b^2*c^2+-4*a*d*(-4*a*d+5*b*c))+-2//15*a*c^-2*x^-3*(c+d*x^2)^-3//2*(-4*a*d+5*b*c))
@test integrate(x^5*(d*x^2)^-1//2*(a+b*x^2)^-1, x) == :(1//3*b^-1*x^4*(d*x^2)^-1//2+-1*a*b^-2*x^2*(d*x^2)^-1//2+x*a^3//2*b^-5//2*(d*x^2)^-1//2*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^3*(d*x^2)^-1//2*(a+b*x^2)^-1, x) == :(b^-1*x^2*(d*x^2)^-1//2+-1*x*a^(1/2)*b^-3//2*(d*x^2)^-1//2*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x*(d*x^2)^-1//2*(a+b*x^2)^-1, x) == :(x*a^-1//2*b^-1//2*(d*x^2)^-1//2*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-1*(d*x^2)^-1//2*(a+b*x^2)^-1, x) == :(-1*a^-1*(d*x^2)^-1//2+-1*x*a^-3//2*b^(1/2)*(d*x^2)^-1//2*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-3*(d*x^2)^-1//2*(a+b*x^2)^-1, x) == :(b*a^-2*(d*x^2)^-1//2+-1//3*a^-1*x^-2*(d*x^2)^-1//2+x*a^-5//2*b^3//2*(d*x^2)^-1//2*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^4*(a+b*x^2)^-1*(c+d*x^2)^(1/2), x) == :(1//4*b^-1*x^3*(c+d*x^2)^(1/2)+a^3//2*b^-3*(b*c+-1*a*d)^(1/2)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+-1//8*b^-3*d^-3//2*(b^2*c^2+-8*a^2*d^2+4*a*b*c*d)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+1//8*x*b^-2*d^-1*(c+d*x^2)^(1/2)*(b*c+-4*a*d))
@test integrate(x^3*(a+b*x^2)^-1*(c+d*x^2)^(1/2), x) == :(-1*a*b^-2*(c+d*x^2)^(1/2)+1//3*b^-1*d^-1*(c+d*x^2)^3//2+a*b^-5//2*(b*c+-1*a*d)^(1/2)*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^2*(a+b*x^2)^-1*(c+d*x^2)^(1/2), x) == :((1/2)*x*b^-1*(c+d*x^2)^(1/2)+(1/2)*b^-2*d^-1//2*(b*c+-2*a*d)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+-1*a^(1/2)*b^-2*(b*c+-1*a*d)^(1/2)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2)))
@test integrate(x*(a+b*x^2)^-1*(c+d*x^2)^(1/2), x) == :(b^-1*(c+d*x^2)^(1/2)+-1*b^-3//2*(b*c+-1*a*d)^(1/2)*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((a+b*x^2)^-1*(c+d*x^2)^(1/2), x) == :(b^-1*d^(1/2)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+a^-1//2*b^-1*(b*c+-1*a*d)^(1/2)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2)))
@test integrate(x^-1*(a+b*x^2)^-1*(c+d*x^2)^(1/2), x) == :(-1*a^-1*c^(1/2)*arctanh(c^-1//2*(c+d*x^2)^(1/2))+a^-1*b^-1//2*(b*c+-1*a*d)^(1/2)*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-2*(a+b*x^2)^-1*(c+d*x^2)^(1/2), x) == :(-1*a^-1*x^-1*(c+d*x^2)^(1/2)+-1*a^-3//2*(b*c+-1*a*d)^(1/2)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2)))
@test integrate(x^-3*(a+b*x^2)^-1*(c+d*x^2)^(1/2), x) == :(-1//2*a^-1*x^-2*(c+d*x^2)^(1/2)+(1/2)*a^-2*c^-1//2*(-1*a*d+2*b*c)*arctanh(c^-1//2*(c+d*x^2)^(1/2))+-1*a^-2*b^(1/2)*(b*c+-1*a*d)^(1/2)*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-4*(a+b*x^2)^-1*(c+d*x^2)^(1/2), x) == :(-1//3*a^-1*x^-3*(c+d*x^2)^(1/2)+b*a^-5//2*(b*c+-1*a*d)^(1/2)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+1//3*a^-2*c^-1*x^-1*(c+d*x^2)^(1/2)*(-1*a*d+3*b*c))
@test integrate(x^4*(a+b*x^2)^-1*(c+d*x^2)^3//2, x) == :(a^3//2*b^-4*(b*c+-1*a*d)^3//2*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+1//6*d*b^-1*x^5*(c+d*x^2)^(1/2)+1//24*b^-2*x^3*(c+d*x^2)^(1/2)*(-6*a*d+7*b*c)+-1//16*b^-4*d^-3//2*(b*c+-2*a*d)*(b^2*c^2+-8*a^2*d^2+8*a*b*c*d)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+1//16*x*b^-3*d^-1*(c+d*x^2)^(1/2)*(b^2*c^2+8*a^2*d^2+-10*a*b*c*d))
@test integrate(x^3*(a+b*x^2)^-1*(c+d*x^2)^3//2, x) == :(-1//3*a*b^-2*(c+d*x^2)^3//2+1//5*b^-1*d^-1*(c+d*x^2)^5//2+a*b^-7//2*(b*c+-1*a*d)^3//2*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2)+-1*a*b^-3*(c+d*x^2)^(1/2)*(b*c+-1*a*d))
@test integrate(x^2*(a+b*x^2)^-1*(c+d*x^2)^3//2, x) == :(-1*a^(1/2)*b^-3*(b*c+-1*a*d)^3//2*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+1//4*d*b^-1*x^3*(c+d*x^2)^(1/2)+1//8*x*b^-2*(c+d*x^2)^(1/2)*(-4*a*d+5*b*c)+1//8*b^-3*d^-1//2*(3*b^2*c^2+8*a^2*d^2+-12*a*b*c*d)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2))
@test integrate(x*(a+b*x^2)^-1*(c+d*x^2)^3//2, x) == :(1//3*b^-1*(c+d*x^2)^3//2+b^-2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)+-1*b^-5//2*(b*c+-1*a*d)^3//2*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((a+b*x^2)^-1*(c+d*x^2)^3//2, x) == :(a^-1//2*b^-2*(b*c+-1*a*d)^3//2*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+(1/2)*d*x*b^-1*(c+d*x^2)^(1/2)+(1/2)*b^-2*d^(1/2)*(-2*a*d+3*b*c)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2))
@test integrate(x^-1*(a+b*x^2)^-1*(c+d*x^2)^3//2, x) == :(d*b^-1*(c+d*x^2)^(1/2)+-1*a^-1*c^3//2*arctanh(c^-1//2*(c+d*x^2)^(1/2))+a^-1*b^-3//2*(b*c+-1*a*d)^3//2*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-2*(a+b*x^2)^-1*(c+d*x^2)^3//2, x) == :(b^-1*d^3//2*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+-1*c*a^-1*x^-1*(c+d*x^2)^(1/2)+-1*a^-3//2*b^-1*(b*c+-1*a*d)^3//2*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2)))
@test integrate(x^-3*(a+b*x^2)^-1*(c+d*x^2)^3//2, x) == :((1/2)*a^-2*c^(1/2)*(-3*a*d+2*b*c)*arctanh(c^-1//2*(c+d*x^2)^(1/2))+-1*a^-2*b^-1//2*(b*c+-1*a*d)^3//2*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//2*c*a^-1*x^-2*(c+d*x^2)^(1/2))
@test integrate(x^-4*(a+b*x^2)^-1*(c+d*x^2)^3//2, x) == :(a^-5//2*(b*c+-1*a*d)^3//2*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+-1//3*c*a^-1*x^-3*(c+d*x^2)^(1/2)+1//3*a^-2*x^-1*(c+d*x^2)^(1/2)*(-4*a*d+3*b*c))
@test integrate(x^4*(a+b*x^2)^-1*(c+d*x^2)^5//2, x) == :(a^3//2*b^-5*(b*c+-1*a*d)^5//2*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+-1//128*b^-5*d^-3//2*(-128*a^4*d^4+5*b^4*c^4+-240*a^2*b^2*c^2*d^2+40*a*d*b^3*c^3+320*b*c*a^3*d^3)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+1//8*d*b^-1*x^5*(c+d*x^2)^3//2+1//192*b^-3*x^3*(c+d*x^2)^(1/2)*(48*a^2*d^2+59*b^2*c^2+-104*a*b*c*d)+1//48*d*b^-2*x^5*(c+d*x^2)^(1/2)*(-8*a*d+11*b*c)+1//128*x*b^-4*d^-1*(c+d*x^2)^(1/2)*(-64*a^3*d^3+5*b^3*c^3+-88*a*d*b^2*c^2+144*b*c*a^2*d^2))
@test integrate(x^3*(a+b*x^2)^-1*(c+d*x^2)^5//2, x) == :(-1//5*a*b^-2*(c+d*x^2)^5//2+1//7*b^-1*d^-1*(c+d*x^2)^7//2+a*b^-9//2*(b*c+-1*a*d)^5//2*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2)+-1*a*b^-4*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^2+-1//3*a*b^-3*(c+d*x^2)^3//2*(b*c+-1*a*d))
@test integrate(x^2*(a+b*x^2)^-1*(c+d*x^2)^5//2, x) == :(-1*a^(1/2)*b^-4*(b*c+-1*a*d)^5//2*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+1//6*d*b^-1*x^3*(c+d*x^2)^3//2+1//16*x*b^-3*(c+d*x^2)^(1/2)*(8*a^2*d^2+11*b^2*c^2+-18*a*b*c*d)+1//16*b^-4*d^-1//2*(-16*a^3*d^3+5*b^3*c^3+-30*a*d*b^2*c^2+40*b*c*a^2*d^2)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+1//8*d*b^-2*x^3*(c+d*x^2)^(1/2)*(-2*a*d+3*b*c))
@test integrate(x*(a+b*x^2)^-1*(c+d*x^2)^5//2, x) == :(1//5*b^-1*(c+d*x^2)^5//2+b^-3*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^2+-1*b^-7//2*(b*c+-1*a*d)^5//2*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2)+1//3*b^-2*(c+d*x^2)^3//2*(b*c+-1*a*d))
@test integrate((a+b*x^2)^-1*(c+d*x^2)^5//2, x) == :(a^-1//2*b^-3*(b*c+-1*a*d)^5//2*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+1//4*d*x*b^-1*(c+d*x^2)^3//2+1//8*b^-3*d^(1/2)*(8*a^2*d^2+15*b^2*c^2+-20*a*b*c*d)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+1//8*d*x*b^-2*(c+d*x^2)^(1/2)*(-4*a*d+7*b*c))
@test integrate(x^-1*(a+b*x^2)^-1*(c+d*x^2)^5//2, x) == :(-1*a^-1*c^5//2*arctanh(c^-1//2*(c+d*x^2)^(1/2))+1//3*d*b^-1*(c+d*x^2)^3//2+d*b^-2*(c+d*x^2)^(1/2)*(-1*a*d+2*b*c)+a^-1*b^-5//2*(b*c+-1*a*d)^5//2*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-2*(a+b*x^2)^-1*(c+d*x^2)^5//2, x) == :((1/2)*b^-2*d^3//2*(-2*a*d+5*b*c)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+-1*c*a^-1*x^-1*(c+d*x^2)^3//2+-1*a^-3//2*b^-2*(b*c+-1*a*d)^5//2*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+(1/2)*d*x*a^-1*b^-1*(c+d*x^2)^(1/2)*(a*d+2*b*c))
@test integrate(x^-3*(a+b*x^2)^-1*(c+d*x^2)^5//2, x) == :((1/2)*a^-2*c^3//2*(-5*a*d+2*b*c)*arctanh(c^-1//2*(c+d*x^2)^(1/2))+-1*a^-2*b^-3//2*(b*c+-1*a*d)^5//2*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//2*c*a^-1*x^-2*(c+d*x^2)^3//2+(1/2)*d*a^-1*b^-1*(c+d*x^2)^(1/2)*(b*c+2*a*d))
@test integrate(x^-4*(a+b*x^2)^-1*(c+d*x^2)^5//2, x) == :(b^-1*d^5//2*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+a^-5//2*b^-1*(b*c+-1*a*d)^5//2*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+-1//3*c*a^-1*x^-3*(c+d*x^2)^3//2+c*a^-2*x^-1*(c+d*x^2)^(1/2)*(b*c+-2*a*d))
@test integrate(x^5*(a+b*x^2)^-1*(c+d*x^2)^-1//2, x) == :(1//3*b^-1*d^-2*(c+d*x^2)^3//2+-1*a^2*b^-5//2*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2)+-1*b^-2*d^-2*(c+d*x^2)^(1/2)*(a*d+b*c))
@test integrate(x^3*(a+b*x^2)^-1*(c+d*x^2)^-1//2, x) == :(b^-1*d^-1*(c+d*x^2)^(1/2)+a*b^-3//2*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x*(a+b*x^2)^-1*(c+d*x^2)^-1//2, x) == :(-1*b^-1//2*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-1*(a+b*x^2)^-1*(c+d*x^2)^-1//2, x) == :(-1*a^-1*c^-1//2*arctanh(c^-1//2*(c+d*x^2)^(1/2))+a^-1*b^(1/2)*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-3*(a+b*x^2)^-1*(c+d*x^2)^-1//2, x) == :((1/2)*a^-2*c^-3//2*(a*d+2*b*c)*arctanh(c^-1//2*(c+d*x^2)^(1/2))+-1*a^-2*b^3//2*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//2*a^-1*c^-1*x^-2*(c+d*x^2)^(1/2))
@test integrate(x^4*(a+b*x^2)^-1*(c+d*x^2)^-1//2, x) == :(a^3//2*b^-2*(b*c+-1*a*d)^-1//2*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+(1/2)*x*b^-1*d^-1*(c+d*x^2)^(1/2)+-1//2*b^-2*d^-3//2*(b*c+2*a*d)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2))
@test integrate(x^2*(a+b*x^2)^-1*(c+d*x^2)^-1//2, x) == :(b^-1*d^-1//2*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+-1*a^(1/2)*b^-1*(b*c+-1*a*d)^-1//2*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2)))
@test integrate((a+b*x^2)^-1*(c+d*x^2)^-1//2, x) == :(a^-1//2*(b*c+-1*a*d)^-1//2*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2)))
@test integrate(x^-2*(a+b*x^2)^-1*(c+d*x^2)^-1//2, x) == :(-1*b*a^-3//2*(b*c+-1*a*d)^-1//2*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+-1*a^-1*c^-1*x^-1*(c+d*x^2)^(1/2))
@test integrate(x^-4*(a+b*x^2)^-1*(c+d*x^2)^-1//2, x) == :(a^-5//2*b^2*(b*c+-1*a*d)^-1//2*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+-1//3*a^-1*c^-1*x^-3*(c+d*x^2)^(1/2)+1//3*a^-2*c^-2*x^-1*(c+d*x^2)^(1/2)*(2*a*d+3*b*c))
@test integrate(x^4*(a+b*x^2)^-1*(c+d*x^2)^-3//2, x) == :(b^-1*d^-3//2*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+a^3//2*b^-1*(b*c+-1*a*d)^-3//2*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+-1*c*x*d^-1*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-1)
@test integrate(x^3*(a+b*x^2)^-1*(c+d*x^2)^-3//2, x) == :(a*b^-1//2*(b*c+-1*a*d)^-3//2*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2)+-1*c*d^-1*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-1)
@test integrate(x^2*(a+b*x^2)^-1*(c+d*x^2)^-3//2, x) == :(x*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-1+-1*a^(1/2)*(b*c+-1*a*d)^-3//2*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2)))
@test integrate(x*(a+b*x^2)^-1*(c+d*x^2)^-3//2, x) == :((c+d*x^2)^-1//2*(b*c+-1*a*d)^-1+-1*b^(1/2)*(b*c+-1*a*d)^-3//2*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((a+b*x^2)^-1*(c+d*x^2)^-3//2, x) == :(b*a^-1//2*(b*c+-1*a*d)^-3//2*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+-1*d*x*c^-1*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-1)
@test integrate(x^-1*(a+b*x^2)^-1*(c+d*x^2)^-3//2, x) == :(-1*a^-1*c^-3//2*arctanh(c^-1//2*(c+d*x^2)^(1/2))+a^-1*b^3//2*(b*c+-1*a*d)^-3//2*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2)+-1*d*c^-1*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-1)
@test integrate(x^-2*(a+b*x^2)^-1*(c+d*x^2)^-3//2, x) == :(-1*a^-3//2*b^2*(b*c+-1*a*d)^-3//2*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+-1*d*c^-1*x^-1*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-1+-1*a^-1*c^-2*x^-1*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1*(b*c+-2*a*d))
@test integrate(x^-3*(a+b*x^2)^-1*(c+d*x^2)^-3//2, x) == :((1/2)*a^-2*c^-5//2*(2*b*c+3*a*d)*arctanh(c^-1//2*(c+d*x^2)^(1/2))+-1*a^-2*b^5//2*(b*c+-1*a*d)^-3//2*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//2*a^-1*c^-1*x^-2*(c+d*x^2)^-1//2+-1//2*d*a^-1*c^-2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-1*(b*c+-3*a*d))
@test integrate(x^-4*(a+b*x^2)^-1*(c+d*x^2)^-3//2, x) == :(a^-5//2*b^3*(b*c+-1*a*d)^-3//2*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+-1*d*c^-1*x^-3*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-1+-1//3*a^-1*c^-2*x^-3*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1*(b*c+-4*a*d)+1//3*a^-2*c^-3*x^-1*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1*(b*c+2*a*d)*(-4*a*d+3*b*c))
@test integrate(x^4*(a+b*x^2)^-1*(c+d*x^2)^-5//2, x) == :(a^3//2*(b*c+-1*a*d)^-5//2*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+-1//3*c*x*d^-1*(c+d*x^2)^-3//2*(b*c+-1*a*d)^-1+1//3*x*d^-1*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-2*(b*c+-4*a*d))
@test integrate(x^3*(a+b*x^2)^-1*(c+d*x^2)^-5//2, x) == :(-1*a*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-2+a*b^(1/2)*(b*c+-1*a*d)^-5//2*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//3*c*d^-1*(c+d*x^2)^-3//2*(b*c+-1*a*d)^-1)
@test integrate(x^2*(a+b*x^2)^-1*(c+d*x^2)^-5//2, x) == :(x*(c+d*x^2)^-3//2*(-3*a*d+3*b*c)^-1+-1*b*a^(1/2)*(b*c+-1*a*d)^-5//2*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+1//3*x*c^-1*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-2*(a*d+2*b*c))
@test integrate(x*(a+b*x^2)^-1*(c+d*x^2)^-5//2, x) == :((c+d*x^2)^-3//2*(-3*a*d+3*b*c)^-1+b*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-2+-1*b^3//2*(b*c+-1*a*d)^-5//2*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((a+b*x^2)^-1*(c+d*x^2)^-5//2, x) == :(a^-1//2*b^2*(b*c+-1*a*d)^-5//2*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+-1//3*d*x*c^-1*(c+d*x^2)^-3//2*(b*c+-1*a*d)^-1+-1//3*d*x*c^-2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-2*(-2*a*d+5*b*c))
@test integrate(x^-1*(a+b*x^2)^-1*(c+d*x^2)^-5//2, x) == :(-1*a^-1*c^-5//2*arctanh(c^-1//2*(c+d*x^2)^(1/2))+a^-1*b^5//2*(b*c+-1*a*d)^-5//2*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//3*d*c^-1*(c+d*x^2)^-3//2*(b*c+-1*a*d)^-1+-1*d*c^-2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-2*(-1*a*d+2*b*c))
@test integrate(x^-2*(a+b*x^2)^-1*(c+d*x^2)^-5//2, x) == :(-1*a^-3//2*b^3*(b*c+-1*a*d)^-5//2*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+-1//3*d*c^-1*x^-1*(c+d*x^2)^-3//2*(b*c+-1*a*d)^-1+-1//3*d*c^-2*x^-1*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-2*(-4*a*d+7*b*c)+-1//3*a^-1*c^-3*x^-1*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-2*(b*c+-4*a*d)*(-2*a*d+3*b*c))
@test integrate(x^-3*(a+b*x^2)^-1*(c+d*x^2)^-5//2, x) == :((1/2)*a^-2*c^-7//2*(2*b*c+5*a*d)*arctanh(c^-1//2*(c+d*x^2)^(1/2))+-1*a^-2*b^7//2*(b*c+-1*a*d)^-5//2*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//2*a^-1*c^-1*x^-2*(c+d*x^2)^-3//2+-1//2*d*a^-1*c^-3*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-2*(b^2*c^2+5*a^2*d^2+-8*a*b*c*d)+-1//6*d*a^-1*c^-2*(c+d*x^2)^-3//2*(b*c+-1*a*d)^-1*(-5*a*d+3*b*c))
@test integrate(x^-4*(a+b*x^2)^-1*(c+d*x^2)^-5//2, x) == :(a^-5//2*b^4*(b*c+-1*a*d)^-5//2*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+-1//3*d*c^-1*x^-3*(c+d*x^2)^-3//2*(b*c+-1*a*d)^-1+-1*d*c^-2*x^-3*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-2*(-2*a*d+3*b*c)+-1//3*a^-1*c^-3*x^-3*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-2*(b^2*c^2+8*a^2*d^2+-12*a*b*c*d)+1//3*a^-2*c^-4*x^-1*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-2*(b*c+-2*a*d)*(-8*a^2*d^2+3*b^2*c^2+8*a*b*c*d))
@test integrate(x^4*(a+b*x^2)^-2*(c+d*x^2)^(1/2), x) == :(x*b^-2*(c+d*x^2)^(1/2)+(1/2)*b^-3*d^-1//2*(b*c+-4*a*d)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+-1//2*b^-1*x^3*(a+b*x^2)^-1*(c+d*x^2)^(1/2)+-1//2*a^(1/2)*b^-3*(b*c+-1*a*d)^-1//2*(-4*a*d+3*b*c)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2)))
@test integrate(x^3*(a+b*x^2)^-2*(c+d*x^2)^(1/2), x) == :((1/2)*b^-2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1*(-3*a*d+2*b*c)+-1//2*b^-5//2*(b*c+-1*a*d)^-1//2*(-3*a*d+2*b*c)*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2)+(1/2)*a*b^-1*(a+b*x^2)^-1*(c+d*x^2)^3//2*(b*c+-1*a*d)^-1)
@test integrate(x^2*(a+b*x^2)^-2*(c+d*x^2)^(1/2), x) == :(b^-2*d^(1/2)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+-1//2*x*b^-1*(a+b*x^2)^-1*(c+d*x^2)^(1/2)+(1/2)*a^-1//2*b^-2*(b*c+-1*a*d)^-1//2*(b*c+-2*a*d)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2)))
@test integrate(x*(a+b*x^2)^-2*(c+d*x^2)^(1/2), x) == :(-1//2*b^-1*(a+b*x^2)^-1*(c+d*x^2)^(1/2)+-1//2*d*b^-3//2*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((a+b*x^2)^-2*(c+d*x^2)^(1/2), x) == :((1/2)*c*a^-3//2*(b*c+-1*a*d)^-1//2*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+(1/2)*x*a^-1*(a+b*x^2)^-1*(c+d*x^2)^(1/2))
@test integrate(x^-1*(a+b*x^2)^-2*(c+d*x^2)^(1/2), x) == :((1/2)*a^-1*(a+b*x^2)^-1*(c+d*x^2)^(1/2)+-1*a^-2*c^(1/2)*arctanh(c^-1//2*(c+d*x^2)^(1/2))+(1/2)*a^-2*b^-1//2*(b*c+-1*a*d)^-1//2*(-1*a*d+2*b*c)*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-2*(a+b*x^2)^-2*(c+d*x^2)^(1/2), x) == :(-3//2*a^-2*x^-1*(c+d*x^2)^(1/2)+(1/2)*a^-1*x^-1*(a+b*x^2)^-1*(c+d*x^2)^(1/2)+-1//2*a^-5//2*(b*c+-1*a*d)^-1//2*(-2*a*d+3*b*c)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2)))
@test integrate(x^-3*(a+b*x^2)^-2*(c+d*x^2)^(1/2), x) == :((1/2)*a^-3*c^-1//2*(-1*a*d+4*b*c)*arctanh(c^-1//2*(c+d*x^2)^(1/2))+-1*b*a^-2*(a+b*x^2)^-1*(c+d*x^2)^(1/2)+-1//2*a^-1*x^-2*(a+b*x^2)^-1*(c+d*x^2)^(1/2)+-1//2*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^2)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-4*(a+b*x^2)^-2*(c+d*x^2)^(1/2), x) == :(-5//6*a^-2*x^-3*(c+d*x^2)^(1/2)+(1/2)*a^-1*x^-3*(a+b*x^2)^-1*(c+d*x^2)^(1/2)+(1/2)*b*a^-7//2*(b*c+-1*a*d)^-1//2*(-4*a*d+5*b*c)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+1//6*a^-3*c^-1*x^-1*(c+d*x^2)^(1/2)*(-2*a*d+15*b*c))
@test integrate(x^4*(a+b*x^2)^-2*(c+d*x^2)^3//2, x) == :(-1//2*b^-1*x^3*(a+b*x^2)^-1*(c+d*x^2)^3//2+1//8*x*b^-3*(c+d*x^2)^(1/2)*(-12*a*d+9*b*c)+1//8*b^-4*d^-1//2*(3*b^2*c^2+24*a^2*d^2+-24*a*b*c*d)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+3//4*d*b^-2*x^3*(c+d*x^2)^(1/2)+-3//2*a^(1/2)*b^-4*(b*c+-1*a*d)^(1/2)*(b*c+-2*a*d)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2)))
@test integrate(x^3*(a+b*x^2)^-2*(c+d*x^2)^3//2, x) == :((1/2)*b^-3*(c+d*x^2)^(1/2)*(-5*a*d+2*b*c)+-1//2*b^-7//2*(b*c+-1*a*d)^(1/2)*(-5*a*d+2*b*c)*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2)+1//6*b^-2*(c+d*x^2)^3//2*(b*c+-1*a*d)^-1*(-5*a*d+2*b*c)+(1/2)*a*b^-1*(a+b*x^2)^-1*(c+d*x^2)^5//2*(b*c+-1*a*d)^-1)
@test integrate(x^2*(a+b*x^2)^-2*(c+d*x^2)^3//2, x) == :(d*x*b^-2*(c+d*x^2)^(1/2)+(1/2)*b^-3*d^(1/2)*(-4*a*d+3*b*c)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+-1//2*x*b^-1*(a+b*x^2)^-1*(c+d*x^2)^3//2+(1/2)*a^-1//2*b^-3*(b*c+-1*a*d)^(1/2)*(b*c+-4*a*d)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2)))
@test integrate(x*(a+b*x^2)^-2*(c+d*x^2)^3//2, x) == :(-1//2*b^-1*(a+b*x^2)^-1*(c+d*x^2)^3//2+3//2*d*b^-2*(c+d*x^2)^(1/2)+-3//2*d*b^-5//2*(b*c+-1*a*d)^(1/2)*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((a+b*x^2)^-2*(c+d*x^2)^3//2, x) == :(b^-2*d^3//2*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+(1/2)*a^-3//2*b^-2*(b*c+-1*a*d)^(1/2)*(b*c+2*a*d)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+(1/2)*x*a^-1*b^-1*(a+b*x^2)^-1*(c+d*x^2)^(1/2)*(b*c+-1*a*d))
@test integrate(x^-1*(a+b*x^2)^-2*(c+d*x^2)^3//2, x) == :(-1*a^-2*c^3//2*arctanh(c^-1//2*(c+d*x^2)^(1/2))+(1/2)*a^-1*b^-1*(a+b*x^2)^-1*(c+d*x^2)^(1/2)*(b*c+-1*a*d)+(1/2)*a^-2*b^-3//2*(b*c+-1*a*d)^(1/2)*(a*d+2*b*c)*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-2*(a+b*x^2)^-2*(c+d*x^2)^3//2, x) == :(-3//2*c*a^-5//2*(b*c+-1*a*d)^(1/2)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+-1//2*a^-2*b^-1*x^-1*(c+d*x^2)^(1/2)*(-1*a*d+3*b*c)+(1/2)*a^-1*b^-1*x^-1*(a+b*x^2)^-1*(c+d*x^2)^(1/2)*(b*c+-1*a*d))
@test integrate(x^-3*(a+b*x^2)^-2*(c+d*x^2)^3//2, x) == :((1/2)*a^-3*c^(1/2)*(-3*a*d+4*b*c)*arctanh(c^-1//2*(c+d*x^2)^(1/2))+-1//2*a^-2*(a+b*x^2)^-1*(c+d*x^2)^(1/2)*(-1*a*d+2*b*c)+-1//2*c*a^-1*x^-2*(a+b*x^2)^-1*(c+d*x^2)^(1/2)+-1//2*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^2)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-4*(a+b*x^2)^-2*(c+d*x^2)^3//2, x) == :((1/2)*a^-7//2*(b*c+-1*a*d)^(1/2)*(-2*a*d+5*b*c)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+1//6*a^-3*x^-1*(c+d*x^2)^(1/2)*(-11*a*d+15*b*c)+-1//6*a^-2*b^-1*x^-3*(c+d*x^2)^(1/2)*(-3*a*d+5*b*c)+(1/2)*a^-1*b^-1*x^-3*(a+b*x^2)^-1*(c+d*x^2)^(1/2)*(b*c+-1*a*d))
@test integrate(x^4*(a+b*x^2)^-2*(c+d*x^2)^5//2, x) == :(-1//2*b^-1*x^3*(a+b*x^2)^-1*(c+d*x^2)^5//2+1//16*x*b^-4*(c+d*x^2)^(1/2)*(19*b^2*c^2+32*a^2*d^2+-52*a*b*c*d)+1//16*b^-5*d^-1//2*(-64*a^3*d^3+5*b^3*c^3+-60*a*d*b^2*c^2+120*b*c*a^2*d^2)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+2//3*d*b^-2*x^3*(c+d*x^2)^3//2+-1//2*a^(1/2)*b^-5*(b*c+-1*a*d)^3//2*(-8*a*d+3*b*c)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+1//8*d*b^-3*x^3*(c+d*x^2)^(1/2)*(-8*a*d+7*b*c))
@test integrate(x^3*(a+b*x^2)^-2*(c+d*x^2)^5//2, x) == :(1//6*b^-3*(c+d*x^2)^3//2*(-7*a*d+2*b*c)+(1/2)*b^-4*(c+d*x^2)^(1/2)*(b*c+-1*a*d)*(-7*a*d+2*b*c)+-1//2*b^-9//2*(b*c+-1*a*d)^3//2*(-7*a*d+2*b*c)*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2)+1//10*b^-2*(c+d*x^2)^5//2*(b*c+-1*a*d)^-1*(-7*a*d+2*b*c)+(1/2)*a*b^-1*(a+b*x^2)^-1*(c+d*x^2)^7//2*(b*c+-1*a*d)^-1)
@test integrate(x^2*(a+b*x^2)^-2*(c+d*x^2)^5//2, x) == :(-1//2*x*b^-1*(a+b*x^2)^-1*(c+d*x^2)^5//2+1//8*b^-4*d^(1/2)*(15*b^2*c^2+24*a^2*d^2+-40*a*b*c*d)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+3//4*d*x*b^-2*(c+d*x^2)^3//2+(1/2)*a^-1//2*b^-4*(b*c+-1*a*d)^3//2*(b*c+-6*a*d)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+1//8*d*x*b^-3*(c+d*x^2)^(1/2)*(-12*a*d+11*b*c))
@test integrate(x*(a+b*x^2)^-2*(c+d*x^2)^5//2, x) == :(-1//2*b^-1*(a+b*x^2)^-1*(c+d*x^2)^5//2+5//6*d*b^-2*(c+d*x^2)^3//2+-5//2*d*b^-7//2*(b*c+-1*a*d)^3//2*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2)+5//2*d*b^-3*(c+d*x^2)^(1/2)*(b*c+-1*a*d))
@test integrate((a+b*x^2)^-2*(c+d*x^2)^5//2, x) == :((1/2)*b^-3*d^3//2*(-4*a*d+5*b*c)*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+(1/2)*a^-3//2*b^-3*(b*c+-1*a*d)^3//2*(b*c+4*a*d)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+(1/2)*x*a^-1*b^-1*(a+b*x^2)^-1*(c+d*x^2)^3//2*(b*c+-1*a*d)+-1//2*d*x*a^-1*b^-2*(c+d*x^2)^(1/2)*(b*c+-2*a*d))
@test integrate(x^-1*(a+b*x^2)^-2*(c+d*x^2)^5//2, x) == :(-1*a^-2*c^5//2*arctanh(c^-1//2*(c+d*x^2)^(1/2))+(1/2)*a^-1*b^-1*(a+b*x^2)^-1*(c+d*x^2)^3//2*(b*c+-1*a*d)+(1/2)*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^2)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//2*d*a^-1*b^-2*(c+d*x^2)^(1/2)*(b*c+-3*a*d))
@test integrate(x^-2*(a+b*x^2)^-2*(c+d*x^2)^5//2, x) == :(b^-2*d^5//2*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+-1//2*a^-5//2*b^-2*(b*c+-1*a*d)^3//2*(2*a*d+3*b*c)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+(1/2)*a^-1*b^-1*x^-1*(a+b*x^2)^-1*(c+d*x^2)^3//2*(b*c+-1*a*d)+-1//2*c*a^-2*b^-1*x^-1*(c+d*x^2)^(1/2)*(-1*a*d+3*b*c))
@test integrate(x^-3*(a+b*x^2)^-2*(c+d*x^2)^5//2, x) == :((1/2)*a^-3*c^3//2*(-5*a*d+4*b*c)*arctanh(c^-1//2*(c+d*x^2)^(1/2))+-1//2*c*a^-1*x^-2*(a+b*x^2)^-1*(c+d*x^2)^3//2+-1//2*a^-3*b^-3//2*(b*c+-1*a*d)^3//2*(a*d+4*b*c)*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//2*a^-2*b^-1*(a+b*x^2)^-1*(c+d*x^2)^(1/2)*(b*c+-1*a*d)*(-1*a*d+2*b*c))
@test integrate(x^-4*(a+b*x^2)^-2*(c+d*x^2)^5//2, x) == :(5//2*c*a^-7//2*(b*c+-1*a*d)^3//2*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+1//6*a^-3*b^-1*x^-1*(c+d*x^2)^(1/2)*(3*a^2*d^2+15*b^2*c^2+-20*a*b*c*d)+(1/2)*a^-1*b^-1*x^-3*(a+b*x^2)^-1*(c+d*x^2)^3//2*(b*c+-1*a*d)+-1//6*c*a^-2*b^-1*x^-3*(c+d*x^2)^(1/2)*(-3*a*d+5*b*c))
@test integrate(x^4*(a+b*x^2)^-2*(c+d*x^2)^-1//2, x) == :(b^-2*d^-1//2*arctanh(x*d^(1/2)*(c+d*x^2)^-1//2)+-1//2*a^(1/2)*b^-2*(b*c+-1*a*d)^-3//2*(-2*a*d+3*b*c)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+(1/2)*a*x*b^-1*(a+b*x^2)^-1*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1)
@test integrate(x^3*(a+b*x^2)^-2*(c+d*x^2)^-1//2, x) == :(-1//2*b^-3//2*(b*c+-1*a*d)^-3//2*(-1*a*d+2*b*c)*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2)+(1/2)*a*b^-1*(a+b*x^2)^-1*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1)
@test integrate(x^2*(a+b*x^2)^-2*(c+d*x^2)^-1//2, x) == :((1/2)*c*a^-1//2*(b*c+-1*a*d)^-3//2*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+-1*x*(a+b*x^2)^-1*(c+d*x^2)^(1/2)*(-2*a*d+2*b*c)^-1)
@test integrate(x*(a+b*x^2)^-2*(c+d*x^2)^-1//2, x) == :(-1*(a+b*x^2)^-1*(c+d*x^2)^(1/2)*(-2*a*d+2*b*c)^-1+(1/2)*d*b^-1//2*(b*c+-1*a*d)^-3//2*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((a+b*x^2)^-2*(c+d*x^2)^-1//2, x) == :((1/2)*a^-3//2*(b*c+-1*a*d)^-3//2*(b*c+-2*a*d)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+(1/2)*b*x*a^-1*(a+b*x^2)^-1*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1)
@test integrate(x^-1*(a+b*x^2)^-2*(c+d*x^2)^-1//2, x) == :(-1*a^-2*c^-1//2*arctanh(c^-1//2*(c+d*x^2)^(1/2))+(1/2)*b*a^-1*(a+b*x^2)^-1*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1+(1/2)*a^-2*b^(1/2)*(b*c+-1*a*d)^-3//2*(-3*a*d+2*b*c)*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-2*(a+b*x^2)^-2*(c+d*x^2)^-1//2, x) == :(-1//2*b*a^-5//2*(b*c+-1*a*d)^-3//2*(-4*a*d+3*b*c)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+(1/2)*b*a^-1*x^-1*(a+b*x^2)^-1*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1+-1//2*a^-2*c^-1*x^-1*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1*(-2*a*d+3*b*c))
@test integrate(x^-3*(a+b*x^2)^-2*(c+d*x^2)^-1//2, x) == :((1/2)*a^-3*c^-3//2*(a*d+4*b*c)*arctanh(c^-1//2*(c+d*x^2)^(1/2))+-1//2*a^-1*c^-1*x^-2*(a+b*x^2)^-1*(c+d*x^2)^(1/2)+-1//2*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^2)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//2*b*a^-2*c^-1*(a+b*x^2)^-1*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1*(-1*a*d+2*b*c))
@test integrate(x^-4*(a+b*x^2)^-2*(c+d*x^2)^-1//2, x) == :((1/2)*a^-7//2*b^2*(b*c+-1*a*d)^-3//2*(-6*a*d+5*b*c)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+(1/2)*b*a^-1*x^-3*(a+b*x^2)^-1*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1+-1//6*a^-2*c^-1*x^-3*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1*(-2*a*d+5*b*c)+1//6*a^-3*c^-2*x^-1*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1*(-4*a^2*d^2+15*b^2*c^2+-8*a*b*c*d))
@test integrate(x^4*(a+b*x^2)^-2*(c+d*x^2)^-3//2, x) == :(-3//2*c*a^(1/2)*(b*c+-1*a*d)^-5//2*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+(1/2)*x*b^-1*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-2*(a*d+2*b*c)+(1/2)*a*x*b^-1*(a+b*x^2)^-1*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-1)
@test integrate(x^3*(a+b*x^2)^-2*(c+d*x^2)^-3//2, x) == :((1/2)*b^-1*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-2*(a*d+2*b*c)+-1//2*b^-1//2*(b*c+-1*a*d)^-5//2*(a*d+2*b*c)*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2)+(1/2)*a*b^-1*(a+b*x^2)^-1*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-1)
@test integrate(x^2*(a+b*x^2)^-2*(c+d*x^2)^-3//2, x) == :((1/2)*a^-1//2*(b*c+-1*a*d)^-5//2*(b*c+2*a*d)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+-1*x*(a+b*x^2)^-1*(c+d*x^2)^-1//2*(-2*a*d+2*b*c)^-1+-3//2*d*x*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-2)
@test integrate(x*(a+b*x^2)^-2*(c+d*x^2)^-3//2, x) == :(-1*(a+b*x^2)^-1*(c+d*x^2)^-1//2*(-2*a*d+2*b*c)^-1+-3//2*d*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-2+3//2*d*b^(1/2)*(b*c+-1*a*d)^-5//2*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((a+b*x^2)^-2*(c+d*x^2)^-3//2, x) == :((1/2)*b*a^-3//2*(b*c+-1*a*d)^-5//2*(b*c+-4*a*d)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+(1/2)*b*x*a^-1*(a+b*x^2)^-1*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-1+(1/2)*d*x*a^-1*c^-1*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-2*(b*c+2*a*d))
@test integrate(x^-1*(a+b*x^2)^-2*(c+d*x^2)^-3//2, x) == :(-1*a^-2*c^-3//2*arctanh(c^-1//2*(c+d*x^2)^(1/2))+(1/2)*b*a^-1*(a+b*x^2)^-1*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-1+(1/2)*a^-2*b^3//2*(b*c+-1*a*d)^-5//2*(-5*a*d+2*b*c)*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2)+(1/2)*d*a^-1*c^-1*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-2*(b*c+2*a*d))
@test integrate(x^-2*(a+b*x^2)^-2*(c+d*x^2)^-3//2, x) == :(-3//2*a^-5//2*b^2*(b*c+-1*a*d)^-5//2*(b*c+-2*a*d)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+(1/2)*b*a^-1*x^-1*(a+b*x^2)^-1*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-1+-1//2*a^-2*c^-2*x^-1*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-2*(3*b^2*c^2+4*a^2*d^2+-4*a*b*c*d)+(1/2)*d*a^-1*c^-1*x^-1*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-2*(b*c+2*a*d))
@test integrate(x^-3*(a+b*x^2)^-2*(c+d*x^2)^-3//2, x) == :((1/2)*a^-3*c^-5//2*(3*a*d+4*b*c)*arctanh(c^-1//2*(c+d*x^2)^(1/2))+-1//2*a^-1*c^-1*x^-2*(a+b*x^2)^-1*(c+d*x^2)^-1//2+-1//2*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^2)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//2*d*a^-2*c^-2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-2*(2*b^2*c^2+3*a^2*d^2+-2*a*b*c*d)+-1//2*b*a^-2*c^-1*(a+b*x^2)^-1*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-1*(-1*a*d+2*b*c))
@test integrate(x^-4*(a+b*x^2)^-2*(c+d*x^2)^-3//2, x) == :((1/2)*a^-7//2*b^3*(b*c+-1*a*d)^-5//2*(-8*a*d+5*b*c)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+(1/2)*b*a^-1*x^-3*(a+b*x^2)^-1*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-1+-1//6*a^-2*c^-2*x^-3*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-2*(5*b^2*c^2+8*a^2*d^2+-4*a*b*c*d)+1//6*a^-3*c^-3*x^-1*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-2*(15*b^3*c^3+16*a^3*d^3+-14*a*d*b^2*c^2+-8*b*c*a^2*d^2)+(1/2)*d*a^-1*c^-1*x^-3*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-2*(b*c+2*a*d))
@test integrate(x^4*(a+b*x^2)^-2*(c+d*x^2)^-5//2, x) == :(-1//2*a^(1/2)*(b*c+-1*a*d)^-7//2*(2*a*d+3*b*c)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+1//6*x*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-3*(4*b*c+11*a*d)+1//6*x*b^-1*(c+d*x^2)^-3//2*(b*c+-1*a*d)^-2*(2*b*c+3*a*d)+(1/2)*a*x*b^-1*(a+b*x^2)^-1*(c+d*x^2)^-3//2*(b*c+-1*a*d)^-1)
@test integrate(x^3*(a+b*x^2)^-2*(c+d*x^2)^-5//2, x) == :((1/2)*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-3*(2*b*c+3*a*d)+-1//2*b^(1/2)*(b*c+-1*a*d)^-7//2*(2*b*c+3*a*d)*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2)+1//6*b^-1*(c+d*x^2)^-3//2*(b*c+-1*a*d)^-2*(2*b*c+3*a*d)+(1/2)*a*b^-1*(a+b*x^2)^-1*(c+d*x^2)^-3//2*(b*c+-1*a*d)^-1)
@test integrate(x^2*(a+b*x^2)^-2*(c+d*x^2)^-5//2, x) == :(-1*x*(a+b*x^2)^-1*(c+d*x^2)^-3//2*(-2*a*d+2*b*c)^-1+-5//6*d*x*(c+d*x^2)^-3//2*(b*c+-1*a*d)^-2+(1/2)*b*a^-1//2*(b*c+-1*a*d)^-7//2*(b*c+4*a*d)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+-1//6*d*x*c^-1*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-3*(2*a*d+13*b*c))
@test integrate(x*(a+b*x^2)^-2*(c+d*x^2)^-5//2, x) == :(-1*(a+b*x^2)^-1*(c+d*x^2)^-3//2*(-2*a*d+2*b*c)^-1+-5//6*d*(c+d*x^2)^-3//2*(b*c+-1*a*d)^-2+-5//2*b*d*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-3+5//2*d*b^3//2*(b*c+-1*a*d)^-7//2*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((a+b*x^2)^-2*(c+d*x^2)^-5//2, x) == :((1/2)*a^-3//2*b^2*(b*c+-1*a*d)^-7//2*(b*c+-6*a*d)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+(1/2)*b*x*a^-1*(a+b*x^2)^-1*(c+d*x^2)^-3//2*(b*c+-1*a*d)^-1+1//6*d*x*a^-1*c^-1*(c+d*x^2)^-3//2*(b*c+-1*a*d)^-2*(2*a*d+3*b*c)+1//6*d*x*a^-1*c^-2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-3*(-4*a^2*d^2+3*b^2*c^2+16*a*b*c*d))
@test integrate(x^-1*(a+b*x^2)^-2*(c+d*x^2)^-5//2, x) == :(-1*a^-2*c^-5//2*arctanh(c^-1//2*(c+d*x^2)^(1/2))+(1/2)*b*a^-1*(a+b*x^2)^-1*(c+d*x^2)^-3//2*(b*c+-1*a*d)^-1+(1/2)*a^-2*b^5//2*(b*c+-1*a*d)^-7//2*(-7*a*d+2*b*c)*arctanh(b^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1//2)+(1/2)*d*a^-1*c^-2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-3*(b^2*c^2+-2*a^2*d^2+6*a*b*c*d)+1//6*d*a^-1*c^-1*(c+d*x^2)^-3//2*(b*c+-1*a*d)^-2*(2*a*d+3*b*c))
@test integrate(x^-2*(a+b*x^2)^-2*(c+d*x^2)^-5//2, x) == :(-1//2*a^-5//2*b^3*(b*c+-1*a*d)^-7//2*(-8*a*d+3*b*c)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+(1/2)*b*a^-1*x^-1*(a+b*x^2)^-1*(c+d*x^2)^-3//2*(b*c+-1*a*d)^-1+-1//6*a^-2*c^-3*x^-1*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-3*(-16*a^3*d^3+9*b^3*c^3+-18*a*d*b^2*c^2+40*b*c*a^2*d^2)+1//6*d*a^-1*c^-1*x^-1*(c+d*x^2)^-3//2*(b*c+-1*a*d)^-2*(2*a*d+3*b*c)+1//6*d*a^-1*c^-2*x^-1*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-3*(-8*a^2*d^2+3*b^2*c^2+20*a*b*c*d))
@test integrate(x^-3*(a+b*x^2)^-2*(c+d*x^2)^-5//2, x) == :((1/2)*a^-3*c^-7//2*(4*b*c+5*a*d)*arctanh(c^-1//2*(c+d*x^2)^(1/2))+-1//2*a^-1*c^-1*x^-2*(a+b*x^2)^-1*(c+d*x^2)^-3//2+-1//2*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^2)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//6*d*a^-2*c^-2*(c+d*x^2)^-3//2*(b*c+-1*a*d)^-2*(5*a^2*d^2+6*b^2*c^2+-6*a*b*c*d)+-1//2*b*a^-2*c^-1*(a+b*x^2)^-1*(c+d*x^2)^-3//2*(b*c+-1*a*d)^-1*(-1*a*d+2*b*c)+-1//2*d*a^-2*c^-3*(c+d*x^2)^-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^-4*(a+b*x^2)^-2*(c+d*x^2)^-5//2, x) == :(5//2*a^-7//2*b^4*(b*c+-1*a*d)^-7//2*(b*c+-2*a*d)*arctan(x*a^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+(1/2)*b*a^-1*x^-3*(a+b*x^2)^-1*(c+d*x^2)^-3//2*(b*c+-1*a*d)^-1+-1//6*a^-2*c^-3*x^-3*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-3*(-16*a^3*d^3+5*b^3*c^3+-6*a*d*b^2*c^2+32*b*c*a^2*d^2)+1//6*a^-3*c^-4*x^-1*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-3*(-32*a^4*d^4+15*b^4*c^4+-20*a*d*b^3*c^3+-12*a^2*b^2*c^2*d^2+64*b*c*a^3*d^3)+(1/2)*d*a^-1*c^-2*x^-3*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-3*(b^2*c^2+-4*a^2*d^2+8*a*b*c*d)+1//6*d*a^-1*c^-1*x^-3*(c+d*x^2)^-3//2*(b*c+-1*a*d)^-2*(2*a*d+3*b*c))
@test integrate((e*x)^3//2*(a+b*x^2)^(1/2)*(A+B*x^2), x) == :(1//77*b^-1*e^-1*(e*x)^5//2*(a+b*x^2)^(1/2)*(-10*B*a+22*A*b)+2//11*B*b^-1*e^-1*(e*x)^5//2*(a+b*x^2)^3//2+4//231*a*e*b^-2*(e*x)^(1/2)*(a+b*x^2)^(1/2)*(-5*B*a+11*A*b)+-2//231*a^7//4*b^-9//4*e^3//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(-5*B*a+11*A*b)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^(1/2)*(a+b*x^2)^(1/2)*(A+B*x^2), x) == :(1//15*b^-1*e^-1*(e*x)^3//2*(a+b*x^2)^(1/2)*(-2*B*a+6*A*b)+2//9*B*b^-1*e^-1*(e*x)^3//2*(a+b*x^2)^3//2+4//15*a*b^-3//2*(e*x)^(1/2)*(a+b*x^2)^(1/2)*(a^(1/2)+x*b^(1/2))^-1*(-1*B*a+3*A*b)+-4//15*a^5//4*b^-7//4*e^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(-1*B*a+3*A*b)*Elliptic.E(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2)+2//15*a^5//4*b^-7//4*e^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(-1*B*a+3*A*b)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-1//2*(a+b*x^2)^(1/2)*(A+B*x^2), x) == :(1//21*b^-1*e^-1*(e*x)^(1/2)*(a+b*x^2)^(1/2)*(-2*B*a+14*A*b)+2//7*B*b^-1*e^-1*(e*x)^(1/2)*(a+b*x^2)^3//2+2//21*a^3//4*b^-5//4*e^-1//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(-1*B*a+7*A*b)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-3//2*(a+b*x^2)^(1/2)*(A+B*x^2), x) == :(-2*A*a^-1*e^-1*(e*x)^-1//2*(a+b*x^2)^3//2+1//5*a^-1*e^-3*(e*x)^3//2*(a+b*x^2)^(1/2)*(2*B*a+10*A*b)+1//5*b^-1//2*e^-2*(e*x)^(1/2)*(a+b*x^2)^(1/2)*(a^(1/2)+x*b^(1/2))^-1*(4*B*a+20*A*b)+-4//5*a^1//4*b^-3//4*e^-3//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(B*a+5*A*b)*Elliptic.E(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2)+2//5*a^1//4*b^-3//4*e^-3//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(B*a+5*A*b)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-5//2*(a+b*x^2)^(1/2)*(A+B*x^2), x) == :(-2//3*A*a^-1*e^-1*(e*x)^-3//2*(a+b*x^2)^3//2+1//3*a^-1*e^-3*(e*x)^(1/2)*(a+b*x^2)^(1/2)*(2*A*b+2*B*a)+1//3*a^-1//4*b^-1//4*e^-5//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(2*A*b+2*B*a)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-7//2*(a+b*x^2)^(1/2)*(A+B*x^2), x) == :(-2//5*A*a^-1*e^-1*(e*x)^-5//2*(a+b*x^2)^3//2+-1//5*a^-1*e^-3*(e*x)^-1//2*(a+b*x^2)^(1/2)*(2*A*b+10*B*a)+4//5*a^-1*b^(1/2)*e^-4*(e*x)^(1/2)*(a+b*x^2)^(1/2)*(a^(1/2)+x*b^(1/2))^-1*(A*b+5*B*a)+-4//5*a^-3//4*b^1//4*e^-7//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(A*b+5*B*a)*Elliptic.E(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2)+2//5*a^-3//4*b^1//4*e^-7//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(A*b+5*B*a)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate(x^-9//2*(a+b*x^2)^(1/2)*(A+B*x^2), x) == :(-2//7*A*a^-1*x^-7//2*(a+b*x^2)^3//2+1//21*a^-1*x^-3//2*(a+b*x^2)^(1/2)*(-14*B*a+2*A*b)+-2//21*a^-5//4*b^3//4*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(A*b+-7*B*a)*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^-11//2*(a+b*x^2)^(1/2)*(A+B*x^2), x) == :(-2//9*A*a^-1*x^-9//2*(a+b*x^2)^3//2+1//15*a^-1*x^-5//2*(a+b*x^2)^(1/2)*(-6*B*a+2*A*b)+4//15*b*a^-2*x^-1//2*(a+b*x^2)^(1/2)*(A*b+-3*B*a)+-4//15*a^-2*b^3//2*x^(1/2)*(a+b*x^2)^(1/2)*(a^(1/2)+x*b^(1/2))^-1*(A*b+-3*B*a)+-2//15*a^-7//4*b^5//4*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(A*b+-3*B*a)*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2)+4//15*a^-7//4*b^5//4*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(A*b+-3*B*a)*Elliptic.E(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^-13//2*(a+b*x^2)^(1/2)*(A+B*x^2), x) == :(-2//11*A*a^-1*x^-11//2*(a+b*x^2)^3//2+1//77*a^-1*x^-7//2*(a+b*x^2)^(1/2)*(-22*B*a+10*A*b)+4//231*b*a^-2*x^-3//2*(a+b*x^2)^(1/2)*(-11*B*a+5*A*b)+2//231*a^-9//4*b^7//4*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(-11*B*a+5*A*b)*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate((e*x)^3//2*(a+b*x^2)^3//2*(A+B*x^2), x) == :(1//33*b^-1*e^-1*(e*x)^5//2*(a+b*x^2)^3//2*(-2*B*a+6*A*b)+2//15*B*b^-1*e^-1*(e*x)^5//2*(a+b*x^2)^5//2+4//77*a*b^-1*e^-1*(e*x)^5//2*(a+b*x^2)^(1/2)*(-1*B*a+3*A*b)+8//231*e*a^2*b^-2*(e*x)^(1/2)*(a+b*x^2)^(1/2)*(-1*B*a+3*A*b)+-4//231*a^11//4*b^-9//4*e^3//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(-1*B*a+3*A*b)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^(1/2)*(a+b*x^2)^3//2*(A+B*x^2), x) == :(1//117*b^-1*e^-1*(e*x)^3//2*(a+b*x^2)^3//2*(-6*B*a+26*A*b)+2//13*B*b^-1*e^-1*(e*x)^3//2*(a+b*x^2)^5//2+4//195*a*b^-1*e^-1*(e*x)^3//2*(a+b*x^2)^(1/2)*(-3*B*a+13*A*b)+8//195*a^2*b^-3//2*(e*x)^(1/2)*(a+b*x^2)^(1/2)*(a^(1/2)+x*b^(1/2))^-1*(-3*B*a+13*A*b)+-8//195*a^9//4*b^-7//4*e^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(-3*B*a+13*A*b)*Elliptic.E(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2)+4//195*a^9//4*b^-7//4*e^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(-3*B*a+13*A*b)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-1//2*(a+b*x^2)^3//2*(A+B*x^2), x) == :(1//77*b^-1*e^-1*(e*x)^(1/2)*(a+b*x^2)^3//2*(-2*B*a+22*A*b)+2//11*B*b^-1*e^-1*(e*x)^(1/2)*(a+b*x^2)^5//2+4//77*a*b^-1*e^-1*(e*x)^(1/2)*(a+b*x^2)^(1/2)*(-1*B*a+11*A*b)+4//77*a^7//4*b^-5//4*e^-1//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(-1*B*a+11*A*b)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-3//2*(a+b*x^2)^3//2*(A+B*x^2), x) == :(1//15*e^-3*(e*x)^3//2*(a+b*x^2)^(1/2)*(4*B*a+36*A*b)+-2*A*a^-1*e^-1*(e*x)^-1//2*(a+b*x^2)^5//2+1//9*a^-1*e^-3*(e*x)^3//2*(a+b*x^2)^3//2*(2*B*a+18*A*b)+8//15*a*b^-1//2*e^-2*(e*x)^(1/2)*(a+b*x^2)^(1/2)*(a^(1/2)+x*b^(1/2))^-1*(B*a+9*A*b)+-8//15*a^5//4*b^-3//4*e^-3//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(B*a+9*A*b)*Elliptic.E(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2)+4//15*a^5//4*b^-3//4*e^-3//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(B*a+9*A*b)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-5//2*(a+b*x^2)^3//2*(A+B*x^2), x) == :(1//21*e^-3*(e*x)^(1/2)*(a+b*x^2)^(1/2)*(12*B*a+28*A*b)+-2//3*A*a^-1*e^-1*(e*x)^-3//2*(a+b*x^2)^5//2+1//21*a^-1*e^-3*(e*x)^(1/2)*(a+b*x^2)^3//2*(6*B*a+14*A*b)+4//21*a^3//4*b^-1//4*e^-5//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(3*B*a+7*A*b)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-7//2*(a+b*x^2)^3//2*(A+B*x^2), x) == :(-1*a^-1*e^-3*(e*x)^-1//2*(a+b*x^2)^3//2*(2*A*b+2*B*a)+-2//5*A*a^-1*e^-1*(e*x)^-5//2*(a+b*x^2)^5//2+12//5*b*a^-1*e^-5*(e*x)^3//2*(a+b*x^2)^(1/2)*(A*b+B*a)+24//5*b^(1/2)*e^-4*(e*x)^(1/2)*(a+b*x^2)^(1/2)*(a^(1/2)+x*b^(1/2))^-1*(A*b+B*a)+-24//5*a^1//4*b^1//4*e^-7//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(A*b+B*a)*Elliptic.E(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2)+12//5*a^1//4*b^1//4*e^-7//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(A*b+B*a)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^5//2*(a+b*x^2)^-1//2*(A+B*x^2), x) == :(1//45*e*b^-2*(e*x)^3//2*(a+b*x^2)^(1/2)*(-14*B*a+18*A*b)+2//9*B*b^-1*e^-1*(e*x)^7//2*(a+b*x^2)^(1/2)+-2//15*a*b^-5//2*e^2*(e*x)^(1/2)*(a+b*x^2)^(1/2)*(a^(1/2)+x*b^(1/2))^-1*(-7*B*a+9*A*b)+-1//15*a^5//4*b^-11//4*e^5//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(-7*B*a+9*A*b)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2)+2//15*a^5//4*b^-11//4*e^5//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(-7*B*a+9*A*b)*Elliptic.E(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^3//2*(a+b*x^2)^-1//2*(A+B*x^2), x) == :(1//21*e*b^-2*(e*x)^(1/2)*(a+b*x^2)^(1/2)*(-10*B*a+14*A*b)+2//7*B*b^-1*e^-1*(e*x)^5//2*(a+b*x^2)^(1/2)+-1//21*a^3//4*b^-9//4*e^3//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(-5*B*a+7*A*b)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^(1/2)*(a+b*x^2)^-1//2*(A+B*x^2), x) == :(1//5*b^-3//2*(e*x)^(1/2)*(a+b*x^2)^(1/2)*(a^(1/2)+x*b^(1/2))^-1*(-6*B*a+10*A*b)+2//5*B*b^-1*e^-1*(e*x)^3//2*(a+b*x^2)^(1/2)+-2//5*a^1//4*b^-7//4*e^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(-3*B*a+5*A*b)*Elliptic.E(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2)+1//5*a^1//4*b^-7//4*e^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(-3*B*a+5*A*b)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-1//2*(a+b*x^2)^-1//2*(A+B*x^2), x) == :(2//3*B*b^-1*e^-1*(e*x)^(1/2)*(a+b*x^2)^(1/2)+1//3*a^-1//4*b^-5//4*e^-1//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(-1*B*a+3*A*b)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-3//2*(a+b*x^2)^-1//2*(A+B*x^2), x) == :(-2*A*a^-1*e^-1*(e*x)^-1//2*(a+b*x^2)^(1/2)+a^-1*b^-1//2*e^-2*(e*x)^(1/2)*(a+b*x^2)^(1/2)*(a^(1/2)+x*b^(1/2))^-1*(2*A*b+2*B*a)+a^-3//4*b^-3//4*e^-3//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(A*b+B*a)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2)+-1*a^-3//4*b^-3//4*e^-3//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(2*A*b+2*B*a)*Elliptic.E(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-5//2*(a+b*x^2)^-1//2*(A+B*x^2), x) == :(-2//3*A*a^-1*e^-1*(e*x)^-3//2*(a+b*x^2)^(1/2)+-1//3*a^-5//4*b^-1//4*e^-5//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(A*b+-3*B*a)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-7//2*(a+b*x^2)^-1//2*(A+B*x^2), x) == :(-2//5*A*a^-1*e^-1*(e*x)^-5//2*(a+b*x^2)^(1/2)+1//5*a^-2*e^-3*(e*x)^-1//2*(a+b*x^2)^(1/2)*(-10*B*a+6*A*b)+-2//5*a^-2*b^(1/2)*e^-4*(e*x)^(1/2)*(a+b*x^2)^(1/2)*(a^(1/2)+x*b^(1/2))^-1*(-5*B*a+3*A*b)+-1//5*a^-7//4*b^1//4*e^-7//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(-5*B*a+3*A*b)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2)+2//5*a^-7//4*b^1//4*e^-7//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(-5*B*a+3*A*b)*Elliptic.E(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^7//2*(a+b*x^2)^-3//2*(A+B*x^2), x) == :(-1//7*e*b^-2*(e*x)^5//2*(a+b*x^2)^-1//2*(-9*B*a+7*A*b)+1//21*b^-3*e^3*(e*x)^(1/2)*(a+b*x^2)^(1/2)*(-45*B*a+35*A*b)+2//7*B*b^-1*e^-1*(e*x)^9//2*(a+b*x^2)^-1//2+-5//42*a^3//4*b^-13//4*e^7//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(-9*B*a+7*A*b)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^5//2*(a+b*x^2)^-3//2*(A+B*x^2), x) == :(-1//5*e*b^-2*(e*x)^3//2*(a+b*x^2)^-1//2*(-7*B*a+5*A*b)+2//5*B*b^-1*e^-1*(e*x)^7//2*(a+b*x^2)^-1//2+1//5*b^-5//2*e^2*(e*x)^(1/2)*(a+b*x^2)^(1/2)*(a^(1/2)+x*b^(1/2))^-1*(-21*B*a+15*A*b)+-3//5*a^1//4*b^-11//4*e^5//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(-7*B*a+5*A*b)*Elliptic.E(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2)+3//10*a^1//4*b^-11//4*e^5//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(-7*B*a+5*A*b)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^3//2*(a+b*x^2)^-3//2*(A+B*x^2), x) == :(-1//3*e*b^-2*(e*x)^(1/2)*(a+b*x^2)^-1//2*(-5*B*a+3*A*b)+2//3*B*b^-1*e^-1*(e*x)^5//2*(a+b*x^2)^-1//2+1//6*a^-1//4*b^-9//4*e^3//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(-5*B*a+3*A*b)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^(1/2)*(a+b*x^2)^-3//2*(A+B*x^2), x) == :(a^-1*b^-1*e^-1*(e*x)^3//2*(a+b*x^2)^-1//2*(A*b+-1*B*a)+-1*a^-1*b^-3//2*(e*x)^(1/2)*(a+b*x^2)^(1/2)*(a^(1/2)+x*b^(1/2))^-1*(A*b+-3*B*a)+a^-3//4*b^-7//4*e^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(A*b+-3*B*a)*Elliptic.E(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2)+-1//2*a^-3//4*b^-7//4*e^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(A*b+-3*B*a)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-1//2*(a+b*x^2)^-3//2*(A+B*x^2), x) == :(a^-1*b^-1*e^-1*(e*x)^(1/2)*(a+b*x^2)^-1//2*(A*b+-1*B*a)+(1/2)*a^-5//4*b^-5//4*e^-1//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(A*b+B*a)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-3//2*(a+b*x^2)^-3//2*(A+B*x^2), x) == :(-1*a^-2*e^-3*(e*x)^3//2*(a+b*x^2)^-1//2*(-1*B*a+3*A*b)+-2*A*a^-1*e^-1*(e*x)^-1//2*(a+b*x^2)^-1//2+a^-2*b^-1//2*e^-2*(e*x)^(1/2)*(a+b*x^2)^(1/2)*(a^(1/2)+x*b^(1/2))^-1*(-1*B*a+3*A*b)+(1/2)*a^-7//4*b^-3//4*e^-3//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(-1*B*a+3*A*b)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2)+-1*a^-7//4*b^-3//4*e^-3//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(-1*B*a+3*A*b)*Elliptic.E(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-5//2*(a+b*x^2)^-3//2*(A+B*x^2), x) == :(-2//3*A*a^-1*e^-1*(e*x)^-3//2*(a+b*x^2)^-1//2+-1//3*a^-2*e^-3*(e*x)^(1/2)*(a+b*x^2)^-1//2*(-3*B*a+5*A*b)+-1//6*a^-9//4*b^-1//4*e^-5//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(-3*B*a+5*A*b)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-7//2*(a+b*x^2)^-3//2*(A+B*x^2), x) == :(-2//5*A*a^-1*e^-1*(e*x)^-5//2*(a+b*x^2)^-1//2+-1//5*a^-2*e^-3*(e*x)^-1//2*(a+b*x^2)^-1//2*(-5*B*a+7*A*b)+1//5*a^-3*e^-3*(e*x)^-1//2*(a+b*x^2)^(1/2)*(-15*B*a+21*A*b)+-3//5*a^-3*b^(1/2)*e^-4*(e*x)^(1/2)*(a+b*x^2)^(1/2)*(a^(1/2)+x*b^(1/2))^-1*(-5*B*a+7*A*b)+-3//10*a^-11//4*b^1//4*e^-7//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(-5*B*a+7*A*b)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2)+3//5*a^-11//4*b^1//4*e^-7//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(-5*B*a+7*A*b)*Elliptic.E(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^7//2*(a+b*x^2)^-5//2*(A+B*x^2), x) == :(-1//3*e*b^-2*(e*x)^5//2*(a+b*x^2)^-3//2*(A*b+-3*B*a)+-1//6*b^-3*e^3*(e*x)^(1/2)*(a+b*x^2)^-1//2*(-15*B*a+5*A*b)+2//3*B*b^-1*e^-1*(e*x)^9//2*(a+b*x^2)^-3//2+1//12*a^-1//4*b^-13//4*e^7//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(-15*B*a+5*A*b)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^5//2*(a+b*x^2)^-5//2*(A+B*x^2), x) == :(1//3*a^-1*b^-1*e^-1*(e*x)^7//2*(a+b*x^2)^-3//2*(A*b+-1*B*a)+1//6*e*a^-1*b^-2*(e*x)^3//2*(a+b*x^2)^-1//2*(A*b+-7*B*a)+-1//2*a^-1*b^-5//2*e^2*(e*x)^(1/2)*(a+b*x^2)^(1/2)*(a^(1/2)+x*b^(1/2))^-1*(A*b+-7*B*a)+(1/2)*a^-3//4*b^-11//4*e^5//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(A*b+-7*B*a)*Elliptic.E(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2)+-1//4*a^-3//4*b^-11//4*e^5//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(A*b+-7*B*a)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^3//2*(a+b*x^2)^-5//2*(A+B*x^2), x) == :(-1//6*e*a^-1*b^-2*(e*x)^(1/2)*(a+b*x^2)^-1//2*(A*b+5*B*a)+1//3*a^-1*b^-1*e^-1*(e*x)^5//2*(a+b*x^2)^-3//2*(A*b+-1*B*a)+1//12*a^-5//4*b^-9//4*e^3//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(A*b+5*B*a)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^(1/2)*(a+b*x^2)^-5//2*(A+B*x^2), x) == :((1/2)*a^-2*b^-1*e^-1*(e*x)^3//2*(a+b*x^2)^-1//2*(A*b+B*a)+-1//2*a^-2*b^-3//2*(e*x)^(1/2)*(a+b*x^2)^(1/2)*(a^(1/2)+x*b^(1/2))^-1*(A*b+B*a)+1//3*a^-1*b^-1*e^-1*(e*x)^3//2*(a+b*x^2)^-3//2*(A*b+-1*B*a)+(1/2)*a^-7//4*b^-7//4*e^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(A*b+B*a)*Elliptic.E(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2)+-1//4*a^-7//4*b^-7//4*e^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(A*b+B*a)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-1//2*(a+b*x^2)^-5//2*(A+B*x^2), x) == :(1//3*a^-1*b^-1*e^-1*(e*x)^(1/2)*(a+b*x^2)^-3//2*(A*b+-1*B*a)+1//6*a^-2*b^-1*e^-1*(e*x)^(1/2)*(a+b*x^2)^-1//2*(B*a+5*A*b)+1//12*a^-9//4*b^-5//4*e^-1//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(B*a+5*A*b)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-3//2*(a+b*x^2)^-5//2*(A+B*x^2), x) == :(-2*A*a^-1*e^-1*(e*x)^-1//2*(a+b*x^2)^-3//2+-1//2*a^-3*e^-3*(e*x)^3//2*(a+b*x^2)^-1//2*(-1*B*a+7*A*b)+-1//3*a^-2*e^-3*(e*x)^3//2*(a+b*x^2)^-3//2*(-1*B*a+7*A*b)+(1/2)*a^-3*b^-1//2*e^-2*(e*x)^(1/2)*(a+b*x^2)^(1/2)*(a^(1/2)+x*b^(1/2))^-1*(-1*B*a+7*A*b)+-1//2*a^-11//4*b^-3//4*e^-3//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(-1*B*a+7*A*b)*Elliptic.E(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2)+1//4*a^-11//4*b^-3//4*e^-3//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(-1*B*a+7*A*b)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-5//2*(a+b*x^2)^-5//2*(A+B*x^2), x) == :(-2//3*A*a^-1*e^-1*(e*x)^-3//2*(a+b*x^2)^-3//2+-1//3*a^-2*e^-3*(e*x)^(1/2)*(a+b*x^2)^-3//2*(-1*B*a+3*A*b)+-1//6*a^-3*e^-3*(e*x)^(1/2)*(a+b*x^2)^-1//2*(-5*B*a+15*A*b)+-1//12*a^-13//4*b^-1//4*e^-5//2*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a+b*x^2)^-1//2*(a^(1/2)+x*b^(1/2))*(-5*B*a+15*A*b)*Elliptic.F(2*arctan(a^-1//4*b^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^3//2*(a+b*x^2)^2*(c+d*x^2)^(1/2), x) == :(1//77*d^-2*e^-1*(e*x)^5//2*(c+d*x^2)^(1/2)*(22*a^2*d^2+2*b*c*(-10*a*d+3*b*c))+2//15*b^2*d^-1*e^-3*(e*x)^9//2*(c+d*x^2)^3//2+-2//55*b*d^-2*e^-1*(e*x)^5//2*(c+d*x^2)^3//2*(-10*a*d+3*b*c)+4//231*c*e*d^-3*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(11*a^2*d^2+b*c*(-10*a*d+3*b*c))+-2//231*c^7//4*d^-13//4*e^3//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(11*a^2*d^2+b*c*(-10*a*d+3*b*c))*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^(1/2)*(a+b*x^2)^2*(c+d*x^2)^(1/2), x) == :(1//195*d^-2*e^-1*(e*x)^3//2*(c+d*x^2)^(1/2)*(78*a^2*d^2+2*b*c*(-26*a*d+7*b*c))+2//13*b^2*d^-1*e^-3*(e*x)^7//2*(c+d*x^2)^3//2+-2//117*b*d^-2*e^-1*(e*x)^3//2*(c+d*x^2)^3//2*(-26*a*d+7*b*c)+4//195*c*d^-5//2*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(c^(1/2)+x*d^(1/2))^-1*(39*a^2*d^2+b*c*(-26*a*d+7*b*c))+-4//195*c^5//4*d^-11//4*e^(1/2)*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(39*a^2*d^2+b*c*(-26*a*d+7*b*c))*Elliptic.E(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2)+2//195*c^5//4*d^-11//4*e^(1/2)*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(39*a^2*d^2+b*c*(-26*a*d+7*b*c))*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-1//2*(a+b*x^2)^2*(c+d*x^2)^(1/2), x) == :(1//231*d^-2*e^-1*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(10*b^2*c^2+154*a^2*d^2+-44*a*b*c*d)+2//11*b^2*d^-1*e^-3*(e*x)^5//2*(c+d*x^2)^3//2+-2//77*b*d^-2*e^-1*(e*x)^(1/2)*(c+d*x^2)^3//2*(-22*a*d+5*b*c)+2//231*c^3//4*d^-9//4*e^-1//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(5*b^2*c^2+77*a^2*d^2+-22*a*b*c*d)*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-3//2*(a+b*x^2)^2*(c+d*x^2)^(1/2), x) == :(-2*a^2*c^-1*e^-1*(e*x)^-1//2*(c+d*x^2)^3//2+2//9*b^2*d^-1*e^-3*(e*x)^3//2*(c+d*x^2)^3//2+-1//15*c^-1*d^-1*e^-3*(e*x)^3//2*(c+d*x^2)^(1/2)*(2*b^2*c^2+-6*a*d*(2*b*c+5*a*d))+-1//15*d^-3//2*e^-2*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(c^(1/2)+x*d^(1/2))^-1*(4*b^2*c^2+-12*a*d*(2*b*c+5*a*d))+-2//15*c^1//4*d^-7//4*e^-3//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(b^2*c^2+-3*a*d*(2*b*c+5*a*d))*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2)+4//15*c^1//4*d^-7//4*e^-3//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(b^2*c^2+-3*a*d*(2*b*c+5*a*d))*Elliptic.E(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-5//2*(a+b*x^2)^2*(c+d*x^2)^(1/2), x) == :(-2//3*a^2*c^-1*e^-1*(e*x)^-3//2*(c+d*x^2)^3//2+2//7*b^2*d^-1*e^-3*(e*x)^(1/2)*(c+d*x^2)^3//2+-1//21*c^-1*d^-1*e^-3*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(2*b^2*c^2+-14*a*d*(a*d+2*b*c))+-1//21*c^-1//4*d^-5//4*e^-5//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(2*b^2*c^2+-14*a*d*(a*d+2*b*c))*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-7//2*(a+b*x^2)^2*(c+d*x^2)^(1/2), x) == :(-2//5*a^2*c^-1*e^-1*(e*x)^-5//2*(c+d*x^2)^3//2+1//5*c^-2*e^-5*(e*x)^3//2*(c+d*x^2)^(1/2)*(2*b^2*c^2+2*a*d*(a*d+10*b*c))+-2//5*a*c^-2*e^-3*(e*x)^-1//2*(c+d*x^2)^3//2*(a*d+10*b*c)+1//5*c^-1*d^-1//2*e^-4*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(c^(1/2)+x*d^(1/2))^-1*(4*b^2*c^2+4*a*d*(a*d+10*b*c))+-1//5*c^-3//4*d^-3//4*e^-7//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(4*b^2*c^2+4*a*d*(a*d+10*b*c))*Elliptic.E(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2)+1//5*c^-3//4*d^-3//4*e^-7//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(2*b^2*c^2+2*a*d*(a*d+10*b*c))*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate(x^-9//2*(a+b*x^2)^2*(c+d*x^2)^(1/2), x) == :(-2//7*a^2*c^-1*x^-7//2*(c+d*x^2)^3//2+1//21*c^-2*x^(1/2)*(c+d*x^2)^(1/2)*(14*b^2*c^2+2*a*d*(-1*a*d+14*b*c))+-2//21*a*c^-2*x^-3//2*(c+d*x^2)^3//2*(-1*a*d+14*b*c)+1//21*c^-5//4*d^-1//4*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(14*b^2*c^2+2*a*d*(-1*a*d+14*b*c))*Elliptic.F(2*arctan(c^-1//4*d^1//4*x^(1/2)),1/2))
@test integrate(x^-11//2*(a+b*x^2)^2*(c+d*x^2)^(1/2), x) == :(-2//9*a^2*c^-1*x^-9//2*(c+d*x^2)^3//2+-1//15*c^-2*x^-1//2*(c+d*x^2)^(1/2)*(30*b^2*c^2+2*a*d*(-1*a*d+6*b*c))+-2//15*a*c^-2*x^-5//2*(c+d*x^2)^3//2*(-1*a*d+6*b*c)+4//15*c^-2*d^(1/2)*x^(1/2)*(c+d*x^2)^(1/2)*(c^(1/2)+x*d^(1/2))^-1*(15*b^2*c^2+a*d*(-1*a*d+6*b*c))+-4//15*c^-7//4*d^1//4*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(15*b^2*c^2+a*d*(-1*a*d+6*b*c))*Elliptic.E(2*arctan(c^-1//4*d^1//4*x^(1/2)),1/2)+2//15*c^-7//4*d^1//4*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(15*b^2*c^2+a*d*(-1*a*d+6*b*c))*Elliptic.F(2*arctan(c^-1//4*d^1//4*x^(1/2)),1/2))
@test integrate(x^-13//2*(a+b*x^2)^2*(c+d*x^2)^(1/2), x) == :(-2//11*a^2*c^-1*x^-11//2*(c+d*x^2)^3//2+-1//231*c^-2*x^-3//2*(c+d*x^2)^(1/2)*(10*a^2*d^2+154*b^2*c^2+-44*a*b*c*d)+-2//77*a*c^-2*x^-7//2*(c+d*x^2)^3//2*(-5*a*d+22*b*c)+2//231*c^-9//4*d^3//4*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(5*a^2*d^2+77*b^2*c^2+-22*a*b*c*d)*Elliptic.F(2*arctan(c^-1//4*d^1//4*x^(1/2)),1/2))
@test integrate(x^-15//2*(a+b*x^2)^2*(c+d*x^2)^(1/2), x) == :(-2//13*a^2*c^-1*x^-13//2*(c+d*x^2)^3//2+-1//195*c^-2*x^-5//2*(c+d*x^2)^(1/2)*(14*a^2*d^2+78*b^2*c^2+-52*a*b*c*d)+-4//195*d*c^-3*x^-1//2*(c+d*x^2)^(1/2)*(7*a^2*d^2+39*b^2*c^2+-26*a*b*c*d)+-2//117*a*c^-2*x^-9//2*(c+d*x^2)^3//2*(-7*a*d+26*b*c)+4//195*c^-3*d^3//2*x^(1/2)*(c+d*x^2)^(1/2)*(c^(1/2)+x*d^(1/2))^-1*(7*a^2*d^2+39*b^2*c^2+-26*a*b*c*d)+-4//195*c^-11//4*d^5//4*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(7*a^2*d^2+39*b^2*c^2+-26*a*b*c*d)*Elliptic.E(2*arctan(c^-1//4*d^1//4*x^(1/2)),1/2)+2//195*c^-11//4*d^5//4*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(7*a^2*d^2+39*b^2*c^2+-26*a*b*c*d)*Elliptic.F(2*arctan(c^-1//4*d^1//4*x^(1/2)),1/2))
@test integrate((e*x)^5//2*(a+b*x^2)^2*(c+d*x^2)^3//2, x) == :(1//663*d^-2*e^-1*(e*x)^7//2*(c+d*x^2)^3//2*(102*a^2*d^2+2*b*c*(-42*a*d+11*b*c))+2//21*b^2*d^-1*e^-3*(e*x)^11//2*(c+d*x^2)^5//2+-2//357*b*d^-2*e^-1*(e*x)^7//2*(c+d*x^2)^5//2*(-42*a*d+11*b*c)+4//1989*c*d^-2*e^-1*(e*x)^7//2*(c+d*x^2)^(1/2)*(51*a^2*d^2+b*c*(-42*a*d+11*b*c))+8//9945*e*c^2*d^-3*(e*x)^3//2*(c+d*x^2)^(1/2)*(51*a^2*d^2+b*c*(-42*a*d+11*b*c))+-8//3315*c^3*d^-7//2*e^2*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(c^(1/2)+x*d^(1/2))^-1*(51*a^2*d^2+b*c*(-42*a*d+11*b*c))+-4//3315*c^13//4*d^-15//4*e^5//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(51*a^2*d^2+b*c*(-42*a*d+11*b*c))*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2)+8//3315*c^13//4*d^-15//4*e^5//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(51*a^2*d^2+b*c*(-42*a*d+11*b*c))*Elliptic.E(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^3//2*(a+b*x^2)^2*(c+d*x^2)^3//2, x) == :(1//627*d^-2*e^-1*(e*x)^5//2*(c+d*x^2)^3//2*(114*a^2*d^2+2*b*c*(-38*a*d+9*b*c))+2//19*b^2*d^-1*e^-3*(e*x)^9//2*(c+d*x^2)^5//2+-2//285*b*d^-2*e^-1*(e*x)^5//2*(c+d*x^2)^5//2*(-38*a*d+9*b*c)+4//1463*c*d^-2*e^-1*(e*x)^5//2*(c+d*x^2)^(1/2)*(57*a^2*d^2+b*c*(-38*a*d+9*b*c))+8//4389*e*c^2*d^-3*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(57*a^2*d^2+b*c*(-38*a*d+9*b*c))+-4//4389*c^11//4*d^-13//4*e^3//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(57*a^2*d^2+b*c*(-38*a*d+9*b*c))*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^(1/2)*(a+b*x^2)^2*(c+d*x^2)^3//2, x) == :(1//1989*d^-2*e^-1*(e*x)^3//2*(c+d*x^2)^3//2*(442*a^2*d^2+6*b*c*(-34*a*d+7*b*c))+2//17*b^2*d^-1*e^-3*(e*x)^7//2*(c+d*x^2)^5//2+-2//221*b*d^-2*e^-1*(e*x)^3//2*(c+d*x^2)^5//2*(-34*a*d+7*b*c)+4//3315*c*d^-2*e^-1*(e*x)^3//2*(c+d*x^2)^(1/2)*(221*a^2*d^2+3*b*c*(-34*a*d+7*b*c))+8//3315*c^2*d^-5//2*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(c^(1/2)+x*d^(1/2))^-1*(221*a^2*d^2+3*b*c*(-34*a*d+7*b*c))+-8//3315*c^9//4*d^-11//4*e^(1/2)*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(221*a^2*d^2+3*b*c*(-34*a*d+7*b*c))*Elliptic.E(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2)+4//3315*c^9//4*d^-11//4*e^(1/2)*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(221*a^2*d^2+3*b*c*(-34*a*d+7*b*c))*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-1//2*(a+b*x^2)^2*(c+d*x^2)^3//2, x) == :(1//231*d^-2*e^-1*(e*x)^(1/2)*(c+d*x^2)^3//2*(66*a^2*d^2+2*b*c*(b*c+-6*a*d))+2//15*b^2*d^-1*e^-3*(e*x)^5//2*(c+d*x^2)^5//2+-2//33*b*d^-2*e^-1*(e*x)^(1/2)*(c+d*x^2)^5//2*(b*c+-6*a*d)+4//231*c*d^-2*e^-1*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(33*a^2*d^2+b*c*(b*c+-6*a*d))+4//231*c^7//4*d^-9//4*e^-1//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(33*a^2*d^2+b*c*(b*c+-6*a*d))*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-3//2*(a+b*x^2)^2*(c+d*x^2)^3//2, x) == :(-2*a^2*c^-1*e^-1*(e*x)^-1//2*(c+d*x^2)^5//2+-1//195*d^-1*e^-3*(e*x)^3//2*(c+d*x^2)^(1/2)*(12*b^2*c^2+-52*a*d*(2*b*c+9*a*d))+2//13*b^2*d^-1*e^-3*(e*x)^3//2*(c+d*x^2)^5//2+-1//117*c^-1*d^-1*e^-3*(e*x)^3//2*(c+d*x^2)^3//2*(6*b^2*c^2+-26*a*d*(2*b*c+9*a*d))+-8//195*c*d^-3//2*e^-2*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(c^(1/2)+x*d^(1/2))^-1*(3*b^2*c^2+-13*a*d*(2*b*c+9*a*d))+-4//195*c^5//4*d^-7//4*e^-3//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(3*b^2*c^2+-13*a*d*(2*b*c+9*a*d))*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2)+8//195*c^5//4*d^-7//4*e^-3//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(3*b^2*c^2+-13*a*d*(2*b*c+9*a*d))*Elliptic.E(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-5//2*(a+b*x^2)^2*(c+d*x^2)^3//2, x) == :(-2//3*a^2*c^-1*e^-1*(e*x)^-3//2*(c+d*x^2)^5//2+-1//231*d^-1*e^-3*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(12*b^2*c^2+-44*a*d*(6*b*c+7*a*d))+2//11*b^2*d^-1*e^-3*(e*x)^(1/2)*(c+d*x^2)^5//2+-1//231*c^-1*d^-1*e^-3*(e*x)^(1/2)*(c+d*x^2)^3//2*(6*b^2*c^2+-22*a*d*(6*b*c+7*a*d))+-4//231*c^3//4*d^-5//4*e^-5//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(3*b^2*c^2+-11*a*d*(6*b*c+7*a*d))*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-7//2*(a+b*x^2)^2*(c+d*x^2)^3//2, x) == :(-2//5*a^2*c^-1*e^-1*(e*x)^-5//2*(c+d*x^2)^5//2+1//9*c^-2*e^-5*(e*x)^3//2*(c+d*x^2)^3//2*(2*b^2*c^2+18*a*d*(a*d+2*b*c))+1//15*c^-1*e^-5*(e*x)^3//2*(c+d*x^2)^(1/2)*(4*b^2*c^2+36*a*d*(a*d+2*b*c))+-2*a*c^-2*e^-3*(e*x)^-1//2*(c+d*x^2)^5//2*(a*d+2*b*c)+1//15*d^-1//2*e^-4*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(c^(1/2)+x*d^(1/2))^-1*(8*b^2*c^2+72*a*d*(a*d+2*b*c))+-8//15*c^1//4*d^-3//4*e^-7//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(b^2*c^2+9*a*d*(a*d+2*b*c))*Elliptic.E(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2)+4//15*c^1//4*d^-3//4*e^-7//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(b^2*c^2+9*a*d*(a*d+2*b*c))*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^5//2*(a+b*x^2)^2*(c+d*x^2)^-1//2, x) == :(1//585*e*d^-3*(e*x)^3//2*(c+d*x^2)^(1/2)*(234*a^2*d^2+14*b*c*(-26*a*d+11*b*c))+2//13*b^2*d^-1*e^-3*(e*x)^11//2*(c+d*x^2)^(1/2)+-2//117*b*d^-2*e^-1*(e*x)^7//2*(c+d*x^2)^(1/2)*(-26*a*d+11*b*c)+-2//195*c*d^-7//2*e^2*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(c^(1/2)+x*d^(1/2))^-1*(117*a^2*d^2+7*b*c*(-26*a*d+11*b*c))+-1//195*c^5//4*d^-15//4*e^5//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(117*a^2*d^2+7*b*c*(-26*a*d+11*b*c))*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2)+2//195*c^5//4*d^-15//4*e^5//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(117*a^2*d^2+7*b*c*(-26*a*d+11*b*c))*Elliptic.E(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^3//2*(a+b*x^2)^2*(c+d*x^2)^-1//2, x) == :(1//231*e*d^-3*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(154*a^2*d^2+10*b*c*(-22*a*d+9*b*c))+2//11*b^2*d^-1*e^-3*(e*x)^9//2*(c+d*x^2)^(1/2)+-2//77*b*d^-2*e^-1*(e*x)^5//2*(c+d*x^2)^(1/2)*(-22*a*d+9*b*c)+-1//231*c^3//4*d^-13//4*e^3//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(77*a^2*d^2+5*b*c*(-22*a*d+9*b*c))*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^(1/2)*(a+b*x^2)^2*(c+d*x^2)^-1//2, x) == :(1//15*d^-5//2*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(c^(1/2)+x*d^(1/2))^-1*(30*a^2*d^2+2*b*c*(-18*a*d+7*b*c))+2//9*b^2*d^-1*e^-3*(e*x)^7//2*(c+d*x^2)^(1/2)+-2//45*b*d^-2*e^-1*(e*x)^3//2*(c+d*x^2)^(1/2)*(-18*a*d+7*b*c)+-2//15*c^1//4*d^-11//4*e^(1/2)*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(15*a^2*d^2+b*c*(-18*a*d+7*b*c))*Elliptic.E(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2)+1//15*c^1//4*d^-11//4*e^(1/2)*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(15*a^2*d^2+b*c*(-18*a*d+7*b*c))*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-1//2*(a+b*x^2)^2*(c+d*x^2)^-1//2, x) == :(2//7*b^2*d^-1*e^-3*(e*x)^5//2*(c+d*x^2)^(1/2)+-2//21*b*d^-2*e^-1*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(-14*a*d+5*b*c)+1//21*c^-1//4*d^-9//4*e^-1//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(5*b^2*c^2+21*a^2*d^2+-14*a*b*c*d)*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-3//2*(a+b*x^2)^2*(c+d*x^2)^-1//2, x) == :(-2*a^2*c^-1*e^-1*(e*x)^-1//2*(c+d*x^2)^(1/2)+2//5*b^2*d^-1*e^-3*(e*x)^3//2*(c+d*x^2)^(1/2)+-1//5*c^-1*d^-3//2*e^-2*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(c^(1/2)+x*d^(1/2))^-1*(6*b^2*c^2+-10*a*d*(a*d+2*b*c))+-1//5*c^-3//4*d^-7//4*e^-3//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(3*b^2*c^2+-5*a*d*(a*d+2*b*c))*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2)+1//5*c^-3//4*d^-7//4*e^-3//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(6*b^2*c^2+-10*a*d*(a*d+2*b*c))*Elliptic.E(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-5//2*(a+b*x^2)^2*(c+d*x^2)^-1//2, x) == :(-2//3*a^2*c^-1*e^-1*(e*x)^-3//2*(c+d*x^2)^(1/2)+2//3*b^2*d^-1*e^-3*(e*x)^(1/2)*(c+d*x^2)^(1/2)+-1//3*c^-5//4*d^-5//4*e^-5//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(a^2*d^2+b^2*c^2+-6*a*b*c*d)*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-7//2*(a+b*x^2)^2*(c+d*x^2)^-1//2, x) == :(-2//5*a^2*c^-1*e^-1*(e*x)^-5//2*(c+d*x^2)^(1/2)+-2//5*a*c^-2*e^-3*(e*x)^-1//2*(c+d*x^2)^(1/2)*(-3*a*d+10*b*c)+1//5*c^-2*d^-1//2*e^-4*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(c^(1/2)+x*d^(1/2))^-1*(-6*a^2*d^2+10*b^2*c^2+20*a*b*c*d)+-1//5*c^-7//4*d^-3//4*e^-7//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(-6*a^2*d^2+10*b^2*c^2+20*a*b*c*d)*Elliptic.E(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2)+1//5*c^-7//4*d^-3//4*e^-7//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(-3*a^2*d^2+5*b^2*c^2+10*a*b*c*d)*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-9//2*(a+b*x^2)^2*(c+d*x^2)^-1//2, x) == :(-2//7*a^2*c^-1*e^-1*(e*x)^-7//2*(c+d*x^2)^(1/2)+-2//21*a*c^-2*e^-3*(e*x)^-3//2*(c+d*x^2)^(1/2)*(-5*a*d+14*b*c)+1//21*c^-9//4*d^-1//4*e^-9//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(5*a^2*d^2+21*b^2*c^2+-14*a*b*c*d)*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-11//2*(a+b*x^2)^2*(c+d*x^2)^-1//2, x) == :(-2//9*a^2*c^-1*e^-1*(e*x)^-9//2*(c+d*x^2)^(1/2)+-1//15*c^-3*e^-5*(e*x)^-1//2*(c+d*x^2)^(1/2)*(14*a^2*d^2+30*b^2*c^2+-36*a*b*c*d)+-2//45*a*c^-2*e^-3*(e*x)^-5//2*(c+d*x^2)^(1/2)*(-7*a*d+18*b*c)+2//15*c^-3*d^(1/2)*e^-6*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(c^(1/2)+x*d^(1/2))^-1*(7*a^2*d^2+15*b^2*c^2+-18*a*b*c*d)+-2//15*c^-11//4*d^1//4*e^-11//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(7*a^2*d^2+15*b^2*c^2+-18*a*b*c*d)*Elliptic.E(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2)+1//15*c^-11//4*d^1//4*e^-11//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(7*a^2*d^2+15*b^2*c^2+-18*a*b*c*d)*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-13//2*(a+b*x^2)^2*(c+d*x^2)^-1//2, x) == :(-2//11*a^2*c^-1*e^-1*(e*x)^-11//2*(c+d*x^2)^(1/2)+-1//231*c^-3*e^-5*(e*x)^-3//2*(c+d*x^2)^(1/2)*(154*b^2*c^2+-10*a*d*(-9*a*d+22*b*c))+-2//77*a*c^-2*e^-3*(e*x)^-7//2*(c+d*x^2)^(1/2)*(-9*a*d+22*b*c)+-1//231*c^-13//4*d^3//4*e^-13//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(77*b^2*c^2+-5*a*d*(-9*a*d+22*b*c))*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^7//2*(a+b*x^2)^2*(c+d*x^2)^-3//2, x) == :(1//231*d^-4*e^3*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(385*a^2*d^2+585*b^2*c^2+-990*a*b*c*d)+2//11*b^2*d^-2*e^-1*(e*x)^9//2*(c+d*x^2)^(1/2)+c^-1*d^-2*e^-1*(e*x)^9//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^2+-1//77*e*c^-1*d^-3*(e*x)^5//2*(c+d*x^2)^(1/2)*(77*a^2*d^2+117*b^2*c^2+-198*a*b*c*d)+-5//462*c^3//4*d^-17//4*e^7//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(77*a^2*d^2+117*b^2*c^2+-198*a*b*c*d)*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^5//2*(a+b*x^2)^2*(c+d*x^2)^-3//2, x) == :(2//9*b^2*d^-2*e^-1*(e*x)^7//2*(c+d*x^2)^(1/2)+c^-1*d^-2*e^-1*(e*x)^7//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^2+-1//45*e*c^-1*d^-3*(e*x)^3//2*(c+d*x^2)^(1/2)*(45*a^2*d^2+77*b^2*c^2+-126*a*b*c*d)+1//15*d^-7//2*e^2*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(c^(1/2)+x*d^(1/2))^-1*(45*a^2*d^2+77*b^2*c^2+-126*a*b*c*d)+-1//15*c^1//4*d^-15//4*e^5//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(45*a^2*d^2+77*b^2*c^2+-126*a*b*c*d)*Elliptic.E(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2)+1//30*c^1//4*d^-15//4*e^5//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(45*a^2*d^2+77*b^2*c^2+-126*a*b*c*d)*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^3//2*(a+b*x^2)^2*(c+d*x^2)^-3//2, x) == :(2//7*b^2*d^-2*e^-1*(e*x)^5//2*(c+d*x^2)^(1/2)+c^-1*d^-2*e^-1*(e*x)^5//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^2+-1//21*e*c^-1*d^-3*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(21*a^2*d^2+45*b^2*c^2+-70*a*b*c*d)+1//42*c^-1//4*d^-13//4*e^3//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(21*a^2*d^2+45*b^2*c^2+-70*a*b*c*d)*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^(1/2)*(a+b*x^2)^2*(c+d*x^2)^-3//2, x) == :(2//5*b^2*d^-2*e^-1*(e*x)^3//2*(c+d*x^2)^(1/2)+c^-1*d^-2*e^-1*(e*x)^3//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^2+-1//5*c^-1*d^-5//2*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(c^(1/2)+x*d^(1/2))^-1*(5*a^2*d^2+21*b^2*c^2+-30*a*b*c*d)+-1//10*c^-3//4*d^-11//4*e^(1/2)*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(5*a^2*d^2+21*b^2*c^2+-30*a*b*c*d)*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2)+1//5*c^-3//4*d^-11//4*e^(1/2)*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(5*a^2*d^2+21*b^2*c^2+-30*a*b*c*d)*Elliptic.E(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-1//2*(a+b*x^2)^2*(c+d*x^2)^-3//2, x) == :(2//3*b^2*d^-2*e^-1*(e*x)^(1/2)*(c+d*x^2)^(1/2)+c^-1*d^-2*e^-1*(e*x)^(1/2)*(c+d*x^2)^-1//2*(b*c+-1*a*d)^2+-1//6*c^-5//4*d^-9//4*e^-1//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(-3*a^2*d^2+5*b^2*c^2+-6*a*b*c*d)*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-3//2*(a+b*x^2)^2*(c+d*x^2)^-3//2, x) == :(-2*a^2*c^-1*e^-1*(e*x)^-1//2*(c+d*x^2)^-1//2+-1*c^-2*d^-1*e^-3*(e*x)^3//2*(c+d*x^2)^-1//2*(b^2*c^2+3*a^2*d^2+-2*a*b*c*d)+c^-2*d^-3//2*e^-2*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(c^(1/2)+x*d^(1/2))^-1*(3*a^2*d^2+3*b^2*c^2+-2*a*b*c*d)+(1/2)*c^-7//4*d^-7//4*e^-3//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(3*a^2*d^2+3*b^2*c^2+-2*a*b*c*d)*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2)+-1*c^-7//4*d^-7//4*e^-3//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(3*a^2*d^2+3*b^2*c^2+-2*a*b*c*d)*Elliptic.E(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-5//2*(a+b*x^2)^2*(c+d*x^2)^-3//2, x) == :(-2//3*a^2*c^-1*e^-1*(e*x)^-3//2*(c+d*x^2)^-1//2+-1//3*c^-2*d^-1*e^-3*(e*x)^(1/2)*(c+d*x^2)^-1//2*(3*b^2*c^2+5*a^2*d^2+-6*a*b*c*d)+1//6*c^-9//4*d^-5//4*e^-5//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(3*b^2*c^2+a*d*(-5*a*d+6*b*c))*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-7//2*(a+b*x^2)^2*(c+d*x^2)^-3//2, x) == :(-2//5*a^2*c^-1*e^-1*(e*x)^-5//2*(c+d*x^2)^-1//2+1//5*c^-3*e^-5*(e*x)^3//2*(c+d*x^2)^-1//2*(5*b^2*c^2+-3*a*d*(-7*a*d+10*b*c))+-2//5*a*c^-2*e^-3*(e*x)^-1//2*(c+d*x^2)^-1//2*(-7*a*d+10*b*c)+-1//5*c^-3*d^-1//2*e^-4*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(c^(1/2)+x*d^(1/2))^-1*(5*b^2*c^2+-3*a*d*(-7*a*d+10*b*c))+-1//10*c^-11//4*d^-3//4*e^-7//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(5*b^2*c^2+-3*a*d*(-7*a*d+10*b*c))*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2)+1//5*c^-11//4*d^-3//4*e^-7//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(5*b^2*c^2+-3*a*d*(-7*a*d+10*b*c))*Elliptic.E(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^7//2*(a+b*x^2)^2*(c+d*x^2)^-5//2, x) == :(2//7*b^2*d^-2*e^-1*(e*x)^9//2*(c+d*x^2)^-1//2+-1//42*c^-1*d^-4*e^3*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(35*a^2*d^2+195*b^2*c^2+-210*a*b*c*d)+1//3*c^-1*d^-2*e^-1*(e*x)^9//2*(c+d*x^2)^-3//2*(b*c+-1*a*d)^2+1//14*e*c^-1*d^-3*(e*x)^5//2*(c+d*x^2)^-1//2*(7*a^2*d^2+39*b^2*c^2+-42*a*b*c*d)+1//84*c^-1//4*d^-17//4*e^7//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(35*a^2*d^2+195*b^2*c^2+-210*a*b*c*d)*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^5//2*(a+b*x^2)^2*(c+d*x^2)^-5//2, x) == :(2//5*b^2*d^-2*e^-1*(e*x)^7//2*(c+d*x^2)^-1//2+1//3*c^-1*d^-2*e^-1*(e*x)^7//2*(c+d*x^2)^-3//2*(b*c+-1*a*d)^2+1//30*e*c^-1*d^-3*(e*x)^3//2*(c+d*x^2)^-1//2*(5*a^2*d^2+77*b^2*c^2+-70*a*b*c*d)+-1//10*c^-1*d^-7//2*e^2*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(c^(1/2)+x*d^(1/2))^-1*(5*a^2*d^2+77*b^2*c^2+-70*a*b*c*d)+-1//20*c^-3//4*d^-15//4*e^5//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(5*a^2*d^2+77*b^2*c^2+-70*a*b*c*d)*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2)+1//10*c^-3//4*d^-15//4*e^5//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(5*a^2*d^2+77*b^2*c^2+-70*a*b*c*d)*Elliptic.E(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^3//2*(a+b*x^2)^2*(c+d*x^2)^-5//2, x) == :(2//3*b^2*d^-2*e^-1*(e*x)^5//2*(c+d*x^2)^-1//2+1//3*c^-1*d^-2*e^-1*(e*x)^5//2*(c+d*x^2)^-3//2*(b*c+-1*a*d)^2+1//6*e*c^-1*d^-3*(e*x)^(1/2)*(c+d*x^2)^-1//2*(-1*a^2*d^2+15*b^2*c^2+-10*a*b*c*d)+-1//12*c^-5//4*d^-13//4*e^3//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(-1*a^2*d^2+15*b^2*c^2+-10*a*b*c*d)*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^(1/2)*(a+b*x^2)^2*(c+d*x^2)^-5//2, x) == :((1/2)*c^-2*d^-5//2*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(c^(1/2)+x*d^(1/2))^-1*(-1*a^2*d^2+7*b^2*c^2+-2*a*b*c*d)+1//3*c^-1*d^-2*e^-1*(e*x)^3//2*(c+d*x^2)^-3//2*(b*c+-1*a*d)^2+-1//2*c^-2*d^-2*e^-1*(e*x)^3//2*(c+d*x^2)^-1//2*(a*d+3*b*c)*(b*c+-1*a*d)+-1//2*c^-7//4*d^-11//4*e^(1/2)*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(-1*a^2*d^2+7*b^2*c^2+-2*a*b*c*d)*Elliptic.E(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2)+1//4*c^-7//4*d^-11//4*e^(1/2)*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(-1*a^2*d^2+7*b^2*c^2+-2*a*b*c*d)*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-1//2*(a+b*x^2)^2*(c+d*x^2)^-5//2, x) == :(1//3*c^-1*d^-2*e^-1*(e*x)^(1/2)*(c+d*x^2)^-3//2*(b*c+-1*a*d)^2+-1//6*c^-2*d^-2*e^-1*(e*x)^(1/2)*(c+d*x^2)^-1//2*(b*c+-1*a*d)*(5*a*d+7*b*c)+1//12*c^-9//4*d^-9//4*e^-1//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(5*a^2*d^2+5*b^2*c^2+2*a*b*c*d)*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-3//2*(a+b*x^2)^2*(c+d*x^2)^-5//2, x) == :(-2*a^2*c^-1*e^-1*(e*x)^-1//2*(c+d*x^2)^-3//2+(1/2)*c^-3*d^-1*e^-3*(e*x)^3//2*(c+d*x^2)^-1//2*(b^2*c^2+a*d*(-7*a*d+2*b*c))+-1//3*c^-2*d^-1*e^-3*(e*x)^3//2*(c+d*x^2)^-3//2*(b^2*c^2+7*a^2*d^2+-2*a*b*c*d)+-1//2*c^-3*d^-3//2*e^-2*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(c^(1/2)+x*d^(1/2))^-1*(b^2*c^2+a*d*(-7*a*d+2*b*c))+(1/2)*c^-11//4*d^-7//4*e^-3//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(b^2*c^2+a*d*(-7*a*d+2*b*c))*Elliptic.E(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2)+-1//4*c^-11//4*d^-7//4*e^-3//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(b^2*c^2+a*d*(-7*a*d+2*b*c))*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-5//2*(a+b*x^2)^2*(c+d*x^2)^-5//2, x) == :(-2//3*a^2*c^-1*e^-1*(e*x)^-3//2*(c+d*x^2)^-3//2+-1//3*c^-2*d^-1*e^-3*(e*x)^(1/2)*(c+d*x^2)^-3//2*(b^2*c^2+3*a^2*d^2+-2*a*b*c*d)+1//6*c^-3*d^-1*e^-3*(e*x)^(1/2)*(c+d*x^2)^-1//2*(b^2*c^2+5*a*d*(-3*a*d+2*b*c))+1//12*c^-13//4*d^-5//4*e^-5//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(b^2*c^2+5*a*d*(-3*a*d+2*b*c))*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate((e*x)^-7//2*(a+b*x^2)^2*(c+d*x^2)^-5//2, x) == :(-2//5*a^2*c^-1*e^-1*(e*x)^-5//2*(c+d*x^2)^-3//2+1//10*c^-4*e^-5*(e*x)^3//2*(c+d*x^2)^-1//2*(5*b^2*c^2+77*a^2*d^2+-70*a*b*c*d)+1//15*c^-3*e^-5*(e*x)^3//2*(c+d*x^2)^-3//2*(5*b^2*c^2+77*a^2*d^2+-70*a*b*c*d)+-2//5*a*c^-2*e^-3*(e*x)^-1//2*(c+d*x^2)^-3//2*(-11*a*d+10*b*c)+-1//10*c^-4*d^-1//2*e^-4*(e*x)^(1/2)*(c+d*x^2)^(1/2)*(c^(1/2)+x*d^(1/2))^-1*(5*b^2*c^2+77*a^2*d^2+-70*a*b*c*d)+-1//20*c^-15//4*d^-3//4*e^-7//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(5*b^2*c^2+77*a^2*d^2+-70*a*b*c*d)*Elliptic.F(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2)+1//10*c^-15//4*d^-3//4*e^-7//2*((c^(1/2)+x*d^(1/2))^-2*(c+d*x^2))^(1/2)*(c+d*x^2)^-1//2*(c^(1/2)+x*d^(1/2))*(5*b^2*c^2+77*a^2*d^2+-70*a*b*c*d)*Elliptic.E(2*arctan(c^-1//4*d^1//4*e^-1//2*(e*x)^(1/2)),1/2))
@test integrate(x^5*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2, x) == :(-1//16*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^2)^(1/2)*(c+d*x^2)^-1//2)+-1//24*b^-2*d^-2*(a+b*x^2)^3//2*(c+d*x^2)^(1/2)*(3*a*d+5*b*c)+1//6*b^-1*d^-1*x^2*(a+b*x^2)^3//2*(c+d*x^2)^(1/2)+1//16*b^-2*d^-3*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(a^2*d^2+5*b^2*c^2+2*a*b*c*d))
@test integrate(x^3*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2, x) == :(1//4*b^-1*d^-1*(a+b*x^2)^3//2*(c+d*x^2)^(1/2)+-1//8*b^-1*d^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(a*d+3*b*c)+1//8*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^2)^(1/2)*(c+d*x^2)^-1//2))
@test integrate(x*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2, x) == :((1/2)*d^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)+-1//2*b^-1//2*d^-3//2*(b*c+-1*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2))
@test integrate(x^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2, x) == :(b^(1/2)*d^-1//2*arctanh(b^-1//2*d^(1/2)*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2)+-1*a^(1/2)*c^-1//2*arctanh(a^-1//2*c^(1/2)*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2))
@test integrate(x^-3*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2, x) == :(-1//2*a^-1//2*c^-3//2*(b*c+-1*a*d)*arctanh(a^-1//2*c^(1/2)*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2)+-1//2*c^-1*x^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2))
@test integrate(x^-5*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2, x) == :(-1//4*a^-1*c^-1*x^-4*(a+b*x^2)^3//2*(c+d*x^2)^(1/2)+1//8*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^2)^(1/2)*(c+d*x^2)^-1//2)+1//8*a^-1*c^-2*x^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(b*c+3*a*d))
@test integrate(x^4*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2, x) == :(1//5*d^-1*x^3*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)+-1//15*x*b^-1*d^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(-1*a*d+4*b*c)+1//15*x*b^-2*d^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(-2*a^2*d^2+8*b^2*c^2+-3*a*b*c*d)+-1//15*b^-2*c^(1/2)*d^-5//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(-2*a^2*d^2+8*b^2*c^2+-3*a*b*c*d)*Elliptic.E(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1)+1//15*b^-1*c^3//2*d^-5//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(-1*a*d+4*b*c)*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1))
@test integrate(x^2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2, x) == :(1//3*x*d^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)+-1//3*x*b^-1*d^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(-1*a*d+2*b*c)+-1//3*c^3//2*d^-3//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1)+1//3*b^-1*c^(1/2)*d^-3//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(-1*a*d+2*b*c)*Elliptic.E(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1))
@test integrate(x^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2, x) == :(-1*c^-1*x^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)+d*x*c^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2+-1*c^-1//2*d^(1/2)*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*Elliptic.E(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1)+b*a^-1*c^(1/2)*d^-1//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1))
@test integrate(x^-4*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2, x) == :(-1//3*c^-1*x^-3*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)+-1//3*a^-1*c^-2*x^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(b*c+-2*a*d)+1//3*d*x*a^-1*c^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(b*c+-2*a*d)+-1//3*b*a^-1*c^-1//2*d^(1/2)*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1)+-1//3*a^-1*c^-3//2*d^(1/2)*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(b*c+-2*a*d)*Elliptic.E(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1))
@test integrate(x^5*(a+b*x^2)^3//2*(c+d*x^2)^-1//2, x) == :(-1//48*b^-2*d^-2*(a+b*x^2)^5//2*(c+d*x^2)^(1/2)*(3*a*d+7*b*c)+1//8*b^-1*d^-1*x^2*(a+b*x^2)^5//2*(c+d*x^2)^(1/2)+1//128*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^2)^(1/2)*(c+d*x^2)^-1//2)+1//192*b^-2*d^-3*(a+b*x^2)^3//2*(c+d*x^2)^(1/2)*(3*a^2*d^2+35*b^2*c^2+10*a*b*c*d)+-1//128*b^-2*d^-4*(a+b*x^2)^(1/2)*(c+d*x^2)^(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^3*(a+b*x^2)^3//2*(c+d*x^2)^-1//2, x) == :(1//6*b^-1*d^-1*(a+b*x^2)^5//2*(c+d*x^2)^(1/2)+-1//16*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^2)^(1/2)*(c+d*x^2)^-1//2)+-1//24*b^-1*d^-2*(a+b*x^2)^3//2*(c+d*x^2)^(1/2)*(a*d+5*b*c)+1//16*b^-1*d^-3*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(a*d+5*b*c)*(b*c+-1*a*d))
@test integrate(x*(a+b*x^2)^3//2*(c+d*x^2)^-1//2, x) == :(1//4*d^-1*(a+b*x^2)^3//2*(c+d*x^2)^(1/2)+-1//8*d^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(-3*a*d+3*b*c)+3//8*b^-1//2*d^-5//2*(b*c+-1*a*d)^2*arctanh(b^-1//2*d^(1/2)*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2))
@test integrate(x^-1*(a+b*x^2)^3//2*(c+d*x^2)^-1//2, x) == :(-1*a^3//2*c^-1//2*arctanh(a^-1//2*c^(1/2)*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2)+(1/2)*b*d^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)+-1//2*b^(1/2)*d^-3//2*(b*c+-3*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2))
@test integrate(x^-3*(a+b*x^2)^3//2*(c+d*x^2)^-1//2, x) == :(b^3//2*d^-1//2*arctanh(b^-1//2*d^(1/2)*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2)+-1//2*a^(1/2)*c^-3//2*(-1*a*d+3*b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2)+-1//2*a*c^-1*x^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2))
@test integrate(x^-5*(a+b*x^2)^3//2*(c+d*x^2)^-1//2, x) == :(-3//8*a^-1//2*c^-5//2*(b*c+-1*a*d)^2*arctanh(a^-1//2*c^(1/2)*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2)+-1//4*c^-1*x^-4*(a+b*x^2)^3//2*(c+d*x^2)^(1/2)+-1//8*c^-2*x^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(-3*a*d+3*b*c))
@test integrate(x^4*(a+b*x^2)^3//2*(c+d*x^2)^-1//2, x) == :(-1//35*d^-2*x^3*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(-8*a*d+6*b*c)+1//7*b*d^-1*x^5*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)+1//35*x*b^-1*d^-3*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(a^2*d^2+8*b^2*c^2+-11*a*b*c*d)+-1//35*x*b^-2*d^-3*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(-2*a*d+4*b*c)*(-1*a^2*d^2+4*b^2*c^2+-4*a*b*c*d)+-1//35*b^-1*c^3//2*d^-7//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(a^2*d^2+8*b^2*c^2+-11*a*b*c*d)*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1)+2//35*b^-2*c^(1/2)*d^-7//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(-1*a*d+2*b*c)*(-1*a^2*d^2+4*b^2*c^2+-4*a*b*c*d)*Elliptic.E(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1))
@test integrate(x^2*(a+b*x^2)^3//2*(c+d*x^2)^-1//2, x) == :(-1//15*x*d^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(13*a*c+-8*b*c^2*d^-1+-3*d*a^2*b^-1)+-1//15*x*d^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(-6*a*d+4*b*c)+1//5*b*d^-1*x^3*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)+2//15*c^3//2*d^-5//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(-3*a*d+2*b*c)*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1)+-1//15*b^-1*c^(1/2)*d^-5//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(3*a^2*d^2+8*b^2*c^2+-13*a*b*c*d)*Elliptic.E(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1))
@test integrate(x^-2*(a+b*x^2)^3//2*(c+d*x^2)^-1//2, x) == :(x*c^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(a*d+b*c)+-1*a*c^-1*x^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)+-1*c^-1//2*d^-1//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(a*d+b*c)*Elliptic.E(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1)+2*b*c^(1/2)*d^-1//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1))
@test integrate(x^-4*(a+b*x^2)^3//2*(c+d*x^2)^-1//2, x) == :(-1//3*a*c^-1*x^-3*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)+-1//3*c^-2*x^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(-2*a*d+4*b*c)+2//3*d*x*c^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(-1*a*d+2*b*c)+-2//3*c^-3//2*d^(1/2)*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(-1*a*d+2*b*c)*Elliptic.E(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1)+1//3*b*a^-1*c^-1//2*d^-1//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(-1*a*d+3*b*c)*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1))
@test integrate(x^5*(a+b*x^2)^5//2*(c+d*x^2)^-1//2, x) == :(-1//80*b^-2*d^-2*(a+b*x^2)^7//2*(c+d*x^2)^(1/2)*(3*a*d+9*b*c)+-1//256*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^2)^(1/2)*(c+d*x^2)^-1//2)+1//10*b^-1*d^-1*x^2*(a+b*x^2)^7//2*(c+d*x^2)^(1/2)+1//480*b^-2*d^-3*(a+b*x^2)^5//2*(c+d*x^2)^(1/2)*(3*a^2*d^2+63*b^2*c^2+14*a*b*c*d)+-1//384*b^-2*d^-4*(a+b*x^2)^3//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)*(3*a^2*d^2+63*b^2*c^2+14*a*b*c*d)+1//256*b^-2*d^-5*(a+b*x^2)^(1/2)*(c+d*x^2)^(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^3*(a+b*x^2)^5//2*(c+d*x^2)^-1//2, x) == :(1//8*b^-1*d^-1*(a+b*x^2)^7//2*(c+d*x^2)^(1/2)+-1//48*b^-1*d^-2*(a+b*x^2)^5//2*(c+d*x^2)^(1/2)*(a*d+7*b*c)+5//128*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^2)^(1/2)*(c+d*x^2)^-1//2)+-5//128*b^-1*d^-4*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^2*(a*d+7*b*c)+1//192*b^-1*d^-3*(a+b*x^2)^3//2*(c+d*x^2)^(1/2)*(a*d+7*b*c)*(-5*a*d+5*b*c))
@test integrate(x*(a+b*x^2)^5//2*(c+d*x^2)^-1//2, x) == :(1//6*d^-1*(a+b*x^2)^5//2*(c+d*x^2)^(1/2)+-5//16*b^-1//2*d^-7//2*(b*c+-1*a*d)^3*arctanh(b^-1//2*d^(1/2)*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2)+-1//24*d^-2*(a+b*x^2)^3//2*(c+d*x^2)^(1/2)*(-5*a*d+5*b*c)+5//16*d^-3*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^2)
@test integrate(x^-1*(a+b*x^2)^5//2*(c+d*x^2)^-1//2, x) == :(-1*a^5//2*c^-1//2*arctanh(a^-1//2*c^(1/2)*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2)+1//4*b*d^-1*(a+b*x^2)^3//2*(c+d*x^2)^(1/2)+1//8*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^2)^(1/2)*(c+d*x^2)^-1//2)+-1//8*b*d^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(-7*a*d+3*b*c))
@test integrate(x^-3*(a+b*x^2)^5//2*(c+d*x^2)^-1//2, x) == :(-1//2*a^3//2*c^-3//2*(-1*a*d+5*b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2)+-1//2*b^3//2*d^-3//2*(b*c+-5*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2)+-1//2*a*c^-1*x^-2*(a+b*x^2)^3//2*(c+d*x^2)^(1/2)+(1/2)*b*c^-1*d^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(a*d+b*c))
@test integrate(x^-5*(a+b*x^2)^5//2*(c+d*x^2)^-1//2, x) == :(b^5//2*d^-1//2*arctanh(b^-1//2*d^(1/2)*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2)+-1//8*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^2)^(1/2)*(c+d*x^2)^-1//2)+-1//4*a*c^-1*x^-4*(a+b*x^2)^3//2*(c+d*x^2)^(1/2)+-1//8*a*c^-2*x^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(-3*a*d+7*b*c))
@test integrate(x^4*(a+b*x^2)^5//2*(c+d*x^2)^-1//2, x) == :(1//9*b*d^-1*x^5*(a+b*x^2)^3//2*(c+d*x^2)^(1/2)+1//315*d^-3*x^3*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(48*b^2*c^2+75*a^2*d^2+-115*a*b*c*d)+-4//63*b*d^-2*x^5*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(-3*a*d+2*b*c)+-1//315*x*b^-1*d^-4*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(-5*a^3*d^3+64*b^3*c^3+-156*a*d*b^2*c^2+105*b*c*a^2*d^2)+1//315*x*b^-2*d^-4*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(-10*a^4*d^4+128*b^4*c^4+-328*a*d*b^3*c^3+-25*b*c*a^3*d^3+243*a^2*b^2*c^2*d^2)+-1//315*b^-2*c^(1/2)*d^-9//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(-10*a^4*d^4+128*b^4*c^4+-328*a*d*b^3*c^3+-25*b*c*a^3*d^3+243*a^2*b^2*c^2*d^2)*Elliptic.E(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1)+1//315*b^-1*c^3//2*d^-9//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(-5*a^3*d^3+64*b^3*c^3+-156*a*d*b^2*c^2+105*b*c*a^2*d^2)*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1))
@test integrate(x^2*(a+b*x^2)^5//2*(c+d*x^2)^-1//2, x) == :(1//7*b*d^-1*x^3*(a+b*x^2)^3//2*(c+d*x^2)^(1/2)+1//105*x*d^-3*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(24*b^2*c^2+45*a^2*d^2+-61*a*b*c*d)+-2//35*b*d^-2*x^3*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(-5*a*d+3*b*c)+-1//105*x*b^-1*d^-3*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(-15*a^3*d^3+48*b^3*c^3+-128*a*d*b^2*c^2+103*b*c*a^2*d^2)+-1//105*c^3//2*d^-7//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(24*b^2*c^2+45*a^2*d^2+-61*a*b*c*d)*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1)+1//105*b^-1*c^(1/2)*d^-7//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(-15*a^3*d^3+48*b^3*c^3+-128*a*d*b^2*c^2+103*b*c*a^2*d^2)*Elliptic.E(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1))
@test integrate(x^-2*(a+b*x^2)^5//2*(c+d*x^2)^-1//2, x) == :(1//3*x*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(7*a*b+-2*c*b^2*d^-1+3*d*a^2*c^-1)+-1*a*c^-1*x^-1*(a+b*x^2)^3//2*(c+d*x^2)^(1/2)+1//3*b*x*c^-1*d^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(b*c+3*a*d)+1//3*c^-1//2*d^-3//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(-3*a^2*d^2+2*b^2*c^2+-7*a*b*c*d)*Elliptic.E(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1)+-1//3*b*c^(1/2)*d^-3//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(b*c+-9*a*d)*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1))
@test integrate(x^-4*(a+b*x^2)^5//2*(c+d*x^2)^-1//2, x) == :(-1//3*a*c^-1*x^-3*(a+b*x^2)^3//2*(c+d*x^2)^(1/2)+1//3*x*c^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(-2*a^2*d^2+3*b^2*c^2+7*a*b*c*d)+-2//3*a*c^-2*x^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(-1*a*d+3*b*c)+-1//3*c^-3//2*d^-1//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(-2*a^2*d^2+3*b^2*c^2+7*a*b*c*d)*Elliptic.E(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1)+1//3*b*c^-1//2*d^-1//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(-1*a*d+9*b*c)*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1))
@test integrate(x^4*(-1+3*x^2)^(1/2)*(2+-3*x^2)^-1//2, x) == :(-8//135*3^(1/2)*Elliptic.E(arccos((1/2)*x*6^(1/2)),2)+-2//81*3^(1/2)*Elliptic.F(arccos((1/2)*x*6^(1/2)),2)+-7//135*x*(-1+3*x^2)^(1/2)*(2+-3*x^2)^(1/2)+-1//15*x^3*(-1+3*x^2)^(1/2)*(2+-3*x^2)^(1/2))
@test integrate(x^3*(-1+3*x^2)^(1/2)*(2+-3*x^2)^-1//2, x) == :(-7//144*arcsin(3+-6*x^2)+-7//72*(-1+3*x^2)^(1/2)*(2+-3*x^2)^(1/2)+-1//36*(-1+3*x^2)^3//2*(2+-3*x^2)^(1/2))
@test integrate(x^2*(-1+3*x^2)^(1/2)*(2+-3*x^2)^-1//2, x) == :(-1//9*3^(1/2)*Elliptic.E(arccos((1/2)*x*6^(1/2)),2)+-1//27*3^(1/2)*Elliptic.F(arccos((1/2)*x*6^(1/2)),2)+-1//9*x*(-1+3*x^2)^(1/2)*(2+-3*x^2)^(1/2))
@test integrate(x*(-1+3*x^2)^(1/2)*(2+-3*x^2)^-1//2, x) == :(-1//12*arcsin(3+-6*x^2)+-1//6*(-1+3*x^2)^(1/2)*(2+-3*x^2)^(1/2))
@test integrate(x^2*(2+b*x^2)^(1/2)*(3+d*x^2)^-1//2, x) == :(1//3*x*d^-1*(2+b*x^2)^(1/2)*(3+d*x^2)^(1/2)+-1*2^(1/2)*d^-3//2*((3+d*x^2)^-1*(2+b*x^2))^-1//2*(2+b*x^2)^(1/2)*(3+d*x^2)^-1//2*Elliptic.F(arctan(1//3*x*3^(1/2)*d^(1/2)),1+-3//2*b*d^-1)+-1//3*x*b^-1*d^-1*(2+b*x^2)^(1/2)*(3+d*x^2)^-1//2*(-2d+6b)+2//3*2^(1/2)*b^-1*d^-3//2*((3+d*x^2)^-1*(2+b*x^2))^-1//2*(2+b*x^2)^(1/2)*(3+d*x^2)^-1//2*(-1d+3b)*Elliptic.E(arctan(1//3*x*3^(1/2)*d^(1/2)),1+-3//2*b*d^-1))
@test integrate(x^5*(a+b*x^2)^-1//2*(c+d*x^2)^-1//2, x) == :(-1//8*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^2)^(1/2)*(c+d*x^2)^-1//2)+-1//8*b^-2*d^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(3*a*d+3*b*c)+1//4*b^-1*d^-1*x^2*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2))
@test integrate(x^3*(a+b*x^2)^-1//2*(c+d*x^2)^-1//2, x) == :((1/2)*b^-1*d^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)+-1//2*b^-3//2*d^-3//2*(a*d+b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2))
@test integrate(x*(a+b*x^2)^-1//2*(c+d*x^2)^-1//2, x) == :(b^-1//2*d^-1//2*arctanh(b^-1//2*d^(1/2)*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2))
@test integrate(x^-1*(a+b*x^2)^-1//2*(c+d*x^2)^-1//2, x) == :(-1*a^-1//2*c^-1//2*arctanh(a^-1//2*c^(1/2)*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2))
@test integrate(x^-3*(a+b*x^2)^-1//2*(c+d*x^2)^-1//2, x) == :((1/2)*a^-3//2*c^-3//2*(a*d+b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2)+-1//2*a^-1*c^-1*x^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2))
@test integrate(x^-5*(a+b*x^2)^-1//2*(c+d*x^2)^-1//2, x) == :(-1//8*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^2)^(1/2)*(c+d*x^2)^-1//2)+-1//4*a^-1*c^-1*x^-4*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)+1//8*a^-2*c^-2*x^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(3*a*d+3*b*c))
@test integrate(x^6*(a+b*x^2)^-1//2*(c+d*x^2)^-1//2, x) == :(1//5*b^-1*d^-1*x^3*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)+-1//15*x*b^-2*d^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(4*a*d+4*b*c)+1//15*x*b^-3*d^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(8*a^2*d^2+8*b^2*c^2+7*a*b*c*d)+-1//15*b^-3*c^(1/2)*d^-5//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(8*a^2*d^2+8*b^2*c^2+7*a*b*c*d)*Elliptic.E(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1)+4//15*b^-2*c^3//2*d^-5//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(a*d+b*c)*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1))
@test integrate(x^4*(a+b*x^2)^-1//2*(c+d*x^2)^-1//2, x) == :(1//3*x*b^-1*d^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)+-1//3*x*b^-2*d^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(2*a*d+2*b*c)+-1//3*b^-1*c^3//2*d^-3//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1)+2//3*b^-2*c^(1/2)*d^-3//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(a*d+b*c)*Elliptic.E(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1))
@test integrate(x^2*(a+b*x^2)^-1//2*(c+d*x^2)^-1//2, x) == :(x*b^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2+-1*b^-1*c^(1/2)*d^-1//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*Elliptic.E(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1))
@test integrate(x^-2*(a+b*x^2)^-1//2*(c+d*x^2)^-1//2, x) == :(-1*a^-1*c^-1*x^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)+d*x*a^-1*c^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2+-1*a^-1*c^-1//2*d^(1/2)*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*Elliptic.E(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1))
@test integrate(x^-4*(a+b*x^2)^-1//2*(c+d*x^2)^-1//2, x) == :(-1//3*a^-1*c^-1*x^-3*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)+1//3*a^-2*c^-2*x^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(2*a*d+2*b*c)+-2//3*d*x*a^-2*c^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(a*d+b*c)+-1//3*b*a^-2*c^-1//2*d^(1/2)*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1)+2//3*a^-2*c^-3//2*d^(1/2)*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(a*d+b*c)*Elliptic.E(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1))
@test integrate(x^5*(a+b*x^2)^-3//2*(c+d*x^2)^-1//2, x) == :((1/2)*b^-2*d^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)+-1//2*b^-5//2*d^-3//2*(b*c+3*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2)+-1*a^2*b^-2*(a+b*x^2)^-1//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1)
@test integrate(x^3*(a+b*x^2)^-3//2*(c+d*x^2)^-1//2, x) == :(b^-3//2*d^-1//2*arctanh(b^-1//2*d^(1/2)*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2)+a*b^-1*(a+b*x^2)^-1//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1)
@test integrate(x*(a+b*x^2)^-3//2*(c+d*x^2)^-1//2, x) == :(-1*(a+b*x^2)^-1//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1)
@test integrate(x^5*(a+b*x^2)^-5//2*(c+d*x^2)^-1//2, x) == :(b^-5//2*d^-1//2*arctanh(b^-1//2*d^(1/2)*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2)+-1//3*a^2*b^-2*(a+b*x^2)^-3//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1+2//3*a*b^-2*(a+b*x^2)^-1//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-2*(-2*a*d+3*b*c))
@test integrate(x^3*(a+b*x^2)^-5//2*(c+d*x^2)^-1//2, x) == :(-1//3*b^-1*(a+b*x^2)^-1//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-2*(-1*a*d+3*b*c)+1//3*a*b^-1*(a+b*x^2)^-3//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1)
@test integrate(x*(a+b*x^2)^-5//2*(c+d*x^2)^-1//2, x) == :(-1*(a+b*x^2)^-3//2*(c+d*x^2)^(1/2)*(-3*a*d+3*b*c)^-1+2//3*d*(a+b*x^2)^-1//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-2)
@test integrate(x^5*(a+b*x^2)^-7//2*(c+d*x^2)^-1//2, x) == :(-1//5*a^2*b^-2*(a+b*x^2)^-5//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1+-1//15*b^-2*(a+b*x^2)^-1//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-3*(3*a^2*d^2+15*b^2*c^2+-10*a*b*c*d)+2//15*a*b^-2*(a+b*x^2)^-3//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-2*(-3*a*d+5*b*c))
@test integrate(x^3*(a+b*x^2)^-7//2*(c+d*x^2)^-1//2, x) == :(-1//15*b^-1*(a+b*x^2)^-3//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-2*(-1*a*d+5*b*c)+1//5*a*b^-1*(a+b*x^2)^-5//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1+2//15*d*b^-1*(a+b*x^2)^-1//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-3*(-1*a*d+5*b*c))
@test integrate(x*(a+b*x^2)^-7//2*(c+d*x^2)^-1//2, x) == :(-1*(a+b*x^2)^-5//2*(c+d*x^2)^(1/2)*(-5*a*d+5*b*c)^-1+-8//15*d^2*(a+b*x^2)^-1//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-3+4//15*d*(a+b*x^2)^-3//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-2)
@test integrate(x^5*(a+b*x^2)^-9//2*(c+d*x^2)^-1//2, x) == :(-1//7*a^2*b^-2*(a+b*x^2)^-7//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1+-1//105*b^-2*(a+b*x^2)^-3//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-3*(3*a^2*d^2+35*b^2*c^2+-14*a*b*c*d)+2//35*a*b^-2*(a+b*x^2)^-5//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-2*(-4*a*d+7*b*c)+2//105*d*b^-2*(a+b*x^2)^-1//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-4*(3*a^2*d^2+35*b^2*c^2+-14*a*b*c*d))
@test integrate(x*(a+-1*b*x^2)^-1//2*(c+d*x^2)^-1//2, x) == :(-1*b^-1//2*d^-1//2*arctan(b^-1//2*d^(1/2)*(a+-1*b*x^2)^(1/2)*(c+d*x^2)^-1//2))
@test integrate(x*(a+-1*b*x^2)^-1//2*(c+-1*d*x^2)^-1//2, x) == :(-1*b^-1//2*d^-1//2*arctanh(b^-1//2*d^(1/2)*(a+-1*b*x^2)^(1/2)*(c+-1*d*x^2)^-1//2))
@test integrate(x^2*(2+b*x^2)^-1//2*(3+d*x^2)^-1//2, x) == :(x*b^-1*(2+b*x^2)^(1/2)*(3+d*x^2)^-1//2+-1*2^(1/2)*b^-1*d^-1//2*((3+d*x^2)^-1*(2+b*x^2))^-1//2*(2+b*x^2)^(1/2)*(3+d*x^2)^-1//2*Elliptic.E(arctan(1//3*x*3^(1/2)*d^(1/2)),1+-3//2*b*d^-1))
@test integrate(x^2*(4+-1*x^2)^-1//2*(c+d*x^2)^-1//2, x) == :(d^-1*(1+d*c^-1*x^2)^-1//2*(c+d*x^2)^(1/2)*Elliptic.E(arcsin((1/2)*x),-4*d*c^-1)+-1*c*d^-1*(1+d*c^-1*x^2)^(1/2)*(c+d*x^2)^-1//2*Elliptic.F(arcsin((1/2)*x),-4*d*c^-1))
@test integrate(x^2*(4+x^2)^-1//2*(c+d*x^2)^-1//2, x) == :(x*d^-1*(4+x^2)^-1//2*(c+d*x^2)^(1/2)+-1*d^-1*(c^-1*(4+x^2)^-1*(c+d*x^2))^-1//2*(4+x^2)^-1//2*(c+d*x^2)^(1/2)*Elliptic.E(arctan((1/2)*x),1+-4*d*c^-1))
@test integrate(x^2*(1+-1*x^2)^-1//2*(2+3*x^2)^-1//2, x) == :(-1//3*2^(1/2)*Elliptic.F(arcsin(x),-3//2)+1//3*2^(1/2)*Elliptic.E(arcsin(x),-3//2))
@test integrate(x^2*(1+-1*x^2)^-1//2*(2+-3*x^2)^-1//2, x) == :(-1//3*2^(1/2)*Elliptic.E(arcsin(x),3//2)+1//3*2^(1/2)*Elliptic.F(arcsin(x),3//2))
@test integrate(x^2*(2+3*x^2)^-1//2*(4+-1*x^2)^-1//2, x) == :(-1//3*2^(1/2)*Elliptic.F(arcsin((1/2)*x),-6)+1//3*2^(1/2)*Elliptic.E(arcsin((1/2)*x),-6))
@test integrate(x^2*(2+-3*x^2)^-1//2*(4+-1*x^2)^-1//2, x) == :(-1//3*2^(1/2)*Elliptic.E(arcsin((1/2)*x),6)+1//3*2^(1/2)*Elliptic.F(arcsin((1/2)*x),6))
@test integrate(x^2*(1+-4*x^2)^-1//2*(2+3*x^2)^-1//2, x) == :(-1//6*2^(1/2)*Elliptic.F(arcsin(2x),-3//8)+1//6*2^(1/2)*Elliptic.E(arcsin(2x),-3//8))
@test integrate(x^2*(1+-4*x^2)^-1//2*(2+-3*x^2)^-1//2, x) == :(-1//6*2^(1/2)*Elliptic.E(arcsin(2x),3//8)+1//6*2^(1/2)*Elliptic.F(arcsin(2x),3//8))
@test integrate(x^2*(1+x^2)^-1//2*(2+-3*x^2)^-1//2, x) == :(-1//3*3^(1/2)*Elliptic.F(arcsin((1/2)*x*6^(1/2)),-2//3)+1//3*3^(1/2)*Elliptic.E(arcsin((1/2)*x*6^(1/2)),-2//3))
@test integrate(x^2*(2+-3*x^2)^-1//2*(4+x^2)^-1//2, x) == :(-2//3*3^(1/2)*Elliptic.F(arcsin((1/2)*x*6^(1/2)),-1//6)+2//3*3^(1/2)*Elliptic.E(arcsin((1/2)*x*6^(1/2)),-1//6))
@test integrate(x^2*(1+4*x^2)^-1//2*(2+-3*x^2)^-1//2, x) == :(-1//12*3^(1/2)*Elliptic.F(arcsin((1/2)*x*6^(1/2)),-8//3)+1//12*3^(1/2)*Elliptic.E(arcsin((1/2)*x*6^(1/2)),-8//3))
@test integrate(x^2*(1+x^2)^-1//2*(2+3*x^2)^-1//2, x) == :(1//3*x*(1+x^2)^-1//2*(2+3*x^2)^(1/2)+-1//3*2^(1/2)*((1+x^2)^-1*(2+3*x^2))^-1//2*(1+x^2)^-1//2*(2+3*x^2)^(1/2)*Elliptic.E(arctan(x),-1//2))
@test integrate(x^2*(2+3*x^2)^-1//2*(4+x^2)^-1//2, x) == :(1//3*x*(2+3*x^2)^(1/2)*(4+x^2)^-1//2+-1//3*2^(1/2)*((4+x^2)^-1*(2+3*x^2))^-1//2*(2+3*x^2)^(1/2)*(4+x^2)^-1//2*Elliptic.E(arctan((1/2)*x),-5))
@test integrate(x^2*(1+4*x^2)^-1//2*(2+3*x^2)^-1//2, x) == :(1//3*x*(1+4*x^2)^-1//2*(2+3*x^2)^(1/2)+-1//6*2^(1/2)*((1+4*x^2)^-1*(2+3*x^2))^-1//2*(1+4*x^2)^-1//2*(2+3*x^2)^(1/2)*Elliptic.E(arctan(2x),5//8))
@test integrate(x^2*(1+-1*x^2)^-1//2*(-1+2*x^2)^-1//2, x) == :(-1//2*Elliptic.E(arccos(x),2)+-1//2*Elliptic.F(arccos(x),2))
@test integrate(x^5*(1+-1*x^2)^-1//3*(3+x^2)^-1, x) == :(3//2*(1+-1*x^2)^2//3+3//10*(1+-1*x^2)^5//3+-9//8*2^1//3*log(3+x^2)+27//8*2^1//3*log(2^2//3+-1*(1+-1*x^2)^1//3)+9//4*2^1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+(2+-2*x^2)^1//3)))
@test integrate(x^3*(1+-1*x^2)^-1//3*(3+x^2)^-1, x) == :(-3//4*(1+-1*x^2)^2//3+-9//8*2^1//3*log(2^2//3+-1*(1+-1*x^2)^1//3)+3//8*2^1//3*log(3+x^2)+-3//4*2^1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+(2+-2*x^2)^1//3)))
@test integrate(x*(1+-1*x^2)^-1//3*(3+x^2)^-1, x) == :(-1//8*2^1//3*log(3+x^2)+3//8*2^1//3*log(2^2//3+-1*(1+-1*x^2)^1//3)+1//4*2^1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+(2+-2*x^2)^1//3)))
@test integrate(x^-1*(1+-1*x^2)^-1//3*(3+x^2)^-1, x) == :(-1//6*log(x)+1//4*log(1+-1*(1+-1*x^2)^1//3)+-1//8*2^1//3*log(2^2//3+-1*(1+-1*x^2)^1//3)+1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*(1+-1*x^2)^1//3))+1//24*2^1//3*log(3+x^2)+-1//12*2^1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+(2+-2*x^2)^1//3)))
@test integrate(x^-3*(1+-1*x^2)^-1//3*(3+x^2)^-1, x) == :(-1//6*x^-2*(1+-1*x^2)^2//3+-1//72*2^1//3*log(3+x^2)+1//24*2^1//3*log(2^2//3+-1*(1+-1*x^2)^1//3)+1//36*2^1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+(2+-2*x^2)^1//3)))
@test integrate(x^-5*(1+-1*x^2)^-1//3*(3+x^2)^-1, x) == :(-1//27*log(x)+1//18*log(1+-1*(1+-1*x^2)^1//3)+-1//12*x^-4*(1+-1*x^2)^2//3+-1//18*x^-2*(1+-1*x^2)^2//3+-1//72*2^1//3*log(2^2//3+-1*(1+-1*x^2)^1//3)+1//27*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*(1+-1*x^2)^1//3))+1//216*2^1//3*log(3+x^2)+-1//108*2^1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+(2+-2*x^2)^1//3)))
@test integrate(x^4*(1+-1*x^2)^-1//3*(3+x^2)^-1, x) == :(54*x*(7+-7*3^(1/2)+-7*(1+-1*x^2)^1//3)^-1+-3//4*2^1//3*arctanh(x)+-3//7*x*(1+-1*x^2)^2//3+9//4*2^1//3*arctanh(x*(1+2^1//3*(1+-1*x^2)^1//3)^-1)+3//4*2^1//3*3^(1/2)*arctan(3^(1/2)*x^-1)+3//4*2^1//3*3^(1/2)*arctan(3^(1/2)*x^-1*(1+-1*2^1//3*(1+-1*x^2)^1//3))+-18//7*2^(1/2)*3^3//4*x^-1*((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+(1+-1*x^2)^1//3+(1+-1*x^2)^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+-1*(1+-1*x^2)^1//3))^-1//2*(1+-1*(1+-1*x^2)^1//3)*Elliptic.F(arcsin((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-1*(1+3^(1/2)+-1*(1+-1*x^2)^1//3)),-7+4*3^(1/2))+27//7*3^1//4*x^-1*((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+(1+-1*x^2)^1//3+(1+-1*x^2)^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+-1*(1+-1*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(1+-1*(1+-1*x^2)^1//3)*Elliptic.E(arcsin((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-1*(1+3^(1/2)+-1*(1+-1*x^2)^1//3)),-7+4*3^(1/2)))
@test integrate(x^2*(1+-1*x^2)^-1//3*(3+x^2)^-1, x) == :(-3*x*(1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-1+-3//4*2^1//3*arctanh(x*(1+2^1//3*(1+-1*x^2)^1//3)^-1)+1//4*2^1//3*arctanh(x)+-1//4*2^1//3*3^(1/2)*arctan(3^(1/2)*x^-1)+-1//4*2^1//3*3^(1/2)*arctan(3^(1/2)*x^-1*(1+-1*2^1//3*(1+-1*x^2)^1//3))+2^(1/2)*3^3//4*x^-1*((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+(1+-1*x^2)^1//3+(1+-1*x^2)^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+-1*(1+-1*x^2)^1//3))^-1//2*(1+-1*(1+-1*x^2)^1//3)*Elliptic.F(arcsin((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-1*(1+3^(1/2)+-1*(1+-1*x^2)^1//3)),-7+4*3^(1/2))+-3//2*3^1//4*x^-1*((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+(1+-1*x^2)^1//3+(1+-1*x^2)^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+-1*(1+-1*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(1+-1*(1+-1*x^2)^1//3)*Elliptic.E(arcsin((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-1*(1+3^(1/2)+-1*(1+-1*x^2)^1//3)),-7+4*3^(1/2)))
@test integrate((1+-1*x^2)^-1//3*(3+x^2)^-1, x) == :(-1//12*2^1//3*arctanh(x)+1//4*2^1//3*arctanh(x*(1+2^1//3*(1+-1*x^2)^1//3)^-1)+1//12*2^1//3*3^(1/2)*arctan(3^(1/2)*x^-1)+1//12*2^1//3*3^(1/2)*arctan(3^(1/2)*x^-1*(1+-1*2^1//3*(1+-1*x^2)^1//3)))
@test integrate(x^-2*(1+-1*x^2)^-1//3*(3+x^2)^-1, x) == :(x*(3+-3*3^(1/2)+-3*(1+-1*x^2)^1//3)^-1+-1//3*x^-1*(1+-1*x^2)^2//3+-1//12*2^1//3*arctanh(x*(1+2^1//3*(1+-1*x^2)^1//3)^-1)+1//36*2^1//3*arctanh(x)+-1//36*2^1//3*3^(1/2)*arctan(3^(1/2)*x^-1)+-1//36*2^1//3*3^(1/2)*arctan(3^(1/2)*x^-1*(1+-1*2^1//3*(1+-1*x^2)^1//3))+-1//9*2^(1/2)*3^3//4*x^-1*((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+(1+-1*x^2)^1//3+(1+-1*x^2)^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+-1*(1+-1*x^2)^1//3))^-1//2*(1+-1*(1+-1*x^2)^1//3)*Elliptic.F(arcsin((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-1*(1+3^(1/2)+-1*(1+-1*x^2)^1//3)),-7+4*3^(1/2))+1//6*3^1//4*x^-1*((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+(1+-1*x^2)^1//3+(1+-1*x^2)^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+-1*(1+-1*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(1+-1*(1+-1*x^2)^1//3)*Elliptic.E(arcsin((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-1*(1+3^(1/2)+-1*(1+-1*x^2)^1//3)),-7+4*3^(1/2)))
@test integrate(x^-4*(1+-1*x^2)^-1//3*(3+x^2)^-1, x) == :(2*x*(27+-27*3^(1/2)+-27*(1+-1*x^2)^1//3)^-1+-2//27*x^-1*(1+-1*x^2)^2//3+-1//9*x^-3*(1+-1*x^2)^2//3+-1//108*2^1//3*arctanh(x)+1//36*2^1//3*arctanh(x*(1+2^1//3*(1+-1*x^2)^1//3)^-1)+1//108*2^1//3*3^(1/2)*arctan(3^(1/2)*x^-1)+1//108*2^1//3*3^(1/2)*arctan(3^(1/2)*x^-1*(1+-1*2^1//3*(1+-1*x^2)^1//3))+-2//81*2^(1/2)*3^3//4*x^-1*((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+(1+-1*x^2)^1//3+(1+-1*x^2)^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+-1*(1+-1*x^2)^1//3))^-1//2*(1+-1*(1+-1*x^2)^1//3)*Elliptic.F(arcsin((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-1*(1+3^(1/2)+-1*(1+-1*x^2)^1//3)),-7+4*3^(1/2))+1//27*3^1//4*x^-1*((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+(1+-1*x^2)^1//3+(1+-1*x^2)^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+-1*(1+-1*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(1+-1*(1+-1*x^2)^1//3)*Elliptic.E(arcsin((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-1*(1+3^(1/2)+-1*(1+-1*x^2)^1//3)),-7+4*3^(1/2)))
@test integrate(x^7*(1+-1*x^2)^-1//3*(3+x^2)^-2, x) == :(-99//32*2^1//3*log(3+x^2)+297//32*2^1//3*log(2^2//3+-1*(1+-1*x^2)^1//3)+-3*x^4*(1+-1*x^2)^2//3*(30+10*x^2)^-1+9*(1+-1*x^2)^2//3*(120+40*x^2)^-1*(69+14*x^2)+99//16*2^1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+(2+-2*x^2)^1//3)))
@test integrate(x^5*(1+-1*x^2)^-1//3*(3+x^2)^-2, x) == :(-3//4*(1+-1*x^2)^2//3+-9*(1+-1*x^2)^2//3*(24+8*x^2)^-1+-63//32*2^1//3*log(2^2//3+-1*(1+-1*x^2)^1//3)+21//32*2^1//3*log(3+x^2)+-21//16*2^1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+(2+-2*x^2)^1//3)))
@test integrate(x^3*(1+-1*x^2)^-1//3*(3+x^2)^-2, x) == :(3*(1+-1*x^2)^2//3*(24+8*x^2)^-1+-3//32*2^1//3*log(3+x^2)+9//32*2^1//3*log(2^2//3+-1*(1+-1*x^2)^1//3)+3//16*2^1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+(2+-2*x^2)^1//3)))
@test integrate(x*(1+-1*x^2)^-1//3*(3+x^2)^-2, x) == :(-1*(1+-1*x^2)^2//3*(24+8*x^2)^-1+-1//96*2^1//3*log(3+x^2)+1//32*2^1//3*log(2^2//3+-1*(1+-1*x^2)^1//3)+1//48*2^1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+(2+-2*x^2)^1//3)))
@test integrate(x^-1*(1+-1*x^2)^-1//3*(3+x^2)^-2, x) == :(-1//18*log(x)+1//12*log(1+-1*(1+-1*x^2)^1//3)+(1+-1*x^2)^2//3*(72+24*x^2)^-1+-5//96*2^1//3*log(2^2//3+-1*(1+-1*x^2)^1//3)+1//18*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*(1+-1*x^2)^1//3))+5//288*2^1//3*log(3+x^2)+-5//144*2^1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+(2+-2*x^2)^1//3)))
@test integrate(x^-3*(1+-1*x^2)^-1//3*(3+x^2)^-2, x) == :(-1//36*log(1+-1*(1+-1*x^2)^1//3)+1//54*log(x)+-5*(1+-1*x^2)^2//3*(216+72*x^2)^-1+-1//54*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*(1+-1*x^2)^1//3))+-1//96*2^1//3*log(3+x^2)+1//32*2^1//3*log(2^2//3+-1*(1+-1*x^2)^1//3)+-1//6*x^-2*(1+-1*x^2)^2//3*(3+x^2)^-1+1//48*2^1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+(2+-2*x^2)^1//3)))
@test integrate(x^-5*(1+-1*x^2)^-1//3*(3+x^2)^-2, x) == :(-1//54*log(x)+1//36*log(1+-1*(1+-1*x^2)^1//3)+(1+-1*x^2)^2//3*(648+216*x^2)^-1+-13//864*2^1//3*log(2^2//3+-1*(1+-1*x^2)^1//3)+1//54*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*(1+-1*x^2)^1//3))+13//2592*2^1//3*log(3+x^2)+-13//1296*2^1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+(2+-2*x^2)^1//3))+-1//12*x^-4*(1+-1*x^2)^2//3*(3+x^2)^-1+-1//36*x^-2*(1+-1*x^2)^2//3*(3+x^2)^-1)
@test integrate(x^4*(1+-1*x^2)^-1//3*(3+x^2)^-2, x) == :(-27*x*(8+-8*3^(1/2)+-8*(1+-1*x^2)^1//3)^-1+-15//16*2^1//3*arctanh(x*(1+2^1//3*(1+-1*x^2)^1//3)^-1)+5//16*2^1//3*arctanh(x)+3*x*(1+-1*x^2)^2//3*(24+8*x^2)^-1+-5//16*2^1//3*3^(1/2)*arctan(3^(1/2)*x^-1)+-5//16*2^1//3*3^(1/2)*arctan(3^(1/2)*x^-1*(1+-1*2^1//3*(1+-1*x^2)^1//3))+-27//16*3^1//4*x^-1*((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+(1+-1*x^2)^1//3+(1+-1*x^2)^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+-1*(1+-1*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(1+-1*(1+-1*x^2)^1//3)*Elliptic.E(arcsin((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-1*(1+3^(1/2)+-1*(1+-1*x^2)^1//3)),-7+4*3^(1/2))+9//8*2^(1/2)*3^3//4*x^-1*((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+(1+-1*x^2)^1//3+(1+-1*x^2)^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+-1*(1+-1*x^2)^1//3))^-1//2*(1+-1*(1+-1*x^2)^1//3)*Elliptic.F(arcsin((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-1*(1+3^(1/2)+-1*(1+-1*x^2)^1//3)),-7+4*3^(1/2)))
@test integrate(x^2*(1+-1*x^2)^-1//3*(3+x^2)^-2, x) == :(x*(8+-8*3^(1/2)+-8*(1+-1*x^2)^1//3)^-1+-1//48*2^1//3*arctanh(x)+1//16*2^1//3*arctanh(x*(1+2^1//3*(1+-1*x^2)^1//3)^-1)+-1*x*(1+-1*x^2)^2//3*(24+8*x^2)^-1+1//48*2^1//3*3^(1/2)*arctan(3^(1/2)*x^-1)+1//48*2^1//3*3^(1/2)*arctan(3^(1/2)*x^-1*(1+-1*2^1//3*(1+-1*x^2)^1//3))+-1//24*2^(1/2)*3^3//4*x^-1*((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+(1+-1*x^2)^1//3+(1+-1*x^2)^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+-1*(1+-1*x^2)^1//3))^-1//2*(1+-1*(1+-1*x^2)^1//3)*Elliptic.F(arcsin((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-1*(1+3^(1/2)+-1*(1+-1*x^2)^1//3)),-7+4*3^(1/2))+1//16*3^1//4*x^-1*((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+(1+-1*x^2)^1//3+(1+-1*x^2)^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+-1*(1+-1*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(1+-1*(1+-1*x^2)^1//3)*Elliptic.E(arcsin((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-1*(1+3^(1/2)+-1*(1+-1*x^2)^1//3)),-7+4*3^(1/2)))
@test integrate((1+-1*x^2)^-1//3*(3+x^2)^-2, x) == :(-1*x*(24+-24*3^(1/2)+-24*(1+-1*x^2)^1//3)^-1+-1//48*2^1//3*arctanh(x)+1//16*2^1//3*arctanh(x*(1+2^1//3*(1+-1*x^2)^1//3)^-1)+x*(1+-1*x^2)^2//3*(72+24*x^2)^-1+1//48*2^1//3*3^(1/2)*arctan(3^(1/2)*x^-1)+1//48*2^1//3*3^(1/2)*arctan(3^(1/2)*x^-1*(1+-1*2^1//3*(1+-1*x^2)^1//3))+-1//48*3^1//4*x^-1*((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+(1+-1*x^2)^1//3+(1+-1*x^2)^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+-1*(1+-1*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(1+-1*(1+-1*x^2)^1//3)*Elliptic.E(arcsin((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-1*(1+3^(1/2)+-1*(1+-1*x^2)^1//3)),-7+4*3^(1/2))+1//72*2^(1/2)*3^3//4*x^-1*((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+(1+-1*x^2)^1//3+(1+-1*x^2)^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+-1*(1+-1*x^2)^1//3))^-1//2*(1+-1*(1+-1*x^2)^1//3)*Elliptic.F(arcsin((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-1*(1+3^(1/2)+-1*(1+-1*x^2)^1//3)),-7+4*3^(1/2)))
@test integrate(x^-2*(1+-1*x^2)^-1//3*(3+x^2)^-2, x) == :(x*(8+-8*3^(1/2)+-8*(1+-1*x^2)^1//3)^-1+-7//144*2^1//3*arctanh(x*(1+2^1//3*(1+-1*x^2)^1//3)^-1)+-1//8*x^-1*(1+-1*x^2)^2//3+7//432*2^1//3*arctanh(x)+-7//432*2^1//3*3^(1/2)*arctan(3^(1/2)*x^-1)+-7//432*2^1//3*3^(1/2)*arctan(3^(1/2)*x^-1*(1+-1*2^1//3*(1+-1*x^2)^1//3))+1//24*x^-1*(1+-1*x^2)^2//3*(3+x^2)^-1+-1//24*2^(1/2)*3^3//4*x^-1*((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+(1+-1*x^2)^1//3+(1+-1*x^2)^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+-1*(1+-1*x^2)^1//3))^-1//2*(1+-1*(1+-1*x^2)^1//3)*Elliptic.F(arcsin((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-1*(1+3^(1/2)+-1*(1+-1*x^2)^1//3)),-7+4*3^(1/2))+1//16*3^1//4*x^-1*((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+(1+-1*x^2)^1//3+(1+-1*x^2)^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+-1*(1+-1*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(1+-1*(1+-1*x^2)^1//3)*Elliptic.E(arcsin((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-1*(1+3^(1/2)+-1*(1+-1*x^2)^1//3)),-7+4*3^(1/2)))
@test integrate(x^-4*(1+-1*x^2)^-1//3*(3+x^2)^-2, x) == :(-11*x*(648+-648*3^(1/2)+-648*(1+-1*x^2)^1//3)^-1+-11//216*x^-3*(1+-1*x^2)^2//3+-11//1296*2^1//3*arctanh(x)+11//432*2^1//3*arctanh(x*(1+2^1//3*(1+-1*x^2)^1//3)^-1)+11//648*x^-1*(1+-1*x^2)^2//3+1//24*x^-3*(1+-1*x^2)^2//3*(3+x^2)^-1+11//1296*2^1//3*3^(1/2)*arctan(3^(1/2)*x^-1)+11//1296*2^1//3*3^(1/2)*arctan(3^(1/2)*x^-1*(1+-1*2^1//3*(1+-1*x^2)^1//3))+-11//1296*3^1//4*x^-1*((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+(1+-1*x^2)^1//3+(1+-1*x^2)^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+-1*(1+-1*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(1+-1*(1+-1*x^2)^1//3)*Elliptic.E(arcsin((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-1*(1+3^(1/2)+-1*(1+-1*x^2)^1//3)),-7+4*3^(1/2))+1//1944*2^(1/2)*3^3//4*x^-1*((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+(1+-1*x^2)^1//3+(1+-1*x^2)^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-2*(1+-1*(1+-1*x^2)^1//3))^-1//2*(11+-11*(1+-1*x^2)^1//3)*Elliptic.F(arcsin((1+-1*3^(1/2)+-1*(1+-1*x^2)^1//3)^-1*(1+3^(1/2)+-1*(1+-1*x^2)^1//3)),-7+4*3^(1/2)))
@test integrate(x^7*(2+-3*x^2)^-1//4*(4+-3*x^2)^-1, x) == :(-16//567*(2+-3*x^2)^7//4+2//891*(2+-3*x^2)^11//4+56//243*(2+-3*x^2)^3//4+32//81*2^1//4*arctan((1/2)*2^1//4*(2+-3*x^2)^-1//4*(2^(1/2)+-1*(2+-3*x^2)^(1/2)))+32//81*2^1//4*arctanh((1/2)*2^1//4*(2+-3*x^2)^-1//4*(2^(1/2)+(2+-3*x^2)^(1/2))))
@test integrate(x^5*(2+-3*x^2)^-1//4*(4+-3*x^2)^-1, x) == :(-2//189*(2+-3*x^2)^7//4+4//27*(2+-3*x^2)^3//4+8//27*2^1//4*arctan((1/2)*2^1//4*(2+-3*x^2)^-1//4*(2^(1/2)+-1*(2+-3*x^2)^(1/2)))+8//27*2^1//4*arctanh((1/2)*2^1//4*(2+-3*x^2)^-1//4*(2^(1/2)+(2+-3*x^2)^(1/2))))
@test integrate(x^3*(2+-3*x^2)^-1//4*(4+-3*x^2)^-1, x) == :(2//27*(2+-3*x^2)^3//4+2//9*2^1//4*arctan((1/2)*2^1//4*(2+-3*x^2)^-1//4*(2^(1/2)+-1*(2+-3*x^2)^(1/2)))+2//9*2^1//4*arctanh((1/2)*2^1//4*(2+-3*x^2)^-1//4*(2^(1/2)+(2+-3*x^2)^(1/2))))
@test integrate(x*(2+-3*x^2)^-1//4*(4+-3*x^2)^-1, x) == :(1//6*2^1//4*arctan((1/2)*2^1//4*(2+-3*x^2)^-1//4*(2^(1/2)+-1*(2+-3*x^2)^(1/2)))+1//6*2^1//4*arctanh((1/2)*2^1//4*(2+-3*x^2)^-1//4*(2^(1/2)+(2+-3*x^2)^(1/2))))
@test integrate(x^-1*(2+-3*x^2)^-1//4*(4+-3*x^2)^-1, x) == :(-1//8*2^3//4*arctanh((1/2)*2^3//4*(2+-3*x^2)^1//4)+1//8*2^1//4*arctan((1/2)*2^1//4*(2+-3*x^2)^-1//4*(2^(1/2)+-1*(2+-3*x^2)^(1/2)))+1//8*2^1//4*arctanh((1/2)*2^1//4*(2+-3*x^2)^-1//4*(2^(1/2)+(2+-3*x^2)^(1/2)))+1//8*2^3//4*arctan((1/2)*2^3//4*(2+-3*x^2)^1//4))
@test integrate(x^-3*(2+-3*x^2)^-1//4*(4+-3*x^2)^-1, x) == :(-9//64*2^3//4*arctanh((1/2)*2^3//4*(2+-3*x^2)^1//4)+-1//16*x^-2*(2+-3*x^2)^3//4+3//32*2^1//4*arctan((1/2)*2^1//4*(2+-3*x^2)^-1//4*(2^(1/2)+-1*(2+-3*x^2)^(1/2)))+3//32*2^1//4*arctanh((1/2)*2^1//4*(2+-3*x^2)^-1//4*(2^(1/2)+(2+-3*x^2)^(1/2)))+9//64*2^3//4*arctan((1/2)*2^3//4*(2+-3*x^2)^1//4))
@test integrate(x^4*(2+-3*x^2)^-1//4*(4+-3*x^2)^-1, x) == :(2//45*x*(2+-3*x^2)^3//4+-16//45*2^1//4*3^(1/2)*Elliptic.E((1/2)*arcsin((1/2)*x*6^(1/2)),2)+4//27*2^1//4*3^(1/2)*arctan(1//3*3^(1/2)*x^-1*(2+-3*x^2)^-1//4*(2^3//4+-1*2^1//4*(2+-3*x^2)^(1/2)))+4//27*2^1//4*3^(1/2)*arctanh(1//3*3^(1/2)*x^-1*(2+-3*x^2)^-1//4*(2^3//4+2^1//4*(2+-3*x^2)^(1/2))))
@test integrate(x^2*(2+-3*x^2)^-1//4*(4+-3*x^2)^-1, x) == :(-2//9*2^1//4*3^(1/2)*Elliptic.E((1/2)*arcsin((1/2)*x*6^(1/2)),2)+1//9*2^1//4*3^(1/2)*arctan(1//3*3^(1/2)*x^-1*(2+-3*x^2)^-1//4*(2^3//4+-1*2^1//4*(2+-3*x^2)^(1/2)))+1//9*2^1//4*3^(1/2)*arctanh(1//3*3^(1/2)*x^-1*(2+-3*x^2)^-1//4*(2^3//4+2^1//4*(2+-3*x^2)^(1/2))))
@test integrate((2+-3*x^2)^-1//4*(4+-3*x^2)^-1, x) == :(1//12*2^1//4*3^(1/2)*arctan(1//6*2^3//4*3^(1/2)*x^-1*(2+-3*x^2)^-1//4*(2+-1*2^(1/2)*(2+-3*x^2)^(1/2)))+1//12*2^1//4*3^(1/2)*arctanh(1//6*2^3//4*3^(1/2)*x^-1*(2+-3*x^2)^-1//4*(2+2^(1/2)*(2+-3*x^2)^(1/2))))
@test integrate(x^-2*(2+-3*x^2)^-1//4*(4+-3*x^2)^-1, x) == :(-1//8*x^-1*(2+-3*x^2)^3//4+-1//8*2^1//4*3^(1/2)*Elliptic.E((1/2)*arcsin((1/2)*x*6^(1/2)),2)+1//16*2^1//4*3^(1/2)*arctan(1//3*3^(1/2)*x^-1*(2+-3*x^2)^-1//4*(2^3//4+-1*2^1//4*(2+-3*x^2)^(1/2)))+1//16*2^1//4*3^(1/2)*arctanh(1//3*3^(1/2)*x^-1*(2+-3*x^2)^-1//4*(2^3//4+2^1//4*(2+-3*x^2)^(1/2))))
@test integrate(x^-4*(2+-3*x^2)^-1//4*(4+-3*x^2)^-1, x) == :(-3//16*x^-1*(2+-3*x^2)^3//4+-1//24*x^-3*(2+-3*x^2)^3//4+-3//16*2^1//4*3^(1/2)*Elliptic.E((1/2)*arcsin((1/2)*x*6^(1/2)),2)+3//64*2^1//4*3^(1/2)*arctan(1//3*3^(1/2)*x^-1*(2+-3*x^2)^-1//4*(2^3//4+-1*2^1//4*(2+-3*x^2)^(1/2)))+3//64*2^1//4*3^(1/2)*arctanh(1//3*3^(1/2)*x^-1*(2+-3*x^2)^-1//4*(2^3//4+2^1//4*(2+-3*x^2)^(1/2))))
@test integrate(x^7*(-1+3*x^2)^-1//4*(-2+3*x^2)^-1, x) == :(-8//81*arctanh((-1+3*x^2)^1//4)+2//891*(-1+3*x^2)^11//4+8//81*arctan((-1+3*x^2)^1//4)+8//567*(-1+3*x^2)^7//4+14//243*(-1+3*x^2)^3//4)
@test integrate(x^5*(-1+3*x^2)^-1//4*(-2+3*x^2)^-1, x) == :(-4//27*arctanh((-1+3*x^2)^1//4)+2//27*(-1+3*x^2)^3//4+2//189*(-1+3*x^2)^7//4+4//27*arctan((-1+3*x^2)^1//4))
@test integrate(x^3*(-1+3*x^2)^-1//4*(-2+3*x^2)^-1, x) == :(-2//9*arctanh((-1+3*x^2)^1//4)+2//9*arctan((-1+3*x^2)^1//4)+2//27*(-1+3*x^2)^3//4)
@test integrate(x*(-1+3*x^2)^-1//4*(-2+3*x^2)^-1, x) == :(-1//3*arctanh((-1+3*x^2)^1//4)+1//3*arctan((-1+3*x^2)^1//4))
@test integrate(x^-1*(-1+3*x^2)^-1//4*(-2+3*x^2)^-1, x) == :((1/2)*arctan((-1+3*x^2)^1//4)+-1//2*arctanh((-1+3*x^2)^1//4)+-1//4*2^(1/2)*arctan(1+2^(1/2)*(-1+3*x^2)^1//4)+-1//8*2^(1/2)*log(1+(-1+3*x^2)^(1/2)+-1*2^(1/2)*(-1+3*x^2)^1//4)+1//4*2^(1/2)*arctan(1+-1*2^(1/2)*(-1+3*x^2)^1//4)+1//8*2^(1/2)*log(1+(-1+3*x^2)^(1/2)+2^(1/2)*(-1+3*x^2)^1//4))
@test integrate(x^-3*(-1+3*x^2)^-1//4*(-2+3*x^2)^-1, x) == :(-3//4*arctanh((-1+3*x^2)^1//4)+3//4*arctan((-1+3*x^2)^1//4)+-9//16*2^(1/2)*arctan(1+2^(1/2)*(-1+3*x^2)^1//4)+-9//32*2^(1/2)*log(1+(-1+3*x^2)^(1/2)+-1*2^(1/2)*(-1+3*x^2)^1//4)+-1//4*x^-2*(-1+3*x^2)^3//4+9//16*2^(1/2)*arctan(1+-1*2^(1/2)*(-1+3*x^2)^1//4)+9//32*2^(1/2)*log(1+(-1+3*x^2)^(1/2)+2^(1/2)*(-1+3*x^2)^1//4))
@test integrate(x^4*(-1+3*x^2)^-1//4*(-2+3*x^2)^-1, x) == :(-1//27*6^(1/2)*arctan((1/2)*x*6^(1/2)*(-1+3*x^2)^-1//4)+-1//27*6^(1/2)*arctanh((1/2)*x*6^(1/2)*(-1+3*x^2)^-1//4)+2//45*x*(-1+3*x^2)^3//4+8*x*(-1+3*x^2)^1//4*(15+15*(-1+3*x^2)^(1/2))^-1+-8//45*3^(1/2)*x^-1*(x^2*(1+(-1+3*x^2)^(1/2))^-2)^(1/2)*(1+(-1+3*x^2)^(1/2))*Elliptic.E(2*arctan((-1+3*x^2)^1//4),1/2)+4//45*3^(1/2)*x^-1*(x^2*(1+(-1+3*x^2)^(1/2))^-2)^(1/2)*(1+(-1+3*x^2)^(1/2))*Elliptic.F(2*arctan((-1+3*x^2)^1//4),1/2))
@test integrate(x^2*(-1+3*x^2)^-1//4*(-2+3*x^2)^-1, x) == :(-1//18*6^(1/2)*arctan((1/2)*x*6^(1/2)*(-1+3*x^2)^-1//4)+-1//18*6^(1/2)*arctanh((1/2)*x*6^(1/2)*(-1+3*x^2)^-1//4)+2*x*(-1+3*x^2)^1//4*(3+3*(-1+3*x^2)^(1/2))^-1+-2//9*3^(1/2)*x^-1*(x^2*(1+(-1+3*x^2)^(1/2))^-2)^(1/2)*(1+(-1+3*x^2)^(1/2))*Elliptic.E(2*arctan((-1+3*x^2)^1//4),1/2)+1//9*3^(1/2)*x^-1*(x^2*(1+(-1+3*x^2)^(1/2))^-2)^(1/2)*(1+(-1+3*x^2)^(1/2))*Elliptic.F(2*arctan((-1+3*x^2)^1//4),1/2))
@test integrate((-1+3*x^2)^-1//4*(-2+3*x^2)^-1, x) == :(-1//12*6^(1/2)*arctan((1/2)*x*6^(1/2)*(-1+3*x^2)^-1//4)+-1//12*6^(1/2)*arctanh((1/2)*x*6^(1/2)*(-1+3*x^2)^-1//4))
@test integrate(x^-2*(-1+3*x^2)^-1//4*(-2+3*x^2)^-1, x) == :(-1//2*x^-1*(-1+3*x^2)^3//4+-1//8*6^(1/2)*arctan((1/2)*x*6^(1/2)*(-1+3*x^2)^-1//4)+-1//8*6^(1/2)*arctanh((1/2)*x*6^(1/2)*(-1+3*x^2)^-1//4)+3*x*(-1+3*x^2)^1//4*(2+2*(-1+3*x^2)^(1/2))^-1+-1//2*3^(1/2)*x^-1*(x^2*(1+(-1+3*x^2)^(1/2))^-2)^(1/2)*(1+(-1+3*x^2)^(1/2))*Elliptic.E(2*arctan((-1+3*x^2)^1//4),1/2)+1//4*3^(1/2)*x^-1*(x^2*(1+(-1+3*x^2)^(1/2))^-2)^(1/2)*(1+(-1+3*x^2)^(1/2))*Elliptic.F(2*arctan((-1+3*x^2)^1//4),1/2))
@test integrate(x^-4*(-1+3*x^2)^-1//4*(-2+3*x^2)^-1, x) == :(-3//2*x^-1*(-1+3*x^2)^3//4+-3//16*6^(1/2)*arctan((1/2)*x*6^(1/2)*(-1+3*x^2)^-1//4)+-3//16*6^(1/2)*arctanh((1/2)*x*6^(1/2)*(-1+3*x^2)^-1//4)+-1//6*x^-3*(-1+3*x^2)^3//4+9*x*(-1+3*x^2)^1//4*(2+2*(-1+3*x^2)^(1/2))^-1+-3//2*3^(1/2)*x^-1*(x^2*(1+(-1+3*x^2)^(1/2))^-2)^(1/2)*(1+(-1+3*x^2)^(1/2))*Elliptic.E(2*arctan((-1+3*x^2)^1//4),1/2)+3//4*3^(1/2)*x^-1*(x^2*(1+(-1+3*x^2)^(1/2))^-2)^(1/2)*(1+(-1+3*x^2)^(1/2))*Elliptic.F(2*arctan((-1+3*x^2)^1//4),1/2))
@test integrate(x^2*(2+3*x^2)^-3//4*(4+3*x^2)^-1, x) == :(-1//18*2^3//4*3^(1/2)*arctan(1//6*3^(1/2)*x^-1*(2+3*x^2)^-1//4*(2*2^3//4+2*2^1//4*(2+3*x^2)^(1/2)))+1//18*2^3//4*3^(1/2)*arctanh(1//6*3^(1/2)*x^-1*(2+3*x^2)^-1//4*(2*2^3//4+-2*2^1//4*(2+3*x^2)^(1/2))))
@test integrate(x^2*(2+-3*x^2)^-3//4*(4+-3*x^2)^-1, x) == :(-1//18*2^3//4*3^(1/2)*arctanh(1//6*2^3//4*3^(1/2)*x^-1*(2+-3*x^2)^-1//4*(2+2^(1/2)*(2+-3*x^2)^(1/2)))+1//18*2^3//4*3^(1/2)*arctan(1//6*2^3//4*3^(1/2)*x^-1*(2+-3*x^2)^-1//4*(2+-1*2^(1/2)*(2+-3*x^2)^(1/2))))
@test integrate(x^2*(2+b*x^2)^-3//4*(4+b*x^2)^-1, x) == :((1/2)*2^3//4*b^-3//2*arctanh((1/2)*b^-1//2*x^-1*(2+b*x^2)^-1//4*(2*2^3//4+-2*2^1//4*(2+b*x^2)^(1/2)))+-1//2*2^3//4*b^-3//2*arctan((1/2)*b^-1//2*x^-1*(2+b*x^2)^-1//4*(2*2^3//4+2*2^1//4*(2+b*x^2)^(1/2))))
@test integrate(x^2*(2+-1*b*x^2)^-3//4*(4+-1*b*x^2)^-1, x) == :((1/2)*2^3//4*b^-3//2*arctan((1/2)*2^3//4*b^-1//2*x^-1*(2+-1*b*x^2)^-1//4*(2+-1*2^(1/2)*(2+-1*b*x^2)^(1/2)))+-1//2*2^3//4*b^-3//2*arctanh((1/2)*2^3//4*b^-1//2*x^-1*(2+-1*b*x^2)^-1//4*(2+2^(1/2)*(2+-1*b*x^2)^(1/2))))
@test integrate(x^2*(a+3*x^2)^-3//4*(2a+3*x^2)^-1, x) == :(-1//9*3^(1/2)*a^-1//4*arctan(1//3*3^(1/2)*a^3//4*x^-1*(a+3*x^2)^-1//4*(1+a^-1//2*(a+3*x^2)^(1/2)))+1//9*3^(1/2)*a^-1//4*arctanh(1//3*3^(1/2)*a^3//4*x^-1*(a+3*x^2)^-1//4*(1+-1*a^-1//2*(a+3*x^2)^(1/2))))
@test integrate(x^2*(a+-3*x^2)^-3//4*(-3*x^2+2a)^-1, x) == :(-1//9*3^(1/2)*a^-1//4*arctanh(1//3*3^(1/2)*a^3//4*x^-1*(a+-3*x^2)^-1//4*(1+a^-1//2*(a+-3*x^2)^(1/2)))+1//9*3^(1/2)*a^-1//4*arctan(1//3*3^(1/2)*a^3//4*x^-1*(a+-3*x^2)^-1//4*(1+-1*a^-1//2*(a+-3*x^2)^(1/2))))
@test integrate(x^2*(a+b*x^2)^-3//4*(2a+b*x^2)^-1, x) == :(a^-1//4*b^-3//2*arctanh(a^3//4*b^-1//2*x^-1*(a+b*x^2)^-1//4*(1+-1*a^-1//2*(a+b*x^2)^(1/2)))+-1*a^-1//4*b^-3//2*arctan(a^3//4*b^-1//2*x^-1*(a+b*x^2)^-1//4*(1+a^-1//2*(a+b*x^2)^(1/2))))
@test integrate(x^2*(a+-1*b*x^2)^-3//4*(2a+-1*b*x^2)^-1, x) == :(a^-1//4*b^-3//2*arctan(a^3//4*b^-1//2*x^-1*(a+-1*b*x^2)^-1//4*(1+-1*a^-1//2*(a+-1*b*x^2)^(1/2)))+-1*a^-1//4*b^-3//2*arctanh(a^3//4*b^-1//2*x^-1*(a+-1*b*x^2)^-1//4*(1+a^-1//2*(a+-1*b*x^2)^(1/2))))
@test integrate(x^7*(2+-3*x^2)^-3//4*(4+-3*x^2)^-1, x) == :(-16//405*(2+-3*x^2)^5//4+2//729*(2+-3*x^2)^9//4+56//81*(2+-3*x^2)^1//4+-16//81*2^3//4*arctan(1+(4+-6*x^2)^1//4)+-8//81*2^3//4*log(2^(1/2)+(2+-3*x^2)^(1/2)+2^3//4*(2+-3*x^2)^1//4)+8//81*2^3//4*log(2^(1/2)+(2+-3*x^2)^(1/2)+-1*2^3//4*(2+-3*x^2)^1//4)+16//81*2^3//4*arctan(1+-1*2^1//4*(2+-3*x^2)^1//4))
@test integrate(x^5*(2+-3*x^2)^-3//4*(4+-3*x^2)^-1, x) == :(-2//135*(2+-3*x^2)^5//4+4//9*(2+-3*x^2)^1//4+-4//27*2^3//4*arctan(1+(4+-6*x^2)^1//4)+-2//27*2^3//4*log(2^(1/2)+(2+-3*x^2)^(1/2)+2^3//4*(2+-3*x^2)^1//4)+2//27*2^3//4*log(2^(1/2)+(2+-3*x^2)^(1/2)+-1*2^3//4*(2+-3*x^2)^1//4)+4//27*2^3//4*arctan(1+-1*2^1//4*(2+-3*x^2)^1//4))
@test integrate(x^3*(2+-3*x^2)^-3//4*(4+-3*x^2)^-1, x) == :(2//9*(2+-3*x^2)^1//4+-1//9*2^3//4*arctan(1+(4+-6*x^2)^1//4)+-1//18*2^3//4*log(2^(1/2)+(2+-3*x^2)^(1/2)+2^3//4*(2+-3*x^2)^1//4)+1//9*2^3//4*arctan(1+-1*2^1//4*(2+-3*x^2)^1//4)+1//18*2^3//4*log(2^(1/2)+(2+-3*x^2)^(1/2)+-1*2^3//4*(2+-3*x^2)^1//4))
@test integrate(x*(2+-3*x^2)^-3//4*(4+-3*x^2)^-1, x) == :(-1//12*2^3//4*arctan(1+(4+-6*x^2)^1//4)+-1//24*2^3//4*log(2^(1/2)+(2+-3*x^2)^(1/2)+2^3//4*(2+-3*x^2)^1//4)+1//12*2^3//4*arctan(1+-1*2^1//4*(2+-3*x^2)^1//4)+1//24*2^3//4*log(2^(1/2)+(2+-3*x^2)^(1/2)+-1*2^3//4*(2+-3*x^2)^1//4))
@test integrate(x^-1*(2+-3*x^2)^-3//4*(4+-3*x^2)^-1, x) == :(-1//8*2^1//4*arctan((1/2)*2^3//4*(2+-3*x^2)^1//4)+-1//8*2^1//4*arctanh((1/2)*2^3//4*(2+-3*x^2)^1//4)+-1//16*2^3//4*arctan(1+(4+-6*x^2)^1//4)+-1//32*2^3//4*log(2^(1/2)+(2+-3*x^2)^(1/2)+2^3//4*(2+-3*x^2)^1//4)+1//16*2^3//4*arctan(1+-1*2^1//4*(2+-3*x^2)^1//4)+1//32*2^3//4*log(2^(1/2)+(2+-3*x^2)^(1/2)+-1*2^3//4*(2+-3*x^2)^1//4))
@test integrate(x^-3*(2+-3*x^2)^-3//4*(4+-3*x^2)^-1, x) == :(-15//64*2^1//4*arctan((1/2)*2^3//4*(2+-3*x^2)^1//4)+-15//64*2^1//4*arctanh((1/2)*2^3//4*(2+-3*x^2)^1//4)+-3//64*2^3//4*arctan(1+(4+-6*x^2)^1//4)+-3//128*2^3//4*log(2^(1/2)+(2+-3*x^2)^(1/2)+2^3//4*(2+-3*x^2)^1//4)+-1//16*x^-2*(2+-3*x^2)^1//4+3//64*2^3//4*arctan(1+-1*2^1//4*(2+-3*x^2)^1//4)+3//128*2^3//4*log(2^(1/2)+(2+-3*x^2)^(1/2)+-1*2^3//4*(2+-3*x^2)^1//4))
@test integrate(x^6*(2+-3*x^2)^-3//4*(4+-3*x^2)^-1, x) == :(2//63*x^3*(2+-3*x^2)^1//4+80//567*x*(2+-3*x^2)^1//4+-160//1701*2^3//4*3^(1/2)*Elliptic.F((1/2)*arcsin((1/2)*x*6^(1/2)),2)+-8//81*2^3//4*3^(1/2)*arctanh(1//3*3^(1/2)*x^-1*(2+-3*x^2)^-1//4*(2^3//4+2^1//4*(2+-3*x^2)^(1/2)))+8//81*2^3//4*3^(1/2)*arctan(1//3*3^(1/2)*x^-1*(2+-3*x^2)^-1//4*(2^3//4+-1*2^1//4*(2+-3*x^2)^(1/2))))
@test integrate(x^4*(2+-3*x^2)^-3//4*(4+-3*x^2)^-1, x) == :(2//27*x*(2+-3*x^2)^1//4+-4//81*2^3//4*3^(1/2)*Elliptic.F((1/2)*arcsin((1/2)*x*6^(1/2)),2)+-2//27*2^3//4*3^(1/2)*arctanh(1//3*3^(1/2)*x^-1*(2+-3*x^2)^-1//4*(2^3//4+2^1//4*(2+-3*x^2)^(1/2)))+2//27*2^3//4*3^(1/2)*arctan(1//3*3^(1/2)*x^-1*(2+-3*x^2)^-1//4*(2^3//4+-1*2^1//4*(2+-3*x^2)^(1/2))))
@test integrate(x^2*(2+-3*x^2)^-3//4*(4+-3*x^2)^-1, x) == :(-1//18*2^3//4*3^(1/2)*arctanh(1//6*2^3//4*3^(1/2)*x^-1*(2+-3*x^2)^-1//4*(2+2^(1/2)*(2+-3*x^2)^(1/2)))+1//18*2^3//4*3^(1/2)*arctan(1//6*2^3//4*3^(1/2)*x^-1*(2+-3*x^2)^-1//4*(2+-1*2^(1/2)*(2+-3*x^2)^(1/2))))
@test integrate((2+-3*x^2)^-3//4*(4+-3*x^2)^-1, x) == :(-1//24*2^3//4*3^(1/2)*arctanh(1//3*3^(1/2)*x^-1*(2+-3*x^2)^-1//4*(2^3//4+2^1//4*(2+-3*x^2)^(1/2)))+1//12*2^3//4*3^(1/2)*Elliptic.F((1/2)*arcsin((1/2)*x*6^(1/2)),2)+1//24*2^3//4*3^(1/2)*arctan(1//3*3^(1/2)*x^-1*(2+-3*x^2)^-1//4*(2^3//4+-1*2^1//4*(2+-3*x^2)^(1/2))))
@test integrate(x^-2*(2+-3*x^2)^-3//4*(4+-3*x^2)^-1, x) == :(-1//8*x^-1*(2+-3*x^2)^1//4+-1//32*2^3//4*3^(1/2)*arctanh(1//3*3^(1/2)*x^-1*(2+-3*x^2)^-1//4*(2^3//4+2^1//4*(2+-3*x^2)^(1/2)))+1//8*2^3//4*3^(1/2)*Elliptic.F((1/2)*arcsin((1/2)*x*6^(1/2)),2)+1//32*2^3//4*3^(1/2)*arctan(1//3*3^(1/2)*x^-1*(2+-3*x^2)^-1//4*(2^3//4+-1*2^1//4*(2+-3*x^2)^(1/2))))
@test integrate(x^-4*(2+-3*x^2)^-3//4*(4+-3*x^2)^-1, x) == :(-1//4*x^-1*(2+-3*x^2)^1//4+-1//24*x^-3*(2+-3*x^2)^1//4+-3//128*2^3//4*3^(1/2)*arctanh(1//3*3^(1/2)*x^-1*(2+-3*x^2)^-1//4*(2^3//4+2^1//4*(2+-3*x^2)^(1/2)))+3//128*2^3//4*3^(1/2)*arctan(1//3*3^(1/2)*x^-1*(2+-3*x^2)^-1//4*(2^3//4+-1*2^1//4*(2+-3*x^2)^(1/2)))+11//64*2^3//4*3^(1/2)*Elliptic.F((1/2)*arcsin((1/2)*x*6^(1/2)),2))
@test integrate(x^2*(-1+3*x^2)^-3//4*(-2+3*x^2)^-1, x) == :(-1//18*6^(1/2)*arctanh((1/2)*x*6^(1/2)*(-1+3*x^2)^-1//4)+1//18*6^(1/2)*arctan((1/2)*x*6^(1/2)*(-1+3*x^2)^-1//4))
@test integrate(x^2*(-1+-3*x^2)^-3//4*(-2+-3*x^2)^-1, x) == :(-1//18*6^(1/2)*arctanh((1/2)*x*6^(1/2)*(-1+-3*x^2)^-1//4)+1//18*6^(1/2)*arctan((1/2)*x*6^(1/2)*(-1+-3*x^2)^-1//4))
@test integrate(x^2*(-1+b*x^2)^-3//4*(-2+b*x^2)^-1, x) == :((1/2)*2^(1/2)*b^-3//2*arctan((1/2)*x*2^(1/2)*b^(1/2)*(-1+b*x^2)^-1//4)+-1//2*2^(1/2)*b^-3//2*arctanh((1/2)*x*2^(1/2)*b^(1/2)*(-1+b*x^2)^-1//4))
@test integrate(x^2*(-1+-1*b*x^2)^-3//4*(-2+-1*b*x^2)^-1, x) == :((1/2)*2^(1/2)*b^-3//2*arctan((1/2)*x*2^(1/2)*b^(1/2)*(-1+-1*b*x^2)^-1//4)+-1//2*2^(1/2)*b^-3//2*arctanh((1/2)*x*2^(1/2)*b^(1/2)*(-1+-1*b*x^2)^-1//4))
@test integrate(x^2*(-1a+3*x^2)^-3//4*(-2a+3*x^2)^-1, x) == :(-1//18*6^(1/2)*a^-1//4*arctanh((1/2)*x*6^(1/2)*a^-1//4*(-1a+3*x^2)^-1//4)+1//18*6^(1/2)*a^-1//4*arctan((1/2)*x*6^(1/2)*a^-1//4*(-1a+3*x^2)^-1//4))
@test integrate(x^2*(-1a+-3*x^2)^-3//4*(-3*x^2+-2a)^-1, x) == :(-1//18*6^(1/2)*a^-1//4*arctanh((1/2)*x*6^(1/2)*a^-1//4*(-1a+-3*x^2)^-1//4)+1//18*6^(1/2)*a^-1//4*arctan((1/2)*x*6^(1/2)*a^-1//4*(-1a+-3*x^2)^-1//4))
@test integrate(x^2*(-1a+b*x^2)^-3//4*(-2a+b*x^2)^-1, x) == :((1/2)*2^(1/2)*a^-1//4*b^-3//2*arctan((1/2)*x*2^(1/2)*a^-1//4*b^(1/2)*(-1a+b*x^2)^-1//4)+-1//2*2^(1/2)*a^-1//4*b^-3//2*arctanh((1/2)*x*2^(1/2)*a^-1//4*b^(1/2)*(-1a+b*x^2)^-1//4))
@test integrate(x^2*(-1a+-1*b*x^2)^-3//4*(-2a+-1*b*x^2)^-1, x) == :((1/2)*2^(1/2)*a^-1//4*b^-3//2*arctan((1/2)*x*2^(1/2)*a^-1//4*b^(1/2)*(-1a+-1*b*x^2)^-1//4)+-1//2*2^(1/2)*a^-1//4*b^-3//2*arctanh((1/2)*x*2^(1/2)*a^-1//4*b^(1/2)*(-1a+-1*b*x^2)^-1//4))
@test integrate(x^7*(-1+3*x^2)^-3//4*(-2+3*x^2)^-1, x) == :(-8//81*arctan((-1+3*x^2)^1//4)+-8//81*arctanh((-1+3*x^2)^1//4)+2//729*(-1+3*x^2)^9//4+8//405*(-1+3*x^2)^5//4+14//81*(-1+3*x^2)^1//4)
@test integrate(x^5*(-1+3*x^2)^-3//4*(-2+3*x^2)^-1, x) == :(-4//27*arctan((-1+3*x^2)^1//4)+-4//27*arctanh((-1+3*x^2)^1//4)+2//9*(-1+3*x^2)^1//4+2//135*(-1+3*x^2)^5//4)
@test integrate(x^3*(-1+3*x^2)^-3//4*(-2+3*x^2)^-1, x) == :(-2//9*arctan((-1+3*x^2)^1//4)+-2//9*arctanh((-1+3*x^2)^1//4)+2//9*(-1+3*x^2)^1//4)
@test integrate(x*(-1+3*x^2)^-3//4*(-2+3*x^2)^-1, x) == :(-1//3*arctan((-1+3*x^2)^1//4)+-1//3*arctanh((-1+3*x^2)^1//4))
@test integrate(x^-1*(-1+3*x^2)^-3//4*(-2+3*x^2)^-1, x) == :(-1//2*arctan((-1+3*x^2)^1//4)+-1//2*arctanh((-1+3*x^2)^1//4)+-1//4*2^(1/2)*arctan(1+2^(1/2)*(-1+3*x^2)^1//4)+-1//8*2^(1/2)*log(1+(-1+3*x^2)^(1/2)+2^(1/2)*(-1+3*x^2)^1//4)+1//4*2^(1/2)*arctan(1+-1*2^(1/2)*(-1+3*x^2)^1//4)+1//8*2^(1/2)*log(1+(-1+3*x^2)^(1/2)+-1*2^(1/2)*(-1+3*x^2)^1//4))
@test integrate(x^-3*(-1+3*x^2)^-3//4*(-2+3*x^2)^-1, x) == :(-3//4*arctan((-1+3*x^2)^1//4)+-3//4*arctanh((-1+3*x^2)^1//4)+-15//16*2^(1/2)*arctan(1+2^(1/2)*(-1+3*x^2)^1//4)+-15//32*2^(1/2)*log(1+(-1+3*x^2)^(1/2)+2^(1/2)*(-1+3*x^2)^1//4)+-1//4*x^-2*(-1+3*x^2)^1//4+15//16*2^(1/2)*arctan(1+-1*2^(1/2)*(-1+3*x^2)^1//4)+15//32*2^(1/2)*log(1+(-1+3*x^2)^(1/2)+-1*2^(1/2)*(-1+3*x^2)^1//4))
@test integrate(x^6*(-1+3*x^2)^-3//4*(-2+3*x^2)^-1, x) == :(-2//81*6^(1/2)*arctanh((1/2)*x*6^(1/2)*(-1+3*x^2)^-1//4)+2//63*x^3*(-1+3*x^2)^1//4+2//81*6^(1/2)*arctan((1/2)*x*6^(1/2)*(-1+3*x^2)^-1//4)+40//567*x*(-1+3*x^2)^1//4+40//1701*3^(1/2)*x^-1*(x^2*(1+(-1+3*x^2)^(1/2))^-2)^(1/2)*(1+(-1+3*x^2)^(1/2))*Elliptic.F(2*arctan((-1+3*x^2)^1//4),1/2))
@test integrate(x^4*(-1+3*x^2)^-3//4*(-2+3*x^2)^-1, x) == :(-1//27*6^(1/2)*arctanh((1/2)*x*6^(1/2)*(-1+3*x^2)^-1//4)+1//27*6^(1/2)*arctan((1/2)*x*6^(1/2)*(-1+3*x^2)^-1//4)+2//27*x*(-1+3*x^2)^1//4+2//81*3^(1/2)*x^-1*(x^2*(1+(-1+3*x^2)^(1/2))^-2)^(1/2)*(1+(-1+3*x^2)^(1/2))*Elliptic.F(2*arctan((-1+3*x^2)^1//4),1/2))
@test integrate(x^2*(-1+3*x^2)^-3//4*(-2+3*x^2)^-1, x) == :(-1//18*6^(1/2)*arctanh((1/2)*x*6^(1/2)*(-1+3*x^2)^-1//4)+1//18*6^(1/2)*arctan((1/2)*x*6^(1/2)*(-1+3*x^2)^-1//4))
@test integrate((-1+3*x^2)^-3//4*(-2+3*x^2)^-1, x) == :(-1//12*6^(1/2)*arctanh((1/2)*x*6^(1/2)*(-1+3*x^2)^-1//4)+1//12*6^(1/2)*arctan((1/2)*x*6^(1/2)*(-1+3*x^2)^-1//4)+-1//6*3^(1/2)*x^-1*(x^2*(1+(-1+3*x^2)^(1/2))^-2)^(1/2)*(1+(-1+3*x^2)^(1/2))*Elliptic.F(2*arctan((-1+3*x^2)^1//4),1/2))
@test integrate(x^-2*(-1+3*x^2)^-3//4*(-2+3*x^2)^-1, x) == :(-1//2*x^-1*(-1+3*x^2)^1//4+-1//8*6^(1/2)*arctanh((1/2)*x*6^(1/2)*(-1+3*x^2)^-1//4)+1//8*6^(1/2)*arctan((1/2)*x*6^(1/2)*(-1+3*x^2)^-1//4)+-1//2*3^(1/2)*x^-1*(x^2*(1+(-1+3*x^2)^(1/2))^-2)^(1/2)*(1+(-1+3*x^2)^(1/2))*Elliptic.F(2*arctan((-1+3*x^2)^1//4),1/2))
@test integrate(x^-4*(-1+3*x^2)^-3//4*(-2+3*x^2)^-1, x) == :(-2*x^-1*(-1+3*x^2)^1//4+-3//16*6^(1/2)*arctanh((1/2)*x*6^(1/2)*(-1+3*x^2)^-1//4)+-1//6*x^-3*(-1+3*x^2)^1//4+3//16*6^(1/2)*arctan((1/2)*x*6^(1/2)*(-1+3*x^2)^-1//4)+-11//8*3^(1/2)*x^-1*(x^2*(1+(-1+3*x^2)^(1/2))^-2)^(1/2)*(1+(-1+3*x^2)^(1/2))*Elliptic.F(2*arctan((-1+3*x^2)^1//4),1/2))
@test integrate((e*x)^5//2*(a+b*x^2)^-3//4*(c+d*x^2), x) == :(-3//32*a*b^-11//4*e^5//2*(-7*a*d+8*b*c)*arctanh(b^1//4*e^-1//2*(e*x)^(1/2)*(a+b*x^2)^-1//4)+1//4*d*b^-1*e^-1*(e*x)^7//2*(a+b*x^2)^1//4+1//16*e*b^-2*(e*x)^3//2*(a+b*x^2)^1//4*(-7*a*d+8*b*c)+3//32*a*b^-11//4*e^5//2*(-7*a*d+8*b*c)*arctan(b^1//4*e^-1//2*(e*x)^(1/2)*(a+b*x^2)^-1//4))
@test integrate((e*x)^(1/2)*(a+b*x^2)^-3//4*(c+d*x^2), x) == :(-1//4*b^-7//4*e^(1/2)*(-3*a*d+4*b*c)*arctan(b^1//4*e^-1//2*(e*x)^(1/2)*(a+b*x^2)^-1//4)+1//4*b^-7//4*e^(1/2)*(-3*a*d+4*b*c)*arctanh(b^1//4*e^-1//2*(e*x)^(1/2)*(a+b*x^2)^-1//4)+(1/2)*d*b^-1*e^-1*(e*x)^3//2*(a+b*x^2)^1//4)
@test integrate((e*x)^-3//2*(a+b*x^2)^-3//4*(c+d*x^2), x) == :(d*b^-3//4*e^-3//2*arctanh(b^1//4*e^-1//2*(e*x)^(1/2)*(a+b*x^2)^-1//4)+-1*d*b^-3//4*e^-3//2*arctan(b^1//4*e^-1//2*(e*x)^(1/2)*(a+b*x^2)^-1//4)+-2*c*a^-1*e^-1*(e*x)^-1//2*(a+b*x^2)^1//4)
@test integrate((e*x)^-7//2*(a+b*x^2)^-3//4*(c+d*x^2), x) == :(-2//5*c*a^-1*e^-1*(e*x)^-5//2*(a+b*x^2)^1//4+1//5*a^-2*e^-3*(e*x)^-1//2*(a+b*x^2)^1//4*(-10*a*d+8*b*c))
@test integrate((e*x)^-11//2*(a+b*x^2)^-3//4*(c+d*x^2), x) == :(-2//9*c*a^-1*e^-1*(e*x)^-9//2*(a+b*x^2)^1//4+-1//45*a^-3*e^-3*(e*x)^-5//2*(a+b*x^2)^5//4*(-72*a*d+64*b*c)+1//9*a^-2*e^-3*(e*x)^-5//2*(a+b*x^2)^1//4*(-18*a*d+16*b*c))
@test integrate((e*x)^-15//2*(a+b*x^2)^-3//4*(c+d*x^2), x) == :(-2//13*c*a^-1*e^-1*(e*x)^-13//2*(a+b*x^2)^1//4+-1//65*a^-3*e^-3*(e*x)^-9//2*(a+b*x^2)^5//4*(-208*a*d+192*b*c)+1//13*a^-2*e^-3*(e*x)^-9//2*(a+b*x^2)^1//4*(-26*a*d+24*b*c)+1//585*a^-4*e^-3*(e*x)^-9//2*(a+b*x^2)^9//4*(-832*a*d+768*b*c))
@test integrate((e*x)^7//2*(a+b*x^2)^-3//4*(c+d*x^2), x) == :(1//5*d*b^-1*e^-1*(e*x)^9//2*(a+b*x^2)^1//4+1//30*e*b^-2*(e*x)^5//2*(a+b*x^2)^1//4*(-9*a*d+10*b*c)+-1//12*a*b^-3*e^3*(e*x)^(1/2)*(a+b*x^2)^1//4*(-9*a*d+10*b*c)+-1//12*a^3//2*b^-5//2*e^2*(e*x)^3//2*(1+a*b^-1*x^-2)^3//4*(a+b*x^2)^-3//4*(-9*a*d+10*b*c)*Elliptic.F((1/2)*arccot(x*a^-1//2*b^(1/2)),2))
@test integrate((e*x)^3//2*(a+b*x^2)^-3//4*(c+d*x^2), x) == :(1//3*d*b^-1*e^-1*(e*x)^5//2*(a+b*x^2)^1//4+1//6*e*b^-2*(e*x)^(1/2)*(a+b*x^2)^1//4*(-5*a*d+6*b*c)+1//6*a^(1/2)*b^-3//2*(e*x)^3//2*(1+a*b^-1*x^-2)^3//4*(a+b*x^2)^-3//4*(-5*a*d+6*b*c)*Elliptic.F((1/2)*arccot(x*a^-1//2*b^(1/2)),2))
@test integrate((e*x)^-1//2*(a+b*x^2)^-3//4*(c+d*x^2), x) == :(d*b^-1*e^-1*(e*x)^(1/2)*(a+b*x^2)^1//4+-1*a^-1//2*b^-1//2*e^-2*(e*x)^3//2*(1+a*b^-1*x^-2)^3//4*(a+b*x^2)^-3//4*(-1*a*d+2*b*c)*Elliptic.F((1/2)*arccot(x*a^-1//2*b^(1/2)),2))
@test integrate((e*x)^-5//2*(a+b*x^2)^-3//4*(c+d*x^2), x) == :(-2//3*c*a^-1*e^-1*(e*x)^-3//2*(a+b*x^2)^1//4+2//3*a^-3//2*b^(1/2)*e^-4*(e*x)^3//2*(1+a*b^-1*x^-2)^3//4*(a+b*x^2)^-3//4*(-3*a*d+2*b*c)*Elliptic.F((1/2)*arccot(x*a^-1//2*b^(1/2)),2))
@test integrate((e*x)^-9//2*(a+b*x^2)^-3//4*(c+d*x^2), x) == :(-2//7*c*a^-1*e^-1*(e*x)^-7//2*(a+b*x^2)^1//4+1//21*a^-2*e^-3*(e*x)^-3//2*(a+b*x^2)^1//4*(-14*a*d+12*b*c)+-4//21*a^-5//2*b^3//2*e^-6*(e*x)^3//2*(1+a*b^-1*x^-2)^3//4*(a+b*x^2)^-3//4*(-7*a*d+6*b*c)*Elliptic.F((1/2)*arccot(x*a^-1//2*b^(1/2)),2))
@test integrate((e*x)^-13//2*(a+b*x^2)^-3//4*(c+d*x^2), x) == :(-2//11*c*a^-1*e^-1*(e*x)^-11//2*(a+b*x^2)^1//4+1//77*a^-2*e^-3*(e*x)^-7//2*(a+b*x^2)^1//4*(-22*a*d+20*b*c)+-4//77*b*a^-3*e^-5*(e*x)^-3//2*(a+b*x^2)^1//4*(-11*a*d+10*b*c)+8//77*a^-7//2*b^5//2*e^-8*(e*x)^3//2*(1+a*b^-1*x^-2)^3//4*(a+b*x^2)^-3//4*(-11*a*d+10*b*c)*Elliptic.F((1/2)*arccot(x*a^-1//2*b^(1/2)),2))
@test integrate((e*x)^3//2*(a+b*x^2)^-5//4*(c+d*x^2), x) == :(1//4*b^-9//4*e^3//2*(-5*a*d+4*b*c)*arctan(b^1//4*e^-1//2*(e*x)^(1/2)*(a+b*x^2)^-1//4)+1//4*b^-9//4*e^3//2*(-5*a*d+4*b*c)*arctanh(b^1//4*e^-1//2*(e*x)^(1/2)*(a+b*x^2)^-1//4)+(1/2)*d*b^-1*e^-1*(e*x)^5//2*(a+b*x^2)^-1//4+-1//2*e*b^-2*(e*x)^(1/2)*(a+b*x^2)^-1//4*(-5*a*d+4*b*c))
@test integrate((e*x)^-1//2*(a+b*x^2)^-5//4*(c+d*x^2), x) == :(d*b^-5//4*e^-1//2*arctan(b^1//4*e^-1//2*(e*x)^(1/2)*(a+b*x^2)^-1//4)+d*b^-5//4*e^-1//2*arctanh(b^1//4*e^-1//2*(e*x)^(1/2)*(a+b*x^2)^-1//4)+a^-1*b^-1*e^-1*(e*x)^(1/2)*(a+b*x^2)^-1//4*(-2*a*d+2*b*c))
@test integrate((e*x)^-5//2*(a+b*x^2)^-5//4*(c+d*x^2), x) == :(-2//3*c*a^-1*e^-1*(e*x)^-3//2*(a+b*x^2)^-1//4+-1//3*a^-2*e^-3*(e*x)^(1/2)*(a+b*x^2)^-1//4*(-6*a*d+8*b*c))
@test integrate((e*x)^-9//2*(a+b*x^2)^-5//4*(c+d*x^2), x) == :(-2//7*c*a^-1*e^-1*(e*x)^-7//2*(a+b*x^2)^-1//4+-1//7*a^-2*e^-3*(e*x)^-3//2*(a+b*x^2)^-1//4*(-14*a*d+16*b*c)+1//21*a^-3*e^-3*(e*x)^-3//2*(a+b*x^2)^3//4*(-56*a*d+64*b*c))
@test integrate((e*x)^-13//2*(a+b*x^2)^-5//4*(c+d*x^2), x) == :(-2//11*c*a^-1*e^-1*(e*x)^-11//2*(a+b*x^2)^-1//4+-1//11*a^-2*e^-3*(e*x)^-7//2*(a+b*x^2)^-1//4*(-22*a*d+24*b*c)+-1//231*a^-4*e^-3*(e*x)^-7//2*(a+b*x^2)^7//4*(-704*a*d+768*b*c)+1//33*a^-3*e^-3*(e*x)^-7//2*(a+b*x^2)^3//4*(-176*a*d+192*b*c))
@test integrate((e*x)^9//2*(a+b*x^2)^-5//4*(c+d*x^2), x) == :(1//5*d*b^-1*e^-1*(e*x)^11//2*(a+b*x^2)^-1//4+1//30*e*b^-2*(e*x)^7//2*(a+b*x^2)^-1//4*(-11*a*d+10*b*c)+-7//60*a*b^-3*e^3*(e*x)^3//2*(a+b*x^2)^-1//4*(-11*a*d+10*b*c)+-7//20*a^3//2*b^-7//2*e^4*(e*x)^(1/2)*(1+a*b^-1*x^-2)^1//4*(a+b*x^2)^-1//4*(-11*a*d+10*b*c)*Elliptic.E((1/2)*arccot(x*a^-1//2*b^(1/2)),2))
@test integrate((e*x)^5//2*(a+b*x^2)^-5//4*(c+d*x^2), x) == :(1//3*d*b^-1*e^-1*(e*x)^7//2*(a+b*x^2)^-1//4+1//6*e*b^-2*(e*x)^3//2*(a+b*x^2)^-1//4*(-7*a*d+6*b*c)+(1/2)*a^(1/2)*b^-5//2*e^2*(e*x)^(1/2)*(1+a*b^-1*x^-2)^1//4*(a+b*x^2)^-1//4*(-7*a*d+6*b*c)*Elliptic.E((1/2)*arccot(x*a^-1//2*b^(1/2)),2))
@test integrate((e*x)^(1/2)*(a+b*x^2)^-5//4*(c+d*x^2), x) == :(d*b^-1*e^-1*(e*x)^3//2*(a+b*x^2)^-1//4+-1*a^-1//2*b^-3//2*(e*x)^(1/2)*(1+a*b^-1*x^-2)^1//4*(a+b*x^2)^-1//4*(-3*a*d+2*b*c)*Elliptic.E((1/2)*arccot(x*a^-1//2*b^(1/2)),2))
@test integrate((e*x)^-3//2*(a+b*x^2)^-5//4*(c+d*x^2), x) == :(-2*c*a^-1*e^-1*(e*x)^-1//2*(a+b*x^2)^-1//4+a^-3//2*b^-1//2*e^-2*(e*x)^(1/2)*(1+a*b^-1*x^-2)^1//4*(a+b*x^2)^-1//4*(-2*a*d+4*b*c)*Elliptic.E((1/2)*arccot(x*a^-1//2*b^(1/2)),2))
@test integrate((e*x)^-7//2*(a+b*x^2)^-5//4*(c+d*x^2), x) == :(-2//5*c*a^-1*e^-1*(e*x)^-5//2*(a+b*x^2)^-1//4+1//5*a^-2*e^-3*(e*x)^-1//2*(a+b*x^2)^-1//4*(-10*a*d+12*b*c)+-4//5*a^-5//2*b^(1/2)*e^-4*(e*x)^(1/2)*(1+a*b^-1*x^-2)^1//4*(a+b*x^2)^-1//4*(-5*a*d+6*b*c)*Elliptic.E((1/2)*arccot(x*a^-1//2*b^(1/2)),2))
@test integrate((e*x)^-11//2*(a+b*x^2)^-5//4*(c+d*x^2), x) == :(-2//9*c*a^-1*e^-1*(e*x)^-9//2*(a+b*x^2)^-1//4+1//45*a^-2*e^-3*(e*x)^-5//2*(a+b*x^2)^-1//4*(-18*a*d+20*b*c)+-4//15*b*a^-3*e^-5*(e*x)^-1//2*(a+b*x^2)^-1//4*(-9*a*d+10*b*c)+8//15*a^-7//2*b^3//2*e^-6*(e*x)^(1/2)*(1+a*b^-1*x^-2)^1//4*(a+b*x^2)^-1//4*(-9*a*d+10*b*c)*Elliptic.E((1/2)*arccot(x*a^-1//2*b^(1/2)),2))
@test integrate((e*x)^5//2*(a+b*x^2)^-7//4*(c+d*x^2), x) == :(-1//4*b^-11//4*e^5//2*(-7*a*d+4*b*c)*arctan(b^1//4*e^-1//2*(e*x)^(1/2)*(a+b*x^2)^-1//4)+1//4*b^-11//4*e^5//2*(-7*a*d+4*b*c)*arctanh(b^1//4*e^-1//2*(e*x)^(1/2)*(a+b*x^2)^-1//4)+-1//6*e*a^-1*b^-2*(e*x)^3//2*(a+b*x^2)^1//4*(-7*a*d+4*b*c)+1//3*a^-1*b^-1*e^-1*(e*x)^7//2*(a+b*x^2)^-3//4*(-2*a*d+2*b*c))
@test integrate((e*x)^(1/2)*(a+b*x^2)^-7//4*(c+d*x^2), x) == :(d*b^-7//4*e^(1/2)*arctanh(b^1//4*e^-1//2*(e*x)^(1/2)*(a+b*x^2)^-1//4)+-1*d*b^-7//4*e^(1/2)*arctan(b^1//4*e^-1//2*(e*x)^(1/2)*(a+b*x^2)^-1//4)+1//3*a^-1*b^-1*e^-1*(e*x)^3//2*(a+b*x^2)^-3//4*(-2*a*d+2*b*c))
@test integrate((e*x)^-3//2*(a+b*x^2)^-7//4*(c+d*x^2), x) == :(-2*c*a^-1*e^-1*(e*x)^-1//2*(a+b*x^2)^-3//4+-1//3*a^-2*e^-3*(e*x)^3//2*(a+b*x^2)^-3//4*(-2*a*d+8*b*c))
@test integrate((e*x)^-7//2*(a+b*x^2)^-7//4*(c+d*x^2), x) == :(-2//5*c*a^-1*e^-1*(e*x)^-5//2*(a+b*x^2)^-3//4+-1//15*a^-2*e^-3*(e*x)^-1//2*(a+b*x^2)^-3//4*(-10*a*d+16*b*c)+1//15*a^-3*e^-3*(e*x)^-1//2*(a+b*x^2)^1//4*(-40*a*d+64*b*c))
@test integrate((e*x)^-11//2*(a+b*x^2)^-7//4*(c+d*x^2), x) == :(-2//9*c*a^-1*e^-1*(e*x)^-9//2*(a+b*x^2)^-3//4+-1//9*a^-2*e^-3*(e*x)^-5//2*(a+b*x^2)^-3//4*(-6*a*d+8*b*c)+-1//45*a^-4*e^-3*(e*x)^-5//2*(a+b*x^2)^5//4*(-192*a*d+256*b*c)+1//9*a^-3*e^-3*(e*x)^-5//2*(a+b*x^2)^1//4*(-48*a*d+64*b*c))
@test integrate((e*x)^7//2*(a+b*x^2)^-7//4*(c+d*x^2), x) == :(1//6*b^-3*e^3*(e*x)^(1/2)*(a+b*x^2)^1//4*(-15*a*d+10*b*c)+-1//3*e*a^-1*b^-2*(e*x)^5//2*(a+b*x^2)^1//4*(-3*a*d+2*b*c)+1//3*a^-1*b^-1*e^-1*(e*x)^9//2*(a+b*x^2)^-3//4*(-2*a*d+2*b*c)+5//6*a^(1/2)*b^-5//2*e^2*(e*x)^3//2*(1+a*b^-1*x^-2)^3//4*(a+b*x^2)^-3//4*(-3*a*d+2*b*c)*Elliptic.F((1/2)*arccot(x*a^-1//2*b^(1/2)),2))
@test integrate((e*x)^3//2*(a+b*x^2)^-7//4*(c+d*x^2), x) == :(-1//3*e*a^-1*b^-2*(e*x)^(1/2)*(a+b*x^2)^1//4*(-5*a*d+2*b*c)+1//3*a^-1*b^-1*e^-1*(e*x)^5//2*(a+b*x^2)^-3//4*(-2*a*d+2*b*c)+-1//3*a^-1//2*b^-3//2*(e*x)^3//2*(1+a*b^-1*x^-2)^3//4*(a+b*x^2)^-3//4*(-5*a*d+2*b*c)*Elliptic.F((1/2)*arccot(x*a^-1//2*b^(1/2)),2))
@test integrate((e*x)^-1//2*(a+b*x^2)^-7//4*(c+d*x^2), x) == :(1//3*a^-1*b^-1*e^-1*(e*x)^(1/2)*(a+b*x^2)^-3//4*(-2*a*d+2*b*c)+-1//3*a^-3//2*b^-1//2*e^-2*(e*x)^3//2*(1+a*b^-1*x^-2)^3//4*(a+b*x^2)^-3//4*(2*a*d+4*b*c)*Elliptic.F((1/2)*arccot(x*a^-1//2*b^(1/2)),2))
@test integrate((e*x)^-5//2*(a+b*x^2)^-7//4*(c+d*x^2), x) == :(-2//3*c*a^-1*e^-1*(e*x)^-3//2*(a+b*x^2)^-3//4+-1//3*a^-2*e^-3*(e*x)^(1/2)*(a+b*x^2)^-3//4*(-2*a*d+4*b*c)+4//3*a^-5//2*b^(1/2)*e^-4*(e*x)^3//2*(1+a*b^-1*x^-2)^3//4*(a+b*x^2)^-3//4*(-1*a*d+2*b*c)*Elliptic.F((1/2)*arccot(x*a^-1//2*b^(1/2)),2))
@test integrate((e*x)^-9//2*(a+b*x^2)^-7//4*(c+d*x^2), x) == :(-2//7*c*a^-1*e^-1*(e*x)^-7//2*(a+b*x^2)^-3//4+-1//21*a^-2*e^-3*(e*x)^-3//2*(a+b*x^2)^-3//4*(-14*a*d+20*b*c)+1//21*a^-3*e^-3*(e*x)^-3//2*(a+b*x^2)^1//4*(-28*a*d+40*b*c)+-8//21*a^-7//2*b^3//2*e^-6*(e*x)^3//2*(1+a*b^-1*x^-2)^3//4*(a+b*x^2)^-3//4*(-7*a*d+10*b*c)*Elliptic.F((1/2)*arccot(x*a^-1//2*b^(1/2)),2))
@test integrate((e*x)^7//2*(a+b*x^2)^-9//4*(c+d*x^2), x) == :(1//4*b^-13//4*e^7//2*(-9*a*d+4*b*c)*arctan(b^1//4*e^-1//2*(e*x)^(1/2)*(a+b*x^2)^-1//4)+1//4*b^-13//4*e^7//2*(-9*a*d+4*b*c)*arctanh(b^1//4*e^-1//2*(e*x)^(1/2)*(a+b*x^2)^-1//4)+-1//2*b^-3*e^3*(e*x)^(1/2)*(a+b*x^2)^-1//4*(-9*a*d+4*b*c)+-1//10*e*a^-1*b^-2*(e*x)^5//2*(a+b*x^2)^-1//4*(-9*a*d+4*b*c)+1//5*a^-1*b^-1*e^-1*(e*x)^9//2*(a+b*x^2)^-5//4*(-2*a*d+2*b*c))
@test integrate((e*x)^3//2*(a+b*x^2)^-9//4*(c+d*x^2), x) == :(d*b^-9//4*e^3//2*arctan(b^1//4*e^-1//2*(e*x)^(1/2)*(a+b*x^2)^-1//4)+d*b^-9//4*e^3//2*arctanh(b^1//4*e^-1//2*(e*x)^(1/2)*(a+b*x^2)^-1//4)+-2*d*e*b^-2*(e*x)^(1/2)*(a+b*x^2)^-1//4+1//5*a^-1*b^-1*e^-1*(e*x)^5//2*(a+b*x^2)^-5//4*(-2*a*d+2*b*c))
@test integrate((e*x)^-1//2*(a+b*x^2)^-9//4*(c+d*x^2), x) == :(1//5*a^-1*b^-1*e^-1*(e*x)^(1/2)*(a+b*x^2)^-5//4*(-2*a*d+2*b*c)+1//5*a^-2*b^-1*e^-1*(e*x)^(1/2)*(a+b*x^2)^-1//4*(2*a*d+8*b*c))
@test integrate((e*x)^-5//2*(a+b*x^2)^-9//4*(c+d*x^2), x) == :(-2//3*c*a^-1*e^-1*(e*x)^-3//2*(a+b*x^2)^-5//4+-1//15*a^-3*e^-3*(e*x)^(1/2)*(a+b*x^2)^-1//4*(-24*a*d+64*b*c)+-1//15*a^-2*e^-3*(e*x)^(1/2)*(a+b*x^2)^-5//4*(-6*a*d+16*b*c))
@test integrate((e*x)^-9//2*(a+b*x^2)^-9//4*(c+d*x^2), x) == :(-2//7*c*a^-1*e^-1*(e*x)^-7//2*(a+b*x^2)^-5//4+-1//35*a^-3*e^-3*(e*x)^-3//2*(a+b*x^2)^-1//4*(-112*a*d+192*b*c)+-1//35*a^-2*e^-3*(e*x)^-3//2*(a+b*x^2)^-5//4*(-14*a*d+24*b*c)+1//105*a^-4*e^-3*(e*x)^-3//2*(a+b*x^2)^3//4*(-448*a*d+768*b*c))
@test integrate((e*x)^-13//2*(a+b*x^2)^-9//4*(c+d*x^2), x) == :(-2//11*c*a^-1*e^-1*(e*x)^-11//2*(a+b*x^2)^-5//4+-1//55*a^-3*e^-3*(e*x)^-7//2*(a+b*x^2)^-1//4*(-264*a*d+384*b*c)+-1//55*a^-2*e^-3*(e*x)^-7//2*(a+b*x^2)^-5//4*(-22*a*d+32*b*c)+-1//385*a^-5*e^-3*(e*x)^-7//2*(a+b*x^2)^7//4*(-2816*a*d+4096*b*c)+1//55*a^-4*e^-3*(e*x)^-7//2*(a+b*x^2)^3//4*(-704*a*d+1024*b*c))
@test integrate((e*x)^13//2*(a+b*x^2)^-9//4*(c+d*x^2), x) == :(1//30*b^-3*e^3*(e*x)^7//2*(a+b*x^2)^-1//4*(-33*a*d+22*b*c)+-77//60*a*b^-4*e^5*(e*x)^3//2*(a+b*x^2)^-1//4*(-3*a*d+2*b*c)+-1//5*e*a^-1*b^-2*(e*x)^11//2*(a+b*x^2)^-1//4*(-3*a*d+2*b*c)+1//5*a^-1*b^-1*e^-1*(e*x)^15//2*(a+b*x^2)^-5//4*(-2*a*d+2*b*c)+-77//20*a^3//2*b^-9//2*e^6*(e*x)^(1/2)*(1+a*b^-1*x^-2)^1//4*(a+b*x^2)^-1//4*(-3*a*d+2*b*c)*Elliptic.E((1/2)*arccot(x*a^-1//2*b^(1/2)),2))
@test integrate((e*x)^9//2*(a+b*x^2)^-9//4*(c+d*x^2), x) == :(1//30*b^-3*e^3*(e*x)^3//2*(a+b*x^2)^-1//4*(-77*a*d+42*b*c)+-1//15*e*a^-1*b^-2*(e*x)^7//2*(a+b*x^2)^-1//4*(-11*a*d+6*b*c)+1//5*a^-1*b^-1*e^-1*(e*x)^11//2*(a+b*x^2)^-5//4*(-2*a*d+2*b*c)+7//10*a^(1/2)*b^-7//2*e^4*(e*x)^(1/2)*(1+a*b^-1*x^-2)^1//4*(a+b*x^2)^-1//4*(-11*a*d+6*b*c)*Elliptic.E((1/2)*arccot(x*a^-1//2*b^(1/2)),2))
@test integrate((e*x)^5//2*(a+b*x^2)^-9//4*(c+d*x^2), x) == :(-1//5*e*a^-1*b^-2*(e*x)^3//2*(a+b*x^2)^-1//4*(-7*a*d+2*b*c)+1//5*a^-1*b^-1*e^-1*(e*x)^7//2*(a+b*x^2)^-5//4*(-2*a*d+2*b*c)+-1//5*a^-1//2*b^-5//2*e^2*(e*x)^(1/2)*(1+a*b^-1*x^-2)^1//4*(a+b*x^2)^-1//4*(-21*a*d+6*b*c)*Elliptic.E((1/2)*arccot(x*a^-1//2*b^(1/2)),2))
@test integrate((e*x)^(1/2)*(a+b*x^2)^-9//4*(c+d*x^2), x) == :(1//5*a^-1*b^-1*e^-1*(e*x)^3//2*(a+b*x^2)^-5//4*(-2*a*d+2*b*c)+-1//5*a^-3//2*b^-3//2*(e*x)^(1/2)*(1+a*b^-1*x^-2)^1//4*(a+b*x^2)^-1//4*(4*b*c+6*a*d)*Elliptic.E((1/2)*arccot(x*a^-1//2*b^(1/2)),2))
@test integrate((e*x)^-3//2*(a+b*x^2)^-9//4*(c+d*x^2), x) == :(-2*c*a^-1*e^-1*(e*x)^-1//2*(a+b*x^2)^-5//4+-1//5*a^-2*e^-3*(e*x)^3//2*(a+b*x^2)^-5//4*(-2*a*d+12*b*c)+1//5*a^-5//2*b^-1//2*e^-2*(e*x)^(1/2)*(1+a*b^-1*x^-2)^1//4*(a+b*x^2)^-1//4*(-4*a*d+24*b*c)*Elliptic.E((1/2)*arccot(x*a^-1//2*b^(1/2)),2))
@test integrate((e*x)^-7//2*(a+b*x^2)^-9//4*(c+d*x^2), x) == :(-2//5*c*a^-1*e^-1*(e*x)^-5//2*(a+b*x^2)^-5//4+-1//5*a^-2*e^-3*(e*x)^-1//2*(a+b*x^2)^-5//4*(-2*a*d+4*b*c)+1//5*a^-3*e^-3*(e*x)^-1//2*(a+b*x^2)^-1//4*(-12*a*d+24*b*c)+-24//5*a^-7//2*b^(1/2)*e^-4*(e*x)^(1/2)*(1+a*b^-1*x^-2)^1//4*(a+b*x^2)^-1//4*(-1*a*d+2*b*c)*Elliptic.E((1/2)*arccot(x*a^-1//2*b^(1/2)),2))
@test integrate((e*x)^-11//2*(a+b*x^2)^-9//4*(c+d*x^2), x) == :(-2//9*c*a^-1*e^-1*(e*x)^-9//2*(a+b*x^2)^-5//4+-1//45*a^-2*e^-3*(e*x)^-5//2*(a+b*x^2)^-5//4*(-18*a*d+28*b*c)+1//45*a^-3*e^-3*(e*x)^-5//2*(a+b*x^2)^-1//4*(-36*a*d+56*b*c)+-8//15*b*a^-4*e^-5*(e*x)^-1//2*(a+b*x^2)^-1//4*(-9*a*d+14*b*c)+16//15*a^-9//2*b^3//2*e^-6*(e*x)^(1/2)*(1+a*b^-1*x^-2)^1//4*(a+b*x^2)^-1//4*(-9*a*d+14*b*c)*Elliptic.E((1/2)*arccot(x*a^-1//2*b^(1/2)),2))

max_stars_repo_path: test/1 Algebraic functions/1.1 Binomial products/1.1.2 Quadratic/1.1.2.4 (e x)^m (a+b x^2)^p (c+d x^2)^q.jl