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

@test integrate((c+d*x^2)^4*(a+b*x^2), x) == :(a*x*c^4+1//3*c^3*x^3*(b*c+4*a*d)+1//9*d^3*x^9*(a*d+4*b*c)+1//11*b*d^4*x^11+2//5*d*c^2*x^5*(2*b*c+3*a*d)+2//7*c*d^2*x^7*(2*a*d+3*b*c))
@test integrate((c+d*x^2)^3*(a+b*x^2), x) == :(a*x*c^3+1//3*c^2*x^3*(b*c+3*a*d)+1//7*d^2*x^7*(a*d+3*b*c)+1//9*b*d^3*x^9+3//5*c*d*x^5*(a*d+b*c))
@test integrate((c+d*x^2)^2*(a+b*x^2), x) == :(a*x*c^2+1//3*c*x^3*(b*c+2*a*d)+1//5*d*x^5*(a*d+2*b*c)+1//7*b*d^2*x^7)
@test integrate((a+b*x^2)*(c+d*x^2), x) == :(x^3*(1//3*a*d+1//3*b*c)+a*c*x+1//5*b*d*x^5)
@test integrate((c+d*x^2)^-1*(a+b*x^2), x) == :(b*x*d^-1+-1*c^-1//2*d^-3//2*(b*c+-1*a*d)*arctan(x*c^-1//2*d^(1/2)))
@test integrate((c+d*x^2)^-2*(a+b*x^2), x) == :((1/2)*c^-3//2*d^-3//2*(a*d+b*c)*arctan(x*c^-1//2*d^(1/2))+-1//2*x*c^-1*d^-1*(c+d*x^2)^-1*(b*c+-1*a*d))
@test integrate((c+d*x^2)^-3*(a+b*x^2), x) == :(1//8*c^-5//2*d^-3//2*(b*c+3*a*d)*arctan(x*c^-1//2*d^(1/2))+-1//4*x*c^-1*d^-1*(c+d*x^2)^-2*(b*c+-1*a*d)+1//8*x*c^-2*d^-1*(c+d*x^2)^-1*(b*c+3*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((a+b*x^2)^2*(c+d*x^2)^2, x) == :(x^5*(1//5*a^2*d^2+1//5*b^2*c^2+4//5*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((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((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((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((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((a+b*x^2)^3*(c+d*x^2)^3, x) == :(x*a^3*c^3+x^7*(1//7*a*d+1//7*b*c)*(a^2*d^2+b^2*c^2+8*a*b*c*d)+1//13*b^3*d^3*x^13+a^2*c^2*x^3*(a*d+b*c)+1//3*b*d*x^9*(a^2*d^2+b^2*c^2+3*a*b*c*d)+3//5*a*c*x^5*(a^2*d^2+b^2*c^2+3*a*b*c*d)+3//11*b^2*d^2*x^11*(a*d+b*c))
@test integrate((a+b*x^2)^3*(c+d*x^2)^2, x) == :(x*a^3*c^2+1//5*a*x^5*(a^2*d^2+3*b^2*c^2+6*a*b*c*d)+1//7*b*x^7*(b^2*c^2+3*a^2*d^2+6*a*b*c*d)+1//11*b^3*d^2*x^11+1//3*c*a^2*x^3*(2*a*d+3*b*c)+1//9*d*b^2*x^9*(2*b*c+3*a*d))
@test integrate((a+b*x^2)^3*(c+d*x^2), x) == :(c*x*a^3+1//3*a^2*x^3*(a*d+3*b*c)+1//7*b^2*x^7*(b*c+3*a*d)+1//9*d*b^3*x^9+3//5*a*b*x^5*(a*d+b*c))
@test integrate((a+b*x^2)^3*(c+d*x^2)^-1, x) == :(1//5*b^3*d^-1*x^5+b*x*d^-3*(b^2*c^2+3*a^2*d^2+-3*a*b*c*d)+-1*c^-1//2*d^-7//2*(b*c+-1*a*d)^3*arctan(x*c^-1//2*d^(1/2))+-1//3*b^2*d^-2*x^3*(b*c+-3*a*d))
@test integrate((a+b*x^2)^3*(c+d*x^2)^-2, x) == :(1//3*b^3*d^-2*x^3+-1*x*b^2*d^-3*(-3*a*d+2*b*c)+(1/2)*c^-3//2*d^-7//2*(b*c+-1*a*d)^2*(a*d+5*b*c)*arctan(x*c^-1//2*d^(1/2))+-1//2*x*c^-1*d^-3*(c+d*x^2)^-1*(b*c+-1*a*d)^3)
@test integrate((a+b*x^2)^3*(c+d*x^2)^-3, x) == :(x*b^3*d^-3+-1//4*x*c^-1*d^-3*(c+d*x^2)^-2*(b*c+-1*a*d)^3+-1//8*c^-5//2*d^-7//2*((a*d+b*c)^2+4*b^2*c^2)*(-3*a*d+3*b*c)*arctan(x*c^-1//2*d^(1/2))+3//8*x*c^-2*d^-3*(c+d*x^2)^-1*(b*c+-1*a*d)^2*(a*d+3*b*c))
@test integrate((a+b*x^2)^-1*(c+d*x^2)^4, x) == :(1//7*b^-1*d^4*x^7+a^-1//2*b^-9//2*(b*c+-1*a*d)^4*arctan(x*a^-1//2*b^(1/2))+1//3*b^-3*d^2*x^3*(a^2*d^2+6*b^2*c^2+-4*a*b*c*d)+1//5*b^-2*d^3*x^5*(-1*a*d+4*b*c)+d*x*b^-4*(-1*a*d+2*b*c)*(a^2*d^2+2*b^2*c^2+-2*a*b*c*d))
@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((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((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((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((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((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((a+b*x^2)^-2*(c+d*x^2)^5, x) == :(1//7*b^-2*d^5*x^7+x*b^-5*d^2*(-4*a^3*d^3+10*b^3*c^3+-20*a*d*b^2*c^2+15*b*c*a^2*d^2)+1//3*b^-4*d^3*x^3*(3*a^2*d^2+10*b^2*c^2+-10*a*b*c*d)+1//5*b^-3*d^4*x^5*(-2*a*d+5*b*c)+(1/2)*x*a^-1*b^-5*(a+b*x^2)^-1*(b*c+-1*a*d)^5+(1/2)*a^-3//2*b^-11//2*(b*c+-1*a*d)^4*(b*c+9*a*d)*arctan(x*a^-1//2*b^(1/2)))
@test integrate((a+b*x^2)^-2*(c+d*x^2)^4, x) == :(1//5*b^-2*d^4*x^5+x*b^-4*d^2*(3*a^2*d^2+6*b^2*c^2+-8*a*b*c*d)+2//3*b^-3*d^3*x^3*(-1*a*d+2*b*c)+(1/2)*x*a^-1*b^-4*(a+b*x^2)^-1*(b*c+-1*a*d)^4+(1/2)*a^-3//2*b^-9//2*(b*c+-1*a*d)^3*(b*c+7*a*d)*arctan(x*a^-1//2*b^(1/2)))
@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((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((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((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((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((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((a+b*x^2)^-3*(c+d*x^2)^5, x) == :(1//5*b^-3*d^5*x^5+x*b^-5*d^3*(6*a^2*d^2+10*b^2*c^2+-15*a*b*c*d)+1//3*b^-4*d^4*x^3*(-3*a*d+5*b*c)+1//4*x*a^-1*b^-5*(a+b*x^2)^-2*(b*c+-1*a*d)^5+1//8*a^-5//2*b^-11//2*(b*c+-1*a*d)^3*(3*b^2*c^2+63*a^2*d^2+14*a*b*c*d)*arctan(x*a^-1//2*b^(1/2))+1//8*x*a^-2*b^-5*(a+b*x^2)^-1*(b*c+-1*a*d)^4*(3*b*c+17*a*d))
@test integrate((a+b*x^2)^-3*(c+d*x^2)^4, x) == :(1//3*b^-3*d^4*x^3+x*b^-4*d^3*(-3*a*d+4*b*c)+1//4*x*a^-1*b^-4*(a+b*x^2)^-2*(b*c+-1*a*d)^4+1//8*a^-5//2*b^-9//2*(b*c+-1*a*d)^2*(3*b^2*c^2+35*a^2*d^2+10*a*b*c*d)*arctan(x*a^-1//2*b^(1/2))+1//8*x*a^-2*b^-4*(a+b*x^2)^-1*(b*c+-1*a*d)^3*(3*b*c+13*a*d))
@test integrate((a+b*x^2)^-3*(c+d*x^2)^3, x) == :(x*b^-3*d^3+1//4*x*a^-1*b^-3*(a+b*x^2)^-2*(b*c+-1*a*d)^3+1//8*a^-5//2*b^-7//2*((a*d+b*c)^2+4*a^2*d^2)*(-3*a*d+3*b*c)*arctan(x*a^-1//2*b^(1/2))+3//8*x*a^-2*b^-3*(a+b*x^2)^-1*(b*c+-1*a*d)^2*(b*c+3*a*d))
@test integrate((a+b*x^2)^-3*(c+d*x^2)^2, x) == :(x*(8a+8*b*x^2)^-1*(-3*b^-2*d^2+3*a^-2*c^2)+1//8*a^-5//2*b^-5//2*(3*a^2*d^2+3*b^2*c^2+2*a*b*c*d)*arctan(x*a^-1//2*b^(1/2))+1//4*x*a^-1*b^-1*(a+b*x^2)^-2*(c+d*x^2)*(b*c+-1*a*d))
@test integrate((a+b*x^2)^-3*(c+d*x^2), x) == :(1//8*a^-5//2*b^-3//2*(a*d+3*b*c)*arctan(x*a^-1//2*b^(1/2))+1//4*x*a^-1*b^-1*(a+b*x^2)^-2*(b*c+-1*a*d)+1//8*x*a^-2*b^-1*(a+b*x^2)^-1*(a*d+3*b*c))
@test integrate((a+b*x^2)^-3*(c+d*x^2)^-1, x) == :(-1*c^-1//2*d^5//2*(b*c+-1*a*d)^-3*arctan(x*c^-1//2*d^(1/2))+1//4*b*x*a^-1*(a+b*x^2)^-2*(b*c+-1*a*d)^-1+1//8*a^-5//2*b^(1/2)*(b*c+-1*a*d)^-3*(3*b^2*c^2+15*a^2*d^2+-10*a*b*c*d)*arctan(x*a^-1//2*b^(1/2))+1//8*b*x*a^-2*(a+b*x^2)^-1*(b*c+-1*a*d)^-2*(-7*a*d+3*b*c))
@test integrate((a+b*x^2)^-3*(c+d*x^2)^-2, x) == :(-1//2*c^-3//2*d^5//2*(b*c+-1*a*d)^-4*(-1*a*d+7*b*c)*arctan(x*c^-1//2*d^(1/2))+1//8*a^-5//2*b^3//2*(b*c+-1*a*d)^-4*(3*b^2*c^2+35*a^2*d^2+-14*a*b*c*d)*arctan(x*a^-1//2*b^(1/2))+1//4*b*x*a^-1*(a+b*x^2)^-2*(c+d*x^2)^-1*(b*c+-1*a*d)^-1+3//8*b*x*a^-2*(a+b*x^2)^-1*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(b*c+-3*a*d)+1//8*d*x*a^-2*c^-1*(c+d*x^2)^-1*(b*c+-1*a*d)^-3*(a*d+3*b*c)*(b*c+-4*a*d))
@test integrate((a+b*x^2)^-3*(c+d*x^2)^-3, x) == :(-3//8*c^-5//2*d^5//2*(b*c+-1*a*d)^-5*(a^2*d^2+21*b^2*c^2+-6*a*b*c*d)*arctan(x*c^-1//2*d^(1/2))+3//8*a^-5//2*b^5//2*(b*c+-1*a*d)^-5*(b^2*c^2+21*a^2*d^2+-6*a*b*c*d)*arctan(x*a^-1//2*b^(1/2))+1//4*b*x*a^-1*(a+b*x^2)^-2*(c+d*x^2)^-2*(b*c+-1*a*d)^-1+1//8*b*x*a^-2*(a+b*x^2)^-1*(c+d*x^2)^-2*(b*c+-1*a*d)^-2*(-11*a*d+3*b*c)+1//8*d*x*a^-2*c^-1*(c+d*x^2)^-2*(b*c+-1*a*d)^-3*(-2*a^2*d^2+3*b^2*c^2+-13*a*b*c*d)+3//8*d*x*a^-2*c^-2*(c+d*x^2)^-1*(b*c+-1*a*d)^-4*(a*d+b*c)*(a^2*d^2+b^2*c^2+-6*a*b*c*d))
@test integrate((1+x^2)^-4*(-1+x^2)^3, x) == :(-2*x*(3+3*x^2)^-1+-1//3*x*(1+x^2)^-3*(1+-1*x^2)^2)
@test integrate((1+x^2)^-5*(-1+x^2)^4, x) == :(3//8*arctan(x)+1//4*x*(1+x^2)^-4*(1+-1*x^2)^3+3//8*x*(1+x^2)^-2*(1+-1*x^2))
@test integrate((a+b*x^2)^(1/2)*(c+d*x^2)^3, x) == :(1//128*a*b^-7//2*(-5*a^3*d^3+64*b^3*c^3+-48*a*d*b^2*c^2+24*b*c*a^2*d^2)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+1//128*x*b^-3*(a+b*x^2)^(1/2)*(-5*a^3*d^3+64*b^3*c^3+-48*a*d*b^2*c^2+24*b*c*a^2*d^2)+1//8*d*x*b^-1*(a+b*x^2)^3//2*(c+d*x^2)^2+1//192*d*x*b^-3*(a+b*x^2)^3//2*(15*a^2*d^2+72*b^2*c^2+-52*a*b*c*d)+1//48*d*x*b^-2*(a+b*x^2)^3//2*(c+d*x^2)*(-5*a*d+12*b*c))
@test integrate((a+b*x^2)^(1/2)*(c+d*x^2)^2, x) == :(1//16*a*b^-5//2*(a^2*d^2+8*b^2*c^2+-4*a*b*c*d)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+1//16*x*b^-2*(a+b*x^2)^(1/2)*(a^2*d^2+8*b^2*c^2+-4*a*b*c*d)+1//6*d*x*b^-1*(a+b*x^2)^3//2*(c+d*x^2)+1//24*d*x*b^-2*(a+b*x^2)^3//2*(-3*a*d+8*b*c))
@test integrate((a+b*x^2)^(1/2)*(c+d*x^2), x) == :(1//4*d*x*b^-1*(a+b*x^2)^3//2+1//8*a*b^-3//2*(-1*a*d+4*b*c)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+1//8*x*b^-1*(a+b*x^2)^(1/2)*(-1*a*d+4*b*c))
@test integrate((a+b*x^2)^(1/2), x) == :((1/2)*x*(a+b*x^2)^(1/2)+(1/2)*a*b^-1//2*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2))
@test integrate((a+b*x^2)^(1/2)*(c+d*x^2)^-1, x) == :(b^(1/2)*d^-1*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+-1*c^-1//2*d^-1*(b*c+-1*a*d)^(1/2)*arctanh(x*c^-1//2*(a+b*x^2)^-1//2*(b*c+-1*a*d)^(1/2)))
@test integrate((a+b*x^2)^(1/2)*(c+d*x^2)^-2, x) == :((1/2)*a*c^-3//2*(b*c+-1*a*d)^-1//2*arctanh(x*c^-1//2*(a+b*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+(1/2)*x*c^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^-1)
@test integrate((a+b*x^2)^(1/2)*(c+d*x^2)^-3, x) == :(1//8*a*c^-5//2*(b*c+-1*a*d)^-3//2*(-3*a*d+4*b*c)*arctanh(x*c^-1//2*(a+b*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+-1//4*d*x*c^-1*(a+b*x^2)^3//2*(c+d*x^2)^-2*(b*c+-1*a*d)^-1+1//8*x*c^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1*(b*c+-1*a*d)^-1*(-3*a*d+4*b*c))
@test integrate((a+b*x^2)^(1/2)*(c+d*x^2)^-4, x) == :(1//6*x*c^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^-3+1//16*a*c^-7//2*(b*c+-1*a*d)^-5//2*(5*a^2*d^2+8*b^2*c^2+-12*a*b*c*d)*arctanh(x*c^-1//2*(a+b*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+1//24*x*c^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^-2*(b*c+-1*a*d)^-1*(-5*a*d+4*b*c)+1//48*x*c^-3*(a+b*x^2)^(1/2)*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(-5*a*d+2*b*c)*(-3*a*d+4*b*c))
@test integrate((a+b*x^2)^3//2*(c+d*x^2)^3, x) == :(1//10*d*x*b^-1*(a+b*x^2)^5//2*(c+d*x^2)^2+1//128*x*b^-3*(a+b*x^2)^3//2*(-1*a*d+4*b*c)*(a^2*d^2+8*b^2*c^2+-2*a*b*c*d)+1//160*d*x*b^-3*(a+b*x^2)^5//2*(5*a^2*d^2+36*b^2*c^2+-20*a*b*c*d)+3//256*a^2*b^-7//2*(-1*a*d+4*b*c)*(a^2*d^2+8*b^2*c^2+-2*a*b*c*d)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+1//80*d*x*b^-2*(a+b*x^2)^5//2*(c+d*x^2)*(-5*a*d+14*b*c)+3//256*a*x*b^-3*(a+b*x^2)^(1/2)*(-1*a*d+4*b*c)*(a^2*d^2+8*b^2*c^2+-2*a*b*c*d))
@test integrate((a+b*x^2)^3//2*(c+d*x^2)^2, x) == :(1//128*a^2*b^-5//2*(3*a^2*d^2+48*b^2*c^2+-16*a*b*c*d)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+1//192*x*b^-2*(a+b*x^2)^3//2*(3*a^2*d^2+48*b^2*c^2+-16*a*b*c*d)+1//8*d*x*b^-1*(a+b*x^2)^5//2*(c+d*x^2)+1//48*d*x*b^-2*(a+b*x^2)^5//2*(-3*a*d+10*b*c)+1//128*a*x*b^-2*(a+b*x^2)^(1/2)*(3*a^2*d^2+48*b^2*c^2+-16*a*b*c*d))
@test integrate((a+b*x^2)^3//2*(c+d*x^2), x) == :(1//6*d*x*b^-1*(a+b*x^2)^5//2+1//16*a^2*b^-3//2*(-1*a*d+6*b*c)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+1//24*x*b^-1*(a+b*x^2)^3//2*(-1*a*d+6*b*c)+1//16*a*x*b^-1*(a+b*x^2)^(1/2)*(-1*a*d+6*b*c))
@test integrate((a+b*x^2)^3//2, x) == :(1//4*x*(a+b*x^2)^3//2+3//8*a*x*(a+b*x^2)^(1/2)+3//8*a^2*b^-1//2*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2))
@test integrate((a+b*x^2)^3//2*(c+d*x^2)^-1, x) == :(c^-1//2*d^-2*(b*c+-1*a*d)^3//2*arctanh(x*c^-1//2*(a+b*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+(1/2)*b*x*d^-1*(a+b*x^2)^(1/2)+-1//2*b^(1/2)*d^-2*(-3*a*d+2*b*c)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2))
@test integrate((a+b*x^2)^3//2*(c+d*x^2)^-2, x) == :(b^3//2*d^-2*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+-1//2*c^-3//2*d^-2*(b*c+-1*a*d)^(1/2)*(a*d+2*b*c)*arctanh(x*c^-1//2*(a+b*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+-1//2*x*c^-1*d^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^-1*(b*c+-1*a*d))
@test integrate((a+b*x^2)^3//2*(c+d*x^2)^-3, x) == :(1//4*x*c^-1*(a+b*x^2)^3//2*(c+d*x^2)^-2+3//8*a^2*c^-5//2*(b*c+-1*a*d)^-1//2*arctanh(x*c^-1//2*(a+b*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+3//8*a*x*c^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1)
@test integrate((a+b*x^2)^3//2*(c+d*x^2)^-4, x) == :(1//16*a^2*c^-7//2*(b*c+-1*a*d)^-3//2*(-5*a*d+6*b*c)*arctanh(x*c^-1//2*(a+b*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+-1//6*d*x*c^-1*(a+b*x^2)^5//2*(c+d*x^2)^-3*(b*c+-1*a*d)^-1+1//24*x*c^-2*(a+b*x^2)^3//2*(c+d*x^2)^-2*(b*c+-1*a*d)^-1*(-5*a*d+6*b*c)+1//16*a*x*c^-3*(a+b*x^2)^(1/2)*(c+d*x^2)^-1*(b*c+-1*a*d)^-1*(-5*a*d+6*b*c))
@test integrate((a+b*x^2)^3//2*(c+d*x^2)^-5, x) == :(1//128*a^2*c^-9//2*(b*c+-1*a*d)^-5//2*(35*a^2*d^2+48*b^2*c^2+-80*a*b*c*d)*arctanh(x*c^-1//2*(a+b*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+-1//8*x*c^-1*d^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^-4*(b*c+-1*a*d)+1//48*x*c^-2*d^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^-3*(2*b*c+7*a*d)+1//192*x*c^-3*d^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^-2*(b*c+-1*a*d)^-1*(-35*a^2*d^2+8*b^2*c^2+24*a*b*c*d)+1//384*x*c^-4*d^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(16*b^3*c^3+105*a^3*d^3+-170*b*c*a^2*d^2+40*a*d*b^2*c^2))
@test integrate((a+b*x^2)^5//2*(c+d*x^2)^3, x) == :(1//1024*a^3*b^-7//2*(-5*a^3*d^3+320*b^3*c^3+-120*a*d*b^2*c^2+36*b*c*a^2*d^2)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+1//1920*x*b^-3*(a+b*x^2)^5//2*(-5*a^3*d^3+320*b^3*c^3+-120*a*d*b^2*c^2+36*b*c*a^2*d^2)+1//12*d*x*b^-1*(a+b*x^2)^7//2*(c+d*x^2)^2+1//960*d*x*b^-3*(a+b*x^2)^7//2*(15*a^2*d^2+152*b^2*c^2+-68*a*b*c*d)+1//1024*x*a^2*b^-3*(a+b*x^2)^(1/2)*(-5*a^3*d^3+320*b^3*c^3+-120*a*d*b^2*c^2+36*b*c*a^2*d^2)+1//1536*a*x*b^-3*(a+b*x^2)^3//2*(-5*a^3*d^3+320*b^3*c^3+-120*a*d*b^2*c^2+36*b*c*a^2*d^2)+1//120*d*x*b^-2*(a+b*x^2)^7//2*(c+d*x^2)*(-5*a*d+16*b*c))
@test integrate((a+b*x^2)^5//2*(c+d*x^2)^2, x) == :(1//256*a^3*b^-5//2*(3*a^2*d^2+80*b^2*c^2+-20*a*b*c*d)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+1//480*x*b^-2*(a+b*x^2)^5//2*(3*a^2*d^2+80*b^2*c^2+-20*a*b*c*d)+1//10*d*x*b^-1*(a+b*x^2)^7//2*(c+d*x^2)+1//256*x*a^2*b^-2*(a+b*x^2)^(1/2)*(3*a^2*d^2+80*b^2*c^2+-20*a*b*c*d)+1//384*a*x*b^-2*(a+b*x^2)^3//2*(3*a^2*d^2+80*b^2*c^2+-20*a*b*c*d)+3//80*d*x*b^-2*(a+b*x^2)^7//2*(-1*a*d+4*b*c))
@test integrate((a+b*x^2)^5//2*(c+d*x^2), x) == :(1//8*d*x*b^-1*(a+b*x^2)^7//2+1//48*x*b^-1*(a+b*x^2)^5//2*(-1*a*d+8*b*c)+5//128*a^3*b^-3//2*(-1*a*d+8*b*c)*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*a*d+8*b*c)+5//192*a*x*b^-1*(a+b*x^2)^3//2*(-1*a*d+8*b*c))
@test integrate((a+b*x^2)^5//2, x) == :(1//6*x*(a+b*x^2)^5//2+5//16*x*a^2*(a+b*x^2)^(1/2)+5//16*a^3*b^-1//2*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+5//24*a*x*(a+b*x^2)^3//2)
@test integrate((a+b*x^2)^5//2*(c+d*x^2)^-1, x) == :(-1*c^-1//2*d^-3*(b*c+-1*a*d)^5//2*arctanh(x*c^-1//2*(a+b*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+1//4*b*x*d^-1*(a+b*x^2)^3//2+1//8*b^(1/2)*d^-3*(8*b^2*c^2+15*a^2*d^2+-20*a*b*c*d)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+-1//8*b*x*d^-2*(a+b*x^2)^(1/2)*(-7*a*d+4*b*c))
@test integrate((a+b*x^2)^5//2*(c+d*x^2)^-2, x) == :(-1//2*b^3//2*d^-3*(-5*a*d+4*b*c)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+(1/2)*c^-3//2*d^-3*(b*c+-1*a*d)^3//2*(a*d+4*b*c)*arctanh(x*c^-1//2*(a+b*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+(1/2)*b*x*c^-1*d^-2*(a+b*x^2)^(1/2)*(-1*a*d+2*b*c)+-1//2*x*c^-1*d^-1*(a+b*x^2)^3//2*(c+d*x^2)^-1*(b*c+-1*a*d))
@test integrate((a+b*x^2)^5//2*(c+d*x^2)^-3, x) == :(b^5//2*d^-3*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+-1//8*c^-5//2*d^-3*(b*c+-1*a*d)^(1/2)*(3*a^2*d^2+8*b^2*c^2+4*a*b*c*d)*arctanh(x*c^-1//2*(a+b*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+-1//4*x*c^-1*d^-1*(a+b*x^2)^3//2*(c+d*x^2)^-2*(b*c+-1*a*d)+-1//8*x*c^-2*d^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1*(b*c+-1*a*d)*(3*a*d+4*b*c))
@test integrate((a+b*x^2)^5//2*(c+d*x^2)^-4, x) == :(1//6*x*c^-1*(a+b*x^2)^5//2*(c+d*x^2)^-3+5//16*a^3*c^-7//2*(b*c+-1*a*d)^-1//2*arctanh(x*c^-1//2*(a+b*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+5//16*x*a^2*c^-3*(a+b*x^2)^(1/2)*(c+d*x^2)^-1+5//24*a*x*c^-2*(a+b*x^2)^3//2*(c+d*x^2)^-2)
@test integrate((a+b*x^2)^5//2*(c+d*x^2)^-5, x) == :(5//128*a^3*c^-9//2*(b*c+-1*a*d)^-3//2*(-7*a*d+8*b*c)*arctanh(x*c^-1//2*(a+b*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+-1//8*d*x*c^-1*(a+b*x^2)^7//2*(c+d*x^2)^-4*(b*c+-1*a*d)^-1+1//48*x*c^-2*(a+b*x^2)^5//2*(c+d*x^2)^-3*(b*c+-1*a*d)^-1*(-7*a*d+8*b*c)+5//128*x*a^2*c^-4*(a+b*x^2)^(1/2)*(c+d*x^2)^-1*(b*c+-1*a*d)^-1*(-7*a*d+8*b*c)+5//192*a*x*c^-3*(a+b*x^2)^3//2*(c+d*x^2)^-2*(b*c+-1*a*d)^-1*(-7*a*d+8*b*c))
@test integrate((1+x^2)^-1*(1+-1*x^2)^(1/2), x) == :(-1*arcsin(x)+2^(1/2)*arctan(x*2^(1/2)*(1+-1*x^2)^-1//2))
@test integrate((1+x^2)^(1/2)*(-1+x^2)^-1, x) == :(-1*2^(1/2)*arctanh(x*2^(1/2)*(1+x^2)^-1//2)+arcsinh(x))
@test integrate((1+-1*x^2)^(1/2)*(-1+2*x^2)^-1, x) == :(-1//2*arcsin(x)+-1//2*arctanh(x*(1+-1*x^2)^-1//2))
@test integrate((a+b*x^2)^-1//2*(c+d*x^2)^3, x) == :(1//16*b^-7//2*(-1*a*d+2*b*c)*(5*a^2*d^2+8*b^2*c^2+-8*a*b*c*d)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+1//6*d*x*b^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^2+1//48*d*x*b^-3*(a+b*x^2)^(1/2)*(15*a^2*d^2+44*b^2*c^2+-44*a*b*c*d)+5//24*d*x*b^-2*(a+b*x^2)^(1/2)*(c+d*x^2)*(-1*a*d+2*b*c))
@test integrate((a+b*x^2)^-1//2*(c+d*x^2)^2, x) == :(1//8*b^-5//2*(3*a^2*d^2+8*b^2*c^2+-8*a*b*c*d)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+1//4*d*x*b^-1*(a+b*x^2)^(1/2)*(c+d*x^2)+3//8*d*x*b^-2*(a+b*x^2)^(1/2)*(-1*a*d+2*b*c))
@test integrate((a+b*x^2)^-1//2*(c+d*x^2), x) == :((1/2)*b^-3//2*(-1*a*d+2*b*c)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+(1/2)*d*x*b^-1*(a+b*x^2)^(1/2))
@test integrate((a+b*x^2)^-1//2, x) == :(b^-1//2*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2))
@test integrate((a+b*x^2)^-1//2*(c+d*x^2)^-1, x) == :(c^-1//2*(b*c+-1*a*d)^-1//2*arctanh(x*c^-1//2*(a+b*x^2)^-1//2*(b*c+-1*a*d)^(1/2)))
@test integrate((a+b*x^2)^-1//2*(c+d*x^2)^-2, x) == :((1/2)*c^-3//2*(b*c+-1*a*d)^-3//2*(-1*a*d+2*b*c)*arctanh(x*c^-1//2*(a+b*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+-1//2*d*x*c^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^-1*(b*c+-1*a*d)^-1)
@test integrate((a+b*x^2)^-1//2*(c+d*x^2)^-3, x) == :(1//8*c^-5//2*(b*c+-1*a*d)^-5//2*(3*a^2*d^2+8*b^2*c^2+-8*a*b*c*d)*arctanh(x*c^-1//2*(a+b*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+-1//4*d*x*c^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^-2*(b*c+-1*a*d)^-1+-3//8*d*x*c^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(-1*a*d+2*b*c))
@test integrate((a+b*x^2)^-3//2*(c+d*x^2)^4, x) == :(1//16*d*b^-9//2*(-35*a^3*d^3+64*b^3*c^3+-144*a*d*b^2*c^2+120*b*c*a^2*d^2)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+x*a^-1*b^-1*(a+b*x^2)^-1//2*(c+d*x^2)^3*(b*c+-1*a*d)+-1//48*d*x*a^-1*b^-4*(a+b*x^2)^(1/2)*(-105*a^3*d^3+48*b^3*c^3+-248*a*d*b^2*c^2+290*b*c*a^2*d^2)+-1//6*d*x*a^-1*b^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^2*(-7*a*d+6*b*c)+-1//24*d*x*a^-1*b^-3*(a+b*x^2)^(1/2)*(c+d*x^2)*(24*b^2*c^2+35*a^2*d^2+-64*a*b*c*d))
@test integrate((a+b*x^2)^-3//2*(c+d*x^2)^3, x) == :(3//8*d*b^-7//2*(5*a^2*d^2+8*b^2*c^2+-12*a*b*c*d)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+x*a^-1*b^-1*(a+b*x^2)^-1//2*(c+d*x^2)^2*(b*c+-1*a*d)+-1//4*d*x*a^-1*b^-2*(a+b*x^2)^(1/2)*(c+d*x^2)*(-5*a*d+4*b*c)+-1//8*d*x*a^-1*b^-3*(a+b*x^2)^(1/2)*(-5*a*d+2*b*c)*(-3*a*d+4*b*c))
@test integrate((a+b*x^2)^-3//2*(c+d*x^2), x) == :(d*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*(b*c+-1*a*d))
@test integrate((a+b*x^2)^-3//2, x) == :(x*a^-1*(a+b*x^2)^-1//2)
@test integrate((a+b*x^2)^-3//2*(c+d*x^2)^-1, x) == :(-1*d*c^-1//2*(b*c+-1*a*d)^-3//2*arctanh(x*c^-1//2*(a+b*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+b*x*a^-1*(a+b*x^2)^-1//2*(b*c+-1*a*d)^-1)
@test integrate((a+b*x^2)^-3//2*(c+d*x^2)^-2, x) == :(-1//2*d*c^-3//2*(b*c+-1*a*d)^-5//2*(-1*a*d+4*b*c)*arctanh(x*c^-1//2*(a+b*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+-1//2*d*x*c^-1*(a+b*x^2)^-1//2*(c+d*x^2)^-1*(b*c+-1*a*d)^-1+(1/2)*b*x*a^-1*c^-1*(a+b*x^2)^-1//2*(b*c+-1*a*d)^-2*(a*d+2*b*c))
@test integrate((a+b*x^2)^-3//2*(c+d*x^2)^-3, x) == :(-3//8*d*c^-5//2*(b*c+-1*a*d)^-7//2*(a^2*d^2+8*b^2*c^2+-4*a*b*c*d)*arctanh(x*c^-1//2*(a+b*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+-1//4*d*x*c^-1*(a+b*x^2)^-1//2*(c+d*x^2)^-2*(b*c+-1*a*d)^-1+1//4*b*x*a^-1*c^-1*(a+b*x^2)^-1//2*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(a*d+4*b*c)+1//8*d*x*a^-1*c^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1*(b*c+-1*a*d)^-3*(-1*a*d+4*b*c)*(2*b*c+3*a*d))
@test integrate((a+b*x^2)^-5//2*(c+d*x^2)^4, x) == :(1//8*b^-9//2*d^2*(35*a^2*d^2+48*b^2*c^2+-80*a*b*c*d)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+-1//24*d*x*a^-2*b^-4*(a+b*x^2)^(1/2)*(16*b^3*c^3+105*a^3*d^3+-170*b*c*a^2*d^2+40*a*d*b^2*c^2)+1//3*x*a^-1*b^-1*(a+b*x^2)^-3//2*(c+d*x^2)^3*(b*c+-1*a*d)+-1//12*d*x*a^-2*b^-3*(a+b*x^2)^(1/2)*(c+d*x^2)*(-35*a^2*d^2+8*b^2*c^2+24*a*b*c*d)+1//3*x*a^-2*b^-2*(a+b*x^2)^-1//2*(c+d*x^2)^2*(b*c+-1*a*d)*(2*b*c+7*a*d))
@test integrate((a+b*x^2)^-5//2*(c+d*x^2)^3, x) == :((1/2)*b^-7//2*d^2*(-5*a*d+6*b*c)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+-1//6*d*x*a^-2*b^-3*(a+b*x^2)^(1/2)*(-15*a^2*d^2+4*b^2*c^2+8*a*b*c*d)+1//3*x*a^-1*b^-1*(a+b*x^2)^-3//2*(c+d*x^2)^2*(b*c+-1*a*d)+1//3*x*a^-2*b^-2*(a+b*x^2)^-1//2*(c+d*x^2)*(b*c+-1*a*d)*(2*b*c+5*a*d))
@test integrate((a+b*x^2)^-5//2*(c+d*x^2)^2, x) == :(b^-5//2*d^2*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+1//3*x*a^-1*b^-1*(a+b*x^2)^-3//2*(c+d*x^2)*(b*c+-1*a*d)+1//3*x*a^-2*b^-2*(a+b*x^2)^-1//2*(b*c+-1*a*d)*(2*b*c+3*a*d))
@test integrate((a+b*x^2)^-5//2*(c+d*x^2), x) == :(1//3*x*a^-1*(a+b*x^2)^-3//2*(c+d*x^2)+2//3*c*x*a^-2*(a+b*x^2)^-1//2)
@test integrate((a+b*x^2)^-5//2, x) == :(1//3*x*a^-1*(a+b*x^2)^-3//2+2//3*x*a^-2*(a+b*x^2)^-1//2)
@test integrate((a+b*x^2)^-5//2*(c+d*x^2)^-1, x) == :(c^-1//2*d^2*(b*c+-1*a*d)^-5//2*arctanh(x*c^-1//2*(a+b*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+1//3*b*x*a^-1*(a+b*x^2)^-3//2*(b*c+-1*a*d)^-1+1//3*b*x*a^-2*(a+b*x^2)^-1//2*(b*c+-1*a*d)^-2*(-5*a*d+2*b*c))
@test integrate((a+b*x^2)^-5//2*(c+d*x^2)^-2, x) == :((1/2)*c^-3//2*d^2*(b*c+-1*a*d)^-7//2*(-1*a*d+6*b*c)*arctanh(x*c^-1//2*(a+b*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+-1//2*d*x*c^-1*(a+b*x^2)^-3//2*(c+d*x^2)^-1*(b*c+-1*a*d)^-1+1//6*b*x*a^-1*c^-1*(a+b*x^2)^-3//2*(b*c+-1*a*d)^-2*(2*b*c+3*a*d)+1//6*b*x*a^-2*c^-1*(a+b*x^2)^-1//2*(b*c+-1*a*d)^-3*(-3*a^2*d^2+4*b^2*c^2+-16*a*b*c*d))
@test integrate((a+b*x^2)^-5//2*(c+d*x^2)^-3, x) == :(1//8*c^-5//2*d^2*(b*c+-1*a*d)^-9//2*(3*a^2*d^2+48*b^2*c^2+-16*a*b*c*d)*arctanh(x*c^-1//2*(a+b*x^2)^-1//2*(b*c+-1*a*d)^(1/2))+-1//4*d*x*c^-1*(a+b*x^2)^-3//2*(c+d*x^2)^-2*(b*c+-1*a*d)^-1+1//12*b*x*a^-1*c^-1*(a+b*x^2)^-3//2*(c+d*x^2)^-1*(b*c+-1*a*d)^-2*(3*a*d+4*b*c)+1//12*b*x*a^-2*c^-1*(a+b*x^2)^-1//2*(c+d*x^2)^-1*(b*c+-1*a*d)^-3*(-3*a^2*d^2+8*b^2*c^2+-40*a*b*c*d)+1//24*d*x*a^-2*c^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1*(b*c+-1*a*d)^-4*(9*a^3*d^3+16*b^3*c^3+-88*a*d*b^2*c^2+-42*b*c*a^2*d^2))
@test integrate((a+b*x^2)^3*(c+d*x^2)^-11//2, x) == :(-1//9*d*x*c^-1*(a+b*x^2)^4*(c+d*x^2)^-9//2*(b*c+-1*a*d)^-1+1//63*x*c^-2*(a+b*x^2)^3*(c+d*x^2)^-7//2*(b*c+-1*a*d)^-1*(-8*a*d+9*b*c)+16//315*x*a^3*c^-5*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-1*(-8*a*d+9*b*c)+2//105*a*x*c^-3*(a+b*x^2)^2*(c+d*x^2)^-5//2*(b*c+-1*a*d)^-1*(-8*a*d+9*b*c)+8//315*x*a^2*c^-4*(c+d*x^2)^-3//2*(b*c+-1*a*d)^-1*(a+b*x^2)*(-8*a*d+9*b*c))
@test integrate((a+b*x^2)^2*(c+d*x^2)^-9//2, x) == :(-1//7*d*x*c^-1*(a+b*x^2)^3*(c+d*x^2)^-7//2*(b*c+-1*a*d)^-1+1//35*x*c^-2*(a+b*x^2)^2*(c+d*x^2)^-5//2*(b*c+-1*a*d)^-1*(-6*a*d+7*b*c)+8//105*x*a^2*c^-4*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-1*(-6*a*d+7*b*c)+4//105*a*x*c^-3*(c+d*x^2)^-3//2*(b*c+-1*a*d)^-1*(a+b*x^2)*(-6*a*d+7*b*c))
@test integrate((c+d*x^2)^-7//2*(a+b*x^2), x) == :(-1//5*x*c^-1*d^-1*(c+d*x^2)^-5//2*(b*c+-1*a*d)+1//15*x*c^-3*d^-1*(c+d*x^2)^-1//2*(2*b*c+8*a*d)+1//15*x*c^-2*d^-1*(c+d*x^2)^-3//2*(b*c+4*a*d))
@test integrate((c+d*x^2)^-5//2, x) == :(1//3*x*c^-1*(c+d*x^2)^-3//2+2//3*x*c^-2*(c+d*x^2)^-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((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((a+b*x^2)^-3*(c+d*x^2)^(1/2), x) == :(1//8*c*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//4*b*x*a^-1*(a+b*x^2)^-2*(c+d*x^2)^3//2*(b*c+-1*a*d)^-1+1//8*x*a^-2*(a+b*x^2)^-1*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1*(-4*a*d+3*b*c))
@test integrate((a+b*x^2)^-4*(c+d*x^2)^3//2, x) == :(1//16*a^-7//2*c^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//6*b*x*a^-1*(a+b*x^2)^-3*(c+d*x^2)^5//2*(b*c+-1*a*d)^-1+1//24*x*a^-2*(a+b*x^2)^-2*(c+d*x^2)^3//2*(b*c+-1*a*d)^-1*(-6*a*d+5*b*c)+1//16*c*x*a^-3*(a+b*x^2)^-1*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1*(-6*a*d+5*b*c))
@test integrate((c+d*x^2)^-1//2*(b*x^2+b*c*d^-1)^-1, x) == :(d*x*b^-1*c^-1*(c+d*x^2)^-1//2)
@test integrate((1+x^2)^-1*(1+-1*x^2)^-1//2, x) == :((1/2)*2^(1/2)*arctan(x*2^(1/2)*(1+-1*x^2)^-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((1+x^2)^-3//2*(-1+x^2), x) == :(-2*x*(1+x^2)^-1//2+arcsinh(x))
@test integrate((a+-1*b*x^2)^2//3*(3a+b*x^2)^3, x) == :(-72576*x*a^4*(-1235*(a+-1*b*x^2)^1//3+1235*a^1//3*(1+-1*3^(1/2)))^-1+-23544//6175*x*a^2*(a+-1*b*x^2)^5//3+-3//25*x*(a+-1*b*x^2)^5//3*(3a+b*x^2)^2+18144//1235*x*a^3*(a+-1*b*x^2)^2//3+-378//475*a*x*(a+-1*b*x^2)^5//3*(3a+b*x^2)+-36288//1235*3^1//4*a^13//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.E(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+24192//1235*2^(1/2)*3^3//4*a^13//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.F(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+-1*b*x^2)^2//3*(3a+b*x^2)^2, x) == :(-31104*x*a^3*(-1729*(a+-1*b*x^2)^1//3+1729*a^1//3*(1+-1*3^(1/2)))^-1+-252//247*a*x*(a+-1*b*x^2)^5//3+-3//19*x*(a+-1*b*x^2)^5//3*(3a+b*x^2)+7776//1729*x*a^2*(a+-1*b*x^2)^2//3+-15552//1729*3^1//4*a^10//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.E(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+10368//1729*2^(1/2)*3^3//4*a^10//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.F(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+-1*b*x^2)^2//3*(3a+b*x^2), x) == :(-3//13*x*(a+-1*b*x^2)^5//3+-72*x*a^2*(-13*(a+-1*b*x^2)^1//3+13*a^1//3*(1+-1*3^(1/2)))^-1+18//13*a*x*(a+-1*b*x^2)^2//3+-36//13*3^1//4*a^7//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.E(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+24//13*2^(1/2)*3^3//4*a^7//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.F(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+-1*b*x^2)^2//3*(3a+b*x^2)^-1, x) == :(3*x*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1+2^1//3*a^1//6*b^-1//2*arctanh(x*a^-1//6*b^(1/2)*(a^1//3+2^1//3*(a+-1*b*x^2)^1//3)^-1)+-1//3*2^1//3*a^1//6*b^-1//2*arctanh(x*a^-1//2*b^(1/2))+1//3*2^1//3*3^(1/2)*a^1//6*b^-1//2*arctan(3^(1/2)*a^(1/2)*b^-1//2*x^-1)+1//3*2^1//3*3^(1/2)*a^1//6*b^-1//2*arctan(3^(1/2)*a^1//6*b^-1//2*x^-1*(a^1//3+-1*2^1//3*(a+-1*b*x^2)^1//3))+-1*2^(1/2)*3^3//4*a^1//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.F(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+3//2*3^1//4*a^1//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.E(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+-1*b*x^2)^2//3*(3a+b*x^2)^-2, x) == :(-1//6*x*a^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1+1//6*x*a^-1*(a+-1*b*x^2)^2//3*(3a+b*x^2)^-1+-1//12*3^1//4*a^-2//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.E(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+1//18*2^(1/2)*3^3//4*a^-2//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.F(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+-1*b*x^2)^2//3*(3a+b*x^2)^-3, x) == :(-1//36*x*a^-2*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1+-1//432*2^1//3*a^-11//6*b^-1//2*arctanh(x*a^-1//2*b^(1/2))+1//12*x*a^-1*(a+-1*b*x^2)^2//3*(3a+b*x^2)^-2+1//36*x*a^-2*(a+-1*b*x^2)^2//3*(3a+b*x^2)^-1+1//144*2^1//3*a^-11//6*b^-1//2*arctanh(x*a^-1//6*b^(1/2)*(a^1//3+2^1//3*(a+-1*b*x^2)^1//3)^-1)+1//432*2^1//3*3^(1/2)*a^-11//6*b^-1//2*arctan(3^(1/2)*a^(1/2)*b^-1//2*x^-1)+1//432*2^1//3*3^(1/2)*a^-11//6*b^-1//2*arctan(3^(1/2)*a^1//6*b^-1//2*x^-1*(a^1//3+-1*2^1//3*(a+-1*b*x^2)^1//3))+-1//72*3^1//4*a^-5//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.E(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+1//108*2^(1/2)*3^3//4*a^-5//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.F(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+-1*b*x^2)^2//3*(3a+b*x^2)^-4, x) == :(-1//144*x*a^-3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1+-7//7776*2^1//3*a^-17//6*b^-1//2*arctanh(x*a^-1//2*b^(1/2))+1//18*x*a^-1*(a+-1*b*x^2)^2//3*(3a+b*x^2)^-3+1//54*x*a^-2*(a+-1*b*x^2)^2//3*(3a+b*x^2)^-2+1//144*x*a^-3*(a+-1*b*x^2)^2//3*(3a+b*x^2)^-1+7//2592*2^1//3*a^-17//6*b^-1//2*arctanh(x*a^-1//6*b^(1/2)*(a^1//3+2^1//3*(a+-1*b*x^2)^1//3)^-1)+7//7776*2^1//3*3^(1/2)*a^-17//6*b^-1//2*arctan(3^(1/2)*a^(1/2)*b^-1//2*x^-1)+7//7776*2^1//3*3^(1/2)*a^-17//6*b^-1//2*arctan(3^(1/2)*a^1//6*b^-1//2*x^-1*(a^1//3+-1*2^1//3*(a+-1*b*x^2)^1//3))+-1//288*3^1//4*a^-8//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.E(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+1//432*2^(1/2)*3^3//4*a^-8//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.F(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+-1*b*x^2)^5//3*(3a+b*x^2)^3, x) == :(-11238912*x*a^5*(-267995*(a+-1*b*x^2)^1//3+267995*a^1//3*(1+-1*3^(1/2)))^-1+-33264//14725*x*a^2*(a+-1*b*x^2)^8//3+-3//31*x*(a+-1*b*x^2)^8//3*(3a+b*x^2)^2+1404864//191425*x*a^3*(a+-1*b*x^2)^5//3+2809728//267995*x*a^4*(a+-1*b*x^2)^2//3+-432//775*a*x*(a+-1*b*x^2)^8//3*(3a+b*x^2)+-5619456//267995*3^1//4*a^16//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.E(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+3746304//267995*2^(1/2)*3^3//4*a^16//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.F(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+-1*b*x^2)^5//3*(3a+b*x^2)^2, x) == :(-114048*x*a^4*(-8645*(a+-1*b*x^2)^1//3+8645*a^1//3*(1+-1*3^(1/2)))^-1+-306//475*a*x*(a+-1*b*x^2)^8//3+-3//25*x*(a+-1*b*x^2)^8//3*(3a+b*x^2)+14256//6175*x*a^2*(a+-1*b*x^2)^5//3+28512//8645*x*a^3*(a+-1*b*x^2)^2//3+-57024//8645*3^1//4*a^13//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.E(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+38016//8645*2^(1/2)*3^3//4*a^13//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.F(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+-1*b*x^2)^5//3*(3a+b*x^2), x) == :(-3//19*x*(a+-1*b*x^2)^8//3+-7200*x*a^3*(-1729*(a+-1*b*x^2)^1//3+1729*a^1//3*(1+-1*3^(1/2)))^-1+180//247*a*x*(a+-1*b*x^2)^5//3+1800//1729*x*a^2*(a+-1*b*x^2)^2//3+-3600//1729*3^1//4*a^10//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.E(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+2400//1729*2^(1/2)*3^3//4*a^10//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.F(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+-1*b*x^2)^5//3*(3a+b*x^2)^-1, x) == :(-3//7*x*(a+-1*b*x^2)^2//3+96*a*x*(-7*(a+-1*b*x^2)^1//3+7*a^1//3*(1+-1*3^(1/2)))^-1+4*2^1//3*a^7//6*b^-1//2*arctanh(x*a^-1//6*b^(1/2)*(a^1//3+2^1//3*(a+-1*b*x^2)^1//3)^-1)+-4//3*2^1//3*a^7//6*b^-1//2*arctanh(x*a^-1//2*b^(1/2))+4//3*2^1//3*3^(1/2)*a^7//6*b^-1//2*arctan(3^(1/2)*a^(1/2)*b^-1//2*x^-1)+4//3*2^1//3*3^(1/2)*a^7//6*b^-1//2*arctan(3^(1/2)*a^1//6*b^-1//2*x^-1*(a^1//3+-1*2^1//3*(a+-1*b*x^2)^1//3))+-32//7*2^(1/2)*3^3//4*a^4//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.F(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+48//7*3^1//4*a^4//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.E(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+-1*b*x^2)^5//3*(3a+b*x^2)^-2, x) == :(-11*x*(-3*(a+-1*b*x^2)^1//3+3*a^1//3*(1+-1*3^(1/2)))^-1+2*x*(a+-1*b*x^2)^2//3*(9a+3*b*x^2)^-1+-1*2^1//3*a^1//6*b^-1//2*arctanh(x*a^-1//6*b^(1/2)*(a^1//3+2^1//3*(a+-1*b*x^2)^1//3)^-1)+1//3*2^1//3*a^1//6*b^-1//2*arctanh(x*a^-1//2*b^(1/2))+-1//3*2^1//3*3^(1/2)*a^1//6*b^-1//2*arctan(3^(1/2)*a^(1/2)*b^-1//2*x^-1)+-1//3*2^1//3*3^(1/2)*a^1//6*b^-1//2*arctan(3^(1/2)*a^1//6*b^-1//2*x^-1*(a^1//3+-1*2^1//3*(a+-1*b*x^2)^1//3))+-11//6*3^1//4*a^1//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.E(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+11//9*2^(1/2)*3^3//4*a^1//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.F(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+-1*b*x^2)^5//3*(3a+b*x^2)^-3, x) == :(1//3*x*(a+-1*b*x^2)^2//3*(3a+b*x^2)^-2+1//18*x*a^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1+-1//18*x*a^-1*(a+-1*b*x^2)^2//3*(3a+b*x^2)^-1+-1//108*2^1//3*a^-5//6*b^-1//2*arctanh(x*a^-1//2*b^(1/2))+1//36*2^1//3*a^-5//6*b^-1//2*arctanh(x*a^-1//6*b^(1/2)*(a^1//3+2^1//3*(a+-1*b*x^2)^1//3)^-1)+1//108*2^1//3*3^(1/2)*a^-5//6*b^-1//2*arctan(3^(1/2)*a^(1/2)*b^-1//2*x^-1)+1//108*2^1//3*3^(1/2)*a^-5//6*b^-1//2*arctan(3^(1/2)*a^1//6*b^-1//2*x^-1*(a^1//3+-1*2^1//3*(a+-1*b*x^2)^1//3))+-1//54*2^(1/2)*3^3//4*a^-2//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.F(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+1//36*3^1//4*a^-2//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.E(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+-1*b*x^2)^-1//3*(3a+b*x^2)^4, x) == :(-3794688*x*a^4*(-8645*(a+-1*b*x^2)^1//3+8645*a^1//3*(1+-1*3^(1/2)))^-1+-1552608//43225*x*a^3*(a+-1*b*x^2)^2//3+-3//25*x*(a+-1*b*x^2)^2//3*(3a+b*x^2)^3+-36288//6175*x*a^2*(a+-1*b*x^2)^2//3*(3a+b*x^2)+-18//19*a*x*(a+-1*b*x^2)^2//3*(3a+b*x^2)^2+-1897344//8645*3^1//4*a^13//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.E(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+1264896//8645*2^(1/2)*3^3//4*a^13//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.F(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+-1*b*x^2)^-1//3*(3a+b*x^2)^3, x) == :(-215136*x*a^3*(-1729*(a+-1*b*x^2)^1//3+1729*a^1//3*(1+-1*3^(1/2)))^-1+-15768//1729*x*a^2*(a+-1*b*x^2)^2//3+-3//19*x*(a+-1*b*x^2)^2//3*(3a+b*x^2)^2+-324//247*a*x*(a+-1*b*x^2)^2//3*(3a+b*x^2)+-107568//1729*3^1//4*a^10//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.E(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+71712//1729*2^(1/2)*3^3//4*a^10//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.F(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+-1*b*x^2)^-1//3*(3a+b*x^2)^2, x) == :(-3240*x*a^2*(-91*(a+-1*b*x^2)^1//3+91*a^1//3*(1+-1*3^(1/2)))^-1+-198//91*a*x*(a+-1*b*x^2)^2//3+-3//13*x*(a+-1*b*x^2)^2//3*(3a+b*x^2)+-1620//91*3^1//4*a^7//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.E(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+1080//91*2^(1/2)*3^3//4*a^7//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.F(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+-1*b*x^2)^-1//3*(3a+b*x^2), x) == :(-3//7*x*(a+-1*b*x^2)^2//3+-72*a*x*(-7*(a+-1*b*x^2)^1//3+7*a^1//3*(1+-1*3^(1/2)))^-1+-36//7*3^1//4*a^4//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.E(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+24//7*2^(1/2)*3^3//4*a^4//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.F(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+-1*b*x^2)^-1//3*(3a+b*x^2)^-1, x) == :(-1//12*2^1//3*a^-5//6*b^-1//2*arctanh(x*a^-1//2*b^(1/2))+1//4*2^1//3*a^-5//6*b^-1//2*arctanh(x*a^-1//6*b^(1/2)*(a^1//3+2^1//3*(a+-1*b*x^2)^1//3)^-1)+1//12*2^1//3*3^(1/2)*a^-5//6*b^-1//2*arctan(3^(1/2)*a^(1/2)*b^-1//2*x^-1)+1//12*2^1//3*3^(1/2)*a^-5//6*b^-1//2*arctan(3^(1/2)*a^1//6*b^-1//2*x^-1*(a^1//3+-1*2^1//3*(a+-1*b*x^2)^1//3)))
@test integrate((a+-1*b*x^2)^-1//3*(3a+b*x^2)^-2, x) == :(-1//24*x*a^-2*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1+-1//48*2^1//3*a^-11//6*b^-1//2*arctanh(x*a^-1//2*b^(1/2))+1//16*2^1//3*a^-11//6*b^-1//2*arctanh(x*a^-1//6*b^(1/2)*(a^1//3+2^1//3*(a+-1*b*x^2)^1//3)^-1)+1//24*x*a^-2*(a+-1*b*x^2)^2//3*(3a+b*x^2)^-1+1//48*2^1//3*3^(1/2)*a^-11//6*b^-1//2*arctan(3^(1/2)*a^(1/2)*b^-1//2*x^-1)+1//48*2^1//3*3^(1/2)*a^-11//6*b^-1//2*arctan(3^(1/2)*a^1//6*b^-1//2*x^-1*(a^1//3+-1*2^1//3*(a+-1*b*x^2)^1//3))+-1//48*3^1//4*a^-5//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.E(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+1//72*2^(1/2)*3^3//4*a^-5//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.F(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+-1*b*x^2)^-1//3*(3a+b*x^2)^-3, x) == :(-5//288*x*a^-3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1+-5//864*2^1//3*a^-17//6*b^-1//2*arctanh(x*a^-1//2*b^(1/2))+1//48*x*a^-2*(a+-1*b*x^2)^2//3*(3a+b*x^2)^-2+5//288*x*a^-3*(a+-1*b*x^2)^2//3*(3a+b*x^2)^-1+5//288*2^1//3*a^-17//6*b^-1//2*arctanh(x*a^-1//6*b^(1/2)*(a^1//3+2^1//3*(a+-1*b*x^2)^1//3)^-1)+5//864*2^1//3*3^(1/2)*a^-17//6*b^-1//2*arctan(3^(1/2)*a^(1/2)*b^-1//2*x^-1)+5//864*2^1//3*3^(1/2)*a^-17//6*b^-1//2*arctan(3^(1/2)*a^1//6*b^-1//2*x^-1*(a^1//3+-1*2^1//3*(a+-1*b*x^2)^1//3))+-5//576*3^1//4*a^-8//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.E(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+1//864*2^(1/2)*3^3//4*a^-8//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(-5*(a+-1*b*x^2)^1//3+5*a^1//3)*Elliptic.F(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+-1*b*x^2)^-4//3*(3a+b*x^2)^3, x) == :(6*x*(a+-1*b*x^2)^-1//3*(3a+b*x^2)^2+20088*x*a^2*(-91*(a+-1*b*x^2)^1//3+91*a^1//3*(1+-1*3^(1/2)))^-1+81//13*x*(a+-1*b*x^2)^2//3*(3a+b*x^2)+2538//91*a*x*(a+-1*b*x^2)^2//3+-6696//91*2^(1/2)*3^3//4*a^7//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.F(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+10044//91*3^1//4*a^7//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.E(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+-1*b*x^2)^-4//3*(3a+b*x^2)^2, x) == :(45//7*x*(a+-1*b*x^2)^2//3+6*x*(a+-1*b*x^2)^-1//3*(3a+b*x^2)+324*a*x*(-7*(a+-1*b*x^2)^1//3+7*a^1//3*(1+-1*3^(1/2)))^-1+-108//7*2^(1/2)*3^3//4*a^4//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.F(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+162//7*3^1//4*a^4//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.E(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+-1*b*x^2)^-4//3*(3a+b*x^2), x) == :(6*x*(a+-1*b*x^2)^-1//3+9*x*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1+-3*2^(1/2)*3^3//4*a^1//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.F(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+9//2*3^1//4*a^1//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.E(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+-1*b*x^2)^-4//3*(3a+b*x^2)^-1, x) == :(3//8*x*a^-2*(a+-1*b*x^2)^-1//3+3//8*x*a^-2*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1+-1//48*2^1//3*a^-11//6*b^-1//2*arctanh(x*a^-1//2*b^(1/2))+1//16*2^1//3*a^-11//6*b^-1//2*arctanh(x*a^-1//6*b^(1/2)*(a^1//3+2^1//3*(a+-1*b*x^2)^1//3)^-1)+1//48*2^1//3*3^(1/2)*a^-11//6*b^-1//2*arctan(3^(1/2)*a^(1/2)*b^-1//2*x^-1)+1//48*2^1//3*3^(1/2)*a^-11//6*b^-1//2*arctan(3^(1/2)*a^1//6*b^-1//2*x^-1*(a^1//3+-1*2^1//3*(a+-1*b*x^2)^1//3))+-1//8*2^(1/2)*3^3//4*a^-5//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.F(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+3//16*3^1//4*a^-5//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.E(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+-1*b*x^2)^-4//3*(3a+b*x^2)^-2, x) == :(1//12*x*a^-3*(a+-1*b*x^2)^-1//3+1//12*x*a^-3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1+-1//96*2^1//3*a^-17//6*b^-1//2*arctanh(x*a^-1//2*b^(1/2))+1//24*x*a^-2*(a+-1*b*x^2)^-1//3*(3a+b*x^2)^-1+1//32*2^1//3*a^-17//6*b^-1//2*arctanh(x*a^-1//6*b^(1/2)*(a^1//3+2^1//3*(a+-1*b*x^2)^1//3)^-1)+1//96*2^1//3*3^(1/2)*a^-17//6*b^-1//2*arctan(3^(1/2)*a^(1/2)*b^-1//2*x^-1)+1//96*2^1//3*3^(1/2)*a^-17//6*b^-1//2*arctan(3^(1/2)*a^1//6*b^-1//2*x^-1*(a^1//3+-1*2^1//3*(a+-1*b*x^2)^1//3))+-1//36*2^(1/2)*3^3//4*a^-8//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.F(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+1//24*3^1//4*a^-8//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.E(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+-1*b*x^2)^-4//3*(3a+b*x^2)^-3, x) == :(19//1152*x*a^-4*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1+-19//1152*x*a^-4*(a+-1*b*x^2)^2//3*(3a+b*x^2)^-1+-7//1728*2^1//3*a^-23//6*b^-1//2*arctanh(x*a^-1//2*b^(1/2))+1//48*x*a^-2*(a+-1*b*x^2)^-1//3*(3a+b*x^2)^-2+7//576*2^1//3*a^-23//6*b^-1//2*arctanh(x*a^-1//6*b^(1/2)*(a^1//3+2^1//3*(a+-1*b*x^2)^1//3)^-1)+17//192*x*a^-3*(a+-1*b*x^2)^-1//3*(3a+b*x^2)^-1+7//1728*2^1//3*3^(1/2)*a^-23//6*b^-1//2*arctan(3^(1/2)*a^(1/2)*b^-1//2*x^-1)+7//1728*2^1//3*3^(1/2)*a^-23//6*b^-1//2*arctan(3^(1/2)*a^1//6*b^-1//2*x^-1*(a^1//3+-1*2^1//3*(a+-1*b*x^2)^1//3))+-1//3456*2^(1/2)*3^3//4*a^-11//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(-19*(a+-1*b*x^2)^1//3+19*a^1//3)*Elliptic.F(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+19//2304*3^1//4*a^-11//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.E(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+-1*b*x^2)^-7//3*(3a+b*x^2)^4, x) == :(-36936*x*a^2*(-91*(a+-1*b*x^2)^1//3+91*a^1//3*(1+-1*3^(1/2)))^-1+-3240//91*a*x*(a+-1*b*x^2)^2//3+-81//13*x*(a+-1*b*x^2)^2//3*(3a+b*x^2)+-9//2*x*(a+-1*b*x^2)^-1//3*(3a+b*x^2)^2+3//2*x*(a+-1*b*x^2)^-4//3*(3a+b*x^2)^3+-18468//91*3^1//4*a^7//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.E(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+12312//91*2^(1/2)*3^3//4*a^7//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.F(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+-1*b*x^2)^-7//3*(3a+b*x^2)^3, x) == :(-27//14*x*(a+-1*b*x^2)^2//3+-324*a*x*(-7*(a+-1*b*x^2)^1//3+7*a^1//3*(1+-1*3^(1/2)))^-1+3//2*x*(a+-1*b*x^2)^-4//3*(3a+b*x^2)^2+-162//7*3^1//4*a^4//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.E(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+108//7*2^(1/2)*3^3//4*a^4//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.F(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+-1*b*x^2)^-7//3*(3a+b*x^2)^2, x) == :(9//2*x*(a+-1*b*x^2)^-1//3+3//2*x*(a+-1*b*x^2)^-4//3*(3a+b*x^2))
@test integrate((a+-1*b*x^2)^-7//3*(3a+b*x^2), x) == :(3//2*x*(a+-1*b*x^2)^-4//3+9//4*x*a^-1*(a+-1*b*x^2)^-1//3+9//4*x*a^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1+-3//4*2^(1/2)*3^3//4*a^-2//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.F(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+9//8*3^1//4*a^-2//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.E(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+-1*b*x^2)^-7//3*(3a+b*x^2)^-1, x) == :(3//32*x*a^-2*(a+-1*b*x^2)^-4//3+21//64*x*a^-3*(a+-1*b*x^2)^-1//3+21//64*x*a^-3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1+-1//192*2^1//3*a^-17//6*b^-1//2*arctanh(x*a^-1//2*b^(1/2))+1//64*2^1//3*a^-17//6*b^-1//2*arctanh(x*a^-1//6*b^(1/2)*(a^1//3+2^1//3*(a+-1*b*x^2)^1//3)^-1)+1//192*2^1//3*3^(1/2)*a^-17//6*b^-1//2*arctan(3^(1/2)*a^(1/2)*b^-1//2*x^-1)+1//192*2^1//3*3^(1/2)*a^-17//6*b^-1//2*arctan(3^(1/2)*a^1//6*b^-1//2*x^-1*(a^1//3+-1*2^1//3*(a+-1*b*x^2)^1//3))+-7//64*2^(1/2)*3^3//4*a^-8//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.F(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+21//128*3^1//4*a^-8//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.E(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+-1*b*x^2)^-7//3*(3a+b*x^2)^-2, x) == :(5//384*x*a^-3*(a+-1*b*x^2)^-4//3+79//768*x*a^-4*(a+-1*b*x^2)^-1//3+79//768*x*a^-4*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1+-1//256*2^1//3*a^-23//6*b^-1//2*arctanh(x*a^-1//2*b^(1/2))+1//24*x*a^-2*(a+-1*b*x^2)^-4//3*(3a+b*x^2)^-1+3//256*2^1//3*a^-23//6*b^-1//2*arctanh(x*a^-1//6*b^(1/2)*(a^1//3+2^1//3*(a+-1*b*x^2)^1//3)^-1)+1//256*2^1//3*3^(1/2)*a^-23//6*b^-1//2*arctan(3^(1/2)*a^(1/2)*b^-1//2*x^-1)+1//256*2^1//3*3^(1/2)*a^-23//6*b^-1//2*arctan(3^(1/2)*a^1//6*b^-1//2*x^-1*(a^1//3+-1*2^1//3*(a+-1*b*x^2)^1//3))+-1//2304*2^(1/2)*3^3//4*a^-11//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(-79*(a+-1*b*x^2)^1//3+79*a^1//3)*Elliptic.F(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+79//1536*3^1//4*a^-11//3*b^-1*x^-1*((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+(a+-1*b*x^2)^2//3+a^1//3*(a+-1*b*x^2)^1//3))^(1/2)*(-1*a^1//3*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+-1*(a+-1*b*x^2)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a^1//3+-1*(a+-1*b*x^2)^1//3)*Elliptic.E(arcsin((-1*(a+-1*b*x^2)^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(-1*(a+-1*b*x^2)^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((-1a+b*x^2)^-1//3*(-3a+-1*b*x^2)^-1, x) == :(-1//4*2^1//3*a^-1//2*b^-1//2*(-1a)^-1//3*arctanh(x*a^-1//2*b^(1/2)*(-1a)^1//3*((-1a)^1//3+2^1//3*(-1a+b*x^2)^1//3)^-1)+1//12*2^1//3*a^-1//2*b^-1//2*(-1a)^-1//3*arctanh(x*a^-1//2*b^(1/2))+-1//12*2^1//3*3^(1/2)*a^-1//2*b^-1//2*(-1a)^-1//3*arctan(3^(1/2)*a^(1/2)*b^-1//2*x^-1)+-1//12*2^1//3*3^(1/2)*a^-1//2*b^-1//2*(-1a)^-1//3*arctan(3^(1/2)*a^(1/2)*b^-1//2*x^-1*(-1a)^-1//3*((-1a)^1//3+-1*2^1//3*(-1a+b*x^2)^1//3)))
@test integrate((a+b*x^2)^-1//3*(3a+-1*b*x^2)^-1, x) == :(-1//12*2^1//3*a^-5//6*b^-1//2*arctan(x*a^-1//2*b^(1/2))+1//4*2^1//3*a^-5//6*b^-1//2*arctan(x*a^-1//6*b^(1/2)*(a^1//3+2^1//3*(a+b*x^2)^1//3)^-1)+-1//12*2^1//3*3^(1/2)*a^-5//6*b^-1//2*arctanh(3^(1/2)*a^(1/2)*b^-1//2*x^-1)+-1//12*2^1//3*3^(1/2)*a^-5//6*b^-1//2*arctanh(3^(1/2)*a^1//6*b^-1//2*x^-1*(a^1//3+-1*2^1//3*(a+b*x^2)^1//3)))
@test integrate((c+-1*d*x^2)^-1*(c+3*d*x^2)^-1//3, x) == :(-1//4*2^1//3*c^-5//6*d^-1//2*arctanh(c^(1/2)*d^-1//2*x^-1)+-1//4*2^1//3*c^-5//6*d^-1//2*arctanh(c^1//6*d^-1//2*x^-1*(c^1//3+-1*2^1//3*(c+3*d*x^2)^1//3))+-1//12*2^1//3*3^(1/2)*c^-5//6*d^-1//2*arctan(x*3^(1/2)*c^-1//2*d^(1/2))+1//4*2^1//3*3^(1/2)*c^-5//6*d^-1//2*arctan(x*3^(1/2)*c^-1//6*d^(1/2)*(c^1//3+2^1//3*(c+3*d*x^2)^1//3)^-1))
@test integrate((a+-1*b*x^2)^-1//3*(3a+b*x^2)^-1, x) == :(-1//12*2^1//3*a^-5//6*b^-1//2*arctanh(x*a^-1//2*b^(1/2))+1//4*2^1//3*a^-5//6*b^-1//2*arctanh(x*a^-1//6*b^(1/2)*(a^1//3+2^1//3*(a+-1*b*x^2)^1//3)^-1)+1//12*2^1//3*3^(1/2)*a^-5//6*b^-1//2*arctan(3^(1/2)*a^(1/2)*b^-1//2*x^-1)+1//12*2^1//3*3^(1/2)*a^-5//6*b^-1//2*arctan(3^(1/2)*a^1//6*b^-1//2*x^-1*(a^1//3+-1*2^1//3*(a+-1*b*x^2)^1//3)))
@test integrate((c+d*x^2)^-1*(c+-3*d*x^2)^-1//3, x) == :(1//4*2^1//3*c^-5//6*d^-1//2*arctan(c^(1/2)*d^-1//2*x^-1)+1//4*2^1//3*c^-5//6*d^-1//2*arctan(c^1//6*d^-1//2*x^-1*(c^1//3+-1*2^1//3*(c+-3*d*x^2)^1//3))+-1//12*2^1//3*3^(1/2)*c^-5//6*d^-1//2*arctanh(x*3^(1/2)*c^-1//2*d^(1/2))+1//4*2^1//3*3^(1/2)*c^-5//6*d^-1//2*arctanh(x*3^(1/2)*c^-1//6*d^(1/2)*(c^1//3+2^1//3*(c+-3*d*x^2)^1//3)^-1))
@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((1+x^2)^-1//3*(3+-1*x^2)^-1, x) == :(-1//12*2^1//3*arctan(x)+1//4*2^1//3*arctan(x*(1+2^1//3*(1+x^2)^1//3)^-1)+-1//12*2^1//3*3^(1/2)*arctanh(3^(1/2)*x^-1)+-1//12*2^1//3*3^(1/2)*arctanh(3^(1/2)*x^-1*(1+-1*2^1//3*(1+x^2)^1//3)))
@test integrate((1+-1*x^2)^-1//3*(3+x^2)^-1*(3+-1x), x) == :(-1//4*2^1//3*log(3+x^2)+3//4*2^1//3*log((1+x)^2//3+2^1//3*(1+-1x)^1//3)+-1//2*2^1//3*3^(1/2)*arctan(1//3*3^(1/2)+-1//3*2^2//3*3^(1/2)*(1+x)^2//3*(1+-1x)^-1//3))
@test integrate((1+-1*x^2)^-1//3*(3+x^2)^-1*(3+x), x) == :(-3//4*2^1//3*log((1+-1x)^2//3+2^1//3*(1+x)^1//3)+1//4*2^1//3*log(3+x^2)+(1/2)*2^1//3*3^(1/2)*arctan(1//3*3^(1/2)+-1//3*2^2//3*3^(1/2)*(1+x)^-1//3*(1+-1x)^2//3))
@test integrate((a+b*x^2)^-1//3*(d*x^2+9*a*d*b^-1)^-1, x) == :(1//12*a^-5//6*b^(1/2)*d^-1*arctan(1//3*x*a^-1//2*b^(1/2))+1//12*a^-5//6*b^(1/2)*d^-1*arctan(1//3*a^-1//6*b^-1//2*x^-1*(a^1//3+-1*(a+b*x^2)^1//3)^2)+-1//12*3^(1/2)*a^-5//6*b^(1/2)*d^-1*arctanh(3^(1/2)*a^1//6*b^-1//2*x^-1*(a^1//3+-1*(a+b*x^2)^1//3)))
@test integrate((a+-1*b*x^2)^-1//3*(d*x^2+-9*a*d*b^-1)^-1, x) == :(-1//12*a^-5//6*b^(1/2)*d^-1*arctanh(1//3*x*a^-1//2*b^(1/2))+1//12*a^-5//6*b^(1/2)*d^-1*arctanh(1//3*a^-1//6*b^-1//2*x^-1*(a^1//3+-1*(a+-1*b*x^2)^1//3)^2)+-1//12*3^(1/2)*a^-5//6*b^(1/2)*d^-1*arctan(3^(1/2)*a^1//6*b^-1//2*x^-1*(a^1//3+-1*(a+-1*b*x^2)^1//3)))
@test integrate((-1a+b*x^2)^-1//3*(d*x^2+-9*a*d*b^-1)^-1, x) == :(-1//12*a^-5//6*b^(1/2)*d^-1*arctanh(1//3*a^-1//6*b^-1//2*x^-1*(a^1//3+(-1a+b*x^2)^1//3)^2)+1//12*a^-5//6*b^(1/2)*d^-1*arctanh(1//3*x*a^-1//2*b^(1/2))+1//12*3^(1/2)*a^-5//6*b^(1/2)*d^-1*arctan(3^(1/2)*a^1//6*b^-1//2*x^-1*(a^1//3+(-1a+b*x^2)^1//3)))
@test integrate((-1a+-1*b*x^2)^-1//3*(d*x^2+9*a*d*b^-1)^-1, x) == :(-1//12*a^-5//6*b^(1/2)*d^-1*arctan(1//3*x*a^-1//2*b^(1/2))+-1//12*a^-5//6*b^(1/2)*d^-1*arctan(1//3*a^-1//6*b^-1//2*x^-1*(a^1//3+(-1a+-1*b*x^2)^1//3)^2)+1//12*3^(1/2)*a^-5//6*b^(1/2)*d^-1*arctanh(3^(1/2)*a^1//6*b^-1//2*x^-1*(a^1//3+(-1a+-1*b*x^2)^1//3)))
@test integrate((2+b*x^2)^-1//3*(d*x^2+18*d*b^-1)^-1, x) == :(1//24*2^1//6*b^(1/2)*d^-1*arctan(1//6*x*2^(1/2)*b^(1/2))+1//24*2^1//6*b^(1/2)*d^-1*arctan(1//6*2^5//6*b^-1//2*x^-1*(2^1//3+-1*(2+b*x^2)^1//3)^2)+-1//24*2^1//6*3^(1/2)*b^(1/2)*d^-1*arctanh(2^1//6*3^(1/2)*b^-1//2*x^-1*(2^1//3+-1*(2+b*x^2)^1//3)))
@test integrate((-2+b*x^2)^-1//3*(d*x^2+-18*d*b^-1)^-1, x) == :(-1//24*2^1//6*b^(1/2)*d^-1*arctanh(1//6*2^5//6*b^-1//2*x^-1*(2^1//3+(-2+b*x^2)^1//3)^2)+1//24*2^1//6*b^(1/2)*d^-1*arctanh(1//6*x*2^(1/2)*b^(1/2))+1//24*2^1//6*3^(1/2)*b^(1/2)*d^-1*arctan(2^1//6*3^(1/2)*b^-1//2*x^-1*(2^1//3+(-2+b*x^2)^1//3)))
@test integrate((2+3*x^2)^-1//3*(6d+d*x^2)^-1, x) == :(-1//8*2^1//6*d^-1*arctanh(2^1//6*x^-1*(2^1//3+-1*(2+3*x^2)^1//3))+1//24*2^1//6*3^(1/2)*d^-1*arctan(1//6*x*6^(1/2))+1//24*2^1//6*3^(1/2)*d^-1*arctan(1//18*2^5//6*3^(1/2)*x^-1*(2^1//3+-1*(2+3*x^2)^1//3)^2))
@test integrate((2+-3*x^2)^-1//3*(-6d+d*x^2)^-1, x) == :(-1//8*2^1//6*d^-1*arctan(2^1//6*x^-1*(2^1//3+-1*(2+-3*x^2)^1//3))+-1//24*2^1//6*3^(1/2)*d^-1*arctanh(1//6*x*6^(1/2))+1//24*2^1//6*3^(1/2)*d^-1*arctanh(1//18*2^5//6*3^(1/2)*x^-1*(2^1//3+-1*(2+-3*x^2)^1//3)^2))
@test integrate((-2+3*x^2)^-1//3*(-6d+d*x^2)^-1, x) == :(1//8*2^1//6*d^-1*arctan(2^1//6*x^-1*(2^1//3+(-2+3*x^2)^1//3))+-1//24*2^1//6*3^(1/2)*d^-1*arctanh(1//18*2^5//6*3^(1/2)*x^-1*(2^1//3+(-2+3*x^2)^1//3)^2)+1//24*2^1//6*3^(1/2)*d^-1*arctanh(1//6*x*6^(1/2)))
@test integrate((-2+-3*x^2)^-1//3*(6d+d*x^2)^-1, x) == :(1//8*2^1//6*d^-1*arctanh(2^1//6*x^-1*(2^1//3+(-2+-3*x^2)^1//3))+-1//24*2^1//6*3^(1/2)*d^-1*arctan(1//6*x*6^(1/2))+-1//24*2^1//6*3^(1/2)*d^-1*arctan(1//18*2^5//6*3^(1/2)*x^-1*(2^1//3+(-2+-3*x^2)^1//3)^2))
@test integrate((1+x^2)^-1//3*(9+x^2)^-1, x) == :(1//12*arctan(1//3*x)+1//12*arctan(1//3*x^-1*(1+-1*(1+x^2)^1//3)^2)+-1//12*3^(1/2)*arctanh(3^(1/2)*x^-1*(1+-1*(1+x^2)^1//3)))
@test integrate((1+b*x^2)^-1//3*(9+b*x^2)^-1, x) == :(1//12*b^-1//2*arctan(1//3*x*b^(1/2))+1//12*b^-1//2*arctan(1//3*b^-1//2*x^-1*(1+-1*(1+b*x^2)^1//3)^2)+-1//12*3^(1/2)*b^-1//2*arctanh(3^(1/2)*b^-1//2*x^-1*(1+-1*(1+b*x^2)^1//3)))
@test integrate((1+-1*x^2)^-1//3*(9+-1*x^2)^-1, x) == :(-1//12*arctanh(1//3*x^-1*(1+-1*(1+-1*x^2)^1//3)^2)+1//12*arctanh(1//3*x)+1//12*3^(1/2)*arctan(3^(1/2)*x^-1*(1+-1*(1+-1*x^2)^1//3)))
@test integrate((a+b*x^2)^3//2*(c+d*x^2)^(1/2), x) == :(1//15*x*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(7*a*c+-2*b*c^2*d^-1+3*d*a^2*b^-1)+-1//15*x*d^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(-6*a*d+2*b*c)+1//5*b*x*d^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^3//2+-1//15*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*(b*c+-9*a*d)*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^-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))
@test integrate((a+b*x^2)^(1/2)*(c+d*x^2)^(1/2), x) == :(1//3*x*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)+1//3*x*b^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(a*d+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*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^-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((a+b*x^2)^-1//2*(c+d*x^2)^(1/2), x) == :(d*x*b^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2+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*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1)+-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((a+b*x^2)^-3//2*(c+d*x^2)^(1/2), x) == :(a^-1//2*b^-1//2*(a*c^-1*(a+b*x^2)^-1*(c+d*x^2))^-1//2*(a+b*x^2)^-1//2*(c+d*x^2)^(1/2)*Elliptic.E(arctan(x*a^-1//2*b^(1/2)),1+-1*a*d*b^-1*c^-1))
@test integrate((a+b*x^2)^-5//2*(c+d*x^2)^(1/2), x) == :(1//3*x*a^-1*(a+b*x^2)^-3//2*(c+d*x^2)^(1/2)+-1//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*(b*c+-1*a*d)^-1*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1)+1//3*a^-3//2*b^-1//2*(a*c^-1*(a+b*x^2)^-1*(c+d*x^2))^-1//2*(a+b*x^2)^-1//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1*(-1*a*d+2*b*c)*Elliptic.E(arctan(x*a^-1//2*b^(1/2)),1+-1*a*d*b^-1*c^-1))
@test integrate((a+b*x^2)^-7//2*(c+d*x^2)^(1/2), x) == :(1//5*x*a^-1*(a+b*x^2)^-5//2*(c+d*x^2)^(1/2)+1//15*x*a^-2*(a+b*x^2)^-3//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1*(-3*a*d+4*b*c)+1//15*a^-5//2*b^-1//2*(a*c^-1*(a+b*x^2)^-1*(c+d*x^2))^-1//2*(a+b*x^2)^-1//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-2*(3*a^2*d^2+8*b^2*c^2+-13*a*b*c*d)*Elliptic.E(arctan(x*a^-1//2*b^(1/2)),1+-1*a*d*b^-1*c^-1)+-2//15*a^-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*(b*c+-1*a*d)^-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))
@test integrate((a+b*x^2)^3//2*(c+d*x^2)^3//2, x) == :(x*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(9//35*a*c+-2//35*d*a^2*b^-1+1//35*b*c^2*d^-1)+1//7*d*x*b^-1*(a+b*x^2)^5//2*(c+d*x^2)^(1/2)+1//35*x*b^-1*(a+b*x^2)^3//2*(c+d*x^2)^(1/2)*(-2*a*d+8*b*c)+-1//35*x*b^-2*d^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(2*a*d+2*b*c)*(a^2*d^2+b^2*c^2+-6*a*b*c*d)+-1//35*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*(a^2*d^2+b^2*c^2+-18*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^-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)*(a^2*d^2+b^2*c^2+-6*a*b*c*d)*Elliptic.E(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1))
@test integrate((a+b*x^2)^(1/2)*(c+d*x^2)^3//2, x) == :(1//5*d*x*b^-1*(a+b*x^2)^3//2*(c+d*x^2)^(1/2)+1//15*x*b^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(-2*a*d+6*b*c)+1//15*x*b^-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)+-1//15*b^-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*(-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//15*b^-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*(-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((a+b*x^2)^-1//2*(c+d*x^2)^3//2, x) == :(1//3*d*x*b^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)+2//3*d*x*b^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(-1*a*d+2*b*c)+-2//3*b^-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*(-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*a^-1*b^-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*(-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((a+b*x^2)^-3//2*(c+d*x^2)^3//2, x) == :(x*a^-1*b^-1*(a+b*x^2)^-1//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)+-1*d*x*a^-1*b^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(b*c+-2*a*d)+a^-1*b^-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*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1)+a^-1*b^-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*(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((a+b*x^2)^-5//2*(c+d*x^2)^3//2, x) == :(1//3*x*a^-1*b^-1*(a+b*x^2)^-3//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)+1//3*a^-3//2*b^-3//2*(a*c^-1*(a+b*x^2)^-1*(c+d*x^2))^-1//2*(a+b*x^2)^-1//2*(c+d*x^2)^(1/2)*(2*a*d+2*b*c)*Elliptic.E(arctan(x*a^-1//2*b^(1/2)),1+-1*a*d*b^-1*c^-1)+-1//3*a^-2*b^-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*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1))
@test integrate((a+b*x^2)^-7//2*(c+d*x^2)^3//2, x) == :(1//5*x*a^-1*b^-1*(a+b*x^2)^-5//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)+1//15*x*a^-2*b^-1*(a+b*x^2)^-3//2*(c+d*x^2)^(1/2)*(2*a*d+4*b*c)+1//15*a^-5//2*b^-3//2*(a*c^-1*(a+b*x^2)^-1*(c+d*x^2))^-1//2*(a+b*x^2)^-1//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1*(-2*a^2*d^2+8*b^2*c^2+-3*a*b*c*d)*Elliptic.E(arctan(x*a^-1//2*b^(1/2)),1+-1*a*d*b^-1*c^-1)+-1//15*a^-3*b^-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+-1*a*d)^-1*(-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((2+b*x^2)^(1/2)*(3+d*x^2)^(1/2), x) == :(1//3*x*(2+b*x^2)^(1/2)*(3+d*x^2)^(1/2)+1//3*x*b^-1*(2+b*x^2)^(1/2)*(3+d*x^2)^-1//2*(2d+3b)+2*2^(1/2)*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.F(arctan(1//3*x*3^(1/2)*d^(1/2)),1+-3//2*b*d^-1)+-1//3*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*(2d+3b)*Elliptic.E(arctan(1//3*x*3^(1/2)*d^(1/2)),1+-3//2*b*d^-1))
@test integrate((2+4*x^2)^(1/2)*(3+-6*x^2)^(1/2), x) == :(2//3*3^(1/2)*Elliptic.F(arcsin(x*2^(1/2)),-1)+1//3*x*6^(1/2)*(1+-4*x^4)^(1/2))
@test integrate((2+4*x^2)^(1/2)*(3+6*x^2)^(1/2), x) == :(x*6^(1/2)+2//3*6^(1/2)*x^3)
@test integrate((2+b*x^2)^(1/2)*(3+d*x^2)^-1//2, x) == :(x*(2+b*x^2)^(1/2)*(3+d*x^2)^-1//2+2^(1/2)*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.F(arctan(1//3*x*3^(1/2)*d^(1/2)),1+-3//2*b*d^-1)+-1*2^(1/2)*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((4+-1*x^2)^(1/2)*(c+d*x^2)^-1//2, x) == :(-1*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)+d^-1*(1+d*c^-1*x^2)^(1/2)*(c+d*x^2)^-1//2*(c+4d)*Elliptic.F(arcsin((1/2)*x),-4*d*c^-1))
@test integrate((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)+4*c^-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.F(arctan((1/2)*x),1+-4*d*c^-1))
@test integrate((1+-1*x^2)^(1/2)*(2+-3*x^2)^-1//2, x) == :(1//3*3^(1/2)*Elliptic.E(arcsin((1/2)*x*6^(1/2)),2//3))
@test integrate((2+-3*x^2)^-1//2*(4+-1*x^2)^(1/2), x) == :(2//3*3^(1/2)*Elliptic.E(arcsin((1/2)*x*6^(1/2)),1//6))
@test integrate((1+-4*x^2)^(1/2)*(2+-3*x^2)^-1//2, x) == :(1//3*3^(1/2)*Elliptic.E(arcsin((1/2)*x*6^(1/2)),8//3))
@test integrate((1+x^2)^(1/2)*(1+-1*x^2)^-1//2, x) == :(Elliptic.E(arcsin(x),-1))
@test integrate((1+x^2)^(1/2)*(2+-3*x^2)^-1//2, x) == :(1//3*3^(1/2)*Elliptic.E(arcsin((1/2)*x*6^(1/2)),-2//3))
@test integrate((2+-3*x^2)^-1//2*(4+x^2)^(1/2), x) == :(2//3*3^(1/2)*Elliptic.E(arcsin((1/2)*x*6^(1/2)),-1//6))
@test integrate((1+4*x^2)^(1/2)*(2+-3*x^2)^-1//2, x) == :(1//3*3^(1/2)*Elliptic.E(arcsin((1/2)*x*6^(1/2)),-8//3))
@test integrate((1+x^2)^-1//2*(1+-1*x^2)^(1/2), x) == :(-1*Elliptic.E(arcsin(x),-1)+2*Elliptic.F(arcsin(x),-1))
@test integrate((1+-1*x^2)^(1/2)*(2+3*x^2)^-1//2, x) == :(-1//3*2^(1/2)*Elliptic.E(arcsin(x),-3//2)+5//6*2^(1/2)*Elliptic.F(arcsin(x),-3//2))
@test integrate((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)+7//3*2^(1/2)*Elliptic.F(arcsin((1/2)*x),-6))
@test integrate((1+-4*x^2)^(1/2)*(2+3*x^2)^-1//2, x) == :(-2//3*2^(1/2)*Elliptic.E(arcsin(2x),-3//8)+11//12*2^(1/2)*Elliptic.F(arcsin(2x),-3//8))
@test integrate((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)+(1/2)*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.F(arctan(x),-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((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+2*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.F(arctan((1/2)*x),-5)+-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((1+4*x^2)^(1/2)*(2+3*x^2)^-1//2, x) == :(4//3*x*(1+4*x^2)^-1//2*(2+3*x^2)^(1/2)+-2//3*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)+1//4*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.F(arctan(2x),5//8))
@test integrate((1+-1*x^2)^(1/2)*(-1+2*x^2)^-1//2, x) == :((1/2)*2^(1/2)*(1+-2*x^2)^(1/2)*(-1+2*x^2)^-1//2*Elliptic.E(arcsin(x*2^(1/2)),1/2))
@test integrate((a+b*x^2)^7//2*(c+d*x^2)^-1//2, x) == :(1//7*b*x*d^-1*(a+b*x^2)^5//2*(c+d*x^2)^(1/2)+-6//35*b*x*d^-2*(a+b*x^2)^3//2*(c+d*x^2)^(1/2)*(b*c+-2*a*d)+-1//105*x*d^-3*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(-16*a*d+8*b*c)*(6*b^2*c^2+11*a^2*d^2+-11*a*b*c*d)+1//105*b*x*d^-3*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(24*b^2*c^2+71*a^2*d^2+-71*a*b*c*d)+-1//105*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*(-7*a*d+3*b*c)*(8*b^2*c^2+15*a^2*d^2+-11*a*b*c*d)*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1)+8//105*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*(b*c+-2*a*d)*(6*b^2*c^2+11*a^2*d^2+-11*a*b*c*d)*Elliptic.E(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1))
@test integrate((a+b*x^2)^5//2*(c+d*x^2)^-1//2, x) == :(1//5*b*x*d^-1*(a+b*x^2)^3//2*(c+d*x^2)^(1/2)+1//15*x*d^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(8*b^2*c^2+23*a^2*d^2+-23*a*b*c*d)+-4//15*b*x*d^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(b*c+-2*a*d)+-1//15*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*b^2*c^2+23*a^2*d^2+-23*a*b*c*d)*Elliptic.E(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1)+1//15*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*(4*b^2*c^2+15*a^2*d^2+-11*a*b*c*d)*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1))
@test integrate((a+b*x^2)^3//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*(-4*a*d+2*b*c)+1//3*b*x*d^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)+-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*(b*c+-3*a*d)*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1)+2//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*(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((a+b*x^2)^(1/2)*(c+d*x^2)^-1//2, x) == :(x*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//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)+-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((a+b*x^2)^-1//2*(c+d*x^2)^-1//2, x) == :(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((a+b*x^2)^-3//2*(c+d*x^2)^-1//2, x) == :(b*x*a^-1*(a+b*x^2)^-1//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1+-1*d*x*a^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-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*(b*c+-1*a*d)^-1*Elliptic.E(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1)+-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*(b*c+-1*a*d)^-1*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1))
@test integrate((a+b*x^2)^-5//2*(c+d*x^2)^-1//2, x) == :(1//3*b*x*a^-1*(a+b*x^2)^-3//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1+2//3*a^-3//2*b^(1/2)*(a*c^-1*(a+b*x^2)^-1*(c+d*x^2))^-1//2*(a+b*x^2)^-1//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-2*(b*c+-2*a*d)*Elliptic.E(arctan(x*a^-1//2*b^(1/2)),1+-1*a*d*b^-1*c^-1)+-1//3*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*(b*c+-1*a*d)^-2*(b*c+-3*a*d)*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1))
@test integrate((a+b*x^2)^-7//2*(c+d*x^2)^-1//2, x) == :(1//5*b*x*a^-1*(a+b*x^2)^-5//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-1+4//15*b*x*a^-2*(a+b*x^2)^-3//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-2*(b*c+-2*a*d)+1//15*a^-5//2*b^(1/2)*(a*c^-1*(a+b*x^2)^-1*(c+d*x^2))^-1//2*(a+b*x^2)^-1//2*(c+d*x^2)^(1/2)*(b*c+-1*a*d)^-3*(8*b^2*c^2+23*a^2*d^2+-23*a*b*c*d)*Elliptic.E(arctan(x*a^-1//2*b^(1/2)),1+-1*a*d*b^-1*c^-1)+-1//15*a^-3*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*(b*c+-1*a*d)^-3*(4*b^2*c^2+15*a^2*d^2+-11*a*b*c*d)*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1))
@test integrate((a+b*x^2)^7//2*(c+d*x^2)^-3//2, x) == :(-1*x*c^-1*d^-1*(a+b*x^2)^5//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)+1//15*x*c^-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//15*b*x*c^-1*d^-3*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(15*a^2*d^2+24*b^2*c^2+-43*a*b*c*d)+-1//15*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)+1//5*b*x*c^-1*d^-2*(a+b*x^2)^3//2*(c+d*x^2)^(1/2)*(-5*a*d+6*b*c)+1//15*b*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*(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))
@test integrate((a+b*x^2)^5//2*(c+d*x^2)^-3//2, x) == :(-1*x*c^-1*d^-1*(a+b*x^2)^3//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)+-1//3*x*c^-1*d^-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)+1//3*b*x*c^-1*d^-2*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)*(-3*a*d+4*b*c)+1//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*(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)+-2//3*b*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*d+2*b*c)*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1))
@test integrate((a+b*x^2)^3//2*(c+d*x^2)^-3//2, x) == :(x*c^-1*d^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(-1*a*d+2*b*c)+-1*x*c^-1*d^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2*(b*c+-1*a*d)+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*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1)+-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((a+b*x^2)^(1/2)*(c+d*x^2)^-3//2, x) == :(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((a+b*x^2)^-1//2*(c+d*x^2)^-3//2, x) == :(-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*(b*c+-1*a*d)^-1*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*(b*c+-1*a*d)^-1*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1))
@test integrate((a+b*x^2)^-3//2*(c+d*x^2)^-3//2, x) == :(b*x*a^-1*(a+b*x^2)^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-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*(b*c+-1*a*d)^-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*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*(b*c+-1*a*d)^-2*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1))
@test integrate((a+b*x^2)^-5//2*(c+d*x^2)^-3//2, x) == :(1//3*b*x*a^-1*(a+b*x^2)^-3//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-1+2//3*b*x*a^-2*(a+b*x^2)^-1//2*(c+d*x^2)^-1//2*(b*c+-1*a*d)^-2*(b*c+-3*a*d)+1//3*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*(b*c+-1*a*d)^-3*(-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*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*(b*c+-1*a*d)^-3*(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((a+b*x^2)^-1//2*(c+d*x^2)^-1//2, x) == :(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((a+-1*b*x^2)^-1//2*(c+d*x^2)^-1//2, x) == :(a^(1/2)*b^-1//2*(1+d*c^-1*x^2)^(1/2)*(1+-1*b*a^-1*x^2)^(1/2)*(a+-1*b*x^2)^-1//2*(c+d*x^2)^-1//2*Elliptic.F(arcsin(x*a^-1//2*b^(1/2)),-1*a*d*b^-1*c^-1))
@test integrate((a+b*x^2)^-1//2*(c+-1*d*x^2)^-1//2, x) == :(c^(1/2)*d^-1//2*(1+b*a^-1*x^2)^(1/2)*(1+-1*d*c^-1*x^2)^(1/2)*(a+b*x^2)^-1//2*(c+-1*d*x^2)^-1//2*Elliptic.F(arcsin(x*c^-1//2*d^(1/2)),-1*b*c*a^-1*d^-1))
@test integrate((a+-1*b*x^2)^-1//2*(c+-1*d*x^2)^-1//2, x) == :(c^(1/2)*d^-1//2*(1+-1*b*a^-1*x^2)^(1/2)*(1+-1*d*c^-1*x^2)^(1/2)*(a+-1*b*x^2)^-1//2*(c+-1*d*x^2)^-1//2*Elliptic.F(arcsin(x*c^-1//2*d^(1/2)),b*c*a^-1*d^-1))
@test integrate((1+-1*x^2)^-1//2*(2+5*x^2)^-1//2, x) == :((1/2)*2^(1/2)*Elliptic.F(arcsin(x),-5//2))
@test integrate((1+-1*x^2)^-1//2*(2+4*x^2)^-1//2, x) == :((1/2)*2^(1/2)*Elliptic.F(arcsin(x),-2))
@test integrate((1+-1*x^2)^-1//2*(2+3*x^2)^-1//2, x) == :((1/2)*2^(1/2)*Elliptic.F(arcsin(x),-3//2))
@test integrate((1+-1*x^2)^-1//2*(2+2*x^2)^-1//2, x) == :((1/2)*2^(1/2)*Elliptic.F(arcsin(x),-1))
@test integrate((1+-1*x^2)^-1//2*(2+x^2)^-1//2, x) == :((1/2)*2^(1/2)*Elliptic.F(arcsin(x),-1//2))
@test integrate((1+-1*x^2)^-1//2*(2+-1*x^2)^-1//2, x) == :((1/2)*2^(1/2)*Elliptic.F(arcsin(x),1/2))
@test integrate((1+-1*x^2)^-1//2*(2+-2*x^2)^-1//2, x) == :((1/2)*2^(1/2)*arctanh(x))
@test integrate((1+-1*x^2)^-1//2*(2+-3*x^2)^-1//2, x) == :((1/2)*2^(1/2)*Elliptic.F(arcsin(x),3//2))
@test integrate((1+-1*x^2)^-1//2*(2+-4*x^2)^-1//2, x) == :((1/2)*2^(1/2)*Elliptic.F(arcsin(x),2))
@test integrate((1+-1*x^2)^-1//2*(2+-5*x^2)^-1//2, x) == :((1/2)*2^(1/2)*Elliptic.F(arcsin(x),5//2))
@test integrate((1+x^2)^-1//2*(2+5*x^2)^-1//2, x) == :((1/2)*2^(1/2)*((1+x^2)^-1*(2+5*x^2))^-1//2*(1+x^2)^-1//2*(2+5*x^2)^(1/2)*Elliptic.F(arctan(x),-3//2))
@test integrate((1+x^2)^-1//2*(2+4*x^2)^-1//2, x) == :((1/2)*2^(1/2)*((1+x^2)^-1*(1+2*x^2))^-1//2*(1+x^2)^-1//2*(1+2*x^2)^(1/2)*Elliptic.F(arctan(x),-1))
@test integrate((1+x^2)^-1//2*(2+3*x^2)^-1//2, x) == :((1/2)*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.F(arctan(x),-1//2))
@test integrate((1+x^2)^-1//2*(2+2*x^2)^-1//2, x) == :((1/2)*2^(1/2)*arctan(x))
@test integrate((1+x^2)^-1//2*(2+x^2)^-1//2, x) == :((1/2)*2^(1/2)*((1+x^2)^-1*(2+x^2))^-1//2*(1+x^2)^-1//2*(2+x^2)^(1/2)*Elliptic.F(arctan(x),1/2))
@test integrate((1+x^2)^-1//2*(2+-1*x^2)^-1//2, x) == :(Elliptic.F(arcsin((1/2)*x*2^(1/2)),-2))
@test integrate((1+x^2)^-1//2*(2+-2*x^2)^-1//2, x) == :((1/2)*2^(1/2)*Elliptic.F(arcsin(x),-1))
@test integrate((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))
@test integrate((1+x^2)^-1//2*(2+-4*x^2)^-1//2, x) == :((1/2)*Elliptic.F(arcsin(x*2^(1/2)),-1//2))
@test integrate((1+x^2)^-1//2*(2+-5*x^2)^-1//2, x) == :(1//5*5^(1/2)*Elliptic.F(arcsin((1/2)*x*10^(1/2)),-2//5))
@test integrate((-1+x^2)^-1//2*(2+5*x^2)^-1//2, x) == :((1/2)*2^(1/2)*(1+-1*x^2)^(1/2)*(-1+x^2)^-1//2*Elliptic.F(arcsin(x),-5//2))
@test integrate((-1+x^2)^-1//2*(2+4*x^2)^-1//2, x) == :((1/2)*2^(1/2)*(1+-1*x^2)^(1/2)*(-1+x^2)^-1//2*Elliptic.F(arcsin(x),-2))
@test integrate((-1+x^2)^-1//2*(2+3*x^2)^-1//2, x) == :((1/2)*2^(1/2)*(1+-1*x^2)^(1/2)*(-1+x^2)^-1//2*Elliptic.F(arcsin(x),-3//2))
@test integrate((-1+x^2)^-1//2*(2+2*x^2)^-1//2, x) == :((1/2)*Elliptic.F(arcsin(x*2^(1/2)*(-1+x^2)^-1//2),1/2))
@test integrate((-1+x^2)^-1//2*(2+x^2)^-1//2, x) == :((1/2)*2^(1/2)*(1+-1*x^2)^(1/2)*(-1+x^2)^-1//2*Elliptic.F(arcsin(x),-1//2))
@test integrate((-1+x^2)^-1//2*(2+-1*x^2)^-1//2, x) == :(-1*Elliptic.F(arccos((1/2)*x*2^(1/2)),2))
@test integrate((-1+x^2)^-1//2*(2+-2*x^2)^-1//2, x) == :(-1//2*2^(1/2)*(1+-1*x^2)^-1//2*(-1+x^2)^(1/2)*arctanh(x))
@test integrate((-1+x^2)^-1//2*(2+-3*x^2)^-1//2, x) == :((1/2)*2^(1/2)*(1+-1*x^2)^(1/2)*(-1+x^2)^-1//2*Elliptic.F(arcsin(x),3//2))
@test integrate((-1+x^2)^-1//2*(2+-4*x^2)^-1//2, x) == :((1/2)*2^(1/2)*(1+-1*x^2)^(1/2)*(-1+x^2)^-1//2*Elliptic.F(arcsin(x),2))
@test integrate((-1+x^2)^-1//2*(2+-5*x^2)^-1//2, x) == :((1/2)*2^(1/2)*(1+-1*x^2)^(1/2)*(-1+x^2)^-1//2*Elliptic.F(arcsin(x),5//2))
@test integrate((-1+-1*x^2)^-1//2*(2+5*x^2)^-1//2, x) == :((1/2)*2^(1/2)*((1+x^2)^-1*(2+5*x^2))^-1//2*(-1+-1*x^2)^-1//2*(2+5*x^2)^(1/2)*Elliptic.F(arctan(x),-3//2))
@test integrate((-1+-1*x^2)^-1//2*(2+4*x^2)^-1//2, x) == :((1/2)*2^(1/2)*((1+x^2)^-1*(1+2*x^2))^-1//2*(1+2*x^2)^(1/2)*(-1+-1*x^2)^-1//2*Elliptic.F(arctan(x),-1))
@test integrate((-1+-1*x^2)^-1//2*(2+3*x^2)^-1//2, x) == :((1/2)*2^(1/2)*((1+x^2)^-1*(2+3*x^2))^-1//2*(-1+-1*x^2)^-1//2*(2+3*x^2)^(1/2)*Elliptic.F(arctan(x),-1//2))
@test integrate((-1+-1*x^2)^-1//2*(2+2*x^2)^-1//2, x) == :((1/2)*2^(1/2)*(1+x^2)^(1/2)*(-1+-1*x^2)^-1//2*arctan(x))
@test integrate((-1+-1*x^2)^-1//2*(2+x^2)^-1//2, x) == :((1/2)*2^(1/2)*((1+x^2)^-1*(2+x^2))^-1//2*(-1+-1*x^2)^-1//2*(2+x^2)^(1/2)*Elliptic.F(arctan(x),1/2))
@test integrate((-1+-1*x^2)^-1//2*(2+-1*x^2)^-1//2, x) == :((1+x^2)^(1/2)*(-1+-1*x^2)^-1//2*Elliptic.F(arcsin((1/2)*x*2^(1/2)),-2))
@test integrate((-1+-1*x^2)^-1//2*(2+-3*x^2)^-1//2, x) == :(1//3*3^(1/2)*(1+x^2)^(1/2)*(-1+-1*x^2)^-1//2*Elliptic.F(arcsin((1/2)*x*6^(1/2)),-2//3))
@test integrate((-1+-1*x^2)^-1//2*(2+-4*x^2)^-1//2, x) == :((1/2)*(1+x^2)^(1/2)*(-1+-1*x^2)^-1//2*Elliptic.F(arcsin(x*2^(1/2)),-1//2))
@test integrate((-1+-1*x^2)^-1//2*(2+-5*x^2)^-1//2, x) == :(1//5*5^(1/2)*(1+x^2)^(1/2)*(-1+-1*x^2)^-1//2*Elliptic.F(arcsin((1/2)*x*10^(1/2)),-2//5))
@test integrate((a+b*x^2)^(1/2)*(c+-1*d*x^2)^-1//2, x) == :(c^(1/2)*d^-1//2*(1+b*a^-1*x^2)^-1//2*(1+-1*d*c^-1*x^2)^(1/2)*(a+b*x^2)^(1/2)*(c+-1*d*x^2)^-1//2*Elliptic.E(arcsin(x*c^-1//2*d^(1/2)),-1*b*c*a^-1*d^-1))
@test integrate((c+-1*d*x^2)^-1//2*(-1a+-1*b*x^2)^(1/2), x) == :(c^(1/2)*d^-1//2*(1+b*a^-1*x^2)^-1//2*(1+-1*d*c^-1*x^2)^(1/2)*(c+-1*d*x^2)^-1//2*(-1a+-1*b*x^2)^(1/2)*Elliptic.E(arcsin(x*c^-1//2*d^(1/2)),-1*b*c*a^-1*d^-1))
@test integrate((a+b*x^2)^(1/2)*(-1c+d*x^2)^-1//2, x) == :(c^(1/2)*d^-1//2*(1+b*a^-1*x^2)^-1//2*(1+-1*d*c^-1*x^2)^(1/2)*(a+b*x^2)^(1/2)*(-1c+d*x^2)^-1//2*Elliptic.E(arcsin(x*c^-1//2*d^(1/2)),-1*b*c*a^-1*d^-1))
@test integrate((-1a+-1*b*x^2)^(1/2)*(-1c+d*x^2)^-1//2, x) == :(c^(1/2)*d^-1//2*(1+b*a^-1*x^2)^-1//2*(1+-1*d*c^-1*x^2)^(1/2)*(-1a+-1*b*x^2)^(1/2)*(-1c+d*x^2)^-1//2*Elliptic.E(arcsin(x*c^-1//2*d^(1/2)),-1*b*c*a^-1*d^-1))
@test integrate((a+-1*b*x^2)^(1/2)*(c+-1*d*x^2)^-1//2, x) == :(c^(1/2)*d^-1//2*(1+-1*b*a^-1*x^2)^-1//2*(1+-1*d*c^-1*x^2)^(1/2)*(a+-1*b*x^2)^(1/2)*(c+-1*d*x^2)^-1//2*Elliptic.E(arcsin(x*c^-1//2*d^(1/2)),b*c*a^-1*d^-1))
@test integrate((c+-1*d*x^2)^-1//2*(-1a+b*x^2)^(1/2), x) == :(c^(1/2)*d^-1//2*(1+-1*b*a^-1*x^2)^-1//2*(1+-1*d*c^-1*x^2)^(1/2)*(c+-1*d*x^2)^-1//2*(-1a+b*x^2)^(1/2)*Elliptic.E(arcsin(x*c^-1//2*d^(1/2)),b*c*a^-1*d^-1))
@test integrate((a+-1*b*x^2)^(1/2)*(-1c+d*x^2)^-1//2, x) == :(c^(1/2)*d^-1//2*(1+-1*b*a^-1*x^2)^-1//2*(1+-1*d*c^-1*x^2)^(1/2)*(a+-1*b*x^2)^(1/2)*(-1c+d*x^2)^-1//2*Elliptic.E(arcsin(x*c^-1//2*d^(1/2)),b*c*a^-1*d^-1))
@test integrate((-1a+b*x^2)^(1/2)*(-1c+d*x^2)^-1//2, x) == :(c^(1/2)*d^-1//2*(1+-1*b*a^-1*x^2)^-1//2*(1+-1*d*c^-1*x^2)^(1/2)*(-1a+b*x^2)^(1/2)*(-1c+d*x^2)^-1//2*Elliptic.E(arcsin(x*c^-1//2*d^(1/2)),b*c*a^-1*d^-1))
@test integrate((a+b*x^2)^(1/2)*(c+d*x^2)^-1//2, x) == :(x*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//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)+-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((c+d*x^2)^-1//2*(-1a+-1*b*x^2)^(1/2), x) == :(x*(c+d*x^2)^-1//2*(-1a+-1*b*x^2)^(1/2)+c^(1/2)*d^-1//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(c+d*x^2)^-1//2*(-1a+-1*b*x^2)^(1/2)*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1)+-1*c^(1/2)*d^-1//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(c+d*x^2)^-1//2*(-1a+-1*b*x^2)^(1/2)*Elliptic.E(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1))
@test integrate((a+b*x^2)^(1/2)*(-1c+-1*d*x^2)^-1//2, x) == :(x*(a+b*x^2)^(1/2)*(-1c+-1*d*x^2)^-1//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)*(-1c+-1*d*x^2)^-1//2*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1)+-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)*(-1c+-1*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((-1a+-1*b*x^2)^(1/2)*(-1c+-1*d*x^2)^-1//2, x) == :(x*(-1a+-1*b*x^2)^(1/2)*(-1c+-1*d*x^2)^-1//2+c^(1/2)*d^-1//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(-1a+-1*b*x^2)^(1/2)*(-1c+-1*d*x^2)^-1//2*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1)+-1*c^(1/2)*d^-1//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(-1a+-1*b*x^2)^(1/2)*(-1c+-1*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((a+-1*b*x^2)^(1/2)*(c+d*x^2)^-1//2, x) == :(-1*a^(1/2)*b^(1/2)*d^-1*(1+d*c^-1*x^2)^-1//2*(1+-1*b*a^-1*x^2)^(1/2)*(a+-1*b*x^2)^-1//2*(c+d*x^2)^(1/2)*Elliptic.E(arcsin(x*a^-1//2*b^(1/2)),-1*a*d*b^-1*c^-1)+a^(1/2)*b^-1//2*d^-1*(1+d*c^-1*x^2)^(1/2)*(1+-1*b*a^-1*x^2)^(1/2)*(a+-1*b*x^2)^-1//2*(c+d*x^2)^-1//2*(a*d+b*c)*Elliptic.F(arcsin(x*a^-1//2*b^(1/2)),-1*a*d*b^-1*c^-1))
@test integrate((c+d*x^2)^-1//2*(-1a+b*x^2)^(1/2), x) == :(a^(1/2)*b^(1/2)*d^-1*(1+d*c^-1*x^2)^-1//2*(1+-1*b*a^-1*x^2)^(1/2)*(c+d*x^2)^(1/2)*(-1a+b*x^2)^-1//2*Elliptic.E(arcsin(x*a^-1//2*b^(1/2)),-1*a*d*b^-1*c^-1)+-1*a^(1/2)*b^-1//2*d^-1*(1+d*c^-1*x^2)^(1/2)*(1+-1*b*a^-1*x^2)^(1/2)*(c+d*x^2)^-1//2*(-1a+b*x^2)^-1//2*(a*d+b*c)*Elliptic.F(arcsin(x*a^-1//2*b^(1/2)),-1*a*d*b^-1*c^-1))
@test integrate((a+-1*b*x^2)^(1/2)*(-1c+-1*d*x^2)^-1//2, x) == :(a^(1/2)*b^(1/2)*d^-1*(1+d*c^-1*x^2)^-1//2*(1+-1*b*a^-1*x^2)^(1/2)*(a+-1*b*x^2)^-1//2*(-1c+-1*d*x^2)^(1/2)*Elliptic.E(arcsin(x*a^-1//2*b^(1/2)),-1*a*d*b^-1*c^-1)+a^(1/2)*b^-1//2*d^-1*(1+d*c^-1*x^2)^(1/2)*(1+-1*b*a^-1*x^2)^(1/2)*(a+-1*b*x^2)^-1//2*(-1c+-1*d*x^2)^-1//2*(a*d+b*c)*Elliptic.F(arcsin(x*a^-1//2*b^(1/2)),-1*a*d*b^-1*c^-1))
@test integrate((-1a+b*x^2)^(1/2)*(-1c+-1*d*x^2)^-1//2, x) == :(-1*a^(1/2)*b^(1/2)*d^-1*(1+d*c^-1*x^2)^-1//2*(1+-1*b*a^-1*x^2)^(1/2)*(-1a+b*x^2)^-1//2*(-1c+-1*d*x^2)^(1/2)*Elliptic.E(arcsin(x*a^-1//2*b^(1/2)),-1*a*d*b^-1*c^-1)+-1*a^(1/2)*b^-1//2*d^-1*(1+d*c^-1*x^2)^(1/2)*(1+-1*b*a^-1*x^2)^(1/2)*(-1a+b*x^2)^-1//2*(-1c+-1*d*x^2)^-1//2*(a*d+b*c)*Elliptic.F(arcsin(x*a^-1//2*b^(1/2)),-1*a*d*b^-1*c^-1))
@test integrate((a+-1*b*x^2)^-1//2*(c+d*x^2)^(1/2), x) == :(a^(1/2)*b^-1//2*(1+d*c^-1*x^2)^-1//2*(1+-1*b*a^-1*x^2)^(1/2)*(a+-1*b*x^2)^-1//2*(c+d*x^2)^(1/2)*Elliptic.E(arcsin(x*a^-1//2*b^(1/2)),-1*a*d*b^-1*c^-1))
@test integrate((a+-1*b*x^2)^-1//2*(-1c+-1*d*x^2)^(1/2), x) == :(a^(1/2)*b^-1//2*(1+d*c^-1*x^2)^-1//2*(1+-1*b*a^-1*x^2)^(1/2)*(a+-1*b*x^2)^-1//2*(-1c+-1*d*x^2)^(1/2)*Elliptic.E(arcsin(x*a^-1//2*b^(1/2)),-1*a*d*b^-1*c^-1))
@test integrate((c+d*x^2)^(1/2)*(-1a+b*x^2)^-1//2, x) == :(a^(1/2)*b^-1//2*(1+d*c^-1*x^2)^-1//2*(1+-1*b*a^-1*x^2)^(1/2)*(c+d*x^2)^(1/2)*(-1a+b*x^2)^-1//2*Elliptic.E(arcsin(x*a^-1//2*b^(1/2)),-1*a*d*b^-1*c^-1))
@test integrate((-1a+b*x^2)^-1//2*(-1c+-1*d*x^2)^(1/2), x) == :(a^(1/2)*b^-1//2*(1+d*c^-1*x^2)^-1//2*(1+-1*b*a^-1*x^2)^(1/2)*(-1a+b*x^2)^-1//2*(-1c+-1*d*x^2)^(1/2)*Elliptic.E(arcsin(x*a^-1//2*b^(1/2)),-1*a*d*b^-1*c^-1))
@test integrate((a+-1*b*x^2)^-1//2*(c+-1*d*x^2)^(1/2), x) == :(a^(1/2)*b^-1//2*(1+-1*b*a^-1*x^2)^(1/2)*(1+-1*d*c^-1*x^2)^-1//2*(a+-1*b*x^2)^-1//2*(c+-1*d*x^2)^(1/2)*Elliptic.E(arcsin(x*a^-1//2*b^(1/2)),a*d*b^-1*c^-1))
@test integrate((a+-1*b*x^2)^-1//2*(-1c+d*x^2)^(1/2), x) == :(a^(1/2)*b^-1//2*(1+-1*b*a^-1*x^2)^(1/2)*(1+-1*d*c^-1*x^2)^-1//2*(a+-1*b*x^2)^-1//2*(-1c+d*x^2)^(1/2)*Elliptic.E(arcsin(x*a^-1//2*b^(1/2)),a*d*b^-1*c^-1))
@test integrate((c+-1*d*x^2)^(1/2)*(-1a+b*x^2)^-1//2, x) == :(a^(1/2)*b^-1//2*(1+-1*b*a^-1*x^2)^(1/2)*(1+-1*d*c^-1*x^2)^-1//2*(c+-1*d*x^2)^(1/2)*(-1a+b*x^2)^-1//2*Elliptic.E(arcsin(x*a^-1//2*b^(1/2)),a*d*b^-1*c^-1))
@test integrate((-1a+b*x^2)^-1//2*(-1c+d*x^2)^(1/2), x) == :(a^(1/2)*b^-1//2*(1+-1*b*a^-1*x^2)^(1/2)*(1+-1*d*c^-1*x^2)^-1//2*(-1a+b*x^2)^-1//2*(-1c+d*x^2)^(1/2)*Elliptic.E(arcsin(x*a^-1//2*b^(1/2)),a*d*b^-1*c^-1))
@test integrate((a+b*x^2)^-1//2*(c+d*x^2)^(1/2), x) == :(d*x*b^-1*(a+b*x^2)^(1/2)*(c+d*x^2)^-1//2+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*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1)+-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((a+b*x^2)^-1//2*(-1c+-1*d*x^2)^(1/2), x) == :(-1*d*x*b^-1*(a+b*x^2)^(1/2)*(-1c+-1*d*x^2)^-1//2+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)*(-1c+-1*d*x^2)^-1//2*Elliptic.E(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1)+-1*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)*(-1c+-1*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((c+d*x^2)^(1/2)*(-1a+-1*b*x^2)^-1//2, x) == :(-1*d*x*b^-1*(c+d*x^2)^-1//2*(-1a+-1*b*x^2)^(1/2)+b^-1*c^(1/2)*d^(1/2)*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(c+d*x^2)^-1//2*(-1a+-1*b*x^2)^(1/2)*Elliptic.E(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1)+-1*a^-1*c^3//2*d^-1//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(c+d*x^2)^-1//2*(-1a+-1*b*x^2)^(1/2)*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1))
@test integrate((-1a+-1*b*x^2)^-1//2*(-1c+-1*d*x^2)^(1/2), x) == :(d*x*b^-1*(-1a+-1*b*x^2)^(1/2)*(-1c+-1*d*x^2)^-1//2+a^-1*c^3//2*d^-1//2*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(-1a+-1*b*x^2)^(1/2)*(-1c+-1*d*x^2)^-1//2*Elliptic.F(arctan(x*c^-1//2*d^(1/2)),1+-1*b*c*a^-1*d^-1)+-1*b^-1*c^(1/2)*d^(1/2)*(c*a^-1*(c+d*x^2)^-1*(a+b*x^2))^-1//2*(-1a+-1*b*x^2)^(1/2)*(-1c+-1*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((a+b*x^2)^-1//2*(c+-1*d*x^2)^(1/2), x) == :(-1*b^-1*c^(1/2)*d^(1/2)*(1+b*a^-1*x^2)^-1//2*(1+-1*d*c^-1*x^2)^(1/2)*(a+b*x^2)^(1/2)*(c+-1*d*x^2)^-1//2*Elliptic.E(arcsin(x*c^-1//2*d^(1/2)),-1*b*c*a^-1*d^-1)+b^-1*c^(1/2)*d^-1//2*(1+b*a^-1*x^2)^(1/2)*(1+-1*d*c^-1*x^2)^(1/2)*(a+b*x^2)^-1//2*(c+-1*d*x^2)^-1//2*(a*d+b*c)*Elliptic.F(arcsin(x*c^-1//2*d^(1/2)),-1*b*c*a^-1*d^-1))
@test integrate((a+b*x^2)^-1//2*(-1c+d*x^2)^(1/2), x) == :(b^-1*c^(1/2)*d^(1/2)*(1+b*a^-1*x^2)^-1//2*(1+-1*d*c^-1*x^2)^(1/2)*(a+b*x^2)^(1/2)*(-1c+d*x^2)^-1//2*Elliptic.E(arcsin(x*c^-1//2*d^(1/2)),-1*b*c*a^-1*d^-1)+-1*b^-1*c^(1/2)*d^-1//2*(1+b*a^-1*x^2)^(1/2)*(1+-1*d*c^-1*x^2)^(1/2)*(a+b*x^2)^-1//2*(-1c+d*x^2)^-1//2*(a*d+b*c)*Elliptic.F(arcsin(x*c^-1//2*d^(1/2)),-1*b*c*a^-1*d^-1))
@test integrate((c+-1*d*x^2)^(1/2)*(-1a+-1*b*x^2)^-1//2, x) == :(b^-1*c^(1/2)*d^(1/2)*(1+b*a^-1*x^2)^-1//2*(1+-1*d*c^-1*x^2)^(1/2)*(c+-1*d*x^2)^-1//2*(-1a+-1*b*x^2)^(1/2)*Elliptic.E(arcsin(x*c^-1//2*d^(1/2)),-1*b*c*a^-1*d^-1)+b^-1*c^(1/2)*d^-1//2*(1+b*a^-1*x^2)^(1/2)*(1+-1*d*c^-1*x^2)^(1/2)*(c+-1*d*x^2)^-1//2*(-1a+-1*b*x^2)^-1//2*(a*d+b*c)*Elliptic.F(arcsin(x*c^-1//2*d^(1/2)),-1*b*c*a^-1*d^-1))
@test integrate((-1a+-1*b*x^2)^-1//2*(-1c+d*x^2)^(1/2), x) == :(-1*b^-1*c^(1/2)*d^(1/2)*(1+b*a^-1*x^2)^-1//2*(1+-1*d*c^-1*x^2)^(1/2)*(-1a+-1*b*x^2)^(1/2)*(-1c+d*x^2)^-1//2*Elliptic.E(arcsin(x*c^-1//2*d^(1/2)),-1*b*c*a^-1*d^-1)+-1*b^-1*c^(1/2)*d^-1//2*(1+b*a^-1*x^2)^(1/2)*(1+-1*d*c^-1*x^2)^(1/2)*(-1a+-1*b*x^2)^-1//2*(-1c+d*x^2)^-1//2*(a*d+b*c)*Elliptic.F(arcsin(x*c^-1//2*d^(1/2)),-1*b*c*a^-1*d^-1))
@test integrate((2+b*x^2)^-1//2*(3+d*x^2)^-1//2, x) == :((1/2)*2^(1/2)*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.F(arctan(1//3*x*3^(1/2)*d^(1/2)),1+-3//2*b*d^-1))
@test integrate((4+-1*x^2)^-1//2*(c+d*x^2)^-1//2, x) == :((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((4+x^2)^-1//2*(c+d*x^2)^-1//2, x) == :(c^-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.F(arctan((1/2)*x),1+-4*d*c^-1))
@test integrate((1+-1*x^2)^-1//2*(-1+2*x^2)^-1//2, x) == :(-1*Elliptic.F(arccos(x),2))
@test integrate((1+c^2*x^2)^-1//2*(1+-1*c^2*x^2)^(1/2), x) == :(-1*c^-1*Elliptic.E(arcsin(c*x),-1)+2*c^-1*Elliptic.F(arcsin(c*x),-1))
@test integrate((2+b*x^2)^(1/2)*(3+d*x^2)^-1//2, x) == :(x*(2+b*x^2)^(1/2)*(3+d*x^2)^-1//2+2^(1/2)*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.F(arctan(1//3*x*3^(1/2)*d^(1/2)),1+-3//2*b*d^-1)+-1*2^(1/2)*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((-1+3*x^2)^(1/2)*(2+-3*x^2)^-1//2, x) == :(-1//3*3^(1/2)*Elliptic.E(arccos((1/2)*x*6^(1/2)),2))
@test integrate((1+-2*c*x^2*(b+(b^2+-4*a*c)^(1/2))^-1)^-1//2*(1+2*c*x^2*(b+-1*(b^2+-4*a*c)^(1/2))^-1)^(1/2), x) == :((1/2)*2^(1/2)*c^-1//2*(b+(b^2+-4*a*c)^(1/2))^(1/2)*Elliptic.E(arcsin(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2),-1*(b+-1*(b^2+-4*a*c)^(1/2))^-1*(b+(b^2+-4*a*c)^(1/2))))
@test integrate((1+-2*c*x^2*(b+(b^2+-4*a*c)^(1/2))^-1)^-1//2*(1+-2*c*x^2*(b+-1*(b^2+-4*a*c)^(1/2))^-1)^(1/2), x) == :((1/2)*2^(1/2)*c^-1//2*(b+(b^2+-4*a*c)^(1/2))^(1/2)*Elliptic.E(arcsin(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2),(b+-1*(b^2+-4*a*c)^(1/2))^-1*(b+(b^2+-4*a*c)^(1/2))))
@test integrate((1+2*c*x^2*(b+(b^2+-4*a*c)^(1/2))^-1)^-1//2*(1+2*c*x^2*(b+-1*(b^2+-4*a*c)^(1/2))^-1)^(1/2), x) == :(x*(1+2*c*x^2*(b+(b^2+-4*a*c)^(1/2))^-1)^-1//2*(1+2*c*x^2*(b+-1*(b^2+-4*a*c)^(1/2))^-1)^(1/2)+(1/2)*2^(1/2)*c^-1//2*((1+2*c*x^2*(b+(b^2+-4*a*c)^(1/2))^-1)^-1*(1+2*c*x^2*(b+-1*(b^2+-4*a*c)^(1/2))^-1))^-1//2*(1+2*c*x^2*(b+(b^2+-4*a*c)^(1/2))^-1)^-1//2*(1+2*c*x^2*(b+-1*(b^2+-4*a*c)^(1/2))^-1)^(1/2)*(b+(b^2+-4*a*c)^(1/2))^(1/2)*Elliptic.F(arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2),-2*(b+-1*(b^2+-4*a*c)^(1/2))^-1*(b^2+-4*a*c)^(1/2))+-1//2*2^(1/2)*c^-1//2*((1+2*c*x^2*(b+(b^2+-4*a*c)^(1/2))^-1)^-1*(1+2*c*x^2*(b+-1*(b^2+-4*a*c)^(1/2))^-1))^-1//2*(1+2*c*x^2*(b+(b^2+-4*a*c)^(1/2))^-1)^-1//2*(1+2*c*x^2*(b+-1*(b^2+-4*a*c)^(1/2))^-1)^(1/2)*(b+(b^2+-4*a*c)^(1/2))^(1/2)*Elliptic.E(arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2),-2*(b+-1*(b^2+-4*a*c)^(1/2))^-1*(b^2+-4*a*c)^(1/2)))
@test integrate((1+-2*c*x^2*(b+-1*(b^2+-4*a*c)^(1/2))^-1)^(1/2)*(1+2*c*x^2*(b+(b^2+-4*a*c)^(1/2))^-1)^-1//2, x) == :(b*2^(1/2)*c^-1//2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*Elliptic.F(arcsin(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2),-1*(b+(b^2+-4*a*c)^(1/2))^-1*(b+-1*(b^2+-4*a*c)^(1/2)))+-1//2*2^(1/2)*c^-1//2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b+(b^2+-4*a*c)^(1/2))*Elliptic.E(arcsin(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2),-1*(b+(b^2+-4*a*c)^(1/2))^-1*(b+-1*(b^2+-4*a*c)^(1/2))))
@test integrate((-1+x^2)^-1//2*(7+x^2+-4*3^(1/2))^-1//2, x) == :((1+-1*x^2)^(1/2)*(-1+x^2)^-1//2*(7+-4*3^(1/2))^-1//2*Elliptic.F(arcsin(x),-7+-4*3^(1/2)))
@test integrate((3+x^2*(-3+3^(1/2)))^-1//2*(3+-3*3^(1/2)+2*3^(1/2)*x^2)^-1//2, x) == :(-1//6*(3+3^(1/2))^(1/2)*Elliptic.F(arccos(x*(1+-1//3*3^(1/2))^(1/2)),1/2+(1/2)*3^(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*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//12*2^1//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((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((2+b*x^2)^-1//4*(4+b*x^2)^-1, x) == :(-1//4*2^1//4*b^-1//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)))+-1//4*2^1//4*b^-1//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))))
@test integrate((2+-1*b*x^2)^-1//4*(4+-1*b*x^2)^-1, x) == :(1//4*2^1//4*b^-1//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//4*2^1//4*b^-1//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((a+3*x^2)^-1//4*(2a+3*x^2)^-1, x) == :(-1//6*3^(1/2)*a^-3//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//6*3^(1/2)*a^-3//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((a+-3*x^2)^-1//4*(-3*x^2+2a)^-1, x) == :(1//6*3^(1/2)*a^-3//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)))+1//6*3^(1/2)*a^-3//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))))
@test integrate((a+b*x^2)^-1//4*(2a+b*x^2)^-1, x) == :(-1//2*a^-3//4*b^-1//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)))+-1//2*a^-3//4*b^-1//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))))
@test integrate((a+-1*b*x^2)^-1//4*(2a+-1*b*x^2)^-1, x) == :((1/2)*a^-3//4*b^-1//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)))+(1/2)*a^-3//4*b^-1//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((-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((-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((-1+b*x^2)^-1//4*(-2+b*x^2)^-1, x) == :(-1//4*2^(1/2)*b^-1//2*arctan((1/2)*x*2^(1/2)*b^(1/2)*(-1+b*x^2)^-1//4)+-1//4*2^(1/2)*b^-1//2*arctanh((1/2)*x*2^(1/2)*b^(1/2)*(-1+b*x^2)^-1//4))
@test integrate((-1+-1*b*x^2)^-1//4*(-2+-1*b*x^2)^-1, x) == :(-1//4*2^(1/2)*b^-1//2*arctan((1/2)*x*2^(1/2)*b^(1/2)*(-1+-1*b*x^2)^-1//4)+-1//4*2^(1/2)*b^-1//2*arctanh((1/2)*x*2^(1/2)*b^(1/2)*(-1+-1*b*x^2)^-1//4))
@test integrate((-1a+3*x^2)^-1//4*(-2a+3*x^2)^-1, x) == :(-1//12*6^(1/2)*a^-3//4*arctan((1/2)*x*6^(1/2)*a^-1//4*(-1a+3*x^2)^-1//4)+-1//12*6^(1/2)*a^-3//4*arctanh((1/2)*x*6^(1/2)*a^-1//4*(-1a+3*x^2)^-1//4))
@test integrate((-1a+-3*x^2)^-1//4*(-3*x^2+-2a)^-1, x) == :(-1//12*6^(1/2)*a^-3//4*arctan((1/2)*x*6^(1/2)*a^-1//4*(-1a+-3*x^2)^-1//4)+-1//12*6^(1/2)*a^-3//4*arctanh((1/2)*x*6^(1/2)*a^-1//4*(-1a+-3*x^2)^-1//4))
@test integrate((-1a+b*x^2)^-1//4*(-2a+b*x^2)^-1, x) == :(-1//4*2^(1/2)*a^-3//4*b^-1//2*arctan((1/2)*x*2^(1/2)*a^-1//4*b^(1/2)*(-1a+b*x^2)^-1//4)+-1//4*2^(1/2)*a^-3//4*b^-1//2*arctanh((1/2)*x*2^(1/2)*a^-1//4*b^(1/2)*(-1a+b*x^2)^-1//4))
@test integrate((-1a+-1*b*x^2)^-1//4*(-2a+-1*b*x^2)^-1, x) == :(-1//4*2^(1/2)*a^-3//4*b^-1//2*arctan((1/2)*x*2^(1/2)*a^-1//4*b^(1/2)*(-1a+-1*b*x^2)^-1//4)+-1//4*2^(1/2)*a^-3//4*b^-1//2*arctanh((1/2)*x*2^(1/2)*a^-1//4*b^(1/2)*(-1a+-1*b*x^2)^-1//4))
@test integrate((-1+x^2)^-1//4*(2+-1*x^2)^-1, x) == :(1//4*2^(1/2)*arctan((1/2)*x*2^(1/2)*(-1+x^2)^-1//4)+1//4*2^(1/2)*arctanh((1/2)*x*2^(1/2)*(-1+x^2)^-1//4))
@test integrate((a+b*x^2)^(-1+-1*b*c*(-2*a*d+2*b*c)^-1)*(c+d*x^2)^(-1+a*d*(-2*a*d+2*b*c)^-1), x) == :(x*a^-1*c^-1*(a+b*x^2)^(-1*b*c*(-2*a*d+2*b*c)^-1)*(c+d*x^2)^(a*d*(-2*a*d+2*b*c)^-1))

max_stars_repo_path: test/1 Algebraic functions/1.1 Binomial products/1.1.2 Quadratic/1.1.2.3 (a+b x^2)^p (c+d x^2)^q.jl