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

@test integrate(x^2*(A+B*x^3)*(a+b*x^3), x) == :(1//6*x^6*(A*b+B*a)+1//3*A*a*x^3+1//9*B*b*x^9)
@test integrate(x*(A+B*x^3)*(a+b*x^3), x) == :(1//5*x^5*(A*b+B*a)+(1/2)*A*a*x^2+1//8*B*b*x^8)
@test integrate((A+B*x^3)*(a+b*x^3), x) == :(1//4*x^4*(A*b+B*a)+A*a*x+1//7*B*b*x^7)
@test integrate(x^-1*(A+B*x^3)*(a+b*x^3), x) == :(1//3*x^3*(A*b+B*a)+A*a*log(x)+1//6*B*b*x^6)
@test integrate(x^-2*(A+B*x^3)*(a+b*x^3), x) == :((1/2)*x^2*(A*b+B*a)+-1*A*a*x^-1+1//5*B*b*x^5)
@test integrate(x^-3*(A+B*x^3)*(a+b*x^3), x) == :(x*(A*b+B*a)+-1//2*A*a*x^-2+1//4*B*b*x^4)
@test integrate(x^-4*(A+B*x^3)*(a+b*x^3), x) == :((A*b+B*a)*log(x)+-1//3*A*a*x^-3+1//3*B*b*x^3)
@test integrate(x^-5*(A+B*x^3)*(a+b*x^3), x) == :(-1*x^-1*(A*b+B*a)+(1/2)*B*b*x^2+-1//4*A*a*x^-4)
@test integrate(x^-6*(A+B*x^3)*(a+b*x^3), x) == :(-1//2*x^-2*(A*b+B*a)+B*b*x+-1//5*A*a*x^-5)
@test integrate(x^-7*(A+B*x^3)*(a+b*x^3), x) == :(-1//3*x^-3*(A*b+B*a)+B*b*log(x)+-1//6*A*a*x^-6)
@test integrate(x^2*(a+b*x^3)^2*(A+B*x^3), x) == :(1//9*b^-2*(a+b*x^3)^3*(A*b+-1*B*a)+1//12*B*b^-2*(a+b*x^3)^4)
@test integrate(x*(a+b*x^3)^2*(A+B*x^3), x) == :((1/2)*A*a^2*x^2+1//5*a*x^5*(B*a+2*A*b)+1//8*b*x^8*(A*b+2*B*a)+1//11*B*b^2*x^11)
@test integrate((a+b*x^3)^2*(A+B*x^3), x) == :(A*x*a^2+1//4*a*x^4*(B*a+2*A*b)+1//7*b*x^7*(A*b+2*B*a)+1//10*B*b^2*x^10)
@test integrate(x^-1*(a+b*x^3)^2*(A+B*x^3), x) == :(A*a^2*log(x)+1//6*A*b^2*x^6+1//9*B*b^-1*(a+b*x^3)^3+2//3*A*a*b*x^3)
@test integrate(x^-2*(a+b*x^3)^2*(A+B*x^3), x) == :((1/2)*a*x^2*(B*a+2*A*b)+-1*A*a^2*x^-1+1//5*b*x^5*(A*b+2*B*a)+1//8*B*b^2*x^8)
@test integrate(x^-3*(a+b*x^3)^2*(A+B*x^3), x) == :(a*x*(B*a+2*A*b)+-1//2*A*a^2*x^-2+1//4*b*x^4*(A*b+2*B*a)+1//7*B*b^2*x^7)
@test integrate(x^-4*(a+b*x^3)^2*(A+B*x^3), x) == :(a*(B*a+2*A*b)*log(x)+-1//3*A*a^2*x^-3+1//3*b*x^3*(A*b+2*B*a)+1//6*B*b^2*x^6)
@test integrate(x^-5*(a+b*x^3)^2*(A+B*x^3), x) == :((1/2)*b*x^2*(A*b+2*B*a)+-1*a*x^-1*(B*a+2*A*b)+-1//4*A*a^2*x^-4+1//5*B*b^2*x^5)
@test integrate(x^-6*(a+b*x^3)^2*(A+B*x^3), x) == :(b*x*(A*b+2*B*a)+-1//2*a*x^-2*(B*a+2*A*b)+-1//5*A*a^2*x^-5+1//4*B*b^2*x^4)
@test integrate(x^-7*(a+b*x^3)^2*(A+B*x^3), x) == :(b*(A*b+2*B*a)*log(x)+-1//3*a*x^-3*(B*a+2*A*b)+-1//6*A*a^2*x^-6+1//3*B*b^2*x^3)
@test integrate(x^-8*(a+b*x^3)^2*(A+B*x^3), x) == :((1/2)*B*b^2*x^2+-1*b*x^-1*(A*b+2*B*a)+-1//4*a*x^-4*(B*a+2*A*b)+-1//7*A*a^2*x^-7)
@test integrate(x^-9*(a+b*x^3)^2*(A+B*x^3), x) == :(B*x*b^2+-1//2*b*x^-2*(A*b+2*B*a)+-1//5*a*x^-5*(B*a+2*A*b)+-1//8*A*a^2*x^-8)
@test integrate(x^9*(a+b*x^3)^5*(A+B*x^3), x) == :(1//10*A*a^5*x^10+1//13*a^4*x^13*(B*a+5*A*b)+1//25*b^4*x^25*(A*b+5*B*a)+1//28*B*b^5*x^28+5//16*b*a^3*x^16*(B*a+2*A*b)+5//22*a*b^3*x^22*(A*b+2*B*a)+10//19*a^2*b^2*x^19*(A*b+B*a))
@test integrate(x^8*(a+b*x^3)^5*(A+B*x^3), x) == :(1//24*b^-4*(a+b*x^3)^8*(A*b+-3*B*a)+1//27*B*b^-4*(a+b*x^3)^9+-1//21*a*b^-4*(a+b*x^3)^7*(-3*B*a+2*A*b)+1//18*a^2*b^-4*(a+b*x^3)^6*(A*b+-1*B*a))
@test integrate(x^7*(a+b*x^3)^5*(A+B*x^3), x) == :(1//8*A*a^5*x^8+1//11*a^4*x^11*(B*a+5*A*b)+1//23*b^4*x^23*(A*b+5*B*a)+1//26*B*b^5*x^26+1//4*a*b^3*x^20*(A*b+2*B*a)+5//14*b*a^3*x^14*(B*a+2*A*b)+10//17*a^2*b^2*x^17*(A*b+B*a))
@test integrate(x^6*(a+b*x^3)^5*(A+B*x^3), x) == :(1//7*A*a^5*x^7+1//10*a^4*x^10*(B*a+5*A*b)+1//22*b^4*x^22*(A*b+5*B*a)+1//25*B*b^5*x^25+5//8*a^2*b^2*x^16*(A*b+B*a)+5//13*b*a^3*x^13*(B*a+2*A*b)+5//19*a*b^3*x^19*(A*b+2*B*a))
@test integrate(x^5*(a+b*x^3)^5*(A+B*x^3), x) == :(1//21*b^-3*(a+b*x^3)^7*(A*b+-2*B*a)+1//24*B*b^-3*(a+b*x^3)^8+-1//18*a*b^-3*(a+b*x^3)^6*(A*b+-1*B*a))
@test integrate(x^4*(a+b*x^3)^5*(A+B*x^3), x) == :(1//5*A*a^5*x^5+1//8*a^4*x^8*(B*a+5*A*b)+1//20*b^4*x^20*(A*b+5*B*a)+1//23*B*b^5*x^23+5//7*a^2*b^2*x^14*(A*b+B*a)+5//11*b*a^3*x^11*(B*a+2*A*b)+5//17*a*b^3*x^17*(A*b+2*B*a))
@test integrate(x^3*(a+b*x^3)^5*(A+B*x^3), x) == :(1//4*A*a^5*x^4+1//7*a^4*x^7*(B*a+5*A*b)+1//19*b^4*x^19*(A*b+5*B*a)+1//22*B*b^5*x^22+(1/2)*b*a^3*x^10*(B*a+2*A*b)+5//16*a*b^3*x^16*(A*b+2*B*a)+10//13*a^2*b^2*x^13*(A*b+B*a))
@test integrate(x^2*(a+b*x^3)^5*(A+B*x^3), x) == :(1//18*b^-2*(a+b*x^3)^6*(A*b+-1*B*a)+1//21*B*b^-2*(a+b*x^3)^7)
@test integrate(x*(a+b*x^3)^5*(A+B*x^3), x) == :((1/2)*A*a^5*x^2+1//5*a^4*x^5*(B*a+5*A*b)+1//17*b^4*x^17*(A*b+5*B*a)+1//20*B*b^5*x^20+5//8*b*a^3*x^8*(B*a+2*A*b)+5//14*a*b^3*x^14*(A*b+2*B*a)+10//11*a^2*b^2*x^11*(A*b+B*a))
@test integrate((a+b*x^3)^5*(A+B*x^3), x) == :(A*x*a^5+1//4*a^4*x^4*(B*a+5*A*b)+1//16*b^4*x^16*(A*b+5*B*a)+1//19*B*b^5*x^19+a^2*b^2*x^10*(A*b+B*a)+5//7*b*a^3*x^7*(B*a+2*A*b)+5//13*a*b^3*x^13*(A*b+2*B*a))
@test integrate(x^-1*(a+b*x^3)^5*(A+B*x^3), x) == :(A*a^5*log(x)+1//15*A*b^5*x^15+1//18*B*b^-1*(a+b*x^3)^6+5//3*A*b*a^4*x^3+5//3*A*a^3*b^2*x^6+5//12*A*a*b^4*x^12+10//9*A*a^2*b^3*x^9)
@test integrate(x^-2*(a+b*x^3)^5*(A+B*x^3), x) == :((1/2)*a^4*x^2*(B*a+5*A*b)+-1*A*a^5*x^-1+1//14*b^4*x^14*(A*b+5*B*a)+1//17*B*b^5*x^17+b*a^3*x^5*(B*a+2*A*b)+5//4*a^2*b^2*x^8*(A*b+B*a)+5//11*a*b^3*x^11*(A*b+2*B*a))
@test integrate(x^-3*(a+b*x^3)^5*(A+B*x^3), x) == :(x*a^4*(B*a+5*A*b)+-1//2*A*a^5*x^-2+1//13*b^4*x^13*(A*b+5*B*a)+1//16*B*b^5*x^16+(1/2)*a*b^3*x^10*(A*b+2*B*a)+5//4*b*a^3*x^4*(B*a+2*A*b)+10//7*a^2*b^2*x^7*(A*b+B*a))
@test integrate(x^-4*(a+b*x^3)^5*(A+B*x^3), x) == :(a^4*(B*a+5*A*b)*log(x)+-1//3*A*a^5*x^-3+1//12*b^4*x^12*(A*b+5*B*a)+1//15*B*b^5*x^15+5//3*b*a^3*x^3*(B*a+2*A*b)+5//3*a^2*b^2*x^6*(A*b+B*a)+5//9*a*b^3*x^9*(A*b+2*B*a))
@test integrate(x^-5*(a+b*x^3)^5*(A+B*x^3), x) == :(-1*a^4*x^-1*(B*a+5*A*b)+-1//4*A*a^5*x^-4+1//11*b^4*x^11*(A*b+5*B*a)+1//14*B*b^5*x^14+2*a^2*b^2*x^5*(A*b+B*a)+5//2*b*a^3*x^2*(B*a+2*A*b)+5//8*a*b^3*x^8*(A*b+2*B*a))
@test integrate(x^-6*(a+b*x^3)^5*(A+B*x^3), x) == :(-1//2*a^4*x^-2*(B*a+5*A*b)+-1//5*A*a^5*x^-5+1//10*b^4*x^10*(A*b+5*B*a)+1//13*B*b^5*x^13+5*b*x*a^3*(B*a+2*A*b)+5//2*a^2*b^2*x^4*(A*b+B*a)+5//7*a*b^3*x^7*(A*b+2*B*a))
@test integrate(x^-7*(a+b*x^3)^5*(A+B*x^3), x) == :(-1//3*a^4*x^-3*(B*a+5*A*b)+-1//6*A*a^5*x^-6+1//9*b^4*x^9*(A*b+5*B*a)+1//12*B*b^5*x^12+5*b*a^3*(B*a+2*A*b)*log(x)+5//6*a*b^3*x^6*(A*b+2*B*a)+10//3*a^2*b^2*x^3*(A*b+B*a))
@test integrate(x^-8*(a+b*x^3)^5*(A+B*x^3), x) == :(-1//4*a^4*x^-4*(B*a+5*A*b)+-1//7*A*a^5*x^-7+1//8*b^4*x^8*(A*b+5*B*a)+1//11*B*b^5*x^11+a*b^3*x^5*(A*b+2*B*a)+-5*b*a^3*x^-1*(B*a+2*A*b)+5*a^2*b^2*x^2*(A*b+B*a))
@test integrate(x^-9*(a+b*x^3)^5*(A+B*x^3), x) == :(-1//5*a^4*x^-5*(B*a+5*A*b)+-1//8*A*a^5*x^-8+1//7*b^4*x^7*(A*b+5*B*a)+1//10*B*b^5*x^10+10*x*a^2*b^2*(A*b+B*a)+-5//2*b*a^3*x^-2*(B*a+2*A*b)+5//4*a*b^3*x^4*(A*b+2*B*a))
@test integrate(x^-10*(a+b*x^3)^5*(A+B*x^3), x) == :(-1//6*a^4*x^-6*(B*a+5*A*b)+-1//9*A*a^5*x^-9+1//6*b^4*x^6*(A*b+5*B*a)+1//9*B*b^5*x^9+10*a^2*b^2*(A*b+B*a)*log(x)+-5//3*b*a^3*x^-3*(B*a+2*A*b)+5//3*a*b^3*x^3*(A*b+2*B*a))
@test integrate(x^-11*(a+b*x^3)^5*(A+B*x^3), x) == :(-1//7*a^4*x^-7*(B*a+5*A*b)+-1//10*A*a^5*x^-10+1//5*b^4*x^5*(A*b+5*B*a)+1//8*B*b^5*x^8+-10*a^2*b^2*x^-1*(A*b+B*a)+-5//4*b*a^3*x^-4*(B*a+2*A*b)+5//2*a*b^3*x^2*(A*b+2*B*a))
@test integrate(x^-12*(a+b*x^3)^5*(A+B*x^3), x) == :(-1//8*a^4*x^-8*(B*a+5*A*b)+-1//11*A*a^5*x^-11+1//4*b^4*x^4*(A*b+5*B*a)+1//7*B*b^5*x^7+-1*b*a^3*x^-5*(B*a+2*A*b)+-5*a^2*b^2*x^-2*(A*b+B*a)+5*a*x*b^3*(A*b+2*B*a))
@test integrate(x^-13*(a+b*x^3)^5*(A+B*x^3), x) == :(-1//9*a^4*x^-9*(B*a+5*A*b)+-1//12*A*a^5*x^-12+1//3*b^4*x^3*(A*b+5*B*a)+1//6*B*b^5*x^6+5*a*b^3*(A*b+2*B*a)*log(x)+-10//3*a^2*b^2*x^-3*(A*b+B*a)+-5//6*b*a^3*x^-6*(B*a+2*A*b))
@test integrate(x^-14*(a+b*x^3)^5*(A+B*x^3), x) == :((1/2)*b^4*x^2*(A*b+5*B*a)+-1//10*a^4*x^-10*(B*a+5*A*b)+-1//13*A*a^5*x^-13+1//5*B*b^5*x^5+-5*a*b^3*x^-1*(A*b+2*B*a)+-5//2*a^2*b^2*x^-4*(A*b+B*a)+-5//7*b*a^3*x^-7*(B*a+2*A*b))
@test integrate(x^-15*(a+b*x^3)^5*(A+B*x^3), x) == :(x*b^4*(A*b+5*B*a)+-1//11*a^4*x^-11*(B*a+5*A*b)+-1//14*A*a^5*x^-14+1//4*B*b^5*x^4+-2*a^2*b^2*x^-5*(A*b+B*a)+-5//2*a*b^3*x^-2*(A*b+2*B*a)+-5//8*b*a^3*x^-8*(B*a+2*A*b))
@test integrate(x^-16*(a+b*x^3)^5*(A+B*x^3), x) == :(b^4*(A*b+5*B*a)*log(x)+-1//12*a^4*x^-12*(B*a+5*A*b)+-1//15*A*a^5*x^-15+1//3*B*b^5*x^3+-5//3*a*b^3*x^-3*(A*b+2*B*a)+-5//3*a^2*b^2*x^-6*(A*b+B*a)+-5//9*b*a^3*x^-9*(B*a+2*A*b))
@test integrate(x^-17*(a+b*x^3)^5*(A+B*x^3), x) == :((1/2)*B*b^5*x^2+-1*b^4*x^-1*(A*b+5*B*a)+-1//13*a^4*x^-13*(B*a+5*A*b)+-1//16*A*a^5*x^-16+-10//7*a^2*b^2*x^-7*(A*b+B*a)+-5//4*a*b^3*x^-4*(A*b+2*B*a)+-1//2*b*a^3*x^-10*(B*a+2*A*b))
@test integrate(x^-18*(a+b*x^3)^5*(A+B*x^3), x) == :(B*x*b^5+-1//2*b^4*x^-2*(A*b+5*B*a)+-1//14*a^4*x^-14*(B*a+5*A*b)+-1//17*A*a^5*x^-17+-1*a*b^3*x^-5*(A*b+2*B*a)+-5//4*a^2*b^2*x^-8*(A*b+B*a)+-5//11*b*a^3*x^-11*(B*a+2*A*b))
@test integrate(x^-19*(a+b*x^3)^5*(A+B*x^3), x) == :(B*b^5*log(x)+-1//15*B*a^5*x^-15+-10//9*B*a^3*b^2*x^-9+-5//3*B*a*b^4*x^-3+-5//3*B*a^2*b^3*x^-6+-5//12*B*b*a^4*x^-12+-1//18*A*a^-1*x^-18*(a+b*x^3)^6)
@test integrate(x^-20*(a+b*x^3)^5*(A+B*x^3), x) == :(-1*B*b^5*x^-1+-1//4*b^4*x^-4*(A*b+5*B*a)+-1//16*a^4*x^-16*(B*a+5*A*b)+-1//19*A*a^5*x^-19+-1*a^2*b^2*x^-10*(A*b+B*a)+-5//7*a*b^3*x^-7*(A*b+2*B*a)+-5//13*b*a^3*x^-13*(B*a+2*A*b))
@test integrate(x^-21*(a+b*x^3)^5*(A+B*x^3), x) == :(-1//2*B*b^5*x^-2+-1//5*b^4*x^-5*(A*b+5*B*a)+-1//17*a^4*x^-17*(B*a+5*A*b)+-1//20*A*a^5*x^-20+-10//11*a^2*b^2*x^-11*(A*b+B*a)+-5//8*a*b^3*x^-8*(A*b+2*B*a)+-5//14*b*a^3*x^-14*(B*a+2*A*b))
@test integrate(x^-22*(a+b*x^3)^5*(A+B*x^3), x) == :(-1//21*A*a^-1*x^-21*(a+b*x^3)^6+1//126*a^-2*x^-18*(a+b*x^3)^6*(A*b+-7*B*a))
@test integrate(x^-23*(a+b*x^3)^5*(A+B*x^3), x) == :(-1//4*B*b^5*x^-4+-1//7*b^4*x^-7*(A*b+5*B*a)+-1//19*a^4*x^-19*(B*a+5*A*b)+-1//22*A*a^5*x^-22+-10//13*a^2*b^2*x^-13*(A*b+B*a)+-5//16*b*a^3*x^-16*(B*a+2*A*b)+-1//2*a*b^3*x^-10*(A*b+2*B*a))
@test integrate(x^6*(a+b*x^3)^-1*(A+B*x^3), x) == :(1//4*b^-2*x^4*(A*b+-1*B*a)+1//7*B*b^-1*x^7+-1*a*x*b^-3*(A*b+-1*B*a)+-1//6*a^4//3*b^-10//3*(A*b+-1*B*a)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^4//3*b^-10//3*(A*b+-1*B*a)*log(a^1//3+x*b^1//3)+-1//3*3^(1/2)*a^4//3*b^-10//3*(A*b+-1*B*a)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^5*(a+b*x^3)^-1*(A+B*x^3), x) == :(1//3*b^-2*x^3*(A*b+-1*B*a)+1//6*B*b^-1*x^6+-1//3*a*b^-3*(A*b+-1*B*a)*log(a+b*x^3))
@test integrate(x^4*(a+b*x^3)^-1*(A+B*x^3), x) == :((1/2)*b^-2*x^2*(A*b+-1*B*a)+1//5*B*b^-1*x^5+-1//6*a^2//3*b^-8//3*(A*b+-1*B*a)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^2//3*b^-8//3*(A*b+-1*B*a)*log(a^1//3+x*b^1//3)+1//3*3^(1/2)*a^2//3*b^-8//3*(A*b+-1*B*a)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^3*(a+b*x^3)^-1*(A+B*x^3), x) == :(x*b^-2*(A*b+-1*B*a)+1//4*B*b^-1*x^4+-1//3*a^1//3*b^-7//3*(A*b+-1*B*a)*log(a^1//3+x*b^1//3)+1//6*a^1//3*b^-7//3*(A*b+-1*B*a)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*3^(1/2)*a^1//3*b^-7//3*(A*b+-1*B*a)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^2*(a+b*x^3)^-1*(A+B*x^3), x) == :(1//3*B*b^-1*x^3+1//3*b^-2*(A*b+-1*B*a)*log(a+b*x^3))
@test integrate(x*(a+b*x^3)^-1*(A+B*x^3), x) == :((1/2)*B*b^-1*x^2+-1//3*a^-1//3*b^-5//3*(A*b+-1*B*a)*log(a^1//3+x*b^1//3)+1//6*a^-1//3*b^-5//3*(A*b+-1*B*a)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//3*3^(1/2)*a^-1//3*b^-5//3*(A*b+-1*B*a)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate((a+b*x^3)^-1*(A+B*x^3), x) == :(B*x*b^-1+-1//6*a^-2//3*b^-4//3*(A*b+-1*B*a)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-2//3*b^-4//3*(A*b+-1*B*a)*log(a^1//3+x*b^1//3)+-1//3*3^(1/2)*a^-2//3*b^-4//3*(A*b+-1*B*a)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-1*(a+b*x^3)^-1*(A+B*x^3), x) == :(A*a^-1*log(x)+-1//3*a^-1*b^-1*(A*b+-1*B*a)*log(a+b*x^3))
@test integrate(x^-2*(a+b*x^3)^-1*(A+B*x^3), x) == :(-1*A*a^-1*x^-1+-1//6*a^-4//3*b^-2//3*(A*b+-1*B*a)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-4//3*b^-2//3*(A*b+-1*B*a)*log(a^1//3+x*b^1//3)+1//3*3^(1/2)*a^-4//3*b^-2//3*(A*b+-1*B*a)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-3*(a+b*x^3)^-1*(A+B*x^3), x) == :(-1//2*A*a^-1*x^-2+-1//3*a^-5//3*b^-1//3*(A*b+-1*B*a)*log(a^1//3+x*b^1//3)+1//6*a^-5//3*b^-1//3*(A*b+-1*B*a)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*3^(1/2)*a^-5//3*b^-1//3*(A*b+-1*B*a)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-4*(a+b*x^3)^-1*(A+B*x^3), x) == :(-1*a^-2*(A*b+-1*B*a)*log(x)+-1//3*A*a^-1*x^-3+1//3*a^-2*(A*b+-1*B*a)*log(a+b*x^3))
@test integrate(x^-5*(a+b*x^3)^-1*(A+B*x^3), x) == :(a^-2*x^-1*(A*b+-1*B*a)+-1//4*A*a^-1*x^-4+-1//3*a^-7//3*b^1//3*(A*b+-1*B*a)*log(a^1//3+x*b^1//3)+1//6*a^-7//3*b^1//3*(A*b+-1*B*a)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//3*3^(1/2)*a^-7//3*b^1//3*(A*b+-1*B*a)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-6*(a+b*x^3)^-1*(A+B*x^3), x) == :((1/2)*a^-2*x^-2*(A*b+-1*B*a)+-1//5*A*a^-1*x^-5+-1//6*a^-8//3*b^2//3*(A*b+-1*B*a)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-8//3*b^2//3*(A*b+-1*B*a)*log(a^1//3+x*b^1//3)+-1//3*3^(1/2)*a^-8//3*b^2//3*(A*b+-1*B*a)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-7*(a+b*x^3)^-1*(A+B*x^3), x) == :(-1//6*A*a^-1*x^-6+1//3*a^-2*x^-3*(A*b+-1*B*a)+b*a^-3*(A*b+-1*B*a)*log(x)+-1//3*b*a^-3*(A*b+-1*B*a)*log(a+b*x^3))
@test integrate(x^-8*(a+b*x^3)^-1*(A+B*x^3), x) == :(-1//7*A*a^-1*x^-7+1//4*a^-2*x^-4*(A*b+-1*B*a)+-1*b*a^-3*x^-1*(A*b+-1*B*a)+-1//6*a^-10//3*b^4//3*(A*b+-1*B*a)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-10//3*b^4//3*(A*b+-1*B*a)*log(a^1//3+x*b^1//3)+1//3*3^(1/2)*a^-10//3*b^4//3*(A*b+-1*B*a)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^9*(a+b*x^3)^-2*(A+B*x^3), x) == :(1//12*b^-3*x^4*(-10*B*a+7*A*b)+-1//3*a*x*b^-4*(-10*B*a+7*A*b)+-1//18*a^4//3*b^-13//3*(-10*B*a+7*A*b)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//21*a^-1*b^-2*x^7*(-10*B*a+7*A*b)+1//9*a^4//3*b^-13//3*(-10*B*a+7*A*b)*log(a^1//3+x*b^1//3)+-1//9*3^(1/2)*a^4//3*b^-13//3*(-10*B*a+7*A*b)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//3*a^-1*b^-1*x^10*(a+b*x^3)^-1*(A*b+-1*B*a))
@test integrate(x^8*(a+b*x^3)^-2*(A+B*x^3), x) == :(1//3*b^-3*x^3*(A*b+-2*B*a)+1//6*B*b^-2*x^6+-1//3*a*b^-4*(-3*B*a+2*A*b)*log(a+b*x^3)+-1//3*a^2*b^-4*(a+b*x^3)^-1*(A*b+-1*B*a))
@test integrate(x^7*(a+b*x^3)^-2*(A+B*x^3), x) == :(1//6*b^-3*x^2*(-8*B*a+5*A*b)+-1//15*a^-1*b^-2*x^5*(-8*B*a+5*A*b)+-1//18*a^2//3*b^-11//3*(-8*B*a+5*A*b)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*a^2//3*b^-11//3*(-8*B*a+5*A*b)*log(a^1//3+x*b^1//3)+1//3*a^-1*b^-1*x^8*(a+b*x^3)^-1*(A*b+-1*B*a)+1//9*3^(1/2)*a^2//3*b^-11//3*(-8*B*a+5*A*b)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^6*(a+b*x^3)^-2*(A+B*x^3), x) == :(1//3*x*b^-3*(-7*B*a+4*A*b)+-1//9*a^1//3*b^-10//3*(-7*B*a+4*A*b)*log(a^1//3+x*b^1//3)+-1//12*a^-1*b^-2*x^4*(-7*B*a+4*A*b)+1//18*a^1//3*b^-10//3*(-7*B*a+4*A*b)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-1*b^-1*x^7*(a+b*x^3)^-1*(A*b+-1*B*a)+1//9*3^(1/2)*a^1//3*b^-10//3*(-7*B*a+4*A*b)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^5*(a+b*x^3)^-2*(A+B*x^3), x) == :(1//3*B*b^-2*x^3+1//3*b^-3*(A*b+-2*B*a)*log(a+b*x^3)+1//3*a*b^-3*(a+b*x^3)^-1*(A*b+-1*B*a))
@test integrate(x^4*(a+b*x^3)^-2*(A+B*x^3), x) == :(-1//6*a^-1*b^-2*x^2*(-5*B*a+2*A*b)+-1//9*a^-1//3*b^-8//3*(-5*B*a+2*A*b)*log(a^1//3+x*b^1//3)+1//18*a^-1//3*b^-8//3*(-5*B*a+2*A*b)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//9*3^(1/2)*a^-1//3*b^-8//3*(-5*B*a+2*A*b)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//3*a^-1*b^-1*x^5*(a+b*x^3)^-1*(A*b+-1*B*a))
@test integrate(x^3*(a+b*x^3)^-2*(A+B*x^3), x) == :(-1//3*x*a^-1*b^-2*(A*b+-4*B*a)+-1//18*a^-2//3*b^-7//3*(A*b+-4*B*a)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*a^-2//3*b^-7//3*(A*b+-4*B*a)*log(a^1//3+x*b^1//3)+-1//9*3^(1/2)*a^-2//3*b^-7//3*(A*b+-4*B*a)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//3*a^-1*b^-1*x^4*(a+b*x^3)^-1*(A*b+-1*B*a))
@test integrate(x^2*(a+b*x^3)^-2*(A+B*x^3), x) == :(1//3*B*b^-2*log(a+b*x^3)+1//3*b^-2*(a+b*x^3)^-1*(B*a+-1*A*b))
@test integrate(x*(a+b*x^3)^-2*(A+B*x^3), x) == :(-1//9*a^-4//3*b^-5//3*(A*b+2*B*a)*log(a^1//3+x*b^1//3)+1//18*a^-4//3*b^-5//3*(A*b+2*B*a)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//9*3^(1/2)*a^-4//3*b^-5//3*(A*b+2*B*a)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//3*a^-1*b^-1*x^2*(a+b*x^3)^-1*(A*b+-1*B*a))
@test integrate((a+b*x^3)^-2*(A+B*x^3), x) == :(-1//18*a^-5//3*b^-4//3*(B*a+2*A*b)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*a^-5//3*b^-4//3*(B*a+2*A*b)*log(a^1//3+x*b^1//3)+-1//9*3^(1/2)*a^-5//3*b^-4//3*(B*a+2*A*b)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//3*x*a^-1*b^-1*(a+b*x^3)^-1*(A*b+-1*B*a))
@test integrate(x^-1*(a+b*x^3)^-2*(A+B*x^3), x) == :(A*a^-2*log(x)+-1//3*A*a^-2*log(a+b*x^3)+1//3*a^-1*b^-1*(a+b*x^3)^-1*(A*b+-1*B*a))
@test integrate(x^-2*(a+b*x^3)^-2*(A+B*x^3), x) == :(-1//18*a^-7//3*b^-2//3*(-1*B*a+4*A*b)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-2*b^-1*x^-1*(B*a+-4*A*b)+1//9*a^-7//3*b^-2//3*(-1*B*a+4*A*b)*log(a^1//3+x*b^1//3)+1//3*a^-1*b^-1*x^-1*(a+b*x^3)^-1*(A*b+-1*B*a)+1//9*3^(1/2)*a^-7//3*b^-2//3*(-1*B*a+4*A*b)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-3*(a+b*x^3)^-2*(A+B*x^3), x) == :(-1//9*a^-8//3*b^-1//3*(-2*B*a+5*A*b)*log(a^1//3+x*b^1//3)+1//6*a^-2*b^-1*x^-2*(-5*A*b+2*B*a)+1//18*a^-8//3*b^-1//3*(-2*B*a+5*A*b)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-1*b^-1*x^-2*(a+b*x^3)^-1*(A*b+-1*B*a)+1//9*3^(1/2)*a^-8//3*b^-1//3*(-2*B*a+5*A*b)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-4*(a+b*x^3)^-2*(A+B*x^3), x) == :(-1*a^-3*(-1*B*a+2*A*b)*log(x)+-1//3*A*a^-2*x^-3+-1//3*a^-2*(a+b*x^3)^-1*(A*b+-1*B*a)+1//3*a^-3*(-1*B*a+2*A*b)*log(a+b*x^3))
@test integrate(x^-5*(a+b*x^3)^-2*(A+B*x^3), x) == :(1//3*a^-3*x^-1*(-4*B*a+7*A*b)+-1//9*a^-10//3*b^1//3*(-4*B*a+7*A*b)*log(a^1//3+x*b^1//3)+1//12*a^-2*b^-1*x^-4*(-7*A*b+4*B*a)+1//18*a^-10//3*b^1//3*(-4*B*a+7*A*b)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//9*3^(1/2)*a^-10//3*b^1//3*(-4*B*a+7*A*b)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//3*a^-1*b^-1*x^-4*(a+b*x^3)^-1*(A*b+-1*B*a))
@test integrate(x^-6*(a+b*x^3)^-2*(A+B*x^3), x) == :(1//6*a^-3*x^-2*(-5*B*a+8*A*b)+-1//18*a^-11//3*b^2//3*(-5*B*a+8*A*b)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*a^-11//3*b^2//3*(-5*B*a+8*A*b)*log(a^1//3+x*b^1//3)+1//15*a^-2*b^-1*x^-5*(-8*A*b+5*B*a)+-1//9*3^(1/2)*a^-11//3*b^2//3*(-5*B*a+8*A*b)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//3*a^-1*b^-1*x^-5*(a+b*x^3)^-1*(A*b+-1*B*a))
@test integrate(x^-7*(a+b*x^3)^-2*(A+B*x^3), x) == :(-1//6*A*a^-2*x^-6+1//3*a^-3*x^-3*(-1*B*a+2*A*b)+b*a^-4*(-2*B*a+3*A*b)*log(x)+-1//3*b*a^-4*(-2*B*a+3*A*b)*log(a+b*x^3)+1//3*b*a^-3*(a+b*x^3)^-1*(A*b+-1*B*a))
@test integrate(x^11*(a+b*x^3)^-3*(A+B*x^3), x) == :(1//3*b^-4*x^3*(A*b+-3*B*a)+1//6*B*b^-3*x^6+-1*a*b^-5*(A*b+-2*B*a)*log(a+b*x^3)+-1//3*a^2*b^-5*(a+b*x^3)^-1*(-4*B*a+3*A*b)+1//6*a^3*b^-5*(a+b*x^3)^-2*(A*b+-1*B*a))
@test integrate(x^8*(a+b*x^3)^-3*(A+B*x^3), x) == :(1//3*B*b^-3*x^3+1//3*b^-4*(A*b+-3*B*a)*log(a+b*x^3)+-1//6*a^2*b^-4*(a+b*x^3)^-2*(A*b+-1*B*a)+1//3*a*b^-4*(a+b*x^3)^-1*(-3*B*a+2*A*b))
@test integrate(x^5*(a+b*x^3)^-3*(A+B*x^3), x) == :(-1//3*b^-3*(a+b*x^3)^-1*(A*b+-2*B*a)+1//3*B*b^-3*log(a+b*x^3)+1//6*a*b^-3*(a+b*x^3)^-2*(A*b+-1*B*a))
@test integrate(x^2*(a+b*x^3)^-3*(A+B*x^3), x) == :(-1*(A+B*x^3)^2*(a+b*x^3)^-2*(-6*B*a+6*A*b)^-1)
@test integrate(x^-1*(a+b*x^3)^-3*(A+B*x^3), x) == :(A*a^-3*log(x)+-1//3*A*a^-3*log(a+b*x^3)+1//3*A*a^-2*(a+b*x^3)^-1+1//6*a^-1*b^-1*(a+b*x^3)^-2*(A*b+-1*B*a))
@test integrate(x^-4*(a+b*x^3)^-3*(A+B*x^3), x) == :(-1*a^-4*(-1*B*a+3*A*b)*log(x)+-1//3*A*a^-3*x^-3+-1//3*a^-3*(a+b*x^3)^-1*(-1*B*a+2*A*b)+-1//6*a^-2*(a+b*x^3)^-2*(A*b+-1*B*a)+1//3*a^-4*(-1*B*a+3*A*b)*log(a+b*x^3))
@test integrate(x^-7*(a+b*x^3)^-3*(A+B*x^3), x) == :(-1//6*A*a^-3*x^-6+1//3*a^-4*x^-3*(-1*B*a+3*A*b)+-1*b*a^-5*(-1*B*a+2*A*b)*log(a+b*x^3)+3*b*a^-5*(-1*B*a+2*A*b)*log(x)+1//3*b*a^-4*(a+b*x^3)^-1*(-2*B*a+3*A*b)+1//6*b*a^-3*(a+b*x^3)^-2*(A*b+-1*B*a))
@test integrate(x^10*(a+b*x^3)^-3*(A+B*x^3), x) == :(1//9*b^-4*x^2*(-22*B*a+10*A*b)+-2//27*a^2//3*b^-14//3*(-11*B*a+5*A*b)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//45*a^-1*b^-3*x^5*(-44*B*a+20*A*b)+4//27*a^2//3*b^-14//3*(-11*B*a+5*A*b)*log(a^1//3+x*b^1//3)+1//6*a^-1*b^-1*x^11*(a+b*x^3)^-2*(A*b+-1*B*a)+1//18*a^-1*b^-2*x^8*(a+b*x^3)^-1*(-11*B*a+5*A*b)+4//27*3^(1/2)*a^2//3*b^-14//3*(-11*B*a+5*A*b)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^9*(a+b*x^3)^-3*(A+B*x^3), x) == :(1//9*x*b^-4*(-35*B*a+14*A*b)+-7//27*a^1//3*b^-13//3*(-5*B*a+2*A*b)*log(a^1//3+x*b^1//3)+-1//36*a^-1*b^-3*x^4*(-35*B*a+14*A*b)+7//54*a^1//3*b^-13//3*(-5*B*a+2*A*b)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//6*a^-1*b^-1*x^10*(a+b*x^3)^-2*(A*b+-1*B*a)+1//9*a^-1*b^-2*x^7*(a+b*x^3)^-1*(-5*B*a+2*A*b)+7//27*3^(1/2)*a^1//3*b^-13//3*(-5*B*a+2*A*b)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^7*(a+b*x^3)^-3*(A+B*x^3), x) == :(-1//27*a^-1//3*b^-11//3*(-20*B*a+5*A*b)*log(a^1//3+x*b^1//3)+1//18*a^-1*b^-3*x^2*(-5*A*b+20*B*a)+1//54*a^-1//3*b^-11//3*(-20*B*a+5*A*b)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//27*3^(1/2)*a^-1//3*b^-11//3*(-20*B*a+5*A*b)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//6*a^-1*b^-1*x^8*(a+b*x^3)^-2*(A*b+-1*B*a)+1//9*a^-1*b^-2*x^5*(a+b*x^3)^-1*(A*b+-4*B*a))
@test integrate(x^6*(a+b*x^3)^-3*(A+B*x^3), x) == :(-1//27*a^-2//3*b^-10//3*(A*b+-7*B*a)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*x*a^-1*b^-3*(-2*A*b+14*B*a)+1//27*a^-2//3*b^-10//3*(-14*B*a+2*A*b)*log(a^1//3+x*b^1//3)+-1//27*3^(1/2)*a^-2//3*b^-10//3*(-14*B*a+2*A*b)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//6*a^-1*b^-1*x^7*(a+b*x^3)^-2*(A*b+-1*B*a)+1//18*a^-1*b^-2*x^4*(a+b*x^3)^-1*(A*b+-7*B*a))
@test integrate(x^4*(a+b*x^3)^-3*(A+B*x^3), x) == :(-1//27*a^-4//3*b^-8//3*(A*b+5*B*a)*log(a^1//3+x*b^1//3)+1//54*a^-4//3*b^-8//3*(A*b+5*B*a)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//18*a^-1*b^-2*x^2*(a+b*x^3)^-1*(A*b+5*B*a)+-1//27*3^(1/2)*a^-4//3*b^-8//3*(A*b+5*B*a)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//6*a^-1*b^-1*x^5*(a+b*x^3)^-2*(A*b+-1*B*a))
@test integrate(x^3*(a+b*x^3)^-3*(A+B*x^3), x) == :(-1//54*a^-5//3*b^-7//3*(A*b+2*B*a)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//27*a^-5//3*b^-7//3*(A*b+2*B*a)*log(a^1//3+x*b^1//3)+-1//9*x*a^-1*b^-2*(a+b*x^3)^-1*(A*b+2*B*a)+-1//27*3^(1/2)*a^-5//3*b^-7//3*(A*b+2*B*a)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//6*a^-1*b^-1*x^4*(a+b*x^3)^-2*(A*b+-1*B*a))
@test integrate(x*(a+b*x^3)^-3*(A+B*x^3), x) == :(-1//27*a^-7//3*b^-5//3*(B*a+2*A*b)*log(a^1//3+x*b^1//3)+1//54*a^-7//3*b^-5//3*(B*a+2*A*b)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//27*3^(1/2)*a^-7//3*b^-5//3*(B*a+2*A*b)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//6*a^-1*b^-1*x^2*(a+b*x^3)^-2*(A*b+-1*B*a)+1//9*a^-2*b^-1*x^2*(a+b*x^3)^-1*(B*a+2*A*b))
@test integrate((a+b*x^3)^-3*(A+B*x^3), x) == :(-1//54*a^-8//3*b^-4//3*(B*a+5*A*b)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//27*a^-8//3*b^-4//3*(B*a+5*A*b)*log(a^1//3+x*b^1//3)+-1//27*3^(1/2)*a^-8//3*b^-4//3*(B*a+5*A*b)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//6*x*a^-1*b^-1*(a+b*x^3)^-2*(A*b+-1*B*a)+1//18*x*a^-2*b^-1*(a+b*x^3)^-1*(B*a+5*A*b))
@test integrate(x^-2*(a+b*x^3)^-3*(A+B*x^3), x) == :(-1//27*a^-10//3*b^-2//3*(-1*B*a+7*A*b)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*a^-3*b^-1*x^-1*(-14*A*b+2*B*a)+1//27*a^-10//3*b^-2//3*(-2*B*a+14*A*b)*log(a^1//3+x*b^1//3)+1//6*a^-1*b^-1*x^-1*(a+b*x^3)^-2*(A*b+-1*B*a)+1//18*a^-2*b^-1*x^-1*(a+b*x^3)^-1*(-1*B*a+7*A*b)+1//27*3^(1/2)*a^-10//3*b^-2//3*(-2*B*a+14*A*b)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-3*(a+b*x^3)^-3*(A+B*x^3), x) == :(-1//27*a^-11//3*b^-1//3*(-5*B*a+20*A*b)*log(a^1//3+x*b^1//3)+1//18*a^-3*b^-1*x^-2*(-20*A*b+5*B*a)+1//54*a^-11//3*b^-1//3*(-5*B*a+20*A*b)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//6*a^-1*b^-1*x^-2*(a+b*x^3)^-2*(A*b+-1*B*a)+1//9*a^-2*b^-1*x^-2*(a+b*x^3)^-1*(-1*B*a+4*A*b)+1//27*3^(1/2)*a^-11//3*b^-1//3*(-5*B*a+20*A*b)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-5*(a+b*x^3)^-3*(A+B*x^3), x) == :(1//9*a^-4*x^-1*(-14*B*a+35*A*b)+-7//27*a^-13//3*b^1//3*(-2*B*a+5*A*b)*log(a^1//3+x*b^1//3)+1//36*a^-3*b^-1*x^-4*(-35*A*b+14*B*a)+7//54*a^-13//3*b^1//3*(-2*B*a+5*A*b)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-7//27*3^(1/2)*a^-13//3*b^1//3*(-2*B*a+5*A*b)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//6*a^-1*b^-1*x^-4*(a+b*x^3)^-2*(A*b+-1*B*a)+1//9*a^-2*b^-1*x^-4*(a+b*x^3)^-1*(-2*B*a+5*A*b))
@test integrate(x^-6*(a+b*x^3)^-3*(A+B*x^3), x) == :(1//9*a^-4*x^-2*(-10*B*a+22*A*b)+-2//27*a^-14//3*b^2//3*(-5*B*a+11*A*b)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//45*a^-3*b^-1*x^-5*(-44*A*b+20*B*a)+4//27*a^-14//3*b^2//3*(-5*B*a+11*A*b)*log(a^1//3+x*b^1//3)+-4//27*3^(1/2)*a^-14//3*b^2//3*(-5*B*a+11*A*b)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//6*a^-1*b^-1*x^-5*(a+b*x^3)^-2*(A*b+-1*B*a)+1//18*a^-2*b^-1*x^-5*(a+b*x^3)^-1*(-5*B*a+11*A*b))
@test integrate(x^8*(a+b*x^3)^-1*(c+d*x^3)^-1, x) == :(1//3*b^-1*d^-1*x^3+-1//3*c^2*d^-2*(b*c+-1*a*d)^-1*log(c+d*x^3)+1//3*a^2*b^-2*(b*c+-1*a*d)^-1*log(a+b*x^3))
@test integrate(x^7*(a+b*x^3)^-1*(c+d*x^3)^-1, x) == :((1/2)*b^-1*d^-1*x^2+-1//3*a^5//3*b^-5//3*(b*c+-1*a*d)^-1*log(a^1//3+x*b^1//3)+-1//6*c^5//3*d^-5//3*(b*c+-1*a*d)^-1*log(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3)+1//3*c^5//3*d^-5//3*(b*c+-1*a*d)^-1*log(c^1//3+x*d^1//3)+1//6*a^5//3*b^-5//3*(b*c+-1*a*d)^-1*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//3*3^(1/2)*a^5//3*b^-5//3*(b*c+-1*a*d)^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//3*3^(1/2)*c^5//3*d^-5//3*(b*c+-1*a*d)^-1*arctan(1//3*3^(1/2)*c^-1//3*(c^1//3+-2*x*d^1//3)))
@test integrate(x^6*(a+b*x^3)^-1*(c+d*x^3)^-1, x) == :(x*b^-1*d^-1+-1//3*c^4//3*d^-4//3*(b*c+-1*a*d)^-1*log(c^1//3+x*d^1//3)+-1//6*a^4//3*b^-4//3*(b*c+-1*a*d)^-1*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^4//3*b^-4//3*(b*c+-1*a*d)^-1*log(a^1//3+x*b^1//3)+1//6*c^4//3*d^-4//3*(b*c+-1*a*d)^-1*log(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3)+-1//3*3^(1/2)*a^4//3*b^-4//3*(b*c+-1*a*d)^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//3*3^(1/2)*c^4//3*d^-4//3*(b*c+-1*a*d)^-1*arctan(1//3*3^(1/2)*c^-1//3*(c^1//3+-2*x*d^1//3)))
@test integrate(x^5*(a+b*x^3)^-1*(c+d*x^3)^-1, x) == :(-1//3*a*b^-1*(b*c+-1*a*d)^-1*log(a+b*x^3)+1//3*c*d^-1*(b*c+-1*a*d)^-1*log(c+d*x^3))
@test integrate(x^4*(a+b*x^3)^-1*(c+d*x^3)^-1, x) == :(-1//3*c^2//3*d^-2//3*(b*c+-1*a*d)^-1*log(c^1//3+x*d^1//3)+-1//6*a^2//3*b^-2//3*(b*c+-1*a*d)^-1*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^2//3*b^-2//3*(b*c+-1*a*d)^-1*log(a^1//3+x*b^1//3)+1//6*c^2//3*d^-2//3*(b*c+-1*a*d)^-1*log(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3)+-1//3*3^(1/2)*c^2//3*d^-2//3*(b*c+-1*a*d)^-1*arctan(1//3*3^(1/2)*c^-1//3*(c^1//3+-2*x*d^1//3))+1//3*3^(1/2)*a^2//3*b^-2//3*(b*c+-1*a*d)^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^3*(a+b*x^3)^-1*(c+d*x^3)^-1, x) == :(-1//3*a^1//3*b^-1//3*(b*c+-1*a*d)^-1*log(a^1//3+x*b^1//3)+-1//6*c^1//3*d^-1//3*(b*c+-1*a*d)^-1*log(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3)+1//3*c^1//3*d^-1//3*(b*c+-1*a*d)^-1*log(c^1//3+x*d^1//3)+1//6*a^1//3*b^-1//3*(b*c+-1*a*d)^-1*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//3*3^(1/2)*c^1//3*d^-1//3*(b*c+-1*a*d)^-1*arctan(1//3*3^(1/2)*c^-1//3*(c^1//3+-2*x*d^1//3))+1//3*3^(1/2)*a^1//3*b^-1//3*(b*c+-1*a*d)^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^2*(a+b*x^3)^-1*(c+d*x^3)^-1, x) == :((-3*a*d+3*b*c)^-1*log(a+b*x^3)+-1*(-3*a*d+3*b*c)^-1*log(c+d*x^3))
@test integrate(x*(a+b*x^3)^-1*(c+d*x^3)^-1, x) == :(-1//3*a^-1//3*b^1//3*(b*c+-1*a*d)^-1*log(a^1//3+x*b^1//3)+-1//6*c^-1//3*d^1//3*(b*c+-1*a*d)^-1*log(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3)+1//3*c^-1//3*d^1//3*(b*c+-1*a*d)^-1*log(c^1//3+x*d^1//3)+1//6*a^-1//3*b^1//3*(b*c+-1*a*d)^-1*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//3*3^(1/2)*a^-1//3*b^1//3*(b*c+-1*a*d)^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//3*3^(1/2)*c^-1//3*d^1//3*(b*c+-1*a*d)^-1*arctan(1//3*3^(1/2)*c^-1//3*(c^1//3+-2*x*d^1//3)))
@test integrate((a+b*x^3)^-1*(c+d*x^3)^-1, x) == :(-1//3*c^-2//3*d^2//3*(b*c+-1*a*d)^-1*log(c^1//3+x*d^1//3)+-1//6*a^-2//3*b^2//3*(b*c+-1*a*d)^-1*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-2//3*b^2//3*(b*c+-1*a*d)^-1*log(a^1//3+x*b^1//3)+1//6*c^-2//3*d^2//3*(b*c+-1*a*d)^-1*log(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3)+-1//3*3^(1/2)*a^-2//3*b^2//3*(b*c+-1*a*d)^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//3*3^(1/2)*c^-2//3*d^2//3*(b*c+-1*a*d)^-1*arctan(1//3*3^(1/2)*c^-1//3*(c^1//3+-2*x*d^1//3)))
@test integrate(x^-1*(a+b*x^3)^-1*(c+d*x^3)^-1, x) == :(a^-1*c^-1*log(x)+-1//3*b*a^-1*(b*c+-1*a*d)^-1*log(a+b*x^3)+1//3*d*c^-1*(b*c+-1*a*d)^-1*log(c+d*x^3))
@test integrate(x^-2*(a+b*x^3)^-1*(c+d*x^3)^-1, x) == :(-1*a^-1*c^-1*x^-1+-1//3*c^-4//3*d^4//3*(b*c+-1*a*d)^-1*log(c^1//3+x*d^1//3)+-1//6*a^-4//3*b^4//3*(b*c+-1*a*d)^-1*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-4//3*b^4//3*(b*c+-1*a*d)^-1*log(a^1//3+x*b^1//3)+1//6*c^-4//3*d^4//3*(b*c+-1*a*d)^-1*log(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3)+-1//3*3^(1/2)*c^-4//3*d^4//3*(b*c+-1*a*d)^-1*arctan(1//3*3^(1/2)*c^-1//3*(c^1//3+-2*x*d^1//3))+1//3*3^(1/2)*a^-4//3*b^4//3*(b*c+-1*a*d)^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-3*(a+b*x^3)^-1*(c+d*x^3)^-1, x) == :(-1//2*a^-1*c^-1*x^-2+-1//3*a^-5//3*b^5//3*(b*c+-1*a*d)^-1*log(a^1//3+x*b^1//3)+-1//6*c^-5//3*d^5//3*(b*c+-1*a*d)^-1*log(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3)+1//3*c^-5//3*d^5//3*(b*c+-1*a*d)^-1*log(c^1//3+x*d^1//3)+1//6*a^-5//3*b^5//3*(b*c+-1*a*d)^-1*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//3*3^(1/2)*c^-5//3*d^5//3*(b*c+-1*a*d)^-1*arctan(1//3*3^(1/2)*c^-1//3*(c^1//3+-2*x*d^1//3))+1//3*3^(1/2)*a^-5//3*b^5//3*(b*c+-1*a*d)^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-4*(a+b*x^3)^-1*(c+d*x^3)^-1, x) == :(-1//3*a^-1*c^-1*x^-3+-1*a^-2*c^-2*(a*d+b*c)*log(x)+-1//3*c^-2*d^2*(b*c+-1*a*d)^-1*log(c+d*x^3)+1//3*a^-2*b^2*(b*c+-1*a*d)^-1*log(a+b*x^3))
@test integrate(x^-5*(a+b*x^3)^-1*(c+d*x^3)^-1, x) == :(-1//4*a^-1*c^-1*x^-4+a^-2*c^-2*x^-1*(a*d+b*c)+-1//3*a^-7//3*b^7//3*(b*c+-1*a*d)^-1*log(a^1//3+x*b^1//3)+-1//6*c^-7//3*d^7//3*(b*c+-1*a*d)^-1*log(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3)+1//3*c^-7//3*d^7//3*(b*c+-1*a*d)^-1*log(c^1//3+x*d^1//3)+1//6*a^-7//3*b^7//3*(b*c+-1*a*d)^-1*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//3*3^(1/2)*a^-7//3*b^7//3*(b*c+-1*a*d)^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//3*3^(1/2)*c^-7//3*d^7//3*(b*c+-1*a*d)^-1*arctan(1//3*3^(1/2)*c^-1//3*(c^1//3+-2*x*d^1//3)))
@test integrate(x^-6*(a+b*x^3)^-1*(c+d*x^3)^-1, x) == :(-1//5*a^-1*c^-1*x^-5+(1/2)*a^-2*c^-2*x^-2*(a*d+b*c)+-1//3*c^-8//3*d^8//3*(b*c+-1*a*d)^-1*log(c^1//3+x*d^1//3)+-1//6*a^-8//3*b^8//3*(b*c+-1*a*d)^-1*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-8//3*b^8//3*(b*c+-1*a*d)^-1*log(a^1//3+x*b^1//3)+1//6*c^-8//3*d^8//3*(b*c+-1*a*d)^-1*log(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3)+-1//3*3^(1/2)*a^-8//3*b^8//3*(b*c+-1*a*d)^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//3*3^(1/2)*c^-8//3*d^8//3*(b*c+-1*a*d)^-1*arctan(1//3*3^(1/2)*c^-1//3*(c^1//3+-2*x*d^1//3)))
@test integrate(x^-7*(a+b*x^3)^-1*(c+d*x^3)^-1, x) == :(-1//6*a^-1*c^-1*x^-6+a^-3*c^-3*(a^2*d^2+b^2*c^2+a*b*c*d)*log(x)+-1//3*a^-3*b^3*(b*c+-1*a*d)^-1*log(a+b*x^3)+1//3*a^-2*c^-2*x^-3*(a*d+b*c)+1//3*c^-3*d^3*(b*c+-1*a*d)^-1*log(c+d*x^3))
@test integrate(x^-8*(a+b*x^3)^-1*(c+d*x^3)^-1, x) == :(-1//7*a^-1*c^-1*x^-7+-1*a^-3*c^-3*x^-1*(a^2*d^2+b^2*c^2+a*b*c*d)+-1//3*c^-10//3*d^10//3*(b*c+-1*a*d)^-1*log(c^1//3+x*d^1//3)+-1//6*a^-10//3*b^10//3*(b*c+-1*a*d)^-1*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-10//3*b^10//3*(b*c+-1*a*d)^-1*log(a^1//3+x*b^1//3)+1//4*a^-2*c^-2*x^-4*(a*d+b*c)+1//6*c^-10//3*d^10//3*(b*c+-1*a*d)^-1*log(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3)+-1//3*3^(1/2)*c^-10//3*d^10//3*(b*c+-1*a*d)^-1*arctan(1//3*3^(1/2)*c^-1//3*(c^1//3+-2*x*d^1//3))+1//3*3^(1/2)*a^-10//3*b^10//3*(b*c+-1*a*d)^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^m*(a+b*x^3)^5*(A+B*x^3), x) == :(A*a^5*x^(1+m)*(1+m)^-1+B*b^5*x^(19+m)*(19+m)^-1+a^4*x^(4+m)*(4+m)^-1*(B*a+5*A*b)+b^4*x^(16+m)*(16+m)^-1*(A*b+5*B*a)+5*a*b^3*x^(13+m)*(13+m)^-1*(A*b+2*B*a)+5*b*a^3*x^(7+m)*(7+m)^-1*(B*a+2*A*b)+10*a^2*b^2*x^(10+m)*(10+m)^-1*(A*b+B*a))
@test integrate(x^m*(a+b*x^3)^2*(A+B*x^3), x) == :(A*a^2*x^(1+m)*(1+m)^-1+B*b^2*x^(10+m)*(10+m)^-1+a*x^(4+m)*(4+m)^-1*(B*a+2*A*b)+b*x^(7+m)*(7+m)^-1*(A*b+2*B*a))
@test integrate(x^m*(A+B*x^3)*(a+b*x^3), x) == :(x^(4+m)*(4+m)^-1*(A*b+B*a)+A*a*x^(1+m)*(1+m)^-1+B*b*x^(7+m)*(7+m)^-1)
@test integrate(x^7//2*(A+B*x^3)*(a+b*x^3), x) == :(1//15*x^15//2*(2*A*b+2*B*a)+2//9*A*a*x^9//2+2//21*B*b*x^21//2)
@test integrate(x^5//2*(A+B*x^3)*(a+b*x^3), x) == :(1//13*x^13//2*(2*A*b+2*B*a)+2//7*A*a*x^7//2+2//19*B*b*x^19//2)
@test integrate(x^3//2*(A+B*x^3)*(a+b*x^3), x) == :(1//11*x^11//2*(2*A*b+2*B*a)+2//5*A*a*x^5//2+2//17*B*b*x^17//2)
@test integrate(x^(1/2)*(A+B*x^3)*(a+b*x^3), x) == :(1//9*x^9//2*(2*A*b+2*B*a)+2//3*A*a*x^3//2+2//15*B*b*x^15//2)
@test integrate(x^-1//2*(A+B*x^3)*(a+b*x^3), x) == :(1//7*x^7//2*(2*A*b+2*B*a)+2*A*a*x^(1/2)+2//13*B*b*x^13//2)
@test integrate(x^-3//2*(A+B*x^3)*(a+b*x^3), x) == :(1//5*x^5//2*(2*A*b+2*B*a)+-2*A*a*x^-1//2+2//11*B*b*x^11//2)
@test integrate(x^-5//2*(A+B*x^3)*(a+b*x^3), x) == :(1//3*x^3//2*(2*A*b+2*B*a)+-2//3*A*a*x^-3//2+2//9*B*b*x^9//2)
@test integrate(x^-7//2*(A+B*x^3)*(a+b*x^3), x) == :(x^(1/2)*(2*A*b+2*B*a)+-2//5*A*a*x^-5//2+2//7*B*b*x^7//2)
@test integrate(x^7//2*(a+b*x^3)^2*(A+B*x^3), x) == :(2//9*A*a^2*x^9//2+2//15*a*x^15//2*(B*a+2*A*b)+2//21*b*x^21//2*(A*b+2*B*a)+2//27*B*b^2*x^27//2)
@test integrate(x^5//2*(a+b*x^3)^2*(A+B*x^3), x) == :(2//7*A*a^2*x^7//2+2//13*a*x^13//2*(B*a+2*A*b)+2//19*b*x^19//2*(A*b+2*B*a)+2//25*B*b^2*x^25//2)
@test integrate(x^3//2*(a+b*x^3)^2*(A+B*x^3), x) == :(2//5*A*a^2*x^5//2+2//11*a*x^11//2*(B*a+2*A*b)+2//17*b*x^17//2*(A*b+2*B*a)+2//23*B*b^2*x^23//2)
@test integrate(x^(1/2)*(a+b*x^3)^2*(A+B*x^3), x) == :(2//3*A*a^2*x^3//2+2//9*a*x^9//2*(B*a+2*A*b)+2//15*b*x^15//2*(A*b+2*B*a)+2//21*B*b^2*x^21//2)
@test integrate(x^-1//2*(a+b*x^3)^2*(A+B*x^3), x) == :(2*A*a^2*x^(1/2)+2//7*a*x^7//2*(B*a+2*A*b)+2//13*b*x^13//2*(A*b+2*B*a)+2//19*B*b^2*x^19//2)
@test integrate(x^-3//2*(a+b*x^3)^2*(A+B*x^3), x) == :(-2*A*a^2*x^-1//2+2//5*a*x^5//2*(B*a+2*A*b)+2//11*b*x^11//2*(A*b+2*B*a)+2//17*B*b^2*x^17//2)
@test integrate(x^-5//2*(a+b*x^3)^2*(A+B*x^3), x) == :(-2//3*A*a^2*x^-3//2+2//3*a*x^3//2*(B*a+2*A*b)+2//9*b*x^9//2*(A*b+2*B*a)+2//15*B*b^2*x^15//2)
@test integrate(x^-7//2*(a+b*x^3)^2*(A+B*x^3), x) == :(2*a*x^(1/2)*(B*a+2*A*b)+-2//5*A*a^2*x^-5//2+2//7*b*x^7//2*(A*b+2*B*a)+2//13*B*b^2*x^13//2)
@test integrate(x^7//2*(a+b*x^3)^3*(A+B*x^3), x) == :(2//9*A*a^3*x^9//2+2//15*a^2*x^15//2*(B*a+3*A*b)+2//27*b^2*x^27//2*(A*b+3*B*a)+2//33*B*b^3*x^33//2+2//7*a*b*x^21//2*(A*b+B*a))
@test integrate(x^5//2*(a+b*x^3)^3*(A+B*x^3), x) == :(2//7*A*a^3*x^7//2+2//13*a^2*x^13//2*(B*a+3*A*b)+2//25*b^2*x^25//2*(A*b+3*B*a)+2//31*B*b^3*x^31//2+6//19*a*b*x^19//2*(A*b+B*a))
@test integrate(x^3//2*(a+b*x^3)^3*(A+B*x^3), x) == :(2//5*A*a^3*x^5//2+2//11*a^2*x^11//2*(B*a+3*A*b)+2//23*b^2*x^23//2*(A*b+3*B*a)+2//29*B*b^3*x^29//2+6//17*a*b*x^17//2*(A*b+B*a))
@test integrate(x^(1/2)*(a+b*x^3)^3*(A+B*x^3), x) == :(2//3*A*a^3*x^3//2+2//9*a^2*x^9//2*(B*a+3*A*b)+2//21*b^2*x^21//2*(A*b+3*B*a)+2//27*B*b^3*x^27//2+2//5*a*b*x^15//2*(A*b+B*a))
@test integrate(x^-1//2*(a+b*x^3)^3*(A+B*x^3), x) == :(2*A*a^3*x^(1/2)+2//7*a^2*x^7//2*(B*a+3*A*b)+2//19*b^2*x^19//2*(A*b+3*B*a)+2//25*B*b^3*x^25//2+6//13*a*b*x^13//2*(A*b+B*a))
@test integrate(x^-3//2*(a+b*x^3)^3*(A+B*x^3), x) == :(-2*A*a^3*x^-1//2+2//5*a^2*x^5//2*(B*a+3*A*b)+2//17*b^2*x^17//2*(A*b+3*B*a)+2//23*B*b^3*x^23//2+6//11*a*b*x^11//2*(A*b+B*a))
@test integrate(x^-5//2*(a+b*x^3)^3*(A+B*x^3), x) == :(-2//3*A*a^3*x^-3//2+2//3*a^2*x^3//2*(B*a+3*A*b)+2//15*b^2*x^15//2*(A*b+3*B*a)+2//21*B*b^3*x^21//2+2//3*a*b*x^9//2*(A*b+B*a))
@test integrate(x^-7//2*(a+b*x^3)^3*(A+B*x^3), x) == :(2*a^2*x^(1/2)*(B*a+3*A*b)+-2//5*A*a^3*x^-5//2+2//13*b^2*x^13//2*(A*b+3*B*a)+2//19*B*b^3*x^19//2+6//7*a*b*x^7//2*(A*b+B*a))
@test integrate(x^7//2*(a+b*x^3)^-1*(A+B*x^3), x) == :(1//3*b^-2*x^3//2*(-2*B*a+2*A*b)+2//9*B*b^-1*x^9//2+-2//3*a^(1/2)*b^-5//2*(A*b+-1*B*a)*arctan(a^-1//2*b^(1/2)*x^3//2))
@test integrate(x^5//2*(a+b*x^3)^-1*(A+B*x^3), x) == :(b^-2*x^(1/2)*(-2*B*a+2*A*b)+2//7*B*b^-1*x^7//2+-2//3*a^1//6*b^-13//6*(A*b+-1*B*a)*arctan(a^-1//6*b^1//6*x^(1/2))+-1//3*a^1//6*b^-13//6*(A*b+-1*B*a)*arctan(3^(1/2)+2*a^-1//6*b^1//6*x^(1/2))+1//3*a^1//6*b^-13//6*(A*b+-1*B*a)*arctan(3^(1/2)+-2*a^-1//6*b^1//6*x^(1/2))+-1//6*3^(1/2)*a^1//6*b^-13//6*(A*b+-1*B*a)*log(a^1//3+x*b^1//3+3^(1/2)*a^1//6*b^1//6*x^(1/2))+1//6*3^(1/2)*a^1//6*b^-13//6*(A*b+-1*B*a)*log(a^1//3+x*b^1//3+-1*3^(1/2)*a^1//6*b^1//6*x^(1/2)))
@test integrate(x^3//2*(a+b*x^3)^-1*(A+B*x^3), x) == :(2//5*B*b^-1*x^5//2+-1//3*a^-1//6*b^-11//6*(A*b+-1*B*a)*arctan(3^(1/2)+-2*a^-1//6*b^1//6*x^(1/2))+1//3*a^-1//6*b^-11//6*(A*b+-1*B*a)*arctan(3^(1/2)+2*a^-1//6*b^1//6*x^(1/2))+1//3*a^-1//6*b^-11//6*(-2*B*a+2*A*b)*arctan(a^-1//6*b^1//6*x^(1/2))+-1//6*3^(1/2)*a^-1//6*b^-11//6*(A*b+-1*B*a)*log(a^1//3+x*b^1//3+3^(1/2)*a^1//6*b^1//6*x^(1/2))+1//6*3^(1/2)*a^-1//6*b^-11//6*(A*b+-1*B*a)*log(a^1//3+x*b^1//3+-1*3^(1/2)*a^1//6*b^1//6*x^(1/2)))
@test integrate(x^(1/2)*(a+b*x^3)^-1*(A+B*x^3), x) == :(2//3*B*b^-1*x^3//2+1//3*a^-1//2*b^-3//2*(-2*B*a+2*A*b)*arctan(a^-1//2*b^(1/2)*x^3//2))
@test integrate(x^-1//2*(a+b*x^3)^-1*(A+B*x^3), x) == :(2*B*b^-1*x^(1/2)+-1//3*a^-5//6*b^-7//6*(A*b+-1*B*a)*arctan(3^(1/2)+-2*a^-1//6*b^1//6*x^(1/2))+1//3*a^-5//6*b^-7//6*(A*b+-1*B*a)*arctan(3^(1/2)+2*a^-1//6*b^1//6*x^(1/2))+1//3*a^-5//6*b^-7//6*(-2*B*a+2*A*b)*arctan(a^-1//6*b^1//6*x^(1/2))+-1//6*3^(1/2)*a^-5//6*b^-7//6*(A*b+-1*B*a)*log(a^1//3+x*b^1//3+-1*3^(1/2)*a^1//6*b^1//6*x^(1/2))+1//6*3^(1/2)*a^-5//6*b^-7//6*(A*b+-1*B*a)*log(a^1//3+x*b^1//3+3^(1/2)*a^1//6*b^1//6*x^(1/2)))
@test integrate(x^-3//2*(a+b*x^3)^-1*(A+B*x^3), x) == :(-2*A*a^-1*x^-1//2+-1//3*a^-7//6*b^-5//6*(A*b+-1*B*a)*arctan(3^(1/2)+2*a^-1//6*b^1//6*x^(1/2))+-1//3*a^-7//6*b^-5//6*(-2*B*a+2*A*b)*arctan(a^-1//6*b^1//6*x^(1/2))+1//3*a^-7//6*b^-5//6*(A*b+-1*B*a)*arctan(3^(1/2)+-2*a^-1//6*b^1//6*x^(1/2))+-1//6*3^(1/2)*a^-7//6*b^-5//6*(A*b+-1*B*a)*log(a^1//3+x*b^1//3+-1*3^(1/2)*a^1//6*b^1//6*x^(1/2))+1//6*3^(1/2)*a^-7//6*b^-5//6*(A*b+-1*B*a)*log(a^1//3+x*b^1//3+3^(1/2)*a^1//6*b^1//6*x^(1/2)))
@test integrate(x^-5//2*(a+b*x^3)^-1*(A+B*x^3), x) == :(-2//3*A*a^-1*x^-3//2+-1//3*a^-3//2*b^-1//2*(-2*B*a+2*A*b)*arctan(a^-1//2*b^(1/2)*x^3//2))
@test integrate(x^-7//2*(a+b*x^3)^-1*(A+B*x^3), x) == :(-2//5*A*a^-1*x^-5//2+-1//3*a^-11//6*b^-1//6*(A*b+-1*B*a)*arctan(3^(1/2)+2*a^-1//6*b^1//6*x^(1/2))+-1//3*a^-11//6*b^-1//6*(-2*B*a+2*A*b)*arctan(a^-1//6*b^1//6*x^(1/2))+1//3*a^-11//6*b^-1//6*(A*b+-1*B*a)*arctan(3^(1/2)+-2*a^-1//6*b^1//6*x^(1/2))+-1//6*3^(1/2)*a^-11//6*b^-1//6*(A*b+-1*B*a)*log(a^1//3+x*b^1//3+3^(1/2)*a^1//6*b^1//6*x^(1/2))+1//6*3^(1/2)*a^-11//6*b^-1//6*(A*b+-1*B*a)*log(a^1//3+x*b^1//3+-1*3^(1/2)*a^1//6*b^1//6*x^(1/2)))
@test integrate(x^7//2*(a+b*x^3)^-2*(A+B*x^3), x) == :(-1//3*a^-1*b^-2*x^3//2*(A*b+-3*B*a)+1//3*a^-1//2*b^-5//2*(A*b+-3*B*a)*arctan(a^-1//2*b^(1/2)*x^3//2)+1//3*a^-1*b^-1*x^9//2*(a+b*x^3)^-1*(A*b+-1*B*a))
@test integrate(x^5//2*(a+b*x^3)^-2*(A+B*x^3), x) == :(-1//3*a^-1*b^-2*x^(1/2)*(A*b+-7*B*a)+-1//18*a^-5//6*b^-13//6*(A*b+-7*B*a)*arctan(3^(1/2)+-2*a^-1//6*b^1//6*x^(1/2))+1//9*a^-5//6*b^-13//6*(A*b+-7*B*a)*arctan(a^-1//6*b^1//6*x^(1/2))+1//18*a^-5//6*b^-13//6*(A*b+-7*B*a)*arctan(3^(1/2)+2*a^-1//6*b^1//6*x^(1/2))+-1//36*3^(1/2)*a^-5//6*b^-13//6*(A*b+-7*B*a)*log(a^1//3+x*b^1//3+-1*3^(1/2)*a^1//6*b^1//6*x^(1/2))+1//3*a^-1*b^-1*x^7//2*(a+b*x^3)^-1*(A*b+-1*B*a)+1//36*3^(1/2)*a^-5//6*b^-13//6*(A*b+-7*B*a)*log(a^1//3+x*b^1//3+3^(1/2)*a^1//6*b^1//6*x^(1/2)))
@test integrate(x^3//2*(a+b*x^3)^-2*(A+B*x^3), x) == :(-1//18*a^-7//6*b^-11//6*(A*b+5*B*a)*arctan(3^(1/2)+-2*a^-1//6*b^1//6*x^(1/2))+1//9*a^-7//6*b^-11//6*(A*b+5*B*a)*arctan(a^-1//6*b^1//6*x^(1/2))+1//18*a^-7//6*b^-11//6*(A*b+5*B*a)*arctan(3^(1/2)+2*a^-1//6*b^1//6*x^(1/2))+-1//36*3^(1/2)*a^-7//6*b^-11//6*(A*b+5*B*a)*log(a^1//3+x*b^1//3+3^(1/2)*a^1//6*b^1//6*x^(1/2))+1//3*a^-1*b^-1*x^5//2*(a+b*x^3)^-1*(A*b+-1*B*a)+1//36*3^(1/2)*a^-7//6*b^-11//6*(A*b+5*B*a)*log(a^1//3+x*b^1//3+-1*3^(1/2)*a^1//6*b^1//6*x^(1/2)))
@test integrate(x^(1/2)*(a+b*x^3)^-2*(A+B*x^3), x) == :(1//3*a^-3//2*b^-3//2*(A*b+B*a)*arctan(a^-1//2*b^(1/2)*x^3//2)+1//3*a^-1*b^-1*x^3//2*(a+b*x^3)^-1*(A*b+-1*B*a))
@test integrate(x^-1//2*(a+b*x^3)^-2*(A+B*x^3), x) == :(-1//18*a^-11//6*b^-7//6*(B*a+5*A*b)*arctan(3^(1/2)+-2*a^-1//6*b^1//6*x^(1/2))+1//9*a^-11//6*b^-7//6*(B*a+5*A*b)*arctan(a^-1//6*b^1//6*x^(1/2))+1//18*a^-11//6*b^-7//6*(B*a+5*A*b)*arctan(3^(1/2)+2*a^-1//6*b^1//6*x^(1/2))+-1//36*3^(1/2)*a^-11//6*b^-7//6*(B*a+5*A*b)*log(a^1//3+x*b^1//3+-1*3^(1/2)*a^1//6*b^1//6*x^(1/2))+1//3*a^-1*b^-1*x^(1/2)*(a+b*x^3)^-1*(A*b+-1*B*a)+1//36*3^(1/2)*a^-11//6*b^-7//6*(B*a+5*A*b)*log(a^1//3+x*b^1//3+3^(1/2)*a^1//6*b^1//6*x^(1/2)))
@test integrate(x^-3//2*(a+b*x^3)^-2*(A+B*x^3), x) == :(-1//3*a^-2*b^-1*x^-1//2*(-1*B*a+7*A*b)+-1//9*a^-13//6*b^-5//6*(-1*B*a+7*A*b)*arctan(a^-1//6*b^1//6*x^(1/2))+-1//18*a^-13//6*b^-5//6*(-1*B*a+7*A*b)*arctan(3^(1/2)+2*a^-1//6*b^1//6*x^(1/2))+1//18*a^-13//6*b^-5//6*(-1*B*a+7*A*b)*arctan(3^(1/2)+-2*a^-1//6*b^1//6*x^(1/2))+-1//36*3^(1/2)*a^-13//6*b^-5//6*(-1*B*a+7*A*b)*log(a^1//3+x*b^1//3+-1*3^(1/2)*a^1//6*b^1//6*x^(1/2))+1//3*a^-1*b^-1*x^-1//2*(a+b*x^3)^-1*(A*b+-1*B*a)+1//36*3^(1/2)*a^-13//6*b^-5//6*(-1*B*a+7*A*b)*log(a^1//3+x*b^1//3+3^(1/2)*a^1//6*b^1//6*x^(1/2)))
@test integrate(x^-5//2*(a+b*x^3)^-2*(A+B*x^3), x) == :(-1//3*a^-5//2*b^-1//2*(-1*B*a+3*A*b)*arctan(a^-1//2*b^(1/2)*x^3//2)+1//3*a^-2*b^-1*x^-3//2*(B*a+-3*A*b)+1//3*a^-1*b^-1*x^-3//2*(a+b*x^3)^-1*(A*b+-1*B*a))
@test integrate(x^-7//2*(a+b*x^3)^-2*(A+B*x^3), x) == :(-1//9*a^-17//6*b^-1//6*(-5*B*a+11*A*b)*arctan(a^-1//6*b^1//6*x^(1/2))+-1//15*a^-2*b^-1*x^-5//2*(-5*B*a+11*A*b)+-1//18*a^-17//6*b^-1//6*(-5*B*a+11*A*b)*arctan(3^(1/2)+2*a^-1//6*b^1//6*x^(1/2))+1//18*a^-17//6*b^-1//6*(-5*B*a+11*A*b)*arctan(3^(1/2)+-2*a^-1//6*b^1//6*x^(1/2))+-1//36*3^(1/2)*a^-17//6*b^-1//6*(-5*B*a+11*A*b)*log(a^1//3+x*b^1//3+3^(1/2)*a^1//6*b^1//6*x^(1/2))+1//3*a^-1*b^-1*x^-5//2*(a+b*x^3)^-1*(A*b+-1*B*a)+1//36*3^(1/2)*a^-17//6*b^-1//6*(-5*B*a+11*A*b)*log(a^1//3+x*b^1//3+-1*3^(1/2)*a^1//6*b^1//6*x^(1/2)))
@test integrate(x^7//2*(a+b*x^3)^-3*(A+B*x^3), x) == :(1//12*a^-3//2*b^-5//2*(A*b+3*B*a)*arctan(a^-1//2*b^(1/2)*x^3//2)+-1//12*a^-1*b^-2*x^3//2*(a+b*x^3)^-1*(A*b+3*B*a)+1//6*a^-1*b^-1*x^9//2*(a+b*x^3)^-2*(A*b+-1*B*a))
@test integrate(x^5//2*(a+b*x^3)^-3*(A+B*x^3), x) == :(-1//216*a^-11//6*b^-13//6*(5*A*b+7*B*a)*arctan(3^(1/2)+-2*a^-1//6*b^1//6*x^(1/2))+1//108*a^-11//6*b^-13//6*(5*A*b+7*B*a)*arctan(a^-1//6*b^1//6*x^(1/2))+1//216*a^-11//6*b^-13//6*(5*A*b+7*B*a)*arctan(3^(1/2)+2*a^-1//6*b^1//6*x^(1/2))+-1//36*a^-1*b^-2*x^(1/2)*(a+b*x^3)^-1*(5*A*b+7*B*a)+-1//432*3^(1/2)*a^-11//6*b^-13//6*(5*A*b+7*B*a)*log(a^1//3+x*b^1//3+-1*3^(1/2)*a^1//6*b^1//6*x^(1/2))+1//6*a^-1*b^-1*x^7//2*(a+b*x^3)^-2*(A*b+-1*B*a)+1//432*3^(1/2)*a^-11//6*b^-13//6*(5*A*b+7*B*a)*log(a^1//3+x*b^1//3+3^(1/2)*a^1//6*b^1//6*x^(1/2)))
@test integrate(x^3//2*(a+b*x^3)^-3*(A+B*x^3), x) == :(-1//216*a^-13//6*b^-11//6*(5*B*a+7*A*b)*arctan(3^(1/2)+-2*a^-1//6*b^1//6*x^(1/2))+1//108*a^-13//6*b^-11//6*(5*B*a+7*A*b)*arctan(a^-1//6*b^1//6*x^(1/2))+1//216*a^-13//6*b^-11//6*(5*B*a+7*A*b)*arctan(3^(1/2)+2*a^-1//6*b^1//6*x^(1/2))+-1//432*3^(1/2)*a^-13//6*b^-11//6*(5*B*a+7*A*b)*log(a^1//3+x*b^1//3+3^(1/2)*a^1//6*b^1//6*x^(1/2))+1//6*a^-1*b^-1*x^5//2*(a+b*x^3)^-2*(A*b+-1*B*a)+1//36*a^-2*b^-1*x^5//2*(a+b*x^3)^-1*(5*B*a+7*A*b)+1//432*3^(1/2)*a^-13//6*b^-11//6*(5*B*a+7*A*b)*log(a^1//3+x*b^1//3+-1*3^(1/2)*a^1//6*b^1//6*x^(1/2)))
@test integrate(x^(1/2)*(a+b*x^3)^-3*(A+B*x^3), x) == :(1//12*a^-5//2*b^-3//2*(B*a+3*A*b)*arctan(a^-1//2*b^(1/2)*x^3//2)+1//6*a^-1*b^-1*x^3//2*(a+b*x^3)^-2*(A*b+-1*B*a)+1//12*a^-2*b^-1*x^3//2*(a+b*x^3)^-1*(B*a+3*A*b))
@test integrate(x^-1//2*(a+b*x^3)^-3*(A+B*x^3), x) == :(-1//216*a^-17//6*b^-7//6*(5*B*a+55*A*b)*arctan(3^(1/2)+-2*a^-1//6*b^1//6*x^(1/2))+1//108*a^-17//6*b^-7//6*(5*B*a+55*A*b)*arctan(a^-1//6*b^1//6*x^(1/2))+1//216*a^-17//6*b^-7//6*(5*B*a+55*A*b)*arctan(3^(1/2)+2*a^-1//6*b^1//6*x^(1/2))+-1//432*3^(1/2)*a^-17//6*b^-7//6*(5*B*a+55*A*b)*log(a^1//3+x*b^1//3+-1*3^(1/2)*a^1//6*b^1//6*x^(1/2))+1//6*a^-1*b^-1*x^(1/2)*(a+b*x^3)^-2*(A*b+-1*B*a)+1//36*a^-2*b^-1*x^(1/2)*(a+b*x^3)^-1*(B*a+11*A*b)+1//432*3^(1/2)*a^-17//6*b^-7//6*(5*B*a+55*A*b)*log(a^1//3+x*b^1//3+3^(1/2)*a^1//6*b^1//6*x^(1/2)))
@test integrate(x^-3//2*(a+b*x^3)^-3*(A+B*x^3), x) == :(-1//36*a^-3*b^-1*x^-1//2*(-7*B*a+91*A*b)+-1//108*a^-19//6*b^-5//6*(-7*B*a+91*A*b)*arctan(a^-1//6*b^1//6*x^(1/2))+-1//216*a^-19//6*b^-5//6*(-7*B*a+91*A*b)*arctan(3^(1/2)+2*a^-1//6*b^1//6*x^(1/2))+1//216*a^-19//6*b^-5//6*(-7*B*a+91*A*b)*arctan(3^(1/2)+-2*a^-1//6*b^1//6*x^(1/2))+-1//432*3^(1/2)*a^-19//6*b^-5//6*(-7*B*a+91*A*b)*log(a^1//3+x*b^1//3+-1*3^(1/2)*a^1//6*b^1//6*x^(1/2))+1//6*a^-1*b^-1*x^-1//2*(a+b*x^3)^-2*(A*b+-1*B*a)+1//36*a^-2*b^-1*x^-1//2*(a+b*x^3)^-1*(-1*B*a+13*A*b)+1//432*3^(1/2)*a^-19//6*b^-5//6*(-7*B*a+91*A*b)*log(a^1//3+x*b^1//3+3^(1/2)*a^1//6*b^1//6*x^(1/2)))
@test integrate(x^-5//2*(a+b*x^3)^-3*(A+B*x^3), x) == :(-1//4*a^-7//2*b^-1//2*(-1*B*a+5*A*b)*arctan(a^-1//2*b^(1/2)*x^3//2)+1//4*a^-3*b^-1*x^-3//2*(B*a+-5*A*b)+1//6*a^-1*b^-1*x^-3//2*(a+b*x^3)^-2*(A*b+-1*B*a)+1//12*a^-2*b^-1*x^-3//2*(a+b*x^3)^-1*(-1*B*a+5*A*b))
@test integrate(x^-7//2*(a+b*x^3)^-3*(A+B*x^3), x) == :(-1//108*a^-23//6*b^-1//6*(-55*B*a+187*A*b)*arctan(a^-1//6*b^1//6*x^(1/2))+-1//180*a^-3*b^-1*x^-5//2*(-55*B*a+187*A*b)+-1//216*a^-23//6*b^-1//6*(-55*B*a+187*A*b)*arctan(3^(1/2)+2*a^-1//6*b^1//6*x^(1/2))+1//216*a^-23//6*b^-1//6*(-55*B*a+187*A*b)*arctan(3^(1/2)+-2*a^-1//6*b^1//6*x^(1/2))+-1//432*3^(1/2)*a^-23//6*b^-1//6*(-55*B*a+187*A*b)*log(a^1//3+x*b^1//3+3^(1/2)*a^1//6*b^1//6*x^(1/2))+1//6*a^-1*b^-1*x^-5//2*(a+b*x^3)^-2*(A*b+-1*B*a)+1//36*a^-2*b^-1*x^-5//2*(a+b*x^3)^-1*(-5*B*a+17*A*b)+1//432*3^(1/2)*a^-23//6*b^-1//6*(-55*B*a+187*A*b)*log(a^1//3+x*b^1//3+-1*3^(1/2)*a^1//6*b^1//6*x^(1/2)))
@test integrate(x^8*(a+b*x^3)^(1/2)*(A+B*x^3), x) == :(1//21*b^-4*(a+b*x^3)^7//2*(-6*B*a+2*A*b)+2//27*B*b^-4*(a+b*x^3)^9//2+-2//15*a*b^-4*(a+b*x^3)^5//2*(-3*B*a+2*A*b)+2//9*a^2*b^-4*(a+b*x^3)^3//2*(A*b+-1*B*a))
@test integrate(x^5*(a+b*x^3)^(1/2)*(A+B*x^3), x) == :(1//15*b^-3*(a+b*x^3)^5//2*(-4*B*a+2*A*b)+2//21*B*b^-3*(a+b*x^3)^7//2+-2//9*a*b^-3*(a+b*x^3)^3//2*(A*b+-1*B*a))
@test integrate(x^2*(a+b*x^3)^(1/2)*(A+B*x^3), x) == :(1//9*b^-2*(a+b*x^3)^3//2*(-2*B*a+2*A*b)+2//15*B*b^-2*(a+b*x^3)^5//2)
@test integrate(x^-1*(a+b*x^3)^(1/2)*(A+B*x^3), x) == :(2//3*A*(a+b*x^3)^(1/2)+-2//3*A*a^(1/2)*arctanh(a^-1//2*(a+b*x^3)^(1/2))+2//9*B*b^-1*(a+b*x^3)^3//2)
@test integrate(x^-4*(a+b*x^3)^(1/2)*(A+B*x^3), x) == :(-1//3*a^-1//2*(A*b+2*B*a)*arctanh(a^-1//2*(a+b*x^3)^(1/2))+1//3*a^-1*(a+b*x^3)^(1/2)*(A*b+2*B*a)+-1//3*A*a^-1*x^-3*(a+b*x^3)^3//2)
@test integrate(x^-7*(a+b*x^3)^(1/2)*(A+B*x^3), x) == :(-1//6*A*a^-1*x^-6*(a+b*x^3)^3//2+1//12*b*a^-3//2*(A*b+-4*B*a)*arctanh(a^-1//2*(a+b*x^3)^(1/2))+1//12*a^-1*x^-3*(a+b*x^3)^(1/2)*(A*b+-4*B*a))
@test integrate(x^3*(a+b*x^3)^(1/2)*(A+B*x^3), x) == :(1//187*b^-1*x^4*(a+b*x^3)^(1/2)*(-16*B*a+34*A*b)+2//17*B*b^-1*x^4*(a+b*x^3)^3//2+6//935*a*x*b^-2*(a+b*x^3)^(1/2)*(-8*B*a+17*A*b)+-4//935*3^3//4*a^2*b^-7//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-8*B*a+17*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+b*x^3)^(1/2)*(A+B*x^3), x) == :(1//55*x*b^-1*(a+b*x^3)^(1/2)*(-4*B*a+22*A*b)+2//11*B*x*b^-1*(a+b*x^3)^3//2+2//55*a*3^3//4*b^-4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-2*B*a+11*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-3*(a+b*x^3)^(1/2)*(A+B*x^3), x) == :(-1//2*A*a^-1*x^-2*(a+b*x^3)^3//2+1//10*x*a^-1*(a+b*x^3)^(1/2)*(4*B*a+5*A*b)+1//10*3^3//4*b^-1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(4*B*a+5*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-6*(a+b*x^3)^(1/2)*(A+B*x^3), x) == :(-1//5*A*a^-1*x^-5*(a+b*x^3)^3//2+1//20*a^-1*x^-2*(a+b*x^3)^(1/2)*(A*b+-10*B*a)+-1//20*3^3//4*a^-1*b^2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(A*b+-10*B*a)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-9*(a+b*x^3)^(1/2)*(A+B*x^3), x) == :(-1//8*A*a^-1*x^-8*(a+b*x^3)^3//2+1//80*a^-1*x^-5*(a+b*x^3)^(1/2)*(-16*B*a+7*A*b)+3//320*b*a^-2*x^-2*(a+b*x^3)^(1/2)*(-16*B*a+7*A*b)+1//320*3^3//4*a^-2*b^5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-16*B*a+7*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^4*(a+b*x^3)^(1/2)*(A+B*x^3), x) == :(1//247*b^-1*x^5*(a+b*x^3)^(1/2)*(-20*B*a+38*A*b)+2//19*B*b^-1*x^5*(a+b*x^3)^3//2+-24//1729*a^2*b^-8//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(-10*B*a+19*A*b)+6//1729*a*b^-2*x^2*(a+b*x^3)^(1/2)*(-10*B*a+19*A*b)+-8//1729*2^(1/2)*3^3//4*a^7//3*b^-8//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-10*B*a+19*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+12//1729*3^1//4*a^7//3*b^-8//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-10*B*a+19*A*b)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(a+b*x^3)^(1/2)*(A+B*x^3), x) == :(1//91*b^-1*x^2*(a+b*x^3)^(1/2)*(-8*B*a+26*A*b)+2//13*B*b^-1*x^2*(a+b*x^3)^3//2+6//91*a*b^-5//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(-4*B*a+13*A*b)+-3//91*3^1//4*a^4//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-4*B*a+13*A*b)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+2//91*2^(1/2)*3^3//4*a^4//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-4*B*a+13*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-2*(a+b*x^3)^(1/2)*(A+B*x^3), x) == :(-1*A*a^-1*x^-1*(a+b*x^3)^3//2+1//7*a^-1*x^2*(a+b*x^3)^(1/2)*(2*B*a+7*A*b)+1//7*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(6*B*a+21*A*b)+-3//14*3^1//4*a^1//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(2*B*a+7*A*b)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//7*2^(1/2)*3^3//4*a^1//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(2*B*a+7*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-5*(a+b*x^3)^(1/2)*(A+B*x^3), x) == :(-1//4*A*a^-1*x^-4*(a+b*x^3)^3//2+-1//8*a^-1*x^-1*(a+b*x^3)^(1/2)*(A*b+8*B*a)+3//8*a^-1*b^1//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(A*b+8*B*a)+-3//16*3^1//4*a^-2//3*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(A*b+8*B*a)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//8*2^(1/2)*3^3//4*a^-2//3*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(A*b+8*B*a)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-8*(a+b*x^3)^(1/2)*(A+B*x^3), x) == :(-1//7*A*a^-1*x^-7*(a+b*x^3)^3//2+1//56*a^-1*x^-4*(a+b*x^3)^(1/2)*(-14*B*a+5*A*b)+-3//112*a^-2*b^4//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(-14*B*a+5*A*b)+3//112*b*a^-2*x^-1*(a+b*x^3)^(1/2)*(-14*B*a+5*A*b)+-1//112*2^(1/2)*3^3//4*a^-5//3*b^4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-14*B*a+5*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+3//224*3^1//4*a^-5//3*b^4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-14*B*a+5*A*b)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-11*(a+b*x^3)^(1/2)*(A+B*x^3), x) == :(-1//10*A*a^-1*x^-10*(a+b*x^3)^3//2+1//140*a^-1*x^-7*(a+b*x^3)^(1/2)*(-20*B*a+11*A*b)+-3//448*a^-3*b^2*x^-1*(a+b*x^3)^(1/2)*(-20*B*a+11*A*b)+3//448*a^-3*b^7//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(-20*B*a+11*A*b)+3//1120*b*a^-2*x^-4*(a+b*x^3)^(1/2)*(-20*B*a+11*A*b)+-3//896*3^1//4*a^-8//3*b^7//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-20*B*a+11*A*b)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//448*2^(1/2)*3^3//4*a^-8//3*b^7//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-20*B*a+11*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^8*(a+b*x^3)^3//2*(A+B*x^3), x) == :(1//27*b^-4*(a+b*x^3)^9//2*(-6*B*a+2*A*b)+2//33*B*b^-4*(a+b*x^3)^11//2+-2//21*a*b^-4*(a+b*x^3)^7//2*(-3*B*a+2*A*b)+2//15*a^2*b^-4*(a+b*x^3)^5//2*(A*b+-1*B*a))
@test integrate(x^5*(a+b*x^3)^3//2*(A+B*x^3), x) == :(1//21*b^-3*(a+b*x^3)^7//2*(-4*B*a+2*A*b)+2//27*B*b^-3*(a+b*x^3)^9//2+-2//15*a*b^-3*(a+b*x^3)^5//2*(A*b+-1*B*a))
@test integrate(x^2*(a+b*x^3)^3//2*(A+B*x^3), x) == :(1//15*b^-2*(a+b*x^3)^5//2*(-2*B*a+2*A*b)+2//21*B*b^-2*(a+b*x^3)^7//2)
@test integrate(x^-1*(a+b*x^3)^3//2*(A+B*x^3), x) == :(2//9*A*(a+b*x^3)^3//2+-2//3*A*a^3//2*arctanh(a^-1//2*(a+b*x^3)^(1/2))+2//3*A*a*(a+b*x^3)^(1/2)+2//15*B*b^-1*(a+b*x^3)^5//2)
@test integrate(x^-4*(a+b*x^3)^3//2*(A+B*x^3), x) == :(1//3*(a+b*x^3)^(1/2)*(2*B*a+3*A*b)+-1//3*a^(1/2)*(2*B*a+3*A*b)*arctanh(a^-1//2*(a+b*x^3)^(1/2))+1//9*a^-1*(a+b*x^3)^3//2*(2*B*a+3*A*b)+-1//3*A*a^-1*x^-3*(a+b*x^3)^5//2)
@test integrate(x^-7*(a+b*x^3)^3//2*(A+B*x^3), x) == :(-1//4*b*a^-1//2*(A*b+4*B*a)*arctanh(a^-1//2*(a+b*x^3)^(1/2))+-1//6*A*a^-1*x^-6*(a+b*x^3)^5//2+-1//12*a^-1*x^-3*(a+b*x^3)^3//2*(A*b+4*B*a)+1//4*b*a^-1*(a+b*x^3)^(1/2)*(A*b+4*B*a))
@test integrate(x^3*(a+b*x^3)^3//2*(A+B*x^3), x) == :(1//391*b^-1*x^4*(a+b*x^3)^3//2*(-16*B*a+46*A*b)+2//23*B*b^-1*x^4*(a+b*x^3)^5//2+18//4301*a*b^-1*x^4*(a+b*x^3)^(1/2)*(-8*B*a+23*A*b)+54//21505*x*a^2*b^-2*(a+b*x^3)^(1/2)*(-8*B*a+23*A*b)+-36//21505*3^3//4*a^3*b^-7//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-8*B*a+23*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+b*x^3)^3//2*(A+B*x^3), x) == :(1//187*x*b^-1*(a+b*x^3)^3//2*(-4*B*a+34*A*b)+2//17*B*x*b^-1*(a+b*x^3)^5//2+18//935*a*x*b^-1*(a+b*x^3)^(1/2)*(-2*B*a+17*A*b)+18//935*3^3//4*a^2*b^-4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-2*B*a+17*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-3*(a+b*x^3)^3//2*(A+B*x^3), x) == :(x*(a+b*x^3)^(1/2)*(9//10*A*b+18//55*B*a)+-1//2*A*a^-1*x^-2*(a+b*x^3)^5//2+1//22*x*a^-1*(a+b*x^3)^3//2*(4*B*a+11*A*b)+9//110*a*3^3//4*b^-1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(4*B*a+11*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-6*(a+b*x^3)^3//2*(A+B*x^3), x) == :(-1//4*a^-1*x^-2*(a+b*x^3)^3//2*(A*b+2*B*a)+-1//5*A*a^-1*x^-5*(a+b*x^3)^5//2+9//20*b*x*a^-1*(a+b*x^3)^(1/2)*(A*b+2*B*a)+9//20*3^3//4*b^2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(A*b+2*B*a)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-9*(a+b*x^3)^3//2*(A+B*x^3), x) == :(-1//8*A*a^-1*x^-8*(a+b*x^3)^5//2+1//80*a^-1*x^-5*(a+b*x^3)^3//2*(A*b+-16*B*a)+9//320*b*a^-1*x^-2*(a+b*x^3)^(1/2)*(A*b+-16*B*a)+-9//320*3^3//4*a^-1*b^5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(A*b+-16*B*a)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^4*(a+b*x^3)^3//2*(A+B*x^3), x) == :(1//95*b^-1*x^5*(a+b*x^3)^3//2*(-4*B*a+10*A*b)+2//25*B*b^-1*x^5*(a+b*x^3)^5//2+-216//8645*a^3*b^-8//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(-2*B*a+5*A*b)+18//1235*a*b^-1*x^5*(a+b*x^3)^(1/2)*(-2*B*a+5*A*b)+54//8645*a^2*b^-2*x^2*(a+b*x^3)^(1/2)*(-2*B*a+5*A*b)+-72//8645*2^(1/2)*3^3//4*a^10//3*b^-8//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-2*B*a+5*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+108//8645*3^1//4*a^10//3*b^-8//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-2*B*a+5*A*b)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(a+b*x^3)^3//2*(A+B*x^3), x) == :(1//247*b^-1*x^2*(a+b*x^3)^3//2*(-8*B*a+38*A*b)+2//19*B*b^-1*x^2*(a+b*x^3)^5//2+18//1729*a*b^-1*x^2*(a+b*x^3)^(1/2)*(-4*B*a+19*A*b)+54//1729*a^2*b^-5//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(-4*B*a+19*A*b)+-27//1729*3^1//4*a^7//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-4*B*a+19*A*b)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+18//1729*2^(1/2)*3^3//4*a^7//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-4*B*a+19*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-2*(a+b*x^3)^3//2*(A+B*x^3), x) == :(x^2*(a+b*x^3)^(1/2)*(9//7*A*b+18//91*B*a)+-1*A*a^-1*x^-1*(a+b*x^3)^5//2+1//13*a^-1*x^2*(a+b*x^3)^3//2*(2*B*a+13*A*b)+27//91*a*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(2*B*a+13*A*b)+-27//182*3^1//4*a^4//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(2*B*a+13*A*b)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+9//91*2^(1/2)*3^3//4*a^4//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(2*B*a+13*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-5*(a+b*x^3)^3//2*(A+B*x^3), x) == :(27*b^1//3*(a+b*x^3)^(1/2)*(56*x*b^1//3+56*a^1//3*(1+3^(1/2)))^-1*(7*A*b+8*B*a)+-1//4*A*a^-1*x^-4*(a+b*x^3)^5//2+-1//8*a^-1*x^-1*(a+b*x^3)^3//2*(7*A*b+8*B*a)+9//56*b*a^-1*x^2*(a+b*x^3)^(1/2)*(7*A*b+8*B*a)+-27//112*3^1//4*a^1//3*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(7*A*b+8*B*a)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+9//56*2^(1/2)*3^3//4*a^1//3*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(7*A*b+8*B*a)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-8*(a+b*x^3)^3//2*(A+B*x^3), x) == :(-1//7*A*a^-1*x^-7*(a+b*x^3)^5//2+-1//56*a^-1*x^-4*(a+b*x^3)^3//2*(A*b+14*B*a)+-9//112*b*a^-1*x^-1*(a+b*x^3)^(1/2)*(A*b+14*B*a)+27//112*a^-1*b^4//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(A*b+14*B*a)+-27//224*3^1//4*a^-2//3*b^4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(A*b+14*B*a)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+9//112*2^(1/2)*3^3//4*a^-2//3*b^4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(A*b+14*B*a)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-11*(a+b*x^3)^3//2*(A+B*x^3), x) == :(-1//10*A*a^-1*x^-10*(a+b*x^3)^5//2+1//28*a^-1*x^-7*(a+b*x^3)^3//2*(A*b+-4*B*a)+-27//448*a^-2*b^7//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(A*b+-4*B*a)+9//224*b*a^-1*x^-4*(a+b*x^3)^(1/2)*(A*b+-4*B*a)+27//448*a^-2*b^2*x^-1*(a+b*x^3)^(1/2)*(A*b+-4*B*a)+-9//448*2^(1/2)*3^3//4*a^-5//3*b^7//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(A*b+-4*B*a)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+27//896*3^1//4*a^-5//3*b^7//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(A*b+-4*B*a)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^8*(a+b*x^3)^-1//2*(A+B*x^3), x) == :(1//15*b^-4*(a+b*x^3)^5//2*(-6*B*a+2*A*b)+2//21*B*b^-4*(a+b*x^3)^7//2+-2//9*a*b^-4*(a+b*x^3)^3//2*(-3*B*a+2*A*b)+2//3*a^2*b^-4*(a+b*x^3)^(1/2)*(A*b+-1*B*a))
@test integrate(x^5*(a+b*x^3)^-1//2*(A+B*x^3), x) == :(1//9*b^-3*(a+b*x^3)^3//2*(-4*B*a+2*A*b)+2//15*B*b^-3*(a+b*x^3)^5//2+-2//3*a*b^-3*(a+b*x^3)^(1/2)*(A*b+-1*B*a))
@test integrate(x^2*(a+b*x^3)^-1//2*(A+B*x^3), x) == :(1//3*b^-2*(a+b*x^3)^(1/2)*(-2*B*a+2*A*b)+2//9*B*b^-2*(a+b*x^3)^3//2)
@test integrate(x^-1*(a+b*x^3)^-1//2*(A+B*x^3), x) == :(-2//3*A*a^-1//2*arctanh(a^-1//2*(a+b*x^3)^(1/2))+2//3*B*b^-1*(a+b*x^3)^(1/2))
@test integrate(x^-4*(a+b*x^3)^-1//2*(A+B*x^3), x) == :(1//3*a^-3//2*(A*b+-2*B*a)*arctanh(a^-1//2*(a+b*x^3)^(1/2))+-1//3*A*a^-1*x^-3*(a+b*x^3)^(1/2))
@test integrate(x^-7*(a+b*x^3)^-1//2*(A+B*x^3), x) == :(-1//6*A*a^-1*x^-6*(a+b*x^3)^(1/2)+-1//12*b*a^-5//2*(-4*B*a+3*A*b)*arctanh(a^-1//2*(a+b*x^3)^(1/2))+1//12*a^-2*x^-3*(a+b*x^3)^(1/2)*(-4*B*a+3*A*b))
@test integrate(x^3*(a+b*x^3)^-1//2*(A+B*x^3), x) == :(1//55*x*b^-2*(a+b*x^3)^(1/2)*(-16*B*a+22*A*b)+2//11*B*b^-1*x^4*(a+b*x^3)^(1/2)+-4//165*a*3^3//4*b^-7//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-8*B*a+11*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+b*x^3)^-1//2*(A+B*x^3), x) == :(2//5*B*x*b^-1*(a+b*x^3)^(1/2)+2//15*3^3//4*b^-4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-2*B*a+5*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-3*(a+b*x^3)^-1//2*(A+B*x^3), x) == :(-1//2*A*a^-1*x^-2*(a+b*x^3)^(1/2)+-1//6*3^3//4*a^-1*b^-1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(A*b+-4*B*a)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-6*(a+b*x^3)^-1//2*(A+B*x^3), x) == :(-1//5*A*a^-1*x^-5*(a+b*x^3)^(1/2)+1//20*a^-2*x^-2*(a+b*x^3)^(1/2)*(-10*B*a+7*A*b)+1//60*3^3//4*a^-2*b^2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-10*B*a+7*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^4*(a+b*x^3)^-1//2*(A+B*x^3), x) == :(1//91*b^-2*x^2*(a+b*x^3)^(1/2)*(-20*B*a+26*A*b)+2//13*B*b^-1*x^5*(a+b*x^3)^(1/2)+-8//91*a*b^-8//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(-10*B*a+13*A*b)+-8//273*2^(1/2)*3^3//4*a^4//3*b^-8//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-10*B*a+13*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+4//91*3^1//4*a^4//3*b^-8//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-10*B*a+13*A*b)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(a+b*x^3)^-1//2*(A+B*x^3), x) == :(1//7*b^-5//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(-8*B*a+14*A*b)+2//7*B*b^-1*x^2*(a+b*x^3)^(1/2)+-1//7*3^1//4*a^1//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-4*B*a+7*A*b)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+2//21*2^(1/2)*3^3//4*a^1//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-4*B*a+7*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-2*(a+b*x^3)^-1//2*(A+B*x^3), x) == :(-1*A*a^-1*x^-1*(a+b*x^3)^(1/2)+a^-1*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(A*b+2*B*a)+-1//2*3^1//4*a^-2//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(A*b+2*B*a)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//3*2^(1/2)*3^3//4*a^-2//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(A*b+2*B*a)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-5*(a+b*x^3)^-1//2*(A+B*x^3), x) == :(-1//4*A*a^-1*x^-4*(a+b*x^3)^(1/2)+1//8*a^-2*x^-1*(a+b*x^3)^(1/2)*(-8*B*a+5*A*b)+-1//8*a^-2*b^1//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(-8*B*a+5*A*b)+-1//24*2^(1/2)*3^3//4*a^-5//3*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-8*B*a+5*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//16*3^1//4*a^-5//3*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-8*B*a+5*A*b)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-8*(a+b*x^3)^-1//2*(A+B*x^3), x) == :(-1//7*A*a^-1*x^-7*(a+b*x^3)^(1/2)+1//56*a^-2*x^-4*(a+b*x^3)^(1/2)*(-14*B*a+11*A*b)+-5//112*b*a^-3*x^-1*(a+b*x^3)^(1/2)*(-14*B*a+11*A*b)+5//112*a^-3*b^4//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(-14*B*a+11*A*b)+-5//224*3^1//4*a^-8//3*b^4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-14*B*a+11*A*b)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+5//336*2^(1/2)*3^3//4*a^-8//3*b^4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-14*B*a+11*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^8*(a+b*x^3)^-3//2*(A+B*x^3), x) == :(1//9*b^-4*(a+b*x^3)^3//2*(-6*B*a+2*A*b)+2//15*B*b^-4*(a+b*x^3)^5//2+-2//3*a*b^-4*(a+b*x^3)^(1/2)*(-3*B*a+2*A*b)+-2//3*a^2*b^-4*(a+b*x^3)^-1//2*(A*b+-1*B*a))
@test integrate(x^5*(a+b*x^3)^-3//2*(A+B*x^3), x) == :(1//3*b^-3*(a+b*x^3)^(1/2)*(-4*B*a+2*A*b)+2//9*B*b^-3*(a+b*x^3)^3//2+2//3*a*b^-3*(a+b*x^3)^-1//2*(A*b+-1*B*a))
@test integrate(x^2*(a+b*x^3)^-3//2*(A+B*x^3), x) == :(1//3*b^-2*(a+b*x^3)^-1//2*(-2*A*b+2*B*a)+2//3*B*b^-2*(a+b*x^3)^(1/2))
@test integrate(x^-1*(a+b*x^3)^-3//2*(A+B*x^3), x) == :(-2//3*A*a^-3//2*arctanh(a^-1//2*(a+b*x^3)^(1/2))+1//3*a^-1*b^-1*(a+b*x^3)^-1//2*(-2*B*a+2*A*b))
@test integrate(x^-4*(a+b*x^3)^-3//2*(A+B*x^3), x) == :(1//3*a^-2*(a+b*x^3)^-1//2*(-3*A*b+2*B*a)+1//3*a^-5//2*(-2*B*a+3*A*b)*arctanh(a^-1//2*(a+b*x^3)^(1/2))+-1//3*A*a^-1*x^-3*(a+b*x^3)^-1//2)
@test integrate(x^-7*(a+b*x^3)^-3//2*(A+B*x^3), x) == :(-1//4*b*a^-7//2*(-4*B*a+5*A*b)*arctanh(a^-1//2*(a+b*x^3)^(1/2))+-1//6*A*a^-1*x^-6*(a+b*x^3)^-1//2+1//4*b*a^-3*(a+b*x^3)^-1//2*(-4*B*a+5*A*b)+1//12*a^-2*x^-3*(a+b*x^3)^-1//2*(-4*B*a+5*A*b))
@test integrate(x^6*(a+b*x^3)^-3//2*(A+B*x^3), x) == :(-1//33*b^-2*x^4*(a+b*x^3)^-1//2*(-28*B*a+22*A*b)+1//165*x*b^-3*(a+b*x^3)^(1/2)*(-224*B*a+176*A*b)+2//11*B*b^-1*x^7*(a+b*x^3)^-1//2+-32//495*a*3^3//4*b^-10//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-14*B*a+11*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^3*(a+b*x^3)^-3//2*(A+B*x^3), x) == :(-1//15*x*b^-2*(a+b*x^3)^-1//2*(-16*B*a+10*A*b)+2//5*B*b^-1*x^4*(a+b*x^3)^-1//2+4//45*3^3//4*b^-7//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-8*B*a+5*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+b*x^3)^-3//2*(A+B*x^3), x) == :(1//3*x*a^-1*b^-1*(a+b*x^3)^-1//2*(-2*B*a+2*A*b)+2//9*3^3//4*a^-1*b^-4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(A*b+2*B*a)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-3*(a+b*x^3)^-3//2*(A+B*x^3), x) == :(-1//2*A*a^-1*x^-2*(a+b*x^3)^-1//2+-1//6*x*a^-2*(a+b*x^3)^-1//2*(-4*B*a+7*A*b)+-1//18*3^3//4*a^-2*b^-1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-4*B*a+7*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-6*(a+b*x^3)^-3//2*(A+B*x^3), x) == :(-1//5*A*a^-1*x^-5*(a+b*x^3)^-1//2+-1//15*a^-2*x^-2*(a+b*x^3)^-1//2*(-10*B*a+13*A*b)+1//60*a^-3*x^-2*(a+b*x^3)^(1/2)*(-70*B*a+91*A*b)+7//180*3^3//4*a^-3*b^2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-10*B*a+13*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^4*(a+b*x^3)^-3//2*(A+B*x^3), x) == :(-1//21*b^-2*x^2*(a+b*x^3)^-1//2*(-20*B*a+14*A*b)+1//21*b^-8//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(-80*B*a+56*A*b)+2//7*B*b^-1*x^5*(a+b*x^3)^-1//2+-4//21*3^1//4*a^1//3*b^-8//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-10*B*a+7*A*b)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+8//63*2^(1/2)*3^3//4*a^1//3*b^-8//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-10*B*a+7*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(a+b*x^3)^-3//2*(A+B*x^3), x) == :(-1//3*a^-1*b^-5//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(-8*B*a+2*A*b)+1//3*a^-1*b^-1*x^2*(a+b*x^3)^-1//2*(-2*B*a+2*A*b)+-2//9*2^(1/2)*3^3//4*a^-2//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(A*b+-4*B*a)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//3*3^1//4*a^-2//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(A*b+-4*B*a)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-2*(a+b*x^3)^-3//2*(A+B*x^3), x) == :(-1*A*a^-1*x^-1*(a+b*x^3)^-1//2+-1//3*a^-2*x^2*(a+b*x^3)^-1//2*(-2*B*a+5*A*b)+1//3*a^-2*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(-2*B*a+5*A*b)+-1//6*3^1//4*a^-5//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-2*B*a+5*A*b)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//9*2^(1/2)*3^3//4*a^-5//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-2*B*a+5*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-5*(a+b*x^3)^-3//2*(A+B*x^3), x) == :(-1//4*A*a^-1*x^-4*(a+b*x^3)^-1//2+-1//12*a^-2*x^-1*(a+b*x^3)^-1//2*(-8*B*a+11*A*b)+1//24*a^-3*x^-1*(a+b*x^3)^(1/2)*(-40*B*a+55*A*b)+-5//24*a^-3*b^1//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(-8*B*a+11*A*b)+-5//72*2^(1/2)*3^3//4*a^-8//3*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-8*B*a+11*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+5//48*3^1//4*a^-8//3*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-8*B*a+11*A*b)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-8*(a+b*x^3)^-3//2*(A+B*x^3), x) == :(-1//7*A*a^-1*x^-7*(a+b*x^3)^-1//2+-1//21*a^-2*x^-4*(a+b*x^3)^-1//2*(-14*B*a+17*A*b)+1//168*a^-3*x^-4*(a+b*x^3)^(1/2)*(-154*B*a+187*A*b)+-55//336*b*a^-4*x^-1*(a+b*x^3)^(1/2)*(-14*B*a+17*A*b)+55//336*a^-4*b^4//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(-14*B*a+17*A*b)+-55//672*3^1//4*a^-11//3*b^4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-14*B*a+17*A*b)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+55//1008*2^(1/2)*3^3//4*a^-11//3*b^4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-14*B*a+17*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^8*(a+b*x^3)^-5//2*(A+B*x^3), x) == :(1//3*b^-4*(a+b*x^3)^(1/2)*(-6*B*a+2*A*b)+2//9*B*b^-4*(a+b*x^3)^3//2+-2//9*a^2*b^-4*(a+b*x^3)^-3//2*(A*b+-1*B*a)+2//3*a*b^-4*(a+b*x^3)^-1//2*(-3*B*a+2*A*b))
@test integrate(x^5*(a+b*x^3)^-5//2*(A+B*x^3), x) == :(-1//3*b^-3*(a+b*x^3)^-1//2*(-4*B*a+2*A*b)+2//3*B*b^-3*(a+b*x^3)^(1/2)+2//9*a*b^-3*(a+b*x^3)^-3//2*(A*b+-1*B*a))
@test integrate(x^2*(a+b*x^3)^-5//2*(A+B*x^3), x) == :(-2//3*B*b^-2*(a+b*x^3)^-1//2+1//9*b^-2*(a+b*x^3)^-3//2*(-2*A*b+2*B*a))
@test integrate(x^-1*(a+b*x^3)^-5//2*(A+B*x^3), x) == :(-2//3*A*a^-5//2*arctanh(a^-1//2*(a+b*x^3)^(1/2))+2//3*A*a^-2*(a+b*x^3)^-1//2+1//9*a^-1*b^-1*(a+b*x^3)^-3//2*(-2*B*a+2*A*b))
@test integrate(x^-4*(a+b*x^3)^-5//2*(A+B*x^3), x) == :(-1//3*a^-3*(a+b*x^3)^-1//2*(-2*B*a+5*A*b)+1//3*a^-7//2*(-2*B*a+5*A*b)*arctanh(a^-1//2*(a+b*x^3)^(1/2))+1//9*a^-2*(a+b*x^3)^-3//2*(-5*A*b+2*B*a)+-1//3*A*a^-1*x^-3*(a+b*x^3)^-3//2)
@test integrate(x^6*(a+b*x^3)^-5//2*(A+B*x^3), x) == :(-1//45*b^-2*x^4*(a+b*x^3)^-3//2*(-28*B*a+10*A*b)+-1//135*x*b^-3*(a+b*x^3)^-1//2*(-224*B*a+80*A*b)+2//5*B*b^-1*x^7*(a+b*x^3)^-3//2+32//405*3^3//4*b^-10//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-14*B*a+5*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^3*(a+b*x^3)^-5//2*(A+B*x^3), x) == :(-1//27*x*a^-1*b^-2*(a+b*x^3)^-1//2*(2*A*b+16*B*a)+1//9*a^-1*b^-1*x^4*(a+b*x^3)^-3//2*(-2*B*a+2*A*b)+4//81*3^3//4*a^-1*b^-7//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(A*b+8*B*a)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+b*x^3)^-5//2*(A+B*x^3), x) == :(1//9*x*a^-1*b^-1*(a+b*x^3)^-3//2*(-2*B*a+2*A*b)+1//27*x*a^-2*b^-1*(a+b*x^3)^-1//2*(4*B*a+14*A*b)+2//81*3^3//4*a^-2*b^-4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(2*B*a+7*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-3*(a+b*x^3)^-5//2*(A+B*x^3), x) == :(-1//2*A*a^-1*x^-2*(a+b*x^3)^-3//2+-1//18*x*a^-2*(a+b*x^3)^-3//2*(-4*B*a+13*A*b)+-1//54*x*a^-3*(a+b*x^3)^-1//2*(-28*B*a+91*A*b)+-7//162*3^3//4*a^-3*b^-1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-4*B*a+13*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-6*(a+b*x^3)^-5//2*(A+B*x^3), x) == :(-1//5*A*a^-1*x^-5*(a+b*x^3)^-3//2+-1//45*a^-2*x^-2*(a+b*x^3)^-3//2*(-10*B*a+19*A*b)+-1//135*a^-3*x^-2*(a+b*x^3)^-1//2*(-130*B*a+247*A*b)+1//540*a^-4*x^-2*(a+b*x^3)^(1/2)*(-910*B*a+1729*A*b)+91//1620*3^3//4*a^-4*b^2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-10*B*a+19*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^7*(a+b*x^3)^-5//2*(A+B*x^3), x) == :(-1//63*b^-2*x^5*(a+b*x^3)^-3//2*(-32*B*a+14*A*b)+-1//189*b^-3*x^2*(a+b*x^3)^-1//2*(-320*B*a+140*A*b)+1//189*b^-11//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(-1280*B*a+560*A*b)+2//7*B*b^-1*x^8*(a+b*x^3)^-3//2+-40//189*3^1//4*a^1//3*b^-11//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-16*B*a+7*A*b)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+80//567*2^(1/2)*3^3//4*a^1//3*b^-11//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-16*B*a+7*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^4*(a+b*x^3)^-5//2*(A+B*x^3), x) == :(-1//27*a^-1*b^-8//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(-80*B*a+8*A*b)+1//9*a^-1*b^-1*x^5*(a+b*x^3)^-3//2*(-2*B*a+2*A*b)+1//27*a^-1*b^-2*x^2*(a+b*x^3)^-1//2*(-20*B*a+2*A*b)+-8//81*2^(1/2)*3^3//4*a^-2//3*b^-8//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(A*b+-10*B*a)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+4//27*3^1//4*a^-2//3*b^-8//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(A*b+-10*B*a)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(a+b*x^3)^-5//2*(A+B*x^3), x) == :(-1//27*a^-2*b^-5//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(8*B*a+10*A*b)+1//9*a^-1*b^-1*x^2*(a+b*x^3)^-3//2*(-2*B*a+2*A*b)+1//27*a^-2*b^-1*x^2*(a+b*x^3)^-1//2*(8*B*a+10*A*b)+-2//81*2^(1/2)*3^3//4*a^-5//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(4*B*a+5*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//27*3^1//4*a^-5//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(4*B*a+5*A*b)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-2*(a+b*x^3)^-5//2*(A+B*x^3), x) == :(-1*A*a^-1*x^-1*(a+b*x^3)^-3//2+-1//9*a^-2*x^2*(a+b*x^3)^-3//2*(-2*B*a+11*A*b)+-1//27*a^-3*x^2*(a+b*x^3)^-1//2*(-10*B*a+55*A*b)+1//27*a^-3*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(-10*B*a+55*A*b)+-5//54*3^1//4*a^-8//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-2*B*a+11*A*b)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+5//81*2^(1/2)*3^3//4*a^-8//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-2*B*a+11*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-5*(a+b*x^3)^-5//2*(A+B*x^3), x) == :(-1//4*A*a^-1*x^-4*(a+b*x^3)^-3//2+-1//36*a^-2*x^-1*(a+b*x^3)^-3//2*(-8*B*a+17*A*b)+-1//108*a^-3*x^-1*(a+b*x^3)^-1//2*(-88*B*a+187*A*b)+1//216*a^-4*x^-1*(a+b*x^3)^(1/2)*(-440*B*a+935*A*b)+-55//216*a^-4*b^1//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(-8*B*a+17*A*b)+-55//648*2^(1/2)*3^3//4*a^-11//3*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-8*B*a+17*A*b)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+55//432*3^1//4*a^-11//3*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-8*B*a+17*A*b)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^8*(c+d*x^3)^(1/2)*(4c+d*x^3)^-1, x) == :(2//15*d^-3*(c+d*x^3)^5//2+-10//9*c*d^-3*(c+d*x^3)^3//2+32//3*c^2*d^-3*(c+d*x^3)^(1/2)+-32//3*3^(1/2)*c^5//2*d^-3*arctan(1//3*3^(1/2)*c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^5*(c+d*x^3)^(1/2)*(4c+d*x^3)^-1, x) == :(2//9*d^-2*(c+d*x^3)^3//2+-8//3*c*d^-2*(c+d*x^3)^(1/2)+8//3*3^(1/2)*c^3//2*d^-2*arctan(1//3*3^(1/2)*c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^2*(c+d*x^3)^(1/2)*(4c+d*x^3)^-1, x) == :(2//3*d^-1*(c+d*x^3)^(1/2)+-2//3*3^(1/2)*c^(1/2)*d^-1*arctan(1//3*3^(1/2)*c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^-1*(c+d*x^3)^(1/2)*(4c+d*x^3)^-1, x) == :(-1//6*c^-1//2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+1//6*3^(1/2)*c^-1//2*arctan(1//3*3^(1/2)*c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^-4*(c+d*x^3)^(1/2)*(4c+d*x^3)^-1, x) == :(-1//12*c^-1*x^-3*(c+d*x^3)^(1/2)+-1//24*d*c^-3//2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+-1//24*d*3^(1/2)*c^-3//2*arctan(1//3*3^(1/2)*c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^4*(c+d*x^3)^(1/2)*(4c+d*x^3)^-1, x) == :(2//7*d^-1*x^2*(c+d*x^3)^(1/2)+-2*2^1//3*c^7//6*d^-5//3*arctanh(c^1//6*(c+d*x^3)^-1//2*(c^1//3+-1*x*2^1//3*d^1//3))+-50//7*c*d^-5//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+2//3*2^1//3*c^7//6*d^-5//3*arctanh(c^-1//2*(c+d*x^3)^(1/2))+-2//3*2^1//3*3^(1/2)*c^7//6*d^-5//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*2^1//3*d^1//3))+2//3*2^1//3*3^(1/2)*c^7//6*d^-5//3*arctan(1//3*3^(1/2)*c^-1//2*(c+d*x^3)^(1/2))+-50//21*2^(1/2)*3^3//4*c^4//3*d^-5//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+25//7*3^1//4*c^4//3*d^-5//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(c+d*x^3)^(1/2)*(4c+d*x^3)^-1, x) == :(2*d^-2//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+(1/2)*2^1//3*c^1//6*d^-2//3*arctanh(c^1//6*(c+d*x^3)^-1//2*(c^1//3+-1*x*2^1//3*d^1//3))+-1//6*2^1//3*c^1//6*d^-2//3*arctanh(c^-1//2*(c+d*x^3)^(1/2))+-1//6*2^1//3*3^(1/2)*c^1//6*d^-2//3*arctan(1//3*3^(1/2)*c^-1//2*(c+d*x^3)^(1/2))+1//6*2^1//3*3^(1/2)*c^1//6*d^-2//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*2^1//3*d^1//3))+-1*3^1//4*c^1//3*d^-2//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+2//3*2^(1/2)*3^3//4*c^1//3*d^-2//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-2*(c+d*x^3)^(1/2)*(4c+d*x^3)^-1, x) == :(-1//4*c^-1*x^-1*(c+d*x^3)^(1/2)+-1//8*2^1//3*c^-5//6*d^1//3*arctanh(c^1//6*(c+d*x^3)^-1//2*(c^1//3+-1*x*2^1//3*d^1//3))+1//4*c^-1*d^1//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+1//24*2^1//3*c^-5//6*d^1//3*arctanh(c^-1//2*(c+d*x^3)^(1/2))+-1//24*2^1//3*3^(1/2)*c^-5//6*d^1//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*2^1//3*d^1//3))+1//24*2^1//3*3^(1/2)*c^-5//6*d^1//3*arctan(1//3*3^(1/2)*c^-1//2*(c+d*x^3)^(1/2))+-1//8*3^1//4*c^-2//3*d^1//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//12*2^(1/2)*3^3//4*c^-2//3*d^1//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^8*(c+d*x^3)^-1//2*(4c+d*x^3)^-1, x) == :(2//9*d^-3*(c+d*x^3)^3//2+-10//3*c*d^-3*(c+d*x^3)^(1/2)+32//9*3^(1/2)*c^3//2*d^-3*arctan(1//3*3^(1/2)*c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^5*(c+d*x^3)^-1//2*(4c+d*x^3)^-1, x) == :(2//3*d^-2*(c+d*x^3)^(1/2)+-8//9*3^(1/2)*c^(1/2)*d^-2*arctan(1//3*3^(1/2)*c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^2*(c+d*x^3)^-1//2*(4c+d*x^3)^-1, x) == :(2//9*3^(1/2)*c^-1//2*d^-1*arctan(1//3*3^(1/2)*c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^-1*(c+d*x^3)^-1//2*(4c+d*x^3)^-1, x) == :(-1//6*c^-3//2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+-1//18*3^(1/2)*c^-3//2*arctan(1//3*3^(1/2)*c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^-4*(c+d*x^3)^-1//2*(4c+d*x^3)^-1, x) == :(-1//12*c^-2*x^-3*(c+d*x^3)^(1/2)+1//8*d*c^-5//2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+1//72*d*3^(1/2)*c^-5//2*arctan(1//3*3^(1/2)*c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^4*(c+d*x^3)^-1//2*(4c+d*x^3)^-1, x) == :(2*d^-5//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-2//9*2^1//3*c^1//6*d^-5//3*arctanh(c^-1//2*(c+d*x^3)^(1/2))+2//3*2^1//3*c^1//6*d^-5//3*arctanh(c^1//6*(c+d*x^3)^-1//2*(c^1//3+-1*x*2^1//3*d^1//3))+-2//9*2^1//3*3^(1/2)*c^1//6*d^-5//3*arctan(1//3*3^(1/2)*c^-1//2*(c+d*x^3)^(1/2))+2//9*2^1//3*3^(1/2)*c^1//6*d^-5//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*2^1//3*d^1//3))+-1*3^1//4*c^1//3*d^-5//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+2//3*2^(1/2)*3^3//4*c^1//3*d^-5//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(c+d*x^3)^-1//2*(4c+d*x^3)^-1, x) == :(-1//6*2^1//3*c^-5//6*d^-2//3*arctanh(c^1//6*(c+d*x^3)^-1//2*(c^1//3+-1*x*2^1//3*d^1//3))+1//18*2^1//3*c^-5//6*d^-2//3*arctanh(c^-1//2*(c+d*x^3)^(1/2))+-1//18*2^1//3*3^(1/2)*c^-5//6*d^-2//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*2^1//3*d^1//3))+1//18*2^1//3*3^(1/2)*c^-5//6*d^-2//3*arctan(1//3*3^(1/2)*c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^-2*(c+d*x^3)^-1//2*(4c+d*x^3)^-1, x) == :(-1//4*c^-2*x^-1*(c+d*x^3)^(1/2)+-1//72*2^1//3*c^-11//6*d^1//3*arctanh(c^-1//2*(c+d*x^3)^(1/2))+1//4*c^-2*d^1//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+1//24*2^1//3*c^-11//6*d^1//3*arctanh(c^1//6*(c+d*x^3)^-1//2*(c^1//3+-1*x*2^1//3*d^1//3))+-1//72*2^1//3*3^(1/2)*c^-11//6*d^1//3*arctan(1//3*3^(1/2)*c^-1//2*(c+d*x^3)^(1/2))+1//72*2^1//3*3^(1/2)*c^-11//6*d^1//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*2^1//3*d^1//3))+-1//8*3^1//4*c^-5//3*d^1//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//12*2^(1/2)*3^3//4*c^-5//3*d^1//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(1+-1*x^3)^-1//2*(4+-1*x^3)^-1, x) == :(-1//6*2^1//3*arctanh((1+-1*x^3)^-1//2*(1+x*2^1//3))+1//18*2^1//3*arctanh((1+-1*x^3)^(1/2))+-1//18*2^1//3*3^(1/2)*arctan(3^(1/2)*(1+-1*x^3)^-1//2*(1+-1*x*2^1//3))+1//18*2^1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+-1*x^3)^(1/2)))
@test integrate(x^11*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1, x) == :(-2//21*d^-4*(c+d*x^3)^7//2+1024*c^7//2*d^-4*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+-1024//3*c^3*d^-4*(c+d*x^3)^(1/2)+-38//3*c^2*d^-4*(c+d*x^3)^3//2+-4//5*c*d^-4*(c+d*x^3)^5//2)
@test integrate(x^8*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1, x) == :(-2//15*d^-3*(c+d*x^3)^5//2+128*c^5//2*d^-3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+-128//3*c^2*d^-3*(c+d*x^3)^(1/2)+-14//9*c*d^-3*(c+d*x^3)^3//2)
@test integrate(x^5*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1, x) == :(-2//9*d^-2*(c+d*x^3)^3//2+16*c^3//2*d^-2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+-16//3*c*d^-2*(c+d*x^3)^(1/2))
@test integrate(x^2*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1, x) == :(-2//3*d^-1*(c+d*x^3)^(1/2)+2*c^(1/2)*d^-1*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^-1*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1, x) == :(-1//12*c^-1//2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+1//4*c^-1//2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^-4*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1, x) == :(-5//96*d*c^-3//2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+-1//24*c^-1*x^-3*(c+d*x^3)^(1/2)+1//32*d*c^-3//2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^-7*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1, x) == :(-1//48*c^-1*x^-6*(c+d*x^3)^(1/2)+1//256*c^-5//2*d^2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+1//256*c^-5//2*d^2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+-1//64*d*c^-2*x^-3*(c+d*x^3)^(1/2))
@test integrate(x^7*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1, x) == :(-32*c^13//6*d^-8//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+32*c^13//6*d^-8//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-2//13*d^-1*x^5*(c+d*x^3)^(1/2)+-32*3^(1/2)*c^13//6*d^-8//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+-12248//91*c^2*d^-8//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-214//91*c*d^-2*x^2*(c+d*x^3)^(1/2)+-12248//273*2^(1/2)*3^3//4*c^7//3*d^-8//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+6124//91*3^1//4*c^7//3*d^-8//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^4*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1, x) == :(-4*c^7//6*d^-5//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+4*c^7//6*d^-5//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-2//7*d^-1*x^2*(c+d*x^3)^(1/2)+-4*3^(1/2)*c^7//6*d^-5//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+-118//7*c*d^-5//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-118//21*2^(1/2)*3^3//4*c^4//3*d^-5//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+59//7*3^1//4*c^4//3*d^-5//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1, x) == :((1/2)*c^1//6*d^-2//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-2*d^-2//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-1//2*c^1//6*d^-2//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+-1//2*3^(1/2)*c^1//6*d^-2//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+3^1//4*c^1//3*d^-2//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+-2//3*2^(1/2)*3^3//4*c^1//3*d^-2//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-2*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1, x) == :(-1//8*c^-1*x^-1*(c+d*x^3)^(1/2)+-1//16*c^-5//6*d^1//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+1//16*c^-5//6*d^1//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-1//16*3^(1/2)*c^-5//6*d^1//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+1//8*c^-1*d^1//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-1//16*3^1//4*c^-2//3*d^1//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//24*2^(1/2)*3^3//4*c^-2//3*d^1//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-5*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1, x) == :(-1//32*c^-1*x^-4*(c+d*x^3)^(1/2)+-1//128*c^-11//6*d^4//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+1//128*c^-11//6*d^4//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-1//16*d*c^-2*x^-1*(c+d*x^3)^(1/2)+-1//128*3^(1/2)*c^-11//6*d^4//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+1//16*c^-2*d^4//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-1//32*3^1//4*c^-5//3*d^4//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//48*2^(1/2)*3^3//4*c^-5//3*d^4//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-8*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1, x) == :(-1//56*c^-1*x^-7*(c+d*x^3)^(1/2)+-1//1024*c^-17//6*d^7//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+1//1024*c^-17//6*d^7//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-19//1792*d*c^-2*x^-4*(c+d*x^3)^(1/2)+-1//112*c^-3*d^7//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-1//1024*3^(1/2)*c^-17//6*d^7//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+1//112*c^-3*d^2*x^-1*(c+d*x^3)^(1/2)+-1//336*2^(1/2)*3^3//4*c^-8//3*d^7//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//224*3^1//4*c^-8//3*d^7//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^11*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-1, x) == :(-2//27*d^-4*(c+d*x^3)^9//2+-3072*c^4*d^-4*(c+d*x^3)^(1/2)+9216*c^9//2*d^-4*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+-1024//9*c^3*d^-4*(c+d*x^3)^3//2+-38//5*c^2*d^-4*(c+d*x^3)^5//2+-4//7*c*d^-4*(c+d*x^3)^7//2)
@test integrate(x^8*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-1, x) == :(-2//21*d^-3*(c+d*x^3)^7//2+-384*c^3*d^-3*(c+d*x^3)^(1/2)+1152*c^7//2*d^-3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+-128//9*c^2*d^-3*(c+d*x^3)^3//2+-14//15*c*d^-3*(c+d*x^3)^5//2)
@test integrate(x^5*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-1, x) == :(-2//15*d^-2*(c+d*x^3)^5//2+-48*c^2*d^-2*(c+d*x^3)^(1/2)+144*c^5//2*d^-2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+-16//9*c*d^-2*(c+d*x^3)^3//2)
@test integrate(x^2*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-1, x) == :(-2//9*d^-1*(c+d*x^3)^3//2+-6*c*d^-1*(c+d*x^3)^(1/2)+18*c^3//2*d^-1*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^-1*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-1, x) == :(-2//3*(c+d*x^3)^(1/2)+-1//12*c^(1/2)*arctanh(c^-1//2*(c+d*x^3)^(1/2))+9//4*c^(1/2)*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^-4*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-1, x) == :(-1//24*x^-3*(c+d*x^3)^(1/2)+-13//96*d*c^-1//2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+9//32*d*c^-1//2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^-7*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-1, x) == :(-1//48*x^-6*(c+d*x^3)^(1/2)+-37//768*c^-3//2*d^2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+9//256*c^-3//2*d^2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+-11//192*d*c^-1*x^-3*(c+d*x^3)^(1/2))
@test integrate(x^7*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-1, x) == :(-2//19*x^8*(c+d*x^3)^(1/2)+-288*c^19//6*d^-8//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+288*c^19//6*d^-8//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-288*3^(1/2)*c^19//6*d^-8//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+-2094648//1729*c^3*d^-8//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-36534//1729*c^2*d^-2*x^2*(c+d*x^3)^(1/2)+-348//247*c*d^-1*x^5*(c+d*x^3)^(1/2)+-698216//1729*2^(1/2)*3^3//4*c^10//3*d^-8//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1047324//1729*3^1//4*c^10//3*d^-8//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^4*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-1, x) == :(-2//13*x^5*(c+d*x^3)^(1/2)+-36*c^13//6*d^-5//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+36*c^13//6*d^-5//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-36*3^(1/2)*c^13//6*d^-5//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+-13782//91*c^2*d^-5//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-240//91*c*d^-1*x^2*(c+d*x^3)^(1/2)+-4594//91*2^(1/2)*3^3//4*c^7//3*d^-5//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+6891//91*3^1//4*c^7//3*d^-5//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-1, x) == :(-2//7*x^2*(c+d*x^3)^(1/2)+-9//2*c^7//6*d^-2//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+9//2*c^7//6*d^-2//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-132//7*c*d^-2//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-9//2*3^(1/2)*c^7//6*d^-2//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+-44//7*2^(1/2)*3^3//4*c^4//3*d^-2//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+66//7*3^1//4*c^4//3*d^-2//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-2*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-1, x) == :(-1//8*x^-1*(c+d*x^3)^(1/2)+-15*d^1//3*(c+d*x^3)^(1/2)*(8*x*d^1//3+8*c^1//3*(1+3^(1/2)))^-1+-9//16*c^1//6*d^1//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+9//16*c^1//6*d^1//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-9//16*3^(1/2)*c^1//6*d^1//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+-5//8*2^(1/2)*3^3//4*c^1//3*d^1//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+15//16*3^1//4*c^1//3*d^1//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-5*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-1, x) == :(-1//32*x^-4*(c+d*x^3)^(1/2)+-9//128*c^-5//6*d^4//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+9//128*c^-5//6*d^4//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-9//128*3^(1/2)*c^-5//6*d^4//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+-3//16*d*c^-1*x^-1*(c+d*x^3)^(1/2)+3//16*c^-1*d^4//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-3//32*3^1//4*c^-2//3*d^4//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//16*2^(1/2)*3^3//4*c^-2//3*d^4//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-8*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-1, x) == :(-1//56*x^-7*(c+d*x^3)^(1/2)+-9//1024*c^-11//6*d^7//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+9//1024*c^-11//6*d^7//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-75//1792*d*c^-1*x^-4*(c+d*x^3)^(1/2)+-9//1024*3^(1/2)*c^-11//6*d^7//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+-3//56*c^-2*d^2*x^-1*(c+d*x^3)^(1/2)+3//56*c^-2*d^7//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-3//112*3^1//4*c^-5//3*d^7//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//56*2^(1/2)*3^3//4*c^-5//3*d^7//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^11*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-1, x) == :(-2//15*d^-4*(c+d*x^3)^5//2+-38*c^2*d^-4*(c+d*x^3)^(1/2)+-4//3*c*d^-4*(c+d*x^3)^3//2+1024//9*c^5//2*d^-4*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^8*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-1, x) == :(-2//9*d^-3*(c+d*x^3)^3//2+-14//3*c*d^-3*(c+d*x^3)^(1/2)+128//9*c^3//2*d^-3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^5*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-1, x) == :(-2//3*d^-2*(c+d*x^3)^(1/2)+16//9*c^(1/2)*d^-2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^2*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-1, x) == :(2//9*c^-1//2*d^-1*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^-1*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-1, x) == :(-1//12*c^-3//2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+1//36*c^-3//2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^-4*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-1, x) == :(-1//24*c^-2*x^-3*(c+d*x^3)^(1/2)+1//32*d*c^-5//2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+1//288*d*c^-5//2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^-7*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-1, x) == :(-7//256*c^-7//2*d^2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+-1//48*c^-2*x^-6*(c+d*x^3)^(1/2)+1//2304*c^-7//2*d^2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+5//192*d*c^-3*x^-3*(c+d*x^3)^(1/2))
@test integrate(x^7*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-1, x) == :(-32//9*c^7//6*d^-8//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+-2//7*d^-2*x^2*(c+d*x^3)^(1/2)+32//9*c^7//6*d^-8//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-104//7*c*d^-8//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-32//9*3^(1/2)*c^7//6*d^-8//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+-104//21*2^(1/2)*3^3//4*c^4//3*d^-8//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+52//7*3^1//4*c^4//3*d^-8//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^4*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-1, x) == :(-2*d^-5//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-4//9*c^1//6*d^-5//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+4//9*c^1//6*d^-5//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-4//9*3^(1/2)*c^1//6*d^-5//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+3^1//4*c^1//3*d^-5//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+-2//3*2^(1/2)*3^3//4*c^1//3*d^-5//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-1, x) == :(-1//18*c^-5//6*d^-2//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+1//18*c^-5//6*d^-2//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-1//18*3^(1/2)*c^-5//6*d^-2//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)))
@test integrate(x^-2*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-1, x) == :(-1//8*c^-2*x^-1*(c+d*x^3)^(1/2)+-1//144*c^-11//6*d^1//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+1//144*c^-11//6*d^1//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-1//144*3^(1/2)*c^-11//6*d^1//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+1//8*c^-2*d^1//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-1//16*3^1//4*c^-5//3*d^1//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//24*2^(1/2)*3^3//4*c^-5//3*d^1//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-5*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-1, x) == :(-1//32*c^-2*x^-4*(c+d*x^3)^(1/2)+-1//1152*c^-17//6*d^4//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+1//1152*c^-17//6*d^4//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-1//16*c^-3*d^4//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-1//1152*3^(1/2)*c^-17//6*d^4//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+1//16*d*c^-3*x^-1*(c+d*x^3)^(1/2)+-1//48*2^(1/2)*3^3//4*c^-8//3*d^4//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//32*3^1//4*c^-8//3*d^4//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-8*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-1, x) == :(-1//56*c^-2*x^-7*(c+d*x^3)^(1/2)+-1//9216*c^-23//6*d^7//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+1//9216*c^-23//6*d^7//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-3//56*c^-4*d^2*x^-1*(c+d*x^3)^(1/2)+-1//9216*3^(1/2)*c^-23//6*d^7//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+3//56*c^-4*d^7//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+37//1792*d*c^-3*x^-4*(c+d*x^3)^(1/2)+-3//112*3^1//4*c^-11//3*d^7//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//56*2^(1/2)*3^3//4*c^-11//3*d^7//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^11*(c+d*x^3)^-3//2*(8c+-1*d*x^3)^-1, x) == :(-2//9*d^-4*(c+d*x^3)^3//2+-4*c*d^-4*(c+d*x^3)^(1/2)+2//27*c^2*d^-4*(c+d*x^3)^-1//2+1024//81*c^3//2*d^-4*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^8*(c+d*x^3)^-3//2*(8c+-1*d*x^3)^-1, x) == :(-2//3*d^-3*(c+d*x^3)^(1/2)+-2//27*c*d^-3*(c+d*x^3)^-1//2+128//81*c^(1/2)*d^-3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^5*(c+d*x^3)^-3//2*(8c+-1*d*x^3)^-1, x) == :(2//27*d^-2*(c+d*x^3)^-1//2+16//81*c^-1//2*d^-2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^2*(c+d*x^3)^-3//2*(8c+-1*d*x^3)^-1, x) == :(-2//27*c^-1*d^-1*(c+d*x^3)^-1//2+2//81*c^-3//2*d^-1*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^-1*(c+d*x^3)^-3//2*(8c+-1*d*x^3)^-1, x) == :(-1//12*c^-5//2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+1//324*c^-5//2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+2//27*c^-2*(c+d*x^3)^-1//2)
@test integrate(x^-4*(c+d*x^3)^-3//2*(8c+-1*d*x^3)^-1, x) == :(-25//216*d*c^-3*(c+d*x^3)^-1//2+-1//24*c^-2*x^-3*(c+d*x^3)^-1//2+1//2592*d*c^-7//2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+11//96*d*c^-7//2*arctanh(c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^-7*(c+d*x^3)^-3//2*(8c+-1*d*x^3)^-1, x) == :(-109//768*c^-9//2*d^2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+-1//48*c^-2*x^-6*(c+d*x^3)^-1//2+1//20736*c^-9//2*d^2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+245//1728*c^-4*d^2*(c+d*x^3)^-1//2+3//64*d*c^-3*x^-3*(c+d*x^3)^-1//2)
@test integrate(x^7*(c+d*x^3)^-3//2*(8c+-1*d*x^3)^-1, x) == :(-56//27*d^-8//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-32//81*c^1//6*d^-8//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+2//27*d^-2*x^2*(c+d*x^3)^-1//2+32//81*c^1//6*d^-8//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-32//81*3^(1/2)*c^1//6*d^-8//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+-56//81*2^(1/2)*3^3//4*c^1//3*d^-8//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+28//27*3^1//4*c^1//3*d^-8//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^4*(c+d*x^3)^-3//2*(8c+-1*d*x^3)^-1, x) == :(-4//81*c^-5//6*d^-5//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+4//81*c^-5//6*d^-5//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-4//81*3^(1/2)*c^-5//6*d^-5//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+-2//27*c^-1*d^-1*x^2*(c+d*x^3)^-1//2+2//27*c^-1*d^-5//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-1//27*3^1//4*c^-2//3*d^-5//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+2//81*2^(1/2)*3^3//4*c^-2//3*d^-5//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(c+d*x^3)^-3//2*(8c+-1*d*x^3)^-1, x) == :(-1//162*c^-11//6*d^-2//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+1//162*c^-11//6*d^-2//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+2//27*c^-2*x^2*(c+d*x^3)^-1//2+-2//27*c^-2*d^-2//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-1//162*3^(1/2)*c^-11//6*d^-2//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+-2//81*2^(1/2)*3^3//4*c^-5//3*d^-2//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//27*3^1//4*c^-5//3*d^-2//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-2*(c+d*x^3)^-3//2*(8c+-1*d*x^3)^-1, x) == :(-43//216*c^-3*x^-1*(c+d*x^3)^(1/2)+-1//1296*c^-17//6*d^1//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+1//1296*c^-17//6*d^1//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+2//27*c^-2*x^-1*(c+d*x^3)^-1//2+-1//1296*3^(1/2)*c^-17//6*d^1//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+43//216*c^-3*d^1//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-43//432*3^1//4*c^-8//3*d^1//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+43//648*2^(1/2)*3^3//4*c^-8//3*d^1//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-5*(c+d*x^3)^-3//2*(8c+-1*d*x^3)^-1, x) == :(-91//864*c^-3*x^-4*(c+d*x^3)^(1/2)+-1//10368*c^-23//6*d^4//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+1//10368*c^-23//6*d^4//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+2//27*c^-2*x^-4*(c+d*x^3)^-1//2+-113//432*c^-4*d^4//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-1//10368*3^(1/2)*c^-23//6*d^4//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+113//432*d*c^-4*x^-1*(c+d*x^3)^(1/2)+-113//1296*2^(1/2)*3^3//4*c^-11//3*d^4//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+113//864*3^1//4*c^-11//3*d^4//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-8*(c+d*x^3)^-3//2*(8c+-1*d*x^3)^-1, x) == :(-139//1512*c^-3*x^-7*(c+d*x^3)^(1/2)+-1//82944*c^-29//6*d^7//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+1//82944*c^-29//6*d^7//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+2//27*c^-2*x^-7*(c+d*x^3)^-1//2+-953//3024*c^-5*d^2*x^-1*(c+d*x^3)^(1/2)+-1//82944*3^(1/2)*c^-29//6*d^7//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+953//3024*c^-5*d^7//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+6095//48384*d*c^-4*x^-4*(c+d*x^3)^(1/2)+-953//6048*3^1//4*c^-14//3*d^7//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+953//9072*2^(1/2)*3^3//4*c^-14//3*d^7//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(a+b*x^3)^(1/2)*(a*(10+6*3^(1/2))+b*x^3)^-1, x) == :(2*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+(1/2)*2^(1/2)*3^1//4*a^1//6*b^-2//3*arctanh((1/2)*2^(1/2)*3^1//4*a^1//6*(a+b*x^3)^-1//2*(a^1//3*(1+3^(1/2))+-2*x*b^1//3))+1//4*2^(1/2)*3^1//4*a^1//6*b^-2//3*arctanh((1/2)*2^(1/2)*3^1//4*a^1//6*(a+b*x^3)^-1//2*(1+-1*3^(1/2))*(a^1//3+x*b^1//3))+1//4*2^(1/2)*3^3//4*a^1//6*b^-2//3*arctan((1/2)*2^(1/2)*3^1//4*a^1//6*(a+b*x^3)^-1//2*(1+3^(1/2))*(a^1//3+x*b^1//3))+1//6*2^(1/2)*3^3//4*a^1//6*b^-2//3*arctan(1//6*2^(1/2)*3^1//4*a^-1//2*(a+b*x^3)^(1/2)*(1+-1*3^(1/2)))+-1*3^1//4*a^1//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+2//3*2^(1/2)*3^3//4*a^1//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(a+-1*b*x^3)^(1/2)*(a*(10+6*3^(1/2))+-1*b*x^3)^-1, x) == :(2*b^-2//3*(a+-1*b*x^3)^(1/2)*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-1+(1/2)*2^(1/2)*3^1//4*a^1//6*b^-2//3*arctanh((1/2)*2^(1/2)*3^1//4*a^1//6*(a+-1*b*x^3)^-1//2*(a^1//3*(1+3^(1/2))+2*x*b^1//3))+1//4*2^(1/2)*3^1//4*a^1//6*b^-2//3*arctanh((1/2)*2^(1/2)*3^1//4*a^1//6*(a+-1*b*x^3)^-1//2*(1+-1*3^(1/2))*(a^1//3+-1*x*b^1//3))+1//4*2^(1/2)*3^3//4*a^1//6*b^-2//3*arctan((1/2)*2^(1/2)*3^1//4*a^1//6*(a+-1*b*x^3)^-1//2*(1+3^(1/2))*(a^1//3+-1*x*b^1//3))+1//6*2^(1/2)*3^3//4*a^1//6*b^-2//3*arctan(1//6*2^(1/2)*3^1//4*a^-1//2*(a+-1*b*x^3)^(1/2)*(1+-1*3^(1/2)))+-1*3^1//4*a^1//3*b^-2//3*((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+-1*b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)),-7+-4*3^(1/2))+2//3*2^(1/2)*3^3//4*a^1//3*b^-2//3*((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(a+-1*b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)),-7+-4*3^(1/2)))
@test integrate(x*(-1a+b*x^3)^(1/2)*(a*(-10+-6*3^(1/2))+b*x^3)^-1, x) == :(-2*b^-2//3*(-1a+b*x^3)^(1/2)*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-1+(1/2)*2^(1/2)*3^1//4*a^1//6*b^-2//3*arctan((1/2)*2^(1/2)*3^1//4*a^1//6*(-1a+b*x^3)^-1//2*(a^1//3*(1+3^(1/2))+2*x*b^1//3))+-1//6*2^(1/2)*3^3//4*a^1//6*b^-2//3*arctanh(1//6*2^(1/2)*3^1//4*a^-1//2*(-1a+b*x^3)^(1/2)*(1+-1*3^(1/2)))+1//4*2^(1/2)*3^1//4*a^1//6*b^-2//3*arctan((1/2)*2^(1/2)*3^1//4*a^1//6*(-1a+b*x^3)^-1//2*(1+-1*3^(1/2))*(a^1//3+-1*x*b^1//3))+1//4*2^(1/2)*3^3//4*a^1//6*b^-2//3*arctanh((1/2)*2^(1/2)*3^1//4*a^1//6*(-1a+b*x^3)^-1//2*(1+3^(1/2))*(a^1//3+-1*x*b^1//3))+3^1//4*a^1//3*b^-2//3*((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(-1a+b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*Elliptic.E(arcsin((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)),-7+4*3^(1/2))+-2//3*2^(1/2)*3^3//4*a^1//3*b^-2//3*((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(-1a+b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*Elliptic.F(arcsin((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)),-7+4*3^(1/2)))
@test integrate(x*(-1a+-1*b*x^3)^(1/2)*(a*(-10+-6*3^(1/2))+-1*b*x^3)^-1, x) == :(-2*b^-2//3*(-1a+-1*b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-1+(1/2)*2^(1/2)*3^1//4*a^1//6*b^-2//3*arctan((1/2)*2^(1/2)*3^1//4*a^1//6*(-1a+-1*b*x^3)^-1//2*(a^1//3*(1+3^(1/2))+-2*x*b^1//3))+-1//6*2^(1/2)*3^3//4*a^1//6*b^-2//3*arctanh(1//6*2^(1/2)*3^1//4*a^-1//2*(-1a+-1*b*x^3)^(1/2)*(1+-1*3^(1/2)))+1//4*2^(1/2)*3^1//4*a^1//6*b^-2//3*arctan((1/2)*2^(1/2)*3^1//4*a^1//6*(-1a+-1*b*x^3)^-1//2*(1+-1*3^(1/2))*(a^1//3+x*b^1//3))+1//4*2^(1/2)*3^3//4*a^1//6*b^-2//3*arctanh((1/2)*2^(1/2)*3^1//4*a^1//6*(-1a+-1*b*x^3)^-1//2*(1+3^(1/2))*(a^1//3+x*b^1//3))+3^1//4*a^1//3*b^-2//3*((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(-1a+-1*b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+-2//3*2^(1/2)*3^3//4*a^1//3*b^-2//3*((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(-1a+-1*b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate(x*(a+b*x^3)^(1/2)*(a*(10+-6*3^(1/2))+b*x^3)^-1, x) == :(2*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+-1//2*2^(1/2)*3^1//4*a^1//6*b^-2//3*arctan((1/2)*2^(1/2)*3^1//4*a^1//6*(a+b*x^3)^-1//2*(a^1//3*(1+-1*3^(1/2))+-2*x*b^1//3))+-1//4*2^(1/2)*3^1//4*a^1//6*b^-2//3*arctan((1/2)*2^(1/2)*3^1//4*a^1//6*(a+b*x^3)^-1//2*(1+3^(1/2))*(a^1//3+x*b^1//3))+1//4*2^(1/2)*3^3//4*a^1//6*b^-2//3*arctanh((1/2)*2^(1/2)*3^1//4*a^1//6*(a+b*x^3)^-1//2*(1+-1*3^(1/2))*(a^1//3+x*b^1//3))+1//6*2^(1/2)*3^3//4*a^1//6*b^-2//3*arctanh(1//6*2^(1/2)*3^1//4*a^-1//2*(a+b*x^3)^(1/2)*(1+3^(1/2)))+-1*3^1//4*a^1//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+2//3*2^(1/2)*3^3//4*a^1//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(a+-1*b*x^3)^(1/2)*(a*(10+-6*3^(1/2))+-1*b*x^3)^-1, x) == :(2*b^-2//3*(a+-1*b*x^3)^(1/2)*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-1+-1//2*2^(1/2)*3^1//4*a^1//6*b^-2//3*arctan((1/2)*2^(1/2)*3^1//4*a^1//6*(a+-1*b*x^3)^-1//2*(a^1//3*(1+-1*3^(1/2))+2*x*b^1//3))+-1//4*2^(1/2)*3^1//4*a^1//6*b^-2//3*arctan((1/2)*2^(1/2)*3^1//4*a^1//6*(a+-1*b*x^3)^-1//2*(1+3^(1/2))*(a^1//3+-1*x*b^1//3))+1//4*2^(1/2)*3^3//4*a^1//6*b^-2//3*arctanh((1/2)*2^(1/2)*3^1//4*a^1//6*(a+-1*b*x^3)^-1//2*(1+-1*3^(1/2))*(a^1//3+-1*x*b^1//3))+1//6*2^(1/2)*3^3//4*a^1//6*b^-2//3*arctanh(1//6*2^(1/2)*3^1//4*a^-1//2*(a+-1*b*x^3)^(1/2)*(1+3^(1/2)))+-1*3^1//4*a^1//3*b^-2//3*((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+-1*b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)),-7+-4*3^(1/2))+2//3*2^(1/2)*3^3//4*a^1//3*b^-2//3*((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(a+-1*b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)),-7+-4*3^(1/2)))
@test integrate(x*(-1a+b*x^3)^(1/2)*(a*(10+-6*3^(1/2))+-1*b*x^3)^-1, x) == :(2*b^-2//3*(-1a+b*x^3)^(1/2)*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-1+(1/2)*2^(1/2)*3^1//4*a^1//6*b^-2//3*arctanh((1/2)*2^(1/2)*3^1//4*a^1//6*(-1a+b*x^3)^-1//2*(a^1//3*(1+-1*3^(1/2))+2*x*b^1//3))+-1//4*2^(1/2)*3^3//4*a^1//6*b^-2//3*arctan((1/2)*2^(1/2)*3^1//4*a^1//6*(-1a+b*x^3)^-1//2*(1+-1*3^(1/2))*(a^1//3+-1*x*b^1//3))+1//4*2^(1/2)*3^1//4*a^1//6*b^-2//3*arctanh((1/2)*2^(1/2)*3^1//4*a^1//6*(-1a+b*x^3)^-1//2*(1+3^(1/2))*(a^1//3+-1*x*b^1//3))+1//6*2^(1/2)*3^3//4*a^1//6*b^-2//3*arctan(1//6*2^(1/2)*3^1//4*a^-1//2*(-1a+b*x^3)^(1/2)*(1+3^(1/2)))+-1*3^1//4*a^1//3*b^-2//3*((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(-1a+b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*Elliptic.E(arcsin((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)),-7+4*3^(1/2))+2//3*2^(1/2)*3^3//4*a^1//3*b^-2//3*((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(-1a+b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*Elliptic.F(arcsin((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)),-7+4*3^(1/2)))
@test integrate(x*(-1a+-1*b*x^3)^(1/2)*(a*(10+-6*3^(1/2))+b*x^3)^-1, x) == :(2*b^-2//3*(-1a+-1*b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-1+(1/2)*2^(1/2)*3^1//4*a^1//6*b^-2//3*arctanh((1/2)*2^(1/2)*3^1//4*a^1//6*(-1a+-1*b*x^3)^-1//2*(a^1//3*(1+-1*3^(1/2))+-2*x*b^1//3))+-1//4*2^(1/2)*3^3//4*a^1//6*b^-2//3*arctan((1/2)*2^(1/2)*3^1//4*a^1//6*(-1a+-1*b*x^3)^-1//2*(1+-1*3^(1/2))*(a^1//3+x*b^1//3))+1//4*2^(1/2)*3^1//4*a^1//6*b^-2//3*arctanh((1/2)*2^(1/2)*3^1//4*a^1//6*(-1a+-1*b*x^3)^-1//2*(1+3^(1/2))*(a^1//3+x*b^1//3))+1//6*2^(1/2)*3^3//4*a^1//6*b^-2//3*arctan(1//6*2^(1/2)*3^1//4*a^-1//2*(-1a+-1*b*x^3)^(1/2)*(1+3^(1/2)))+-1*3^1//4*a^1//3*b^-2//3*((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(-1a+-1*b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+2//3*2^(1/2)*3^3//4*a^1//3*b^-2//3*((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(-1a+-1*b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate(x*(a+b*x^3)^-1//2*(a*(10+6*3^(1/2))+b*x^3)^-1, x) == :(-1//12*2^(1/2)*3^1//4*a^-5//6*b^-2//3*(2+-1*3^(1/2))*arctan((1/2)*2^(1/2)*3^1//4*a^1//6*(a+b*x^3)^-1//2*(1+3^(1/2))*(a^1//3+x*b^1//3))+-1//18*2^(1/2)*3^1//4*a^-5//6*b^-2//3*(2+-1*3^(1/2))*arctan(1//6*2^(1/2)*3^1//4*a^-1//2*(a+b*x^3)^(1/2)*(1+-1*3^(1/2)))+-1//18*2^(1/2)*3^3//4*a^-5//6*b^-2//3*(2+-1*3^(1/2))*arctanh((1/2)*2^(1/2)*3^1//4*a^1//6*(a+b*x^3)^-1//2*(a^1//3*(1+3^(1/2))+-2*x*b^1//3))+-1//36*2^(1/2)*3^3//4*a^-5//6*b^-2//3*(2+-1*3^(1/2))*arctanh((1/2)*2^(1/2)*3^1//4*a^1//6*(a+b*x^3)^-1//2*(1+-1*3^(1/2))*(a^1//3+x*b^1//3)))
@test integrate(x*(a+-1*b*x^3)^-1//2*(a*(10+6*3^(1/2))+-1*b*x^3)^-1, x) == :(-1//12*2^(1/2)*3^1//4*a^-5//6*b^-2//3*(2+-1*3^(1/2))*arctan((1/2)*2^(1/2)*3^1//4*a^1//6*(a+-1*b*x^3)^-1//2*(1+3^(1/2))*(a^1//3+-1*x*b^1//3))+-1//18*2^(1/2)*3^1//4*a^-5//6*b^-2//3*(2+-1*3^(1/2))*arctan(1//6*2^(1/2)*3^1//4*a^-1//2*(a+-1*b*x^3)^(1/2)*(1+-1*3^(1/2)))+-1//18*2^(1/2)*3^3//4*a^-5//6*b^-2//3*(2+-1*3^(1/2))*arctanh((1/2)*2^(1/2)*3^1//4*a^1//6*(a+-1*b*x^3)^-1//2*(a^1//3*(1+3^(1/2))+2*x*b^1//3))+-1//36*2^(1/2)*3^3//4*a^-5//6*b^-2//3*(2+-1*3^(1/2))*arctanh((1/2)*2^(1/2)*3^1//4*a^1//6*(a+-1*b*x^3)^-1//2*(1+-1*3^(1/2))*(a^1//3+-1*x*b^1//3)))
@test integrate(x*(-1a+b*x^3)^-1//2*(a*(-10+-6*3^(1/2))+b*x^3)^-1, x) == :(-1//18*2^(1/2)*3^1//4*a^-5//6*b^-2//3*(2+-1*3^(1/2))*arctanh(1//6*2^(1/2)*3^1//4*a^-1//2*(-1a+b*x^3)^(1/2)*(1+-1*3^(1/2)))+1//12*2^(1/2)*3^1//4*a^-5//6*b^-2//3*(2+-1*3^(1/2))*arctanh((1/2)*2^(1/2)*3^1//4*a^1//6*(-1a+b*x^3)^-1//2*(1+3^(1/2))*(a^1//3+-1*x*b^1//3))+1//18*2^(1/2)*3^3//4*a^-5//6*b^-2//3*(2+-1*3^(1/2))*arctan((1/2)*2^(1/2)*3^1//4*a^1//6*(-1a+b*x^3)^-1//2*(a^1//3*(1+3^(1/2))+2*x*b^1//3))+1//36*2^(1/2)*3^3//4*a^-5//6*b^-2//3*(2+-1*3^(1/2))*arctan((1/2)*2^(1/2)*3^1//4*a^1//6*(-1a+b*x^3)^-1//2*(1+-1*3^(1/2))*(a^1//3+-1*x*b^1//3)))
@test integrate(x*(-1a+-1*b*x^3)^-1//2*(a*(-10+-6*3^(1/2))+-1*b*x^3)^-1, x) == :(-1//18*2^(1/2)*3^1//4*a^-5//6*b^-2//3*(2+-1*3^(1/2))*arctanh(1//6*2^(1/2)*3^1//4*a^-1//2*(-1a+-1*b*x^3)^(1/2)*(1+-1*3^(1/2)))+1//12*2^(1/2)*3^1//4*a^-5//6*b^-2//3*(2+-1*3^(1/2))*arctanh((1/2)*2^(1/2)*3^1//4*a^1//6*(-1a+-1*b*x^3)^-1//2*(1+3^(1/2))*(a^1//3+x*b^1//3))+1//18*2^(1/2)*3^3//4*a^-5//6*b^-2//3*(2+-1*3^(1/2))*arctan((1/2)*2^(1/2)*3^1//4*a^1//6*(-1a+-1*b*x^3)^-1//2*(a^1//3*(1+3^(1/2))+-2*x*b^1//3))+1//36*2^(1/2)*3^3//4*a^-5//6*b^-2//3*(2+-1*3^(1/2))*arctan((1/2)*2^(1/2)*3^1//4*a^1//6*(-1a+-1*b*x^3)^-1//2*(1+-1*3^(1/2))*(a^1//3+x*b^1//3)))
@test integrate(x*(a+b*x^3)^-1//2*(a*(10+-6*3^(1/2))+b*x^3)^-1, x) == :(-1//18*2^(1/2)*3^3//4*a^-5//6*b^-2//3*(2+3^(1/2))*arctan((1/2)*2^(1/2)*3^1//4*a^1//6*(a+b*x^3)^-1//2*(a^1//3*(1+-1*3^(1/2))+-2*x*b^1//3))+-1//36*2^(1/2)*3^3//4*a^-5//6*b^-2//3*(2+3^(1/2))*arctan((1/2)*2^(1/2)*3^1//4*a^1//6*(a+b*x^3)^-1//2*(1+3^(1/2))*(a^1//3+x*b^1//3))+1//12*2^(1/2)*3^1//4*a^-5//6*b^-2//3*(2+3^(1/2))*arctanh((1/2)*2^(1/2)*3^1//4*a^1//6*(a+b*x^3)^-1//2*(1+-1*3^(1/2))*(a^1//3+x*b^1//3))+1//18*2^(1/2)*3^1//4*a^-5//6*b^-2//3*(2+3^(1/2))*arctanh(1//6*2^(1/2)*3^1//4*a^-1//2*(a+b*x^3)^(1/2)*(1+3^(1/2))))
@test integrate(x*(a+-1*b*x^3)^-1//2*(a*(10+-6*3^(1/2))+-1*b*x^3)^-1, x) == :(-1//18*2^(1/2)*3^3//4*a^-5//6*b^-2//3*(2+3^(1/2))*arctan((1/2)*2^(1/2)*3^1//4*a^1//6*(a+-1*b*x^3)^-1//2*(a^1//3*(1+-1*3^(1/2))+2*x*b^1//3))+-1//36*2^(1/2)*3^3//4*a^-5//6*b^-2//3*(2+3^(1/2))*arctan((1/2)*2^(1/2)*3^1//4*a^1//6*(a+-1*b*x^3)^-1//2*(1+3^(1/2))*(a^1//3+-1*x*b^1//3))+1//12*2^(1/2)*3^1//4*a^-5//6*b^-2//3*(2+3^(1/2))*arctanh((1/2)*2^(1/2)*3^1//4*a^1//6*(a+-1*b*x^3)^-1//2*(1+-1*3^(1/2))*(a^1//3+-1*x*b^1//3))+1//18*2^(1/2)*3^1//4*a^-5//6*b^-2//3*(2+3^(1/2))*arctanh(1//6*2^(1/2)*3^1//4*a^-1//2*(a+-1*b*x^3)^(1/2)*(1+3^(1/2))))
@test integrate(x*(-1a+b*x^3)^-1//2*(a*(10+-6*3^(1/2))+-1*b*x^3)^-1, x) == :(-1//18*2^(1/2)*3^1//4*a^-5//6*b^-2//3*(2+3^(1/2))*arctan(1//6*2^(1/2)*3^1//4*a^-1//2*(-1a+b*x^3)^(1/2)*(1+3^(1/2)))+-1//18*2^(1/2)*3^3//4*a^-5//6*b^-2//3*(2+3^(1/2))*arctanh((1/2)*2^(1/2)*3^1//4*a^1//6*(-1a+b*x^3)^-1//2*(a^1//3*(1+-1*3^(1/2))+2*x*b^1//3))+-1//36*2^(1/2)*3^3//4*a^-5//6*b^-2//3*(2+3^(1/2))*arctanh((1/2)*2^(1/2)*3^1//4*a^1//6*(-1a+b*x^3)^-1//2*(1+3^(1/2))*(a^1//3+-1*x*b^1//3))+1//12*2^(1/2)*3^1//4*a^-5//6*b^-2//3*(2+3^(1/2))*arctan((1/2)*2^(1/2)*3^1//4*a^1//6*(-1a+b*x^3)^-1//2*(1+-1*3^(1/2))*(a^1//3+-1*x*b^1//3)))
@test integrate(x*(-1a+-1*b*x^3)^-1//2*(a*(10+-6*3^(1/2))+b*x^3)^-1, x) == :(-1//18*2^(1/2)*3^1//4*a^-5//6*b^-2//3*(2+3^(1/2))*arctan(1//6*2^(1/2)*3^1//4*a^-1//2*(-1a+-1*b*x^3)^(1/2)*(1+3^(1/2)))+-1//18*2^(1/2)*3^3//4*a^-5//6*b^-2//3*(2+3^(1/2))*arctanh((1/2)*2^(1/2)*3^1//4*a^1//6*(-1a+-1*b*x^3)^-1//2*(a^1//3*(1+-1*3^(1/2))+-2*x*b^1//3))+-1//36*2^(1/2)*3^3//4*a^-5//6*b^-2//3*(2+3^(1/2))*arctanh((1/2)*2^(1/2)*3^1//4*a^1//6*(-1a+-1*b*x^3)^-1//2*(1+3^(1/2))*(a^1//3+x*b^1//3))+1//12*2^(1/2)*3^1//4*a^-5//6*b^-2//3*(2+3^(1/2))*arctan((1/2)*2^(1/2)*3^1//4*a^1//6*(-1a+-1*b*x^3)^-1//2*(1+-1*3^(1/2))*(a^1//3+x*b^1//3)))
@test integrate(x^8*(a+b*x^3)^-1*(c+d*x^3)^(1/2), x) == :(2//3*a^2*b^-3*(c+d*x^3)^(1/2)+2//15*b^-1*d^-2*(c+d*x^3)^5//2+-2//3*a^2*b^-7//2*(b*c+-1*a*d)^(1/2)*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//9*b^-2*d^-2*(c+d*x^3)^3//2*(2*a*d+2*b*c))
@test integrate(x^5*(a+b*x^3)^-1*(c+d*x^3)^(1/2), x) == :(-2//3*a*b^-2*(c+d*x^3)^(1/2)+2//9*b^-1*d^-1*(c+d*x^3)^3//2+2//3*a*b^-5//2*(b*c+-1*a*d)^(1/2)*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^2*(a+b*x^3)^-1*(c+d*x^3)^(1/2), x) == :(2//3*b^-1*(c+d*x^3)^(1/2)+-2//3*b^-3//2*(b*c+-1*a*d)^(1/2)*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-1*(a+b*x^3)^-1*(c+d*x^3)^(1/2), x) == :(-2//3*a^-1*c^(1/2)*arctanh(c^-1//2*(c+d*x^3)^(1/2))+2//3*a^-1*b^-1//2*(b*c+-1*a*d)^(1/2)*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-4*(a+b*x^3)^-1*(c+d*x^3)^(1/2), x) == :(-1//3*a^-1*x^-3*(c+d*x^3)^(1/2)+-2//3*a^-2*b^(1/2)*(b*c+-1*a*d)^(1/2)*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2)+1//3*a^-2*c^-1//2*(-1*a*d+2*b*c)*arctanh(c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^8*(a+b*x^3)^-1*(c+d*x^3)^3//2, x) == :(2//9*a^2*b^-3*(c+d*x^3)^3//2+2//21*b^-1*d^-2*(c+d*x^3)^7//2+-2//3*a^2*b^-9//2*(b*c+-1*a*d)^3//2*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//15*b^-2*d^-2*(c+d*x^3)^5//2*(2*a*d+2*b*c)+2//3*a^2*b^-4*(c+d*x^3)^(1/2)*(b*c+-1*a*d))
@test integrate(x^5*(a+b*x^3)^-1*(c+d*x^3)^3//2, x) == :(-2//9*a*b^-2*(c+d*x^3)^3//2+2//15*b^-1*d^-1*(c+d*x^3)^5//2+-2//3*a*b^-3*(c+d*x^3)^(1/2)*(b*c+-1*a*d)+2//3*a*b^-7//2*(b*c+-1*a*d)^3//2*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^2*(a+b*x^3)^-1*(c+d*x^3)^3//2, x) == :(2//9*b^-1*(c+d*x^3)^3//2+-2//3*b^-5//2*(b*c+-1*a*d)^3//2*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2)+1//3*b^-2*(c+d*x^3)^(1/2)*(-2*a*d+2*b*c))
@test integrate(x^-1*(a+b*x^3)^-1*(c+d*x^3)^3//2, x) == :(-2//3*a^-1*c^3//2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+2//3*d*b^-1*(c+d*x^3)^(1/2)+2//3*a^-1*b^-3//2*(b*c+-1*a*d)^3//2*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-4*(a+b*x^3)^-1*(c+d*x^3)^3//2, x) == :(-2//3*a^-2*b^-1//2*(b*c+-1*a*d)^3//2*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//3*c*a^-1*x^-3*(c+d*x^3)^(1/2)+1//3*a^-2*c^(1/2)*(-3*a*d+2*b*c)*arctanh(c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^8*(a+b*x^3)^-1*(c+d*x^3)^-1//2, x) == :(2//9*b^-1*d^-2*(c+d*x^3)^3//2+-2//3*a^2*b^-5//2*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//3*b^-2*d^-2*(c+d*x^3)^(1/2)*(2*a*d+2*b*c))
@test integrate(x^5*(a+b*x^3)^-1*(c+d*x^3)^-1//2, x) == :(2//3*b^-1*d^-1*(c+d*x^3)^(1/2)+2//3*a*b^-3//2*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^2*(a+b*x^3)^-1*(c+d*x^3)^-1//2, x) == :(-2//3*b^-1//2*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-1*(a+b*x^3)^-1*(c+d*x^3)^-1//2, x) == :(-2//3*a^-1*c^-1//2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+2//3*a^-1*b^(1/2)*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-4*(a+b*x^3)^-1*(c+d*x^3)^-1//2, x) == :(-2//3*a^-2*b^3//2*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//3*a^-1*c^-1*x^-3*(c+d*x^3)^(1/2)+1//3*a^-2*c^-3//2*(a*d+2*b*c)*arctanh(c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^8*(a+b*x^3)^-1*(c+d*x^3)^-3//2, x) == :(2//3*b^-1*d^-2*(c+d*x^3)^(1/2)+-2//3*a^2*b^-3//2*(b*c+-1*a*d)^-3//2*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2)+2//3*c^2*d^-2*(c+d*x^3)^-1//2*(b*c+-1*a*d)^-1)
@test integrate(x^5*(a+b*x^3)^-1*(c+d*x^3)^-3//2, x) == :(-2//3*c*d^-1*(c+d*x^3)^-1//2*(b*c+-1*a*d)^-1+2//3*a*b^-1//2*(b*c+-1*a*d)^-3//2*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^2*(a+b*x^3)^-1*(c+d*x^3)^-3//2, x) == :(2*(c+d*x^3)^-1//2*(-3*a*d+3*b*c)^-1+-2//3*b^(1/2)*(b*c+-1*a*d)^-3//2*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-1*(a+b*x^3)^-1*(c+d*x^3)^-3//2, x) == :(-2//3*a^-1*c^-3//2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+-2//3*d*c^-1*(c+d*x^3)^-1//2*(b*c+-1*a*d)^-1+2//3*a^-1*b^3//2*(b*c+-1*a*d)^-3//2*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-4*(a+b*x^3)^-1*(c+d*x^3)^-3//2, x) == :(-2//3*a^-2*b^5//2*(b*c+-1*a*d)^-3//2*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//3*a^-1*c^-1*x^-3*(c+d*x^3)^-1//2+1//3*a^-2*c^-5//2*(2*b*c+3*a*d)*arctanh(c^-1//2*(c+d*x^3)^(1/2))+-1//3*d*a^-1*c^-2*(c+d*x^3)^-1//2*(b*c+-1*a*d)^-1*(b*c+-3*a*d))
@test integrate(x^11*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-2, x) == :(-3968//9*c^5//2*d^-4*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+7//15*d^-2*x^6*(c+d*x^3)^(1/2)+1//3*d^-1*x^9*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1+2//15*c*d^-4*(c+d*x^3)^(1/2)*(1146c+47*d*x^3))
@test integrate(x^8*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-2, x) == :(2//9*d^-3*(c+d*x^3)^3//2+-352//9*c^3//2*d^-3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+352//27*c*d^-3*(c+d*x^3)^(1/2)+64//27*c*d^-3*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-1)
@test integrate(x^5*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-2, x) == :(26//27*d^-2*(c+d*x^3)^(1/2)+-26//9*c^(1/2)*d^-2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+8//27*d^-2*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-1)
@test integrate(x^2*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-2, x) == :(-1//9*c^-1//2*d^-1*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+1//3*d^-1*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1)
@test integrate(x^-1*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-2, x) == :(-1//96*c^-3//2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+5//288*c^-3//2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+1//24*c^-1*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1)
@test integrate(x^-4*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-2, x) == :(-1//128*d*c^-5//2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+7//1152*d*c^-5//2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+-1//24*c^-1*x^-3*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1+1//96*d*c^-2*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1)
@test integrate(x^-7*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-2, x) == :(-1//2048*c^-7//2*d^2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+23//18432*c^-7//2*d^2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+-1//48*c^-1*x^-6*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1+5//1536*c^-3*d^2*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1+-7//384*d*c^-2*x^-3*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1)
@test integrate(x^7*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-2, x) == :(-76//9*c^7//6*d^-8//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+13//21*d^-2*x^2*(c+d*x^3)^(1/2)+76//9*c^7//6*d^-8//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+1//3*d^-1*x^5*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1+76//9*3^(1/2)*c^7//6*d^-8//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+746//21*c*d^-8//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-373//21*3^1//4*c^4//3*d^-8//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+746//63*2^(1/2)*3^3//4*c^4//3*d^-8//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^4*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-2, x) == :(-5//9*c^1//6*d^-5//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+5//9*c^1//6*d^-5//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+7//3*d^-5//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+1//3*d^-1*x^2*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1+5//9*3^(1/2)*c^1//6*d^-5//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+-7//6*3^1//4*c^1//3*d^-5//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+7//9*2^(1/2)*3^3//4*c^1//3*d^-5//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-2, x) == :(-1//144*c^-5//6*d^-2//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+1//144*c^-5//6*d^-2//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+1//24*c^-1*d^-2//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+1//24*c^-1*x^2*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1+1//144*3^(1/2)*c^-5//6*d^-2//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+-1//48*3^1//4*c^-2//3*d^-2//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//72*2^(1/2)*3^3//4*c^-2//3*d^-2//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-2*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-2, x) == :(-1//48*c^-2*x^-1*(c+d*x^3)^(1/2)+-1//144*c^-11//6*d^1//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+1//144*c^-11//6*d^1//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-1//144*3^(1/2)*c^-11//6*d^1//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+1//24*c^-1*x^-1*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1+1//48*c^-2*d^1//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-1//96*3^1//4*c^-5//3*d^1//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//144*2^(1/2)*3^3//4*c^-5//3*d^1//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-5*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-2, x) == :(-17//9216*c^-17//6*d^4//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+-7//768*c^-2*x^-4*(c+d*x^3)^(1/2)+17//9216*c^-17//6*d^4//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-17//9216*3^(1/2)*c^-17//6*d^4//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+-1//96*d*c^-3*x^-1*(c+d*x^3)^(1/2)+1//24*c^-1*x^-4*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1+1//96*c^-3*d^4//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-1//192*3^1//4*c^-8//3*d^4//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//288*2^(1/2)*3^3//4*c^-8//3*d^4//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-8*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-2, x) == :(-13//36864*c^-23//6*d^7//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+-5//672*c^-2*x^-7*(c+d*x^3)^(1/2)+13//36864*c^-23//6*d^7//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-53//21504*d*c^-3*x^-4*(c+d*x^3)^(1/2)+-13//36864*3^(1/2)*c^-23//6*d^7//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+-1//5376*c^-4*d^2*x^-1*(c+d*x^3)^(1/2)+1//24*c^-1*x^-7*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1+1//5376*c^-4*d^7//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-1//10752*3^1//4*c^-11//3*d^7//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//16128*2^(1/2)*3^3//4*c^-11//3*d^7//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^11*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-2, x) == :(-4992*c^7//2*d^-4*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+1664*c^3*d^-4*(c+d*x^3)^(1/2)+3//7*d^-2*x^6*(c+d*x^3)^3//2+1//3*d^-1*x^9*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-1+2//21*c*d^-4*(c+d*x^3)^3//2*(694c+51*d*x^3))
@test integrate(x^8*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-2, x) == :(2//15*d^-3*(c+d*x^3)^5//2+-480*c^5//2*d^-3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+160*c^2*d^-3*(c+d*x^3)^(1/2)+160//27*c*d^-3*(c+d*x^3)^3//2+64//27*c*d^-3*(c+d*x^3)^5//2*(8c+-1*d*x^3)^-1)
@test integrate(x^5*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-2, x) == :(14//27*d^-2*(c+d*x^3)^3//2+-42*c^3//2*d^-2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+14*c*d^-2*(c+d*x^3)^(1/2)+8//27*d^-2*(c+d*x^3)^5//2*(8c+-1*d*x^3)^-1)
@test integrate(x^2*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-2, x) == :(d^-1*(c+d*x^3)^(1/2)+-3*c^(1/2)*d^-1*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+1//3*d^-1*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-1)
@test integrate(x^-1*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-2, x) == :(3*(c+d*x^3)^(1/2)*(64c+-8*d*x^3)^-1+-3//32*c^-1//2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+-1//96*c^-1//2*arctanh(c^-1//2*(c+d*x^3)^(1/2)))
@test integrate(x^-4*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-2, x) == :(-7//384*d*c^-3//2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+-1//24*x^-3*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1+3//128*d*c^-3//2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+5//96*d*c^-1*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1)
@test integrate(x^-7*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-2, x) == :(-17//2048*c^-5//2*d^2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+-1//48*x^-6*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1+15//2048*c^-5//2*d^2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+7//512*c^-2*d^2*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1+-23//384*d*c^-1*x^-3*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1)
@test integrate(x^7*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-2, x) == :(-108*c^13//6*d^-8//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+108*c^13//6*d^-8//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+19//39*d^-1*x^5*(c+d*x^3)^(1/2)+108*3^(1/2)*c^13//6*d^-8//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+1//3*d^-1*x^5*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-1+103//13*c*d^-2*x^2*(c+d*x^3)^(1/2)+5906//13*c^2*d^-8//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-2953//13*3^1//4*c^7//3*d^-8//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+5906//39*2^(1/2)*3^3//4*c^7//3*d^-8//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^4*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-2, x) == :(-9*c^7//6*d^-5//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+9*c^7//6*d^-5//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+13//21*d^-1*x^2*(c+d*x^3)^(1/2)+9*3^(1/2)*c^7//6*d^-5//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+1//3*d^-1*x^2*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-1+265//7*c*d^-5//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-265//14*3^1//4*c^4//3*d^-5//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+265//21*2^(1/2)*3^3//4*c^4//3*d^-5//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-2, x) == :(3*x^2*(c+d*x^3)^(1/2)*(64c+-8*d*x^3)^-1+-9//16*c^1//6*d^-2//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+9//16*c^1//6*d^-2//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+19//8*d^-2//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+9//16*3^(1/2)*c^1//6*d^-2//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+-19//16*3^1//4*c^1//3*d^-2//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+19//24*2^(1/2)*3^3//4*c^1//3*d^-2//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-2*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-2, x) == :(-1//16*c^-1*x^-1*(c+d*x^3)^(1/2)+3//8*x^-1*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1+1//16*c^-1*d^1//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-1//32*3^1//4*c^-2//3*d^1//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//48*2^(1/2)*3^3//4*c^-2//3*d^1//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-5*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-2, x) == :(-13//256*c^-1*x^-4*(c+d*x^3)^(1/2)+-9//1024*c^-11//6*d^4//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+3//8*x^-4*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1+9//1024*c^-11//6*d^4//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-9//1024*3^(1/2)*c^-11//6*d^4//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+-1//32*d*c^-2*x^-1*(c+d*x^3)^(1/2)+1//32*c^-2*d^4//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-1//64*3^1//4*c^-5//3*d^4//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//96*2^(1/2)*3^3//4*c^-5//3*d^4//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-8*(c+d*x^3)^3//2*(8c+-1*d*x^3)^-2, x) == :(-11//224*c^-1*x^-7*(c+d*x^3)^(1/2)+-9//4096*c^-17//6*d^7//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+3//8*x^-7*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1+9//4096*c^-17//6*d^7//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-83//7168*d*c^-2*x^-4*(c+d*x^3)^(1/2)+-19//1792*c^-3*d^2*x^-1*(c+d*x^3)^(1/2)+-9//4096*3^(1/2)*c^-17//6*d^7//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+19//1792*c^-3*d^7//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-19//3584*3^1//4*c^-8//3*d^7//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+19//5376*2^(1/2)*3^3//4*c^-8//3*d^7//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^11*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-2, x) == :(-2944//81*c^3//2*d^-4*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+2//27*d^-4*(c+d*x^3)^(1/2)*(170c+7*d*x^3)+8//27*d^-2*x^6*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1)
@test integrate(x^8*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-2, x) == :(2//3*d^-3*(c+d*x^3)^(1/2)+-224//81*c^(1/2)*d^-3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+64//27*c*d^-3*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1)
@test integrate(x^5*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-2, x) == :(-10//81*c^-1//2*d^-2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+8//27*d^-2*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1)
@test integrate(x^2*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-2, x) == :(1//81*c^-3//2*d^-1*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+1//27*c^-1*d^-1*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1)
@test integrate(x^-1*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-2, x) == :(-1//96*c^-5//2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+13//2592*c^-5//2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+1//216*c^-2*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1)
@test integrate(x^-4*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-2, x) == :(1//384*d*c^-7//2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+11//10368*d*c^-7//2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+-1//24*c^-2*x^-3*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1+5//864*d*c^-3*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1)
@test integrate(x^-7*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-2, x) == :(-19//6144*c^-9//2*d^2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+31//165888*c^-9//2*d^2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+-35//13824*c^-4*d^2*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1+-1//48*c^-2*x^-6*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1+3//128*d*c^-3*x^-3*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1)
@test integrate(x^7*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-2, x) == :(-44//81*c^1//6*d^-8//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+44//81*c^1//6*d^-8//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+62//27*d^-8//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+8//27*d^-2*x^2*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1+44//81*3^(1/2)*c^1//6*d^-8//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+-31//27*3^1//4*c^1//3*d^-8//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+62//81*2^(1/2)*3^3//4*c^1//3*d^-8//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^4*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-2, x) == :(-1//81*c^-5//6*d^-5//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+1//81*c^-5//6*d^-5//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+1//27*c^-1*d^-5//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+1//81*3^(1/2)*c^-5//6*d^-5//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+1//27*c^-1*d^-1*x^2*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1+-1//54*3^1//4*c^-2//3*d^-5//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//81*2^(1/2)*3^3//4*c^-2//3*d^-5//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-2, x) == :(-7//1296*c^-11//6*d^-2//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+7//1296*c^-11//6*d^-2//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-7//1296*3^(1/2)*c^-11//6*d^-2//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+1//216*c^-2*d^-2//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+1//216*c^-2*x^2*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1+-1//432*3^1//4*c^-5//3*d^-2//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//648*2^(1/2)*3^3//4*c^-5//3*d^-2//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-2*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-2, x) == :(-7//432*c^-3*x^-1*(c+d*x^3)^(1/2)+-1//648*c^-17//6*d^1//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+1//648*c^-17//6*d^1//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-1//648*3^(1/2)*c^-17//6*d^1//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+1//216*c^-2*x^-1*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1+7//432*c^-3*d^1//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-7//864*3^1//4*c^-8//3*d^1//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+7//1296*2^(1/2)*3^3//4*c^-8//3*d^1//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-5*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-2, x) == :(-31//6912*c^-3*x^-4*(c+d*x^3)^(1/2)+-25//82944*c^-23//6*d^4//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+25//82944*c^-23//6*d^4//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-25//82944*3^(1/2)*c^-23//6*d^4//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+-5//864*c^-4*d^4//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+1//216*c^-2*x^-4*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1+5//864*d*c^-4*x^-1*(c+d*x^3)^(1/2)+-5//2592*2^(1/2)*3^3//4*c^-11//3*d^4//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+5//1728*3^1//4*c^-11//3*d^4//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-8*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-2, x) == :(-17//6048*c^-3*x^-7*(c+d*x^3)^(1/2)+-17//331776*c^-29//6*d^7//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+17//331776*c^-29//6*d^7//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-289//48384*c^-5*d^2*x^-1*(c+d*x^3)^(1/2)+-17//331776*3^(1/2)*c^-29//6*d^7//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+1//216*c^-2*x^-7*(c+d*x^3)^(1/2)*(8c+-1*d*x^3)^-1+289//48384*c^-5*d^7//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+391//193536*d*c^-4*x^-4*(c+d*x^3)^(1/2)+-289//96768*3^1//4*c^-14//3*d^7//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+289//145152*2^(1/2)*3^3//4*c^-14//3*d^7//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^11*(c+d*x^3)^-3//2*(8c+-1*d*x^3)^-2, x) == :(-640//243*c^(1/2)*d^-4*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+1//81*d^-4*(c+d*x^3)^-1//2*(76c+78*d*x^3)+8//27*d^-2*x^6*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-1)
@test integrate(x^8*(c+d*x^3)^-3//2*(8c+-1*d*x^3)^-2, x) == :(-22//81*d^-3*(c+d*x^3)^-1//2+-32//243*c^-1//2*d^-3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+64//27*c*d^-3*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-1)
@test integrate(x^5*(c+d*x^3)^-3//2*(8c+-1*d*x^3)^-2, x) == :(-2//81*c^-1*d^-2*(c+d*x^3)^-1//2+2//243*c^-3//2*d^-2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+8//27*d^-2*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-1)
@test integrate(x^2*(c+d*x^3)^-3//2*(8c+-1*d*x^3)^-2, x) == :(-1//81*c^-2*d^-1*(c+d*x^3)^-1//2+1//243*c^-5//2*d^-1*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+1//27*c^-1*d^-1*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-1)
@test integrate(x^-1*(c+d*x^3)^-3//2*(8c+-1*d*x^3)^-2, x) == :(-1//96*c^-7//2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+5//648*c^-3*(c+d*x^3)^-1//2+7//7776*c^-7//2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+1//216*c^-2*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-1)
@test integrate(x^-4*(c+d*x^3)^-3//2*(8c+-1*d*x^3)^-2, x) == :(-35//2592*d*c^-4*(c+d*x^3)^-1//2+5//384*d*c^-9//2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+5//31104*d*c^-9//2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+-1//24*c^-2*x^-3*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-1+5//864*d*c^-3*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-1)
@test integrate(x^-7*(c+d*x^3)^-3//2*(8c+-1*d*x^3)^-2, x) == :(-33//2048*c^-11//2*d^2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+13//497664*c^-11//2*d^2*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+665//41472*c^-5*d^2*(c+d*x^3)^-1//2+-71//13824*c^-4*d^2*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-1+-1//48*c^-2*x^-6*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-1+17//384*d*c^-3*x^-3*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-1)
@test integrate(x^7*(c+d*x^3)^-3//2*(8c+-1*d*x^3)^-2, x) == :(-4//243*c^-5//6*d^-8//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+4//243*c^-5//6*d^-8//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+-2//81*c^-1*d^-2*x^2*(c+d*x^3)^-1//2+2//81*c^-1*d^-8//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+4//243*3^(1/2)*c^-5//6*d^-8//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+8//27*d^-2*x^2*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-1+-1//81*3^1//4*c^-2//3*d^-8//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+2//243*2^(1/2)*3^3//4*c^-2//3*d^-8//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^4*(c+d*x^3)^-3//2*(8c+-1*d*x^3)^-2, x) == :(-1//243*c^-11//6*d^-5//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+1//243*c^-11//6*d^-5//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-1//81*c^-2*d^-1*x^2*(c+d*x^3)^-1//2+-1//243*3^(1/2)*c^-11//6*d^-5//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+1//81*c^-2*d^-5//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+1//27*c^-1*d^-1*x^2*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-1+-1//162*3^1//4*c^-5//3*d^-5//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//243*2^(1/2)*3^3//4*c^-5//3*d^-5//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(c+d*x^3)^-3//2*(8c+-1*d*x^3)^-2, x) == :(-5//3888*c^-17//6*d^-2//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+5//648*c^-3*x^2*(c+d*x^3)^-1//2+5//3888*c^-17//6*d^-2//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-5//648*c^-3*d^-2//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-5//3888*3^(1/2)*c^-17//6*d^-2//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+1//216*c^-2*x^2*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-1+-1//1944*2^(1/2)*3^3//4*c^-8//3*d^-2//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(5*c^1//3+5*x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+5//1296*3^1//4*c^-8//3*d^-2//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-2*(c+d*x^3)^-3//2*(8c+-1*d*x^3)^-2, x) == :(-31//1296*c^-4*x^-1*(c+d*x^3)^(1/2)+-1//3888*c^-23//6*d^1//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+1//3888*c^-23//6*d^1//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+5//648*c^-3*x^-1*(c+d*x^3)^-1//2+-1//3888*3^(1/2)*c^-23//6*d^1//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+1//216*c^-2*x^-1*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-1+31//1296*c^-4*d^1//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-31//2592*3^1//4*c^-11//3*d^1//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+31//3888*2^(1/2)*3^3//4*c^-11//3*d^1//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-5*(c+d*x^3)^-3//2*(8c+-1*d*x^3)^-2, x) == :(-253//20736*c^-4*x^-4*(c+d*x^3)^(1/2)+-11//248832*c^-29//6*d^4//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+5//648*c^-3*x^-4*(c+d*x^3)^-1//2+11//248832*c^-29//6*d^4//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-77//2592*c^-5*d^4//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+-11//248832*3^(1/2)*c^-29//6*d^4//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+1//216*c^-2*x^-4*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-1+77//2592*d*c^-5*x^-1*(c+d*x^3)^(1/2)+-77//7776*2^(1/2)*3^3//4*c^-14//3*d^4//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+77//5184*3^1//4*c^-14//3*d^4//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-8*(c+d*x^3)^-3//2*(8c+-1*d*x^3)^-2, x) == :(-191//18144*c^-4*x^-7*(c+d*x^3)^(1/2)+-7//995328*c^-35//6*d^7//3*arctanh(1//3*c^-1//2*(c+d*x^3)^(1/2))+5//648*c^-3*x^-7*(c+d*x^3)^-1//2+7//995328*c^-35//6*d^7//3*arctanh(1//3*c^-1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)^2)+-5179//145152*c^-6*d^2*x^-1*(c+d*x^3)^(1/2)+-7//995328*3^(1/2)*c^-35//6*d^7//3*arctan(3^(1/2)*c^1//6*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3))+1//216*c^-2*x^-7*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-1+5179//145152*c^-6*d^7//3*(c+d*x^3)^(1/2)*(x*d^1//3+c^1//3*(1+3^(1/2)))^-1+8257//580608*d*c^-5*x^-4*(c+d*x^3)^(1/2)+-5179//290304*3^1//4*c^-17//3*d^7//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.E(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+5179//435456*2^(1/2)*3^3//4*c^-17//3*d^7//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^6*(c+d*x^3)^-3//2*(8c+-1*d*x^3)^-2, x) == :(2//81*x*c^-1*d^-2*(c+d*x^3)^-1//2*(8c+-1*d*x^3)^-1*(4c+d*x^3)+-2//243*3^3//4*c^-1*d^-7//3*((x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3))^(1/2)*(c^1//3*(x*d^1//3+c^1//3*(1+3^(1/2)))^-2*(c^1//3+x*d^1//3))^-1//2*(2+3^(1/2))^(1/2)*(c+d*x^3)^-1//2*(c^1//3+x*d^1//3)*Elliptic.F(arcsin((x*d^1//3+c^1//3*(1+3^(1/2)))^-1*(x*d^1//3+c^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^8*(a+b*x^3)^-2*(c+d*x^3)^(1/2), x) == :(2//9*b^-2*d^-1*(c+d*x^3)^3//2+-1//3*a*b^-3*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1*(-5*a*d+4*b*c)+-1//3*a^2*b^-2*(a+b*x^3)^-1*(c+d*x^3)^3//2*(b*c+-1*a*d)^-1+1//3*a*b^-7//2*(b*c+-1*a*d)^-1//2*(-5*a*d+4*b*c)*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^5*(a+b*x^3)^-2*(c+d*x^3)^(1/2), x) == :(-1//3*b^-5//2*(b*c+-1*a*d)^-1//2*(-3*a*d+2*b*c)*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2)+1//3*b^-2*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1*(-3*a*d+2*b*c)+1//3*a*b^-1*(a+b*x^3)^-1*(c+d*x^3)^3//2*(b*c+-1*a*d)^-1)
@test integrate(x^2*(a+b*x^3)^-2*(c+d*x^3)^(1/2), x) == :(-1//3*b^-1*(a+b*x^3)^-1*(c+d*x^3)^(1/2)+-1//3*d*b^-3//2*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-1*(a+b*x^3)^-2*(c+d*x^3)^(1/2), x) == :(-2//3*a^-2*c^(1/2)*arctanh(c^-1//2*(c+d*x^3)^(1/2))+1//3*a^-1*(a+b*x^3)^-1*(c+d*x^3)^(1/2)+1//3*a^-2*b^-1//2*(b*c+-1*a*d)^-1//2*(-1*a*d+2*b*c)*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-4*(a+b*x^3)^-2*(c+d*x^3)^(1/2), x) == :(-2//3*b*a^-2*(a+b*x^3)^-1*(c+d*x^3)^(1/2)+-1//3*a^-1*x^-3*(a+b*x^3)^-1*(c+d*x^3)^(1/2)+1//3*a^-3*c^-1//2*(-1*a*d+4*b*c)*arctanh(c^-1//2*(c+d*x^3)^(1/2))+-1//3*a^-3*b^(1/2)*(b*c+-1*a*d)^-1//2*(-3*a*d+4*b*c)*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^8*(a+b*x^3)^-2*(c+d*x^3)^3//2, x) == :(2//15*b^-2*d^-1*(c+d*x^3)^5//2+-1//3*a*b^-4*(c+d*x^3)^(1/2)*(-7*a*d+4*b*c)+-1//3*a^2*b^-2*(a+b*x^3)^-1*(c+d*x^3)^5//2*(b*c+-1*a*d)^-1+-1//9*a*b^-3*(c+d*x^3)^3//2*(b*c+-1*a*d)^-1*(-7*a*d+4*b*c)+1//3*a*b^-9//2*(b*c+-1*a*d)^(1/2)*(-7*a*d+4*b*c)*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^5*(a+b*x^3)^-2*(c+d*x^3)^3//2, x) == :(1//3*b^-3*(c+d*x^3)^(1/2)*(-5*a*d+2*b*c)+-1//3*b^-7//2*(b*c+-1*a*d)^(1/2)*(-5*a*d+2*b*c)*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2)+1//9*b^-2*(c+d*x^3)^3//2*(b*c+-1*a*d)^-1*(-5*a*d+2*b*c)+1//3*a*b^-1*(a+b*x^3)^-1*(c+d*x^3)^5//2*(b*c+-1*a*d)^-1)
@test integrate(x^2*(a+b*x^3)^-2*(c+d*x^3)^3//2, x) == :(d*b^-2*(c+d*x^3)^(1/2)+-1//3*b^-1*(a+b*x^3)^-1*(c+d*x^3)^3//2+-1*d*b^-5//2*(b*c+-1*a*d)^(1/2)*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-1*(a+b*x^3)^-2*(c+d*x^3)^3//2, x) == :(-2//3*a^-2*c^3//2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+1//3*a^-1*b^-1*(a+b*x^3)^-1*(c+d*x^3)^(1/2)*(b*c+-1*a*d)+1//3*a^-2*b^-3//2*(b*c+-1*a*d)^(1/2)*(a*d+2*b*c)*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-4*(a+b*x^3)^-2*(c+d*x^3)^3//2, x) == :(-1//3*a^-2*(a+b*x^3)^-1*(c+d*x^3)^(1/2)*(-1*a*d+2*b*c)+1//3*a^-3*c^(1/2)*(-3*a*d+4*b*c)*arctanh(c^-1//2*(c+d*x^3)^(1/2))+-1//3*c*a^-1*x^-3*(a+b*x^3)^-1*(c+d*x^3)^(1/2)+-1//3*a^-3*b^-1//2*(b*c+-1*a*d)^(1/2)*(-1*a*d+4*b*c)*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^8*(a+b*x^3)^-2*(c+d*x^3)^-1//2, x) == :(2//3*b^-2*d^-1*(c+d*x^3)^(1/2)+-1//3*a^2*b^-2*(a+b*x^3)^-1*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1+1//3*a*b^-5//2*(b*c+-1*a*d)^-3//2*(-3*a*d+4*b*c)*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^5*(a+b*x^3)^-2*(c+d*x^3)^-1//2, x) == :(-1//3*b^-3//2*(b*c+-1*a*d)^-3//2*(-1*a*d+2*b*c)*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2)+1//3*a*b^-1*(a+b*x^3)^-1*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1)
@test integrate(x^2*(a+b*x^3)^-2*(c+d*x^3)^-1//2, x) == :(-1*(a+b*x^3)^-1*(c+d*x^3)^(1/2)*(-3*a*d+3*b*c)^-1+1//3*d*b^-1//2*(b*c+-1*a*d)^-3//2*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-1*(a+b*x^3)^-2*(c+d*x^3)^-1//2, x) == :(-2//3*a^-2*c^-1//2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+1//3*b*a^-1*(a+b*x^3)^-1*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1+1//3*a^-2*b^(1/2)*(b*c+-1*a*d)^-3//2*(-3*a*d+2*b*c)*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-4*(a+b*x^3)^-2*(c+d*x^3)^-1//2, x) == :(1//3*a^-3*c^-3//2*(a*d+4*b*c)*arctanh(c^-1//2*(c+d*x^3)^(1/2))+-1//3*a^-1*c^-1*x^-3*(a+b*x^3)^-1*(c+d*x^3)^(1/2)+-1//3*a^-3*b^3//2*(b*c+-1*a*d)^-3//2*(-5*a*d+4*b*c)*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//3*b*a^-2*c^-1*(a+b*x^3)^-1*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1*(-1*a*d+2*b*c))
@test integrate(x^8*(a+b*x^3)^-2*(c+d*x^3)^-3//2, x) == :(-1//3*a^2*b^-2*(a+b*x^3)^-1*(c+d*x^3)^-1//2*(b*c+-1*a*d)^-1+1//3*a*b^-3//2*(b*c+-1*a*d)^-5//2*(-1*a*d+4*b*c)*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2)+1//3*b^-2*d^-1*(c+d*x^3)^-1//2*(b*c+-1*a*d)^-2*(-1*a^2*d^2+-2*b^2*c^2))
@test integrate(x^5*(a+b*x^3)^-2*(c+d*x^3)^-3//2, x) == :(-1//3*b^-1//2*(b*c+-1*a*d)^-5//2*(a*d+2*b*c)*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2)+1//3*b^-1*(c+d*x^3)^-1//2*(b*c+-1*a*d)^-2*(a*d+2*b*c)+1//3*a*b^-1*(a+b*x^3)^-1*(c+d*x^3)^-1//2*(b*c+-1*a*d)^-1)
@test integrate(x^2*(a+b*x^3)^-2*(c+d*x^3)^-3//2, x) == :(-1*d*(c+d*x^3)^-1//2*(b*c+-1*a*d)^-2+-1*(a+b*x^3)^-1*(c+d*x^3)^-1//2*(-3*a*d+3*b*c)^-1+d*b^(1/2)*(b*c+-1*a*d)^-5//2*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-1*(a+b*x^3)^-2*(c+d*x^3)^-3//2, x) == :(-2//3*a^-2*c^-3//2*arctanh(c^-1//2*(c+d*x^3)^(1/2))+1//3*b*a^-1*(a+b*x^3)^-1*(c+d*x^3)^-1//2*(b*c+-1*a*d)^-1+1//3*a^-2*b^3//2*(b*c+-1*a*d)^-5//2*(-5*a*d+2*b*c)*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2)+1//3*d*a^-1*c^-1*(c+d*x^3)^-1//2*(b*c+-1*a*d)^-2*(b*c+2*a*d))
@test integrate(x^-4*(a+b*x^3)^-2*(c+d*x^3)^-3//2, x) == :(1//3*a^-3*c^-5//2*(3*a*d+4*b*c)*arctanh(c^-1//2*(c+d*x^3)^(1/2))+-1//3*a^-1*c^-1*x^-3*(a+b*x^3)^-1*(c+d*x^3)^-1//2+-1//3*a^-3*b^5//2*(b*c+-1*a*d)^-5//2*(-7*a*d+4*b*c)*arctanh(b^(1/2)*(c+d*x^3)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//3*d*a^-2*c^-2*(c+d*x^3)^-1//2*(b*c+-1*a*d)^-2*(2*b^2*c^2+3*a^2*d^2+-2*a*b*c*d)+-1//3*b*a^-2*c^-1*(a+b*x^3)^-1*(c+d*x^3)^-1//2*(b*c+-1*a*d)^-1*(-1*a*d+2*b*c))
@test integrate(x^5*(a+b*x^3)^-1//2*(c+d*x^3)^-1//2, x) == :(-1//3*b^-3//2*d^-3//2*(a*d+b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x^3)^(1/2)*(c+d*x^3)^-1//2)+1//3*b^-1*d^-1*(a+b*x^3)^(1/2)*(c+d*x^3)^(1/2))
@test integrate(x^2*(a+b*x^3)^-1//2*(c+d*x^3)^-1//2, x) == :(2//3*b^-1//2*d^-1//2*arctanh(b^-1//2*d^(1/2)*(a+b*x^3)^(1/2)*(c+d*x^3)^-1//2))
@test integrate(x^-1*(a+b*x^3)^-1//2*(c+d*x^3)^-1//2, x) == :(-2//3*a^-1//2*c^-1//2*arctanh(a^-1//2*c^(1/2)*(a+b*x^3)^(1/2)*(c+d*x^3)^-1//2))
@test integrate(x^-4*(a+b*x^3)^-1//2*(c+d*x^3)^-1//2, x) == :(1//3*a^-3//2*c^-3//2*(a*d+b*c)*arctanh(a^-1//2*c^(1/2)*(a+b*x^3)^(1/2)*(c+d*x^3)^-1//2)+-1//3*a^-1*c^-1*x^-3*(a+b*x^3)^(1/2)*(c+d*x^3)^(1/2))
@test integrate((e*x)^7//2*(a+b*x^3)^(1/2)*(A+B*x^3), x) == :(-1//24*a^2*b^-5//2*e^7//2*(-1*B*a+2*A*b)*arctanh(b^(1/2)*e^-3//2*(e*x)^3//2*(a+b*x^3)^-1//2)+1//9*B*b^-1*e^-1*(e*x)^9//2*(a+b*x^3)^3//2+1//12*b^-1*e^-1*(e*x)^9//2*(a+b*x^3)^(1/2)*(-1*B*a+2*A*b)+1//24*a*b^-2*e^2*(e*x)^3//2*(a+b*x^3)^(1/2)*(-1*B*a+2*A*b))
@test integrate((e*x)^5//2*(a+b*x^3)^(1/2)*(A+B*x^3), x) == :(1//8*B*b^-1*e^-1*(e*x)^7//2*(a+b*x^3)^3//2+1//80*b^-1*e^-1*(e*x)^7//2*(a+b*x^3)^(1/2)*(-7*B*a+16*A*b)+3//320*a*b^-2*e^2*(e*x)^(1/2)*(a+b*x^3)^(1/2)*(-7*B*a+16*A*b)+-1//640*3^3//4*a^5//3*b^-2*e^2*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-7*B*a+16*A*b)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((e*x)^3//2*(a+b*x^3)^(1/2)*(A+B*x^3), x) == :(1//7*B*b^-1*e^-1*(e*x)^5//2*(a+b*x^3)^3//2+1//56*b^-1*e^-1*(e*x)^5//2*(a+b*x^3)^(1/2)*(-5*B*a+14*A*b)+1//112*a*e*b^-5//3*(e*x)^(1/2)*(a+b*x^3)^(1/2)*(a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(3+3*3^(1/2))*(-5*B*a+14*A*b)+-3//112*e*3^1//4*a^4//3*b^-5//3*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-5*B*a+14*A*b)*Elliptic.E(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-1//224*e*3^3//4*a^4//3*b^-5//3*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(1+-1*3^(1/2))*(a^1//3+x*b^1//3)*(-5*B*a+14*A*b)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((e*x)^(1/2)*(a+b*x^3)^(1/2)*(A+B*x^3), x) == :(1//6*B*b^-1*e^-1*(e*x)^3//2*(a+b*x^3)^3//2+1//12*a*b^-3//2*e^(1/2)*(-1*B*a+4*A*b)*arctanh(b^(1/2)*e^-3//2*(e*x)^3//2*(a+b*x^3)^-1//2)+1//12*b^-1*e^-1*(e*x)^3//2*(a+b*x^3)^(1/2)*(-1*B*a+4*A*b))
@test integrate((e*x)^-1//2*(a+b*x^3)^(1/2)*(A+B*x^3), x) == :(1//5*B*b^-1*e^-1*(e*x)^(1/2)*(a+b*x^3)^3//2+1//20*b^-1*e^-1*(e*x)^(1/2)*(a+b*x^3)^(1/2)*(-1*B*a+10*A*b)+1//40*3^3//4*a^2//3*b^-1*e^-1*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-1*B*a+10*A*b)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((e*x)^-3//2*(a+b*x^3)^(1/2)*(A+B*x^3), x) == :(-2*A*a^-1*e^-1*(e*x)^-1//2*(a+b*x^3)^3//2+1//4*a^-1*e^-4*(e*x)^5//2*(a+b*x^3)^(1/2)*(B*a+8*A*b)+1//8*b^-2//3*e^-2*(e*x)^(1/2)*(a+b*x^3)^(1/2)*(a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(3+3*3^(1/2))*(B*a+8*A*b)+-3//8*3^1//4*a^1//3*b^-2//3*e^-2*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(B*a+8*A*b)*Elliptic.E(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-1//16*3^3//4*a^1//3*b^-2//3*e^-2*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(1+-1*3^(1/2))*(a^1//3+x*b^1//3)*(B*a+8*A*b)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((e*x)^-5//2*(a+b*x^3)^(1/2)*(A+B*x^3), x) == :(1//3*b^-1//2*e^-5//2*(B*a+2*A*b)*arctanh(b^(1/2)*e^-3//2*(e*x)^3//2*(a+b*x^3)^-1//2)+-2//3*A*a^-1*e^-1*(e*x)^-3//2*(a+b*x^3)^3//2+1//3*a^-1*e^-4*(e*x)^3//2*(a+b*x^3)^(1/2)*(B*a+2*A*b))
@test integrate((e*x)^-7//2*(a+b*x^3)^(1/2)*(A+B*x^3), x) == :(-2//5*A*a^-1*e^-1*(e*x)^-5//2*(a+b*x^3)^3//2+1//10*a^-1*e^-4*(e*x)^(1/2)*(a+b*x^3)^(1/2)*(4*A*b+5*B*a)+1//20*3^3//4*a^-1//3*e^-4*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(4*A*b+5*B*a)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate(x^-9//2*(a+b*x^3)^(1/2)*(A+B*x^3), x) == :(-2//7*A*a^-1*x^-7//2*(a+b*x^3)^3//2+-1//7*a^-1*x^-1//2*(a+b*x^3)^(1/2)*(4*A*b+14*B*a)+1//7*a^-1*b^1//3*x^(1/2)*(a+b*x^3)^(1/2)*(a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(3+3*3^(1/2))*(2*A*b+7*B*a)+-3//7*3^1//4*a^-2//3*b^1//3*x^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(2*A*b+7*B*a)*Elliptic.E(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-1//14*3^3//4*a^-2//3*b^1//3*x^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(1+-1*3^(1/2))*(a^1//3+x*b^1//3)*(2*A*b+7*B*a)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate(x^-11//2*(a+b*x^3)^(1/2)*(A+B*x^3), x) == :(-2//3*B*x^-3//2*(a+b*x^3)^(1/2)+2//3*B*b^(1/2)*arctanh(b^(1/2)*x^3//2*(a+b*x^3)^-1//2)+-2//9*A*a^-1*x^-9//2*(a+b*x^3)^3//2)
@test integrate(x^-13//2*(a+b*x^3)^(1/2)*(A+B*x^3), x) == :(-2//11*A*a^-1*x^-11//2*(a+b*x^3)^3//2+1//55*a^-1*x^-5//2*(a+b*x^3)^(1/2)*(-22*B*a+4*A*b)+-1//55*b*3^3//4*a^-4//3*x^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-11*B*a+2*A*b)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((e*x)^7//2*(a+b*x^3)^3//2*(A+B*x^3), x) == :(-1//192*a^3*b^-5//2*e^7//2*(-3*B*a+8*A*b)*arctanh(b^(1/2)*e^-3//2*(e*x)^3//2*(a+b*x^3)^-1//2)+1//12*B*b^-1*e^-1*(e*x)^9//2*(a+b*x^3)^5//2+1//72*b^-1*e^-1*(e*x)^9//2*(a+b*x^3)^3//2*(-3*B*a+8*A*b)+1//96*a*b^-1*e^-1*(e*x)^9//2*(a+b*x^3)^(1/2)*(-3*B*a+8*A*b)+1//192*a^2*b^-2*e^2*(e*x)^3//2*(a+b*x^3)^(1/2)*(-3*B*a+8*A*b))
@test integrate((e*x)^5//2*(a+b*x^3)^3//2*(A+B*x^3), x) == :(1//11*B*b^-1*e^-1*(e*x)^7//2*(a+b*x^3)^5//2+1//176*b^-1*e^-1*(e*x)^7//2*(a+b*x^3)^3//2*(-7*B*a+22*A*b)+9//1760*a*b^-1*e^-1*(e*x)^7//2*(a+b*x^3)^(1/2)*(-7*B*a+22*A*b)+27//7040*a^2*b^-2*e^2*(e*x)^(1/2)*(a+b*x^3)^(1/2)*(-7*B*a+22*A*b)+-9//14080*3^3//4*a^8//3*b^-2*e^2*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-7*B*a+22*A*b)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((e*x)^3//2*(a+b*x^3)^3//2*(A+B*x^3), x) == :(1//10*B*b^-1*e^-1*(e*x)^5//2*(a+b*x^3)^5//2+1//28*b^-1*e^-1*(e*x)^5//2*(a+b*x^3)^3//2*(-1*B*a+4*A*b)+9//224*a*b^-1*e^-1*(e*x)^5//2*(a+b*x^3)^(1/2)*(-1*B*a+4*A*b)+1//448*e*a^2*b^-5//3*(e*x)^(1/2)*(a+b*x^3)^(1/2)*(a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(27+27*3^(1/2))*(-1*B*a+4*A*b)+-27//448*e*3^1//4*a^7//3*b^-5//3*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-1*B*a+4*A*b)*Elliptic.E(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-9//896*e*3^3//4*a^7//3*b^-5//3*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(1+-1*3^(1/2))*(a^1//3+x*b^1//3)*(-1*B*a+4*A*b)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((e*x)^(1/2)*(a+b*x^3)^3//2*(A+B*x^3), x) == :(1//9*B*b^-1*e^-1*(e*x)^3//2*(a+b*x^3)^5//2+1//24*a^2*b^-3//2*e^(1/2)*(-1*B*a+6*A*b)*arctanh(b^(1/2)*e^-3//2*(e*x)^3//2*(a+b*x^3)^-1//2)+1//36*b^-1*e^-1*(e*x)^3//2*(a+b*x^3)^3//2*(-1*B*a+6*A*b)+1//24*a*b^-1*e^-1*(e*x)^3//2*(a+b*x^3)^(1/2)*(-1*B*a+6*A*b))
@test integrate((e*x)^-1//2*(a+b*x^3)^3//2*(A+B*x^3), x) == :(1//8*B*b^-1*e^-1*(e*x)^(1/2)*(a+b*x^3)^5//2+1//80*b^-1*e^-1*(e*x)^(1/2)*(a+b*x^3)^3//2*(-1*B*a+16*A*b)+9//320*a*b^-1*e^-1*(e*x)^(1/2)*(a+b*x^3)^(1/2)*(-1*B*a+16*A*b)+9//640*3^3//4*a^5//3*b^-1*e^-1*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-1*B*a+16*A*b)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((e*x)^-3//2*(a+b*x^3)^3//2*(A+B*x^3), x) == :(1//56*e^-4*(e*x)^5//2*(a+b*x^3)^(1/2)*(9*B*a+126*A*b)+-2*A*a^-1*e^-1*(e*x)^-1//2*(a+b*x^3)^5//2+1//7*a^-1*e^-4*(e*x)^5//2*(a+b*x^3)^3//2*(B*a+14*A*b)+1//112*a*b^-2//3*e^-2*(e*x)^(1/2)*(a+b*x^3)^(1/2)*(a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(27+27*3^(1/2))*(B*a+14*A*b)+-27//112*3^1//4*a^4//3*b^-2//3*e^-2*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(B*a+14*A*b)*Elliptic.E(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-9//224*3^3//4*a^4//3*b^-2//3*e^-2*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(1+-1*3^(1/2))*(a^1//3+x*b^1//3)*(B*a+14*A*b)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((e*x)^-5//2*(a+b*x^3)^3//2*(A+B*x^3), x) == :(1//4*e^-4*(e*x)^3//2*(a+b*x^3)^(1/2)*(B*a+4*A*b)+-2//3*A*a^-1*e^-1*(e*x)^-3//2*(a+b*x^3)^5//2+1//4*a*b^-1//2*e^-5//2*(B*a+4*A*b)*arctanh(b^(1/2)*e^-3//2*(e*x)^3//2*(a+b*x^3)^-1//2)+1//6*a^-1*e^-4*(e*x)^3//2*(a+b*x^3)^3//2*(B*a+4*A*b))
@test integrate((e*x)^-7//2*(a+b*x^3)^3//2*(A+B*x^3), x) == :(1//20*e^-4*(e*x)^(1/2)*(a+b*x^3)^(1/2)*(9*B*a+18*A*b)+-2//5*A*a^-1*e^-1*(e*x)^-5//2*(a+b*x^3)^5//2+1//5*a^-1*e^-4*(e*x)^(1/2)*(a+b*x^3)^3//2*(B*a+2*A*b)+9//40*3^3//4*a^2//3*e^-4*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(B*a+2*A*b)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((e*x)^7//2*(a+b*x^3)^5//2*(A+B*x^3), x) == :(-1//384*a^4*b^-5//2*e^7//2*(-3*B*a+10*A*b)*arctanh(b^(1/2)*e^-3//2*(e*x)^3//2*(a+b*x^3)^-1//2)+1//15*B*b^-1*e^-1*(e*x)^9//2*(a+b*x^3)^7//2+1//120*b^-1*e^-1*(e*x)^9//2*(a+b*x^3)^5//2*(-3*B*a+10*A*b)+1//144*a*b^-1*e^-1*(e*x)^9//2*(a+b*x^3)^3//2*(-3*B*a+10*A*b)+1//192*a^2*b^-1*e^-1*(e*x)^9//2*(a+b*x^3)^(1/2)*(-3*B*a+10*A*b)+1//384*a^3*b^-2*e^2*(e*x)^3//2*(a+b*x^3)^(1/2)*(-3*B*a+10*A*b))
@test integrate((e*x)^5//2*(a+b*x^3)^5//2*(A+B*x^3), x) == :(1//14*B*b^-1*e^-1*(e*x)^7//2*(a+b*x^3)^7//2+1//44*b^-1*e^-1*(e*x)^7//2*(a+b*x^3)^5//2*(-1*B*a+4*A*b)+15//704*a*b^-1*e^-1*(e*x)^7//2*(a+b*x^3)^3//2*(-1*B*a+4*A*b)+27//1408*a^2*b^-1*e^-1*(e*x)^7//2*(a+b*x^3)^(1/2)*(-1*B*a+4*A*b)+81//5632*a^3*b^-2*e^2*(e*x)^(1/2)*(a+b*x^3)^(1/2)*(-1*B*a+4*A*b)+-27//11264*3^3//4*a^11//3*b^-2*e^2*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-1*B*a+4*A*b)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((e*x)^3//2*(a+b*x^3)^5//2*(A+B*x^3), x) == :(1//13*B*b^-1*e^-1*(e*x)^5//2*(a+b*x^3)^7//2+1//260*b^-1*e^-1*(e*x)^5//2*(a+b*x^3)^5//2*(-5*B*a+26*A*b)+3//728*a*b^-1*e^-1*(e*x)^5//2*(a+b*x^3)^3//2*(-5*B*a+26*A*b)+27//5824*a^2*b^-1*e^-1*(e*x)^5//2*(a+b*x^3)^(1/2)*(-5*B*a+26*A*b)+1//11648*e*a^3*b^-5//3*(e*x)^(1/2)*(a+b*x^3)^(1/2)*(a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(81+81*3^(1/2))*(-5*B*a+26*A*b)+-81//11648*e*3^1//4*a^10//3*b^-5//3*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-5*B*a+26*A*b)*Elliptic.E(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-27//23296*e*3^3//4*a^10//3*b^-5//3*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(1+-1*3^(1/2))*(a^1//3+x*b^1//3)*(-5*B*a+26*A*b)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((e*x)^(1/2)*(a+b*x^3)^5//2*(A+B*x^3), x) == :(1//12*B*b^-1*e^-1*(e*x)^3//2*(a+b*x^3)^7//2+1//72*b^-1*e^-1*(e*x)^3//2*(a+b*x^3)^5//2*(-1*B*a+8*A*b)+5//192*a^3*b^-3//2*e^(1/2)*(-1*B*a+8*A*b)*arctanh(b^(1/2)*e^-3//2*(e*x)^3//2*(a+b*x^3)^-1//2)+5//192*a^2*b^-1*e^-1*(e*x)^3//2*(a+b*x^3)^(1/2)*(-1*B*a+8*A*b)+5//288*a*b^-1*e^-1*(e*x)^3//2*(a+b*x^3)^3//2*(-1*B*a+8*A*b))
@test integrate((e*x)^-1//2*(a+b*x^3)^5//2*(A+B*x^3), x) == :(1//11*B*b^-1*e^-1*(e*x)^(1/2)*(a+b*x^3)^7//2+1//176*b^-1*e^-1*(e*x)^(1/2)*(a+b*x^3)^5//2*(-1*B*a+22*A*b)+3//352*a*b^-1*e^-1*(e*x)^(1/2)*(a+b*x^3)^3//2*(-1*B*a+22*A*b)+27//1408*a^2*b^-1*e^-1*(e*x)^(1/2)*(a+b*x^3)^(1/2)*(-1*B*a+22*A*b)+27//2816*3^3//4*a^8//3*b^-1*e^-1*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-1*B*a+22*A*b)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((e*x)^-3//2*(a+b*x^3)^5//2*(A+B*x^3), x) == :(1//28*e^-4*(e*x)^5//2*(a+b*x^3)^3//2*(3*B*a+60*A*b)+-2*A*a^-1*e^-1*(e*x)^-1//2*(a+b*x^3)^7//2+1//10*a^-1*e^-4*(e*x)^5//2*(a+b*x^3)^5//2*(B*a+20*A*b)+27//224*a*e^-4*(e*x)^5//2*(a+b*x^3)^(1/2)*(B*a+20*A*b)+1//448*a^2*b^-2//3*e^-2*(e*x)^(1/2)*(a+b*x^3)^(1/2)*(a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(81+81*3^(1/2))*(B*a+20*A*b)+-81//448*3^1//4*a^7//3*b^-2//3*e^-2*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(B*a+20*A*b)*Elliptic.E(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-27//896*3^3//4*a^7//3*b^-2//3*e^-2*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(1+-1*3^(1/2))*(a^1//3+x*b^1//3)*(B*a+20*A*b)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((e*x)^-5//2*(a+b*x^3)^5//2*(A+B*x^3), x) == :(1//36*e^-4*(e*x)^3//2*(a+b*x^3)^3//2*(5*B*a+30*A*b)+-2//3*A*a^-1*e^-1*(e*x)^-3//2*(a+b*x^3)^7//2+1//9*a^-1*e^-4*(e*x)^3//2*(a+b*x^3)^5//2*(B*a+6*A*b)+5//24*a*e^-4*(e*x)^3//2*(a+b*x^3)^(1/2)*(B*a+6*A*b)+5//24*a^2*b^-1//2*e^-5//2*(B*a+6*A*b)*arctanh(b^(1/2)*e^-3//2*(e*x)^3//2*(a+b*x^3)^-1//2))
@test integrate((e*x)^-7//2*(a+b*x^3)^5//2*(A+B*x^3), x) == :(1//80*e^-4*(e*x)^(1/2)*(a+b*x^3)^3//2*(15*B*a+48*A*b)+-2//5*A*a^-1*e^-1*(e*x)^-5//2*(a+b*x^3)^7//2+1//40*a^-1*e^-4*(e*x)^(1/2)*(a+b*x^3)^5//2*(5*B*a+16*A*b)+27//320*a*e^-4*(e*x)^(1/2)*(a+b*x^3)^(1/2)*(5*B*a+16*A*b)+27//640*3^3//4*a^5//3*e^-4*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(5*B*a+16*A*b)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((e*x)^7//2*(a+b*x^3)^-1//2*(A+B*x^3), x) == :(-1//12*a*b^-5//2*e^7//2*(-3*B*a+4*A*b)*arctanh(b^(1/2)*e^-3//2*(e*x)^3//2*(a+b*x^3)^-1//2)+1//6*B*b^-1*e^-1*(e*x)^9//2*(a+b*x^3)^(1/2)+1//12*b^-2*e^2*(e*x)^3//2*(a+b*x^3)^(1/2)*(-3*B*a+4*A*b))
@test integrate((e*x)^5//2*(a+b*x^3)^-1//2*(A+B*x^3), x) == :(1//5*B*b^-1*e^-1*(e*x)^7//2*(a+b*x^3)^(1/2)+1//20*b^-2*e^2*(e*x)^(1/2)*(a+b*x^3)^(1/2)*(-7*B*a+10*A*b)+-1//120*3^3//4*a^2//3*b^-2*e^2*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-7*B*a+10*A*b)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((e*x)^3//2*(a+b*x^3)^-1//2*(A+B*x^3), x) == :(1//4*B*b^-1*e^-1*(e*x)^5//2*(a+b*x^3)^(1/2)+1//8*e*b^-5//3*(e*x)^(1/2)*(a+b*x^3)^(1/2)*(a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(1+3^(1/2))*(-5*B*a+8*A*b)+-1//8*e*3^1//4*a^1//3*b^-5//3*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-5*B*a+8*A*b)*Elliptic.E(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-1//48*e*3^3//4*a^1//3*b^-5//3*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(1+-1*3^(1/2))*(a^1//3+x*b^1//3)*(-5*B*a+8*A*b)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((e*x)^(1/2)*(a+b*x^3)^-1//2*(A+B*x^3), x) == :(1//3*b^-3//2*e^(1/2)*(-1*B*a+2*A*b)*arctanh(b^(1/2)*e^-3//2*(e*x)^3//2*(a+b*x^3)^-1//2)+1//3*B*b^-1*e^-1*(e*x)^3//2*(a+b*x^3)^(1/2))
@test integrate((e*x)^-1//2*(a+b*x^3)^-1//2*(A+B*x^3), x) == :((1/2)*B*b^-1*e^-1*(e*x)^(1/2)*(a+b*x^3)^(1/2)+1//12*3^3//4*a^-1//3*b^-1*e^-1*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-1*B*a+4*A*b)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((e*x)^-3//2*(a+b*x^3)^-1//2*(A+B*x^3), x) == :(-2*A*a^-1*e^-1*(e*x)^-1//2*(a+b*x^3)^(1/2)+a^-1*b^-2//3*e^-2*(e*x)^(1/2)*(a+b*x^3)^(1/2)*(a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(1+3^(1/2))*(B*a+2*A*b)+-1*3^1//4*a^-2//3*b^-2//3*e^-2*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(B*a+2*A*b)*Elliptic.E(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-1//6*3^3//4*a^-2//3*b^-2//3*e^-2*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(1+-1*3^(1/2))*(a^1//3+x*b^1//3)*(B*a+2*A*b)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((e*x)^-5//2*(a+b*x^3)^-1//2*(A+B*x^3), x) == :(2//3*B*b^-1//2*e^-5//2*arctanh(b^(1/2)*e^-3//2*(e*x)^3//2*(a+b*x^3)^-1//2)+-2//3*A*a^-1*e^-1*(e*x)^-3//2*(a+b*x^3)^(1/2))
@test integrate((e*x)^-7//2*(a+b*x^3)^-1//2*(A+B*x^3), x) == :(-2//5*A*a^-1*e^-1*(e*x)^-5//2*(a+b*x^3)^(1/2)+-1//15*3^3//4*a^-4//3*e^-4*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-5*B*a+2*A*b)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((e*x)^7//2*(a+b*x^3)^-3//2*(A+B*x^3), x) == :(1//3*b^-5//2*e^7//2*(-3*B*a+2*A*b)*arctanh(b^(1/2)*e^-3//2*(e*x)^3//2*(a+b*x^3)^-1//2)+-1//3*b^-2*e^2*(e*x)^3//2*(a+b*x^3)^-1//2*(-3*B*a+2*A*b)+1//3*B*b^-1*e^-1*(e*x)^9//2*(a+b*x^3)^-1//2)
@test integrate((e*x)^5//2*(a+b*x^3)^-3//2*(A+B*x^3), x) == :((1/2)*B*b^-1*e^-1*(e*x)^7//2*(a+b*x^3)^-1//2+-1//6*b^-2*e^2*(e*x)^(1/2)*(a+b*x^3)^-1//2*(-7*B*a+4*A*b)+1//36*3^3//4*a^-1//3*b^-2*e^2*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-7*B*a+4*A*b)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((e*x)^3//2*(a+b*x^3)^-3//2*(A+B*x^3), x) == :(1//3*a^-1*b^-1*e^-1*(e*x)^5//2*(a+b*x^3)^-1//2*(-2*B*a+2*A*b)+-1//3*e*a^-1*b^-5//3*(e*x)^(1/2)*(a+b*x^3)^(1/2)*(a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(1+3^(1/2))*(-5*B*a+2*A*b)+1//3*e*3^1//4*a^-2//3*b^-5//3*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-5*B*a+2*A*b)*Elliptic.E(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+1//18*e*3^3//4*a^-2//3*b^-5//3*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(1+-1*3^(1/2))*(a^1//3+x*b^1//3)*(-5*B*a+2*A*b)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((e*x)^(1/2)*(a+b*x^3)^-3//2*(A+B*x^3), x) == :(2//3*B*b^-3//2*e^(1/2)*arctanh(b^(1/2)*e^-3//2*(e*x)^3//2*(a+b*x^3)^-1//2)+1//3*a^-1*b^-1*e^-1*(e*x)^3//2*(a+b*x^3)^-1//2*(-2*B*a+2*A*b))
@test integrate((e*x)^-1//2*(a+b*x^3)^-3//2*(A+B*x^3), x) == :(1//3*a^-1*b^-1*e^-1*(e*x)^(1/2)*(a+b*x^3)^-1//2*(-2*B*a+2*A*b)+1//9*3^3//4*a^-4//3*b^-1*e^-1*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(B*a+2*A*b)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((e*x)^-3//2*(a+b*x^3)^-3//2*(A+B*x^3), x) == :(-2*A*a^-1*e^-1*(e*x)^-1//2*(a+b*x^3)^-1//2+-1//3*a^-2*e^-4*(e*x)^5//2*(a+b*x^3)^-1//2*(-2*B*a+8*A*b)+1//3*a^-2*b^-2//3*e^-2*(e*x)^(1/2)*(a+b*x^3)^(1/2)*(a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(2+2*3^(1/2))*(-1*B*a+4*A*b)+-1//3*3^1//4*a^-5//3*b^-2//3*e^-2*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-2*B*a+8*A*b)*Elliptic.E(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-1//9*3^3//4*a^-5//3*b^-2//3*e^-2*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(1+-1*3^(1/2))*(a^1//3+x*b^1//3)*(-1*B*a+4*A*b)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((e*x)^-5//2*(a+b*x^3)^-3//2*(A+B*x^3), x) == :(-2//3*A*a^-1*e^-1*(e*x)^-3//2*(a+b*x^3)^-1//2+-1//3*a^-2*e^-4*(e*x)^3//2*(a+b*x^3)^-1//2*(-2*B*a+4*A*b))
@test integrate((e*x)^-7//2*(a+b*x^3)^-3//2*(A+B*x^3), x) == :(-2//5*A*a^-1*e^-1*(e*x)^-5//2*(a+b*x^3)^-1//2+-1//15*a^-2*e^-4*(e*x)^(1/2)*(a+b*x^3)^-1//2*(-10*B*a+16*A*b)+-1//45*3^3//4*a^-7//3*e^-4*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-10*B*a+16*A*b)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((e*x)^7//2*(a+b*x^3)^-5//2*(A+B*x^3), x) == :(2//3*B*b^-5//2*e^7//2*arctanh(b^(1/2)*e^-3//2*(e*x)^3//2*(a+b*x^3)^-1//2)+-2//3*B*b^-2*e^2*(e*x)^3//2*(a+b*x^3)^-1//2+1//9*a^-1*b^-1*e^-1*(e*x)^9//2*(a+b*x^3)^-3//2*(-2*B*a+2*A*b))
@test integrate((e*x)^5//2*(a+b*x^3)^-5//2*(A+B*x^3), x) == :(-1//27*a^-1*b^-2*e^2*(e*x)^(1/2)*(a+b*x^3)^-1//2*(4*A*b+14*B*a)+1//9*a^-1*b^-1*e^-1*(e*x)^7//2*(a+b*x^3)^-3//2*(-2*B*a+2*A*b)+1//81*3^3//4*a^-4//3*b^-2*e^2*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(2*A*b+7*B*a)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((e*x)^3//2*(a+b*x^3)^-5//2*(A+B*x^3), x) == :(1//9*a^-1*b^-1*e^-1*(e*x)^5//2*(a+b*x^3)^-3//2*(-2*B*a+2*A*b)+1//27*a^-2*b^-1*e^-1*(e*x)^5//2*(a+b*x^3)^-1//2*(8*A*b+10*B*a)+-1//27*e*a^-2*b^-5//3*(e*x)^(1/2)*(a+b*x^3)^(1/2)*(a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(2+2*3^(1/2))*(4*A*b+5*B*a)+1//27*e*3^1//4*a^-5//3*b^-5//3*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(8*A*b+10*B*a)*Elliptic.E(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+1//81*e*3^3//4*a^-5//3*b^-5//3*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(1+-1*3^(1/2))*(a^1//3+x*b^1//3)*(4*A*b+5*B*a)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((e*x)^(1/2)*(a+b*x^3)^-5//2*(A+B*x^3), x) == :(1//9*a^-1*b^-1*e^-1*(e*x)^3//2*(a+b*x^3)^-3//2*(-2*B*a+2*A*b)+1//9*a^-2*b^-1*e^-1*(e*x)^3//2*(a+b*x^3)^-1//2*(2*B*a+4*A*b))
@test integrate((e*x)^-1//2*(a+b*x^3)^-5//2*(A+B*x^3), x) == :(1//9*a^-1*b^-1*e^-1*(e*x)^(1/2)*(a+b*x^3)^-3//2*(-2*B*a+2*A*b)+1//27*a^-2*b^-1*e^-1*(e*x)^(1/2)*(a+b*x^3)^-1//2*(2*B*a+16*A*b)+1//81*3^3//4*a^-7//3*b^-1*e^-1*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(2*B*a+16*A*b)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((e*x)^-3//2*(a+b*x^3)^-5//2*(A+B*x^3), x) == :(-2*A*a^-1*e^-1*(e*x)^-1//2*(a+b*x^3)^-3//2+-1//9*a^-2*e^-4*(e*x)^5//2*(a+b*x^3)^-3//2*(-2*B*a+20*A*b)+-1//27*a^-3*e^-4*(e*x)^5//2*(a+b*x^3)^-1//2*(-8*B*a+80*A*b)+1//27*a^-3*b^-2//3*e^-2*(e*x)^(1/2)*(a+b*x^3)^(1/2)*(a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(8+8*3^(1/2))*(-1*B*a+10*A*b)+-1//27*3^1//4*a^-8//3*b^-2//3*e^-2*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-8*B*a+80*A*b)*Elliptic.E(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-1//81*3^3//4*a^-8//3*b^-2//3*e^-2*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(4+-4*3^(1/2))*(a^1//3+x*b^1//3)*(-1*B*a+10*A*b)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((e*x)^-5//2*(a+b*x^3)^-5//2*(A+B*x^3), x) == :(-2//3*A*a^-1*e^-1*(e*x)^-3//2*(a+b*x^3)^-3//2+-1//9*a^-3*e^-4*(e*x)^3//2*(a+b*x^3)^-1//2*(-4*B*a+16*A*b)+-1//9*a^-2*e^-4*(e*x)^3//2*(a+b*x^3)^-3//2*(-2*B*a+8*A*b))
@test integrate((e*x)^-7//2*(a+b*x^3)^-5//2*(A+B*x^3), x) == :(-2//5*A*a^-1*e^-1*(e*x)^-5//2*(a+b*x^3)^-3//2+-1//45*a^-2*e^-4*(e*x)^(1/2)*(a+b*x^3)^-3//2*(-10*B*a+28*A*b)+-1//135*a^-3*e^-4*(e*x)^(1/2)*(a+b*x^3)^-1//2*(-80*B*a+224*A*b)+-1//405*3^3//4*a^-10//3*e^-4*(e*x)^(1/2)*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-80*B*a+224*A*b)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate(x^14*(1+x^3)^-1*(1+-1*x^3)^-1//3, x) == :(-1//4*(1+-1*x^3)^8//3+1//11*(1+-1*x^3)^11//3+2//5*(1+-1*x^3)^5//3+-1//12*2^2//3*log(1+x^3)+1//4*2^2//3*log(2^1//3+-1*(1+-1*x^3)^1//3)+1//6*2^2//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+2^2//3*(1+-1*x^3)^1//3)))
@test integrate(x^11*(1+x^3)^-1*(1+-1*x^3)^-1//3, x) == :(-1//2*(1+-1*x^3)^2//3+-1//8*(1+-1*x^3)^8//3+1//5*(1+-1*x^3)^5//3+-1//4*2^2//3*log(2^1//3+-1*(1+-1*x^3)^1//3)+1//12*2^2//3*log(1+x^3)+-1//6*2^2//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+2^2//3*(1+-1*x^3)^1//3)))
@test integrate(x^8*(1+x^3)^-1*(1+-1*x^3)^-1//3, x) == :(1//5*(1+-1*x^3)^5//3+-1//12*2^2//3*log(1+x^3)+1//4*2^2//3*log(2^1//3+-1*(1+-1*x^3)^1//3)+1//6*2^2//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+2^2//3*(1+-1*x^3)^1//3)))
@test integrate(x^5*(1+x^3)^-1*(1+-1*x^3)^-1//3, x) == :(-1//2*(1+-1*x^3)^2//3+-1//4*2^2//3*log(2^1//3+-1*(1+-1*x^3)^1//3)+1//12*2^2//3*log(1+x^3)+-1//6*2^2//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+2^2//3*(1+-1*x^3)^1//3)))
@test integrate(x^2*(1+x^3)^-1*(1+-1*x^3)^-1//3, x) == :(-1//12*2^2//3*log(1+x^3)+1//4*2^2//3*log(2^1//3+-1*(1+-1*x^3)^1//3)+1//6*2^2//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+2^2//3*(1+-1*x^3)^1//3)))
@test integrate(x^-1*(1+x^3)^-1*(1+-1*x^3)^-1//3, x) == :((1/2)*log(1+-1*(1+-1*x^3)^1//3)+-1//2*log(x)+-1//4*2^2//3*log(2^1//3+-1*(1+-1*x^3)^1//3)+1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*(1+-1*x^3)^1//3))+1//12*2^2//3*log(1+x^3)+-1//6*2^2//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+2^2//3*(1+-1*x^3)^1//3)))
@test integrate(x^-4*(1+x^3)^-1*(1+-1*x^3)^-1//3, x) == :(-1//3*log(1+-1*(1+-1*x^3)^1//3)+1//3*log(x)+-2//9*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*(1+-1*x^3)^1//3))+-1//3*x^-3*(1+-1*x^3)^2//3+-1//12*2^2//3*log(1+x^3)+1//4*2^2//3*log(2^1//3+-1*(1+-1*x^3)^1//3)+1//6*2^2//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+2^2//3*(1+-1*x^3)^1//3)))
@test integrate(x^6*(1+x^3)^-1*(1+-1*x^3)^-1//3, x) == :(-2//9*log(1+x*(1+-1*x^3)^-1//3)+1//9*log(1+x^2*(1+-1*x^3)^-2//3+-1*x*(1+-1*x^3)^-1//3)+-1//3*x*(1+-1*x^3)^2//3+-1//12*2^2//3*log(1+2^2//3*x^2*(1+-1*x^3)^-2//3+-1*x*2^1//3*(1+-1*x^3)^-1//3)+1//6*2^2//3*log(1+x*2^1//3*(1+-1*x^3)^-1//3)+2//9*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x*(1+-1*x^3)^-1//3))+-1//6*2^2//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x*2^1//3*(1+-1*x^3)^-1//3)))
@test integrate(x^3*(1+x^3)^-1*(1+-1*x^3)^-1//3, x) == :(-1//6*log(1+x^2*(1+-1*x^3)^-2//3+-1*x*(1+-1*x^3)^-1//3)+1//3*log(1+x*(1+-1*x^3)^-1//3)+-1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x*(1+-1*x^3)^-1//3))+-1//6*2^2//3*log(1+x*2^1//3*(1+-1*x^3)^-1//3)+1//12*2^2//3*log(1+2^2//3*x^2*(1+-1*x^3)^-2//3+-1*x*2^1//3*(1+-1*x^3)^-1//3)+1//6*2^2//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x*2^1//3*(1+-1*x^3)^-1//3)))
@test integrate((1+x^3)^-1*(1+-1*x^3)^-1//3, x) == :(-1//12*2^2//3*log(1+2^2//3*x^2*(1+-1*x^3)^-2//3+-1*x*2^1//3*(1+-1*x^3)^-1//3)+1//6*2^2//3*log(1+x*2^1//3*(1+-1*x^3)^-1//3)+-1//6*2^2//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x*2^1//3*(1+-1*x^3)^-1//3)))
@test integrate(x^-3*(1+x^3)^-1*(1+-1*x^3)^-1//3, x) == :(-1//2*x^-2*(1+-1*x^3)^2//3+-1//6*2^2//3*log(1+x*2^1//3*(1+-1*x^3)^-1//3)+1//12*2^2//3*log(1+2^2//3*x^2*(1+-1*x^3)^-2//3+-1*x*2^1//3*(1+-1*x^3)^-1//3)+1//6*2^2//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x*2^1//3*(1+-1*x^3)^-1//3)))
@test integrate(x^-6*(1+x^3)^-1*(1+-1*x^3)^-1//3, x) == :(-1//5*x^-5*(1+-1*x^3)^5//3+-1//12*2^2//3*log(1+2^2//3*x^2*(1+-1*x^3)^-2//3+-1*x*2^1//3*(1+-1*x^3)^-1//3)+1//6*2^2//3*log(1+x*2^1//3*(1+-1*x^3)^-1//3)+-1//6*2^2//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x*2^1//3*(1+-1*x^3)^-1//3)))
@test integrate(x^-9*(1+x^3)^-1*(1+-1*x^3)^-1//3, x) == :(-1//2*x^-2*(1+-1*x^3)^2//3+-1//5*x^-5*(1+-1*x^3)^5//3+-1//6*2^2//3*log(1+x*2^1//3*(1+-1*x^3)^-1//3)+-1//8*x^-8*(1+-1*x^3)^8//3+1//12*2^2//3*log(1+2^2//3*x^2*(1+-1*x^3)^-2//3+-1*x*2^1//3*(1+-1*x^3)^-1//3)+1//6*2^2//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x*2^1//3*(1+-1*x^3)^-1//3)))
@test integrate(x*(1+x^3)^-1*(1+-1*x^3)^-1//3, x) == :(-1//6*2^2//3*log(1+2^1//3*(1+-1*x^3)^-1//3*(1+-1x))+-1//12*2^2//3*log(2^2//3+(1+-1*x^3)^-1//3*(-1+x))+1//12*2^2//3*log(1+2^2//3*(1+-1x)^2*(1+-1*x^3)^-2//3+-1*2^1//3*(1+-1*x^3)^-1//3*(1+-1x))+1//24*2^2//3*log(2*2^1//3+(1+-1x)^2*(1+-1*x^3)^-2//3+2^2//3*(1+-1*x^3)^-1//3*(1+-1x))+1//6*2^2//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*2^1//3*(1+-1*x^3)^-1//3*(1+-1x)))+1//12*2^2//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+2^1//3*(1+-1*x^3)^-1//3*(1+-1x))))
@test integrate(x^11*(1+x^3)^-1*(1+-1*x^3)^-2//3, x) == :(-1*(1+-1*x^3)^1//3+-1//7*(1+-1*x^3)^7//3+1//4*(1+-1*x^3)^4//3+-1//4*2^1//3*log(2^1//3+-1*(1+-1*x^3)^1//3)+1//12*2^1//3*log(1+x^3)+1//6*2^1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+2^2//3*(1+-1*x^3)^1//3)))
@test integrate(x^8*(1+x^3)^-1*(1+-1*x^3)^-2//3, x) == :(1//4*(1+-1*x^3)^4//3+-1//12*2^1//3*log(1+x^3)+1//4*2^1//3*log(2^1//3+-1*(1+-1*x^3)^1//3)+-1//6*2^1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+2^2//3*(1+-1*x^3)^1//3)))
@test integrate(x^5*(1+x^3)^-1*(1+-1*x^3)^-2//3, x) == :(-1*(1+-1*x^3)^1//3+-1//4*2^1//3*log(2^1//3+-1*(1+-1*x^3)^1//3)+1//12*2^1//3*log(1+x^3)+1//6*2^1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+2^2//3*(1+-1*x^3)^1//3)))
@test integrate(x^2*(1+x^3)^-1*(1+-1*x^3)^-2//3, x) == :(-1//12*2^1//3*log(1+x^3)+1//4*2^1//3*log(2^1//3+-1*(1+-1*x^3)^1//3)+-1//6*2^1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+2^2//3*(1+-1*x^3)^1//3)))
@test integrate(x^-1*(1+x^3)^-1*(1+-1*x^3)^-2//3, x) == :((1/2)*log(1+-1*(1+-1*x^3)^1//3)+-1//2*log(x)+-1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*(1+-1*x^3)^1//3))+-1//4*2^1//3*log(2^1//3+-1*(1+-1*x^3)^1//3)+1//12*2^1//3*log(1+x^3)+1//6*2^1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+2^2//3*(1+-1*x^3)^1//3)))
@test integrate(x^-4*(1+x^3)^-1*(1+-1*x^3)^-2//3, x) == :(-1//6*log(1+-1*(1+-1*x^3)^1//3)+1//6*log(x)+-1//3*x^-3*(1+-1*x^3)^1//3+-1//12*2^1//3*log(1+x^3)+1//4*2^1//3*log(2^1//3+-1*(1+-1*x^3)^1//3)+1//9*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*(1+-1*x^3)^1//3))+-1//6*2^1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+2^2//3*(1+-1*x^3)^1//3)))
@test integrate(x^4*(1+x^3)^-1*(1+-1*x^3)^-2//3, x) == :(-1//3*log(1+x*(1+-1*x^3)^-1//3)+1//6*log(1+x^2*(1+-1*x^3)^-2//3+-1*x*(1+-1*x^3)^-1//3)+-1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x*(1+-1*x^3)^-1//3))+-1//12*2^1//3*log(1+2^2//3*x^2*(1+-1*x^3)^-2//3+-1*x*2^1//3*(1+-1*x^3)^-1//3)+1//6*2^1//3*log(1+x*2^1//3*(1+-1*x^3)^-1//3)+1//6*2^1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x*2^1//3*(1+-1*x^3)^-1//3)))
@test integrate(x*(1+x^3)^-1*(1+-1*x^3)^-2//3, x) == :(-1//6*2^1//3*log(1+x*2^1//3*(1+-1*x^3)^-1//3)+1//12*2^1//3*log(1+2^2//3*x^2*(1+-1*x^3)^-2//3+-1*x*2^1//3*(1+-1*x^3)^-1//3)+-1//6*2^1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x*2^1//3*(1+-1*x^3)^-1//3)))
@test integrate(x^-2*(1+x^3)^-1*(1+-1*x^3)^-2//3, x) == :(-1*x^-1*(1+-1*x^3)^1//3+-1//12*2^1//3*log(1+2^2//3*x^2*(1+-1*x^3)^-2//3+-1*x*2^1//3*(1+-1*x^3)^-1//3)+1//6*2^1//3*log(1+x*2^1//3*(1+-1*x^3)^-1//3)+1//6*2^1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x*2^1//3*(1+-1*x^3)^-1//3)))
@test integrate(x^-5*(1+x^3)^-1*(1+-1*x^3)^-2//3, x) == :(-1//4*x^-4*(1+-1*x^3)^4//3+-1//6*2^1//3*log(1+x*2^1//3*(1+-1*x^3)^-1//3)+1//12*2^1//3*log(1+2^2//3*x^2*(1+-1*x^3)^-2//3+-1*x*2^1//3*(1+-1*x^3)^-1//3)+-1//6*2^1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x*2^1//3*(1+-1*x^3)^-1//3)))
@test integrate(x^15*(a+b*x^4)^-1*(c+d*x^4)^-1, x) == :(1//8*b^-1*d^-1*x^8+-1//4*a^3*b^-3*(b*c+-1*a*d)^-1*log(a+b*x^4)+-1//4*b^-2*d^-2*x^4*(a*d+b*c)+1//4*c^3*d^-3*(b*c+-1*a*d)^-1*log(c+d*x^4))
@test integrate(x^11*(a+b*x^4)^-1*(c+d*x^4)^-1, x) == :(1//4*b^-1*d^-1*x^4+-1//4*c^2*d^-2*(b*c+-1*a*d)^-1*log(c+d*x^4)+1//4*a^2*b^-2*(b*c+-1*a*d)^-1*log(a+b*x^4))
@test integrate(x^7*(a+b*x^4)^-1*(c+d*x^4)^-1, x) == :(-1//4*a*b^-1*(b*c+-1*a*d)^-1*log(a+b*x^4)+1//4*c*d^-1*(b*c+-1*a*d)^-1*log(c+d*x^4))
@test integrate(x^3*(a+b*x^4)^-1*(c+d*x^4)^-1, x) == :((-4*a*d+4*b*c)^-1*log(a+b*x^4)+-1*(-4*a*d+4*b*c)^-1*log(c+d*x^4))
@test integrate(x^-1*(a+b*x^4)^-1*(c+d*x^4)^-1, x) == :(a^-1*c^-1*log(x)+-1//4*b*a^-1*(b*c+-1*a*d)^-1*log(a+b*x^4)+1//4*d*c^-1*(b*c+-1*a*d)^-1*log(c+d*x^4))
@test integrate(x^-5*(a+b*x^4)^-1*(c+d*x^4)^-1, x) == :(-1//4*a^-1*c^-1*x^-4+-1*a^-2*c^-2*(a*d+b*c)*log(x)+-1//4*c^-2*d^2*(b*c+-1*a*d)^-1*log(c+d*x^4)+1//4*a^-2*b^2*(b*c+-1*a*d)^-1*log(a+b*x^4))
@test integrate(x^13*(a+b*x^4)^-1*(c+d*x^4)^-1, x) == :(1//6*b^-1*d^-1*x^6+(1/2)*c^5//2*d^-5//2*(b*c+-1*a*d)^-1*arctan(c^-1//2*d^(1/2)*x^2)+-1//2*a^5//2*b^-5//2*(b*c+-1*a*d)^-1*arctan(a^-1//2*b^(1/2)*x^2)+-1//2*b^-2*d^-2*x^2*(a*d+b*c))
@test integrate(x^9*(a+b*x^4)^-1*(c+d*x^4)^-1, x) == :((1/2)*b^-1*d^-1*x^2+(1/2)*a^3//2*b^-3//2*(b*c+-1*a*d)^-1*arctan(a^-1//2*b^(1/2)*x^2)+-1//2*c^3//2*d^-3//2*(b*c+-1*a*d)^-1*arctan(c^-1//2*d^(1/2)*x^2))
@test integrate(x^5*(a+b*x^4)^-1*(c+d*x^4)^-1, x) == :((1/2)*c^(1/2)*d^-1//2*(b*c+-1*a*d)^-1*arctan(c^-1//2*d^(1/2)*x^2)+-1//2*a^(1/2)*b^-1//2*(b*c+-1*a*d)^-1*arctan(a^-1//2*b^(1/2)*x^2))
@test integrate(x*(a+b*x^4)^-1*(c+d*x^4)^-1, x) == :((1/2)*a^-1//2*b^(1/2)*(b*c+-1*a*d)^-1*arctan(a^-1//2*b^(1/2)*x^2)+-1//2*c^-1//2*d^(1/2)*(b*c+-1*a*d)^-1*arctan(c^-1//2*d^(1/2)*x^2))
@test integrate(x^-3*(a+b*x^4)^-1*(c+d*x^4)^-1, x) == :(-1//2*a^-1*c^-1*x^-2+(1/2)*c^-3//2*d^3//2*(b*c+-1*a*d)^-1*arctan(c^-1//2*d^(1/2)*x^2)+-1//2*a^-3//2*b^3//2*(b*c+-1*a*d)^-1*arctan(a^-1//2*b^(1/2)*x^2))
@test integrate(x^-7*(a+b*x^4)^-1*(c+d*x^4)^-1, x) == :(-1//6*a^-1*c^-1*x^-6+(1/2)*a^-2*c^-2*x^-2*(a*d+b*c)+(1/2)*a^-5//2*b^5//2*(b*c+-1*a*d)^-1*arctan(a^-1//2*b^(1/2)*x^2)+-1//2*c^-5//2*d^5//2*(b*c+-1*a*d)^-1*arctan(c^-1//2*d^(1/2)*x^2))
@test integrate(x^8*(a+b*x^4)^-1*(c+d*x^4)^-1, x) == :(x*b^-1*d^-1+-1//4*2^(1/2)*a^5//4*b^-5//4*(b*c+-1*a*d)^-1*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//4*2^(1/2)*c^5//4*d^-5//4*(b*c+-1*a*d)^-1*arctan(1+x*2^(1/2)*c^-1//4*d^1//4)+-1//8*2^(1/2)*a^5//4*b^-5//4*(b*c+-1*a*d)^-1*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+-1//8*2^(1/2)*c^5//4*d^-5//4*(b*c+-1*a*d)^-1*log(c^(1/2)+d^(1/2)*x^2+x*2^(1/2)*c^1//4*d^1//4)+1//4*2^(1/2)*a^5//4*b^-5//4*(b*c+-1*a*d)^-1*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//4*2^(1/2)*c^5//4*d^-5//4*(b*c+-1*a*d)^-1*arctan(1+-1*x*2^(1/2)*c^-1//4*d^1//4)+1//8*2^(1/2)*a^5//4*b^-5//4*(b*c+-1*a*d)^-1*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4)+1//8*2^(1/2)*c^5//4*d^-5//4*(b*c+-1*a*d)^-1*log(c^(1/2)+d^(1/2)*x^2+-1*x*2^(1/2)*c^1//4*d^1//4))
@test integrate(x^6*(a+b*x^4)^-1*(c+d*x^4)^-1, x) == :(-1//4*2^(1/2)*a^3//4*b^-3//4*(b*c+-1*a*d)^-1*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+-1//4*2^(1/2)*c^3//4*d^-3//4*(b*c+-1*a*d)^-1*arctan(1+-1*x*2^(1/2)*c^-1//4*d^1//4)+-1//8*2^(1/2)*a^3//4*b^-3//4*(b*c+-1*a*d)^-1*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+-1//8*2^(1/2)*c^3//4*d^-3//4*(b*c+-1*a*d)^-1*log(c^(1/2)+d^(1/2)*x^2+x*2^(1/2)*c^1//4*d^1//4)+1//4*2^(1/2)*a^3//4*b^-3//4*(b*c+-1*a*d)^-1*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+1//4*2^(1/2)*c^3//4*d^-3//4*(b*c+-1*a*d)^-1*arctan(1+x*2^(1/2)*c^-1//4*d^1//4)+1//8*2^(1/2)*a^3//4*b^-3//4*(b*c+-1*a*d)^-1*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4)+1//8*2^(1/2)*c^3//4*d^-3//4*(b*c+-1*a*d)^-1*log(c^(1/2)+d^(1/2)*x^2+-1*x*2^(1/2)*c^1//4*d^1//4))
@test integrate(x^4*(a+b*x^4)^-1*(c+d*x^4)^-1, x) == :(-1//4*2^(1/2)*a^1//4*b^-1//4*(b*c+-1*a*d)^-1*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+-1//4*2^(1/2)*c^1//4*d^-1//4*(b*c+-1*a*d)^-1*arctan(1+-1*x*2^(1/2)*c^-1//4*d^1//4)+-1//8*2^(1/2)*a^1//4*b^-1//4*(b*c+-1*a*d)^-1*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4)+-1//8*2^(1/2)*c^1//4*d^-1//4*(b*c+-1*a*d)^-1*log(c^(1/2)+d^(1/2)*x^2+-1*x*2^(1/2)*c^1//4*d^1//4)+1//4*2^(1/2)*a^1//4*b^-1//4*(b*c+-1*a*d)^-1*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+1//4*2^(1/2)*c^1//4*d^-1//4*(b*c+-1*a*d)^-1*arctan(1+x*2^(1/2)*c^-1//4*d^1//4)+1//8*2^(1/2)*a^1//4*b^-1//4*(b*c+-1*a*d)^-1*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//8*2^(1/2)*c^1//4*d^-1//4*(b*c+-1*a*d)^-1*log(c^(1/2)+d^(1/2)*x^2+x*2^(1/2)*c^1//4*d^1//4))
@test integrate(x^2*(a+b*x^4)^-1*(c+d*x^4)^-1, x) == :(-1//4*2^(1/2)*a^-1//4*b^1//4*(b*c+-1*a*d)^-1*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//4*2^(1/2)*c^-1//4*d^1//4*(b*c+-1*a*d)^-1*arctan(1+x*2^(1/2)*c^-1//4*d^1//4)+-1//8*2^(1/2)*a^-1//4*b^1//4*(b*c+-1*a*d)^-1*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4)+-1//8*2^(1/2)*c^-1//4*d^1//4*(b*c+-1*a*d)^-1*log(c^(1/2)+d^(1/2)*x^2+-1*x*2^(1/2)*c^1//4*d^1//4)+1//4*2^(1/2)*a^-1//4*b^1//4*(b*c+-1*a*d)^-1*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//4*2^(1/2)*c^-1//4*d^1//4*(b*c+-1*a*d)^-1*arctan(1+-1*x*2^(1/2)*c^-1//4*d^1//4)+1//8*2^(1/2)*a^-1//4*b^1//4*(b*c+-1*a*d)^-1*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//8*2^(1/2)*c^-1//4*d^1//4*(b*c+-1*a*d)^-1*log(c^(1/2)+d^(1/2)*x^2+x*2^(1/2)*c^1//4*d^1//4))
@test integrate((a+b*x^4)^-1*(c+d*x^4)^-1, x) == :(-1//4*2^(1/2)*a^-3//4*b^3//4*(b*c+-1*a*d)^-1*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//4*2^(1/2)*c^-3//4*d^3//4*(b*c+-1*a*d)^-1*arctan(1+x*2^(1/2)*c^-1//4*d^1//4)+-1//8*2^(1/2)*a^-3//4*b^3//4*(b*c+-1*a*d)^-1*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+-1//8*2^(1/2)*c^-3//4*d^3//4*(b*c+-1*a*d)^-1*log(c^(1/2)+d^(1/2)*x^2+x*2^(1/2)*c^1//4*d^1//4)+1//4*2^(1/2)*a^-3//4*b^3//4*(b*c+-1*a*d)^-1*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//4*2^(1/2)*c^-3//4*d^3//4*(b*c+-1*a*d)^-1*arctan(1+-1*x*2^(1/2)*c^-1//4*d^1//4)+1//8*2^(1/2)*a^-3//4*b^3//4*(b*c+-1*a*d)^-1*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4)+1//8*2^(1/2)*c^-3//4*d^3//4*(b*c+-1*a*d)^-1*log(c^(1/2)+d^(1/2)*x^2+-1*x*2^(1/2)*c^1//4*d^1//4))
@test integrate(x^-2*(a+b*x^4)^-1*(c+d*x^4)^-1, x) == :(-1*a^-1*c^-1*x^-1+-1//4*2^(1/2)*a^-5//4*b^5//4*(b*c+-1*a*d)^-1*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+-1//4*2^(1/2)*c^-5//4*d^5//4*(b*c+-1*a*d)^-1*arctan(1+-1*x*2^(1/2)*c^-1//4*d^1//4)+-1//8*2^(1/2)*a^-5//4*b^5//4*(b*c+-1*a*d)^-1*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+-1//8*2^(1/2)*c^-5//4*d^5//4*(b*c+-1*a*d)^-1*log(c^(1/2)+d^(1/2)*x^2+x*2^(1/2)*c^1//4*d^1//4)+1//4*2^(1/2)*a^-5//4*b^5//4*(b*c+-1*a*d)^-1*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+1//4*2^(1/2)*c^-5//4*d^5//4*(b*c+-1*a*d)^-1*arctan(1+x*2^(1/2)*c^-1//4*d^1//4)+1//8*2^(1/2)*a^-5//4*b^5//4*(b*c+-1*a*d)^-1*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4)+1//8*2^(1/2)*c^-5//4*d^5//4*(b*c+-1*a*d)^-1*log(c^(1/2)+d^(1/2)*x^2+-1*x*2^(1/2)*c^1//4*d^1//4))
@test integrate(x^-4*(a+b*x^4)^-1*(c+d*x^4)^-1, x) == :(-1//3*a^-1*c^-1*x^-3+-1//4*2^(1/2)*a^-7//4*b^7//4*(b*c+-1*a*d)^-1*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+-1//4*2^(1/2)*c^-7//4*d^7//4*(b*c+-1*a*d)^-1*arctan(1+-1*x*2^(1/2)*c^-1//4*d^1//4)+-1//8*2^(1/2)*a^-7//4*b^7//4*(b*c+-1*a*d)^-1*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4)+-1//8*2^(1/2)*c^-7//4*d^7//4*(b*c+-1*a*d)^-1*log(c^(1/2)+d^(1/2)*x^2+-1*x*2^(1/2)*c^1//4*d^1//4)+1//4*2^(1/2)*a^-7//4*b^7//4*(b*c+-1*a*d)^-1*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+1//4*2^(1/2)*c^-7//4*d^7//4*(b*c+-1*a*d)^-1*arctan(1+x*2^(1/2)*c^-1//4*d^1//4)+1//8*2^(1/2)*a^-7//4*b^7//4*(b*c+-1*a*d)^-1*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//8*2^(1/2)*c^-7//4*d^7//4*(b*c+-1*a*d)^-1*log(c^(1/2)+d^(1/2)*x^2+x*2^(1/2)*c^1//4*d^1//4))
@test integrate(x^-6*(a+b*x^4)^-1*(c+d*x^4)^-1, x) == :(-1//5*a^-1*c^-1*x^-5+a^-2*c^-2*x^-1*(a*d+b*c)+-1//4*2^(1/2)*a^-9//4*b^9//4*(b*c+-1*a*d)^-1*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//4*2^(1/2)*c^-9//4*d^9//4*(b*c+-1*a*d)^-1*arctan(1+x*2^(1/2)*c^-1//4*d^1//4)+-1//8*2^(1/2)*a^-9//4*b^9//4*(b*c+-1*a*d)^-1*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4)+-1//8*2^(1/2)*c^-9//4*d^9//4*(b*c+-1*a*d)^-1*log(c^(1/2)+d^(1/2)*x^2+-1*x*2^(1/2)*c^1//4*d^1//4)+1//4*2^(1/2)*a^-9//4*b^9//4*(b*c+-1*a*d)^-1*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//4*2^(1/2)*c^-9//4*d^9//4*(b*c+-1*a*d)^-1*arctan(1+-1*x*2^(1/2)*c^-1//4*d^1//4)+1//8*2^(1/2)*a^-9//4*b^9//4*(b*c+-1*a*d)^-1*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//8*2^(1/2)*c^-9//4*d^9//4*(b*c+-1*a*d)^-1*log(c^(1/2)+d^(1/2)*x^2+x*2^(1/2)*c^1//4*d^1//4))
@test integrate(x^7*(a+b*x^4)^-1*(c+d*x^4)^(1/2), x) == :(-1//2*a*b^-2*(c+d*x^4)^(1/2)+1//6*b^-1*d^-1*(c+d*x^4)^3//2+(1/2)*a*b^-5//2*(b*c+-1*a*d)^(1/2)*arctanh(b^(1/2)*(c+d*x^4)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^5*(a+b*x^4)^-1*(c+d*x^4)^(1/2), x) == :(1//4*b^-1*x^2*(c+d*x^4)^(1/2)+-1//2*a^(1/2)*b^-2*(b*c+-1*a*d)^(1/2)*arctan(a^-1//2*x^2*(c+d*x^4)^-1//2*(b*c+-1*a*d)^(1/2))+1//4*b^-2*d^-1//2*(b*c+-2*a*d)*arctanh(d^(1/2)*x^2*(c+d*x^4)^-1//2))
@test integrate(x^3*(a+b*x^4)^-1*(c+d*x^4)^(1/2), x) == :((1/2)*b^-1*(c+d*x^4)^(1/2)+-1//2*b^-3//2*(b*c+-1*a*d)^(1/2)*arctanh(b^(1/2)*(c+d*x^4)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x*(a+b*x^4)^-1*(c+d*x^4)^(1/2), x) == :((1/2)*b^-1*d^(1/2)*arctanh(d^(1/2)*x^2*(c+d*x^4)^-1//2)+(1/2)*a^-1//2*b^-1*(b*c+-1*a*d)^(1/2)*arctan(a^-1//2*x^2*(c+d*x^4)^-1//2*(b*c+-1*a*d)^(1/2)))
@test integrate(x^-1*(a+b*x^4)^-1*(c+d*x^4)^(1/2), x) == :(-1//2*a^-1*c^(1/2)*arctanh(c^-1//2*(c+d*x^4)^(1/2))+(1/2)*a^-1*b^-1//2*(b*c+-1*a*d)^(1/2)*arctanh(b^(1/2)*(c+d*x^4)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-3*(a+b*x^4)^-1*(c+d*x^4)^(1/2), x) == :(-1//2*a^-1*x^-2*(c+d*x^4)^(1/2)+-1//2*a^-3//2*(b*c+-1*a*d)^(1/2)*arctan(a^-1//2*x^2*(c+d*x^4)^-1//2*(b*c+-1*a*d)^(1/2)))
@test integrate(x^-5*(a+b*x^4)^-1*(c+d*x^4)^(1/2), x) == :(-1//4*a^-1*x^-4*(c+d*x^4)^(1/2)+-1//2*a^-2*b^(1/2)*(b*c+-1*a*d)^(1/2)*arctanh(b^(1/2)*(c+d*x^4)^(1/2)*(b*c+-1*a*d)^-1//2)+1//4*a^-2*c^-1//2*(-1*a*d+2*b*c)*arctanh(c^-1//2*(c+d*x^4)^(1/2)))
@test integrate(x^-7*(a+b*x^4)^-1*(c+d*x^4)^(1/2), x) == :(-1//6*a^-1*x^-6*(c+d*x^4)^(1/2)+(1/2)*b*a^-5//2*(b*c+-1*a*d)^(1/2)*arctan(a^-1//2*x^2*(c+d*x^4)^-1//2*(b*c+-1*a*d)^(1/2))+1//6*a^-2*c^-1*x^-2*(c+d*x^4)^(1/2)*(-1*a*d+3*b*c))
@test integrate(x^11*(a+b*x^4)^-1*(c+d*x^4)^-1//2, x) == :(1//6*b^-1*d^-2*(c+d*x^4)^3//2+-1//2*a^2*b^-5//2*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x^4)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//2*b^-2*d^-2*(c+d*x^4)^(1/2)*(a*d+b*c))
@test integrate(x^7*(a+b*x^4)^-1*(c+d*x^4)^-1//2, x) == :((1/2)*b^-1*d^-1*(c+d*x^4)^(1/2)+(1/2)*a*b^-3//2*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x^4)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^3*(a+b*x^4)^-1*(c+d*x^4)^-1//2, x) == :(-1//2*b^-1//2*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x^4)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-1*(a+b*x^4)^-1*(c+d*x^4)^-1//2, x) == :(-1//2*a^-1*c^-1//2*arctanh(c^-1//2*(c+d*x^4)^(1/2))+(1/2)*a^-1*b^(1/2)*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x^4)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-5*(a+b*x^4)^-1*(c+d*x^4)^-1//2, x) == :(-1//2*a^-2*b^3//2*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x^4)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//4*a^-1*c^-1*x^-4*(c+d*x^4)^(1/2)+1//4*a^-2*c^-3//2*(a*d+2*b*c)*arctanh(c^-1//2*(c+d*x^4)^(1/2)))
@test integrate(x^9*(a+b*x^4)^-1*(c+d*x^4)^-1//2, x) == :((1/2)*a^3//2*b^-2*(b*c+-1*a*d)^-1//2*arctan(a^-1//2*x^2*(c+d*x^4)^-1//2*(b*c+-1*a*d)^(1/2))+-1//4*b^-2*d^-3//2*(b*c+2*a*d)*arctanh(d^(1/2)*x^2*(c+d*x^4)^-1//2)+1//4*b^-1*d^-1*x^2*(c+d*x^4)^(1/2))
@test integrate(x^5*(a+b*x^4)^-1*(c+d*x^4)^-1//2, x) == :((1/2)*b^-1*d^-1//2*arctanh(d^(1/2)*x^2*(c+d*x^4)^-1//2)+-1//2*a^(1/2)*b^-1*(b*c+-1*a*d)^-1//2*arctan(a^-1//2*x^2*(c+d*x^4)^-1//2*(b*c+-1*a*d)^(1/2)))
@test integrate(x*(a+b*x^4)^-1*(c+d*x^4)^-1//2, x) == :((1/2)*a^-1//2*(b*c+-1*a*d)^-1//2*arctan(a^-1//2*x^2*(c+d*x^4)^-1//2*(b*c+-1*a*d)^(1/2)))
@test integrate(x^-3*(a+b*x^4)^-1*(c+d*x^4)^-1//2, x) == :(-1//2*b*a^-3//2*(b*c+-1*a*d)^-1//2*arctan(a^-1//2*x^2*(c+d*x^4)^-1//2*(b*c+-1*a*d)^(1/2))+-1//2*a^-1*c^-1*x^-2*(c+d*x^4)^(1/2))
@test integrate(x^-7*(a+b*x^4)^-1*(c+d*x^4)^-1//2, x) == :((1/2)*a^-5//2*b^2*(b*c+-1*a*d)^-1//2*arctan(a^-1//2*x^2*(c+d*x^4)^-1//2*(b*c+-1*a*d)^(1/2))+-1//6*a^-1*c^-1*x^-6*(c+d*x^4)^(1/2)+1//6*a^-2*c^-2*x^-2*(c+d*x^4)^(1/2)*(2*a*d+3*b*c))
@test integrate(x^15*(a+b*x^4)^-2*(c+d*x^4)^-1//2, x) == :(-1//4*a^2*b^-7//2*(b*c+-1*a*d)^-3//2*(-5*a*d+6*b*c)*arctanh(b^(1/2)*(c+d*x^4)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//12*b^-3*d^-2*(c+d*x^4)^(1/2)*(b*c+-1*a*d)^-1*(-15*a^2*d^2+4*b^2*c^2+-1*b*d*x^4*(-5*a*d+2*b*c)+8*a*b*c*d)+1//4*a*b^-1*x^8*(a+b*x^4)^-1*(c+d*x^4)^(1/2)*(b*c+-1*a*d)^-1)
@test integrate(x^11*(a+b*x^4)^-2*(c+d*x^4)^-1//2, x) == :((1/2)*b^-2*d^-1*(c+d*x^4)^(1/2)+-1//4*a^2*b^-2*(a+b*x^4)^-1*(c+d*x^4)^(1/2)*(b*c+-1*a*d)^-1+1//4*a*b^-5//2*(b*c+-1*a*d)^-3//2*(-3*a*d+4*b*c)*arctanh(b^(1/2)*(c+d*x^4)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^7*(a+b*x^4)^-2*(c+d*x^4)^-1//2, x) == :(-1//4*b^-3//2*(b*c+-1*a*d)^-3//2*(-1*a*d+2*b*c)*arctanh(b^(1/2)*(c+d*x^4)^(1/2)*(b*c+-1*a*d)^-1//2)+1//4*a*b^-1*(a+b*x^4)^-1*(c+d*x^4)^(1/2)*(b*c+-1*a*d)^-1)
@test integrate(x^3*(a+b*x^4)^-2*(c+d*x^4)^-1//2, x) == :(-1*(a+b*x^4)^-1*(c+d*x^4)^(1/2)*(-4*a*d+4*b*c)^-1+1//4*d*b^-1//2*(b*c+-1*a*d)^-3//2*arctanh(b^(1/2)*(c+d*x^4)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-1*(a+b*x^4)^-2*(c+d*x^4)^-1//2, x) == :(-1//2*a^-2*c^-1//2*arctanh(c^-1//2*(c+d*x^4)^(1/2))+1//4*b*a^-1*(a+b*x^4)^-1*(c+d*x^4)^(1/2)*(b*c+-1*a*d)^-1+1//4*a^-2*b^(1/2)*(b*c+-1*a*d)^-3//2*(-3*a*d+2*b*c)*arctanh(b^(1/2)*(c+d*x^4)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-5*(a+b*x^4)^-2*(c+d*x^4)^-1//2, x) == :(1//4*a^-3*c^-3//2*(a*d+4*b*c)*arctanh(c^-1//2*(c+d*x^4)^(1/2))+-1//4*a^-1*c^-1*x^-4*(a+b*x^4)^-1*(c+d*x^4)^(1/2)+-1//4*a^-3*b^3//2*(b*c+-1*a*d)^-3//2*(-5*a*d+4*b*c)*arctanh(b^(1/2)*(c+d*x^4)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//4*b*a^-2*c^-1*(a+b*x^4)^-1*(c+d*x^4)^(1/2)*(b*c+-1*a*d)^-1*(-1*a*d+2*b*c))
@test integrate(x^13*(a+b*x^4)^-2*(c+d*x^4)^-1//2, x) == :(-1//4*b^-3*d^-3//2*(b*c+4*a*d)*arctanh(d^(1/2)*x^2*(c+d*x^4)^-1//2)+1//4*a^3//2*b^-3*(b*c+-1*a*d)^-3//2*(-4*a*d+5*b*c)*arctan(a^-1//2*x^2*(c+d*x^4)^-1//2*(b*c+-1*a*d)^(1/2))+1//4*a*b^-1*x^6*(a+b*x^4)^-1*(c+d*x^4)^(1/2)*(b*c+-1*a*d)^-1+1//4*b^-2*d^-1*x^2*(c+d*x^4)^(1/2)*(b*c+-1*a*d)^-1*(b*c+-2*a*d))
@test integrate(x^9*(a+b*x^4)^-2*(c+d*x^4)^-1//2, x) == :((1/2)*b^-2*d^-1//2*arctanh(d^(1/2)*x^2*(c+d*x^4)^-1//2)+-1//4*a^(1/2)*b^-2*(b*c+-1*a*d)^-3//2*(-2*a*d+3*b*c)*arctan(a^-1//2*x^2*(c+d*x^4)^-1//2*(b*c+-1*a*d)^(1/2))+1//4*a*b^-1*x^2*(a+b*x^4)^-1*(c+d*x^4)^(1/2)*(b*c+-1*a*d)^-1)
@test integrate(x^5*(a+b*x^4)^-2*(c+d*x^4)^-1//2, x) == :(-1*x^2*(a+b*x^4)^-1*(c+d*x^4)^(1/2)*(-4*a*d+4*b*c)^-1+1//4*c*a^-1//2*(b*c+-1*a*d)^-3//2*arctan(a^-1//2*x^2*(c+d*x^4)^-1//2*(b*c+-1*a*d)^(1/2)))
@test integrate(x*(a+b*x^4)^-2*(c+d*x^4)^-1//2, x) == :(1//4*a^-3//2*(b*c+-1*a*d)^-3//2*(b*c+-2*a*d)*arctan(a^-1//2*x^2*(c+d*x^4)^-1//2*(b*c+-1*a*d)^(1/2))+1//4*b*a^-1*x^2*(a+b*x^4)^-1*(c+d*x^4)^(1/2)*(b*c+-1*a*d)^-1)
@test integrate(x^-3*(a+b*x^4)^-2*(c+d*x^4)^-1//2, x) == :(-1//4*b*a^-5//2*(b*c+-1*a*d)^-3//2*(-4*a*d+3*b*c)*arctan(a^-1//2*x^2*(c+d*x^4)^-1//2*(b*c+-1*a*d)^(1/2))+-1//4*a^-2*c^-1*x^-2*(c+d*x^4)^(1/2)*(b*c+-1*a*d)^-1*(-2*a*d+3*b*c)+1//4*b*a^-1*x^-2*(a+b*x^4)^-1*(c+d*x^4)^(1/2)*(b*c+-1*a*d)^-1)
@test integrate(x^-7*(a+b*x^4)^-2*(c+d*x^4)^-1//2, x) == :(1//4*a^-7//2*b^2*(b*c+-1*a*d)^-3//2*(-6*a*d+5*b*c)*arctan(a^-1//2*x^2*(c+d*x^4)^-1//2*(b*c+-1*a*d)^(1/2))+-1//12*a^-2*c^-1*x^-6*(c+d*x^4)^(1/2)*(b*c+-1*a*d)^-1*(-2*a*d+5*b*c)+1//4*b*a^-1*x^-6*(a+b*x^4)^-1*(c+d*x^4)^(1/2)*(b*c+-1*a*d)^-1+1//12*a^-3*c^-2*x^-2*(c+d*x^4)^(1/2)*(b*c+-1*a*d)^-1*(-4*a^2*d^2+15*b^2*c^2+-8*a*b*c*d))
@test integrate(x^17*(a+b*x^6)^-1*(c+d*x^6)^-1//2, x) == :(1//9*b^-1*d^-2*(c+d*x^6)^3//2+-1//3*a^2*b^-5//2*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x^6)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//3*b^-2*d^-2*(c+d*x^6)^(1/2)*(a*d+b*c))
@test integrate(x^11*(a+b*x^6)^-1*(c+d*x^6)^-1//2, x) == :(1//3*b^-1*d^-1*(c+d*x^6)^(1/2)+1//3*a*b^-3//2*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x^6)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^5*(a+b*x^6)^-1*(c+d*x^6)^-1//2, x) == :(-1//3*b^-1//2*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x^6)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-1*(a+b*x^6)^-1*(c+d*x^6)^-1//2, x) == :(-1//3*a^-1*c^-1//2*arctanh(c^-1//2*(c+d*x^6)^(1/2))+1//3*a^-1*b^(1/2)*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x^6)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-7*(a+b*x^6)^-1*(c+d*x^6)^-1//2, x) == :(-1//3*a^-2*b^3//2*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x^6)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//6*a^-1*c^-1*x^-6*(c+d*x^6)^(1/2)+1//6*a^-2*c^-3//2*(a*d+2*b*c)*arctanh(c^-1//2*(c+d*x^6)^(1/2)))
@test integrate(x^14*(a+b*x^6)^-1*(c+d*x^6)^-1//2, x) == :(-1//6*b^-2*d^-3//2*(b*c+2*a*d)*arctanh(d^(1/2)*x^3*(c+d*x^6)^-1//2)+1//3*a^3//2*b^-2*(b*c+-1*a*d)^-1//2*arctan(a^-1//2*x^3*(c+d*x^6)^-1//2*(b*c+-1*a*d)^(1/2))+1//6*b^-1*d^-1*x^3*(c+d*x^6)^(1/2))
@test integrate(x^8*(a+b*x^6)^-1*(c+d*x^6)^-1//2, x) == :(1//3*b^-1*d^-1//2*arctanh(d^(1/2)*x^3*(c+d*x^6)^-1//2)+-1//3*a^(1/2)*b^-1*(b*c+-1*a*d)^-1//2*arctan(a^-1//2*x^3*(c+d*x^6)^-1//2*(b*c+-1*a*d)^(1/2)))
@test integrate(x^2*(a+b*x^6)^-1*(c+d*x^6)^-1//2, x) == :(1//3*a^-1//2*(b*c+-1*a*d)^-1//2*arctan(a^-1//2*x^3*(c+d*x^6)^-1//2*(b*c+-1*a*d)^(1/2)))
@test integrate(x^-4*(a+b*x^6)^-1*(c+d*x^6)^-1//2, x) == :(-1//3*b*a^-3//2*(b*c+-1*a*d)^-1//2*arctan(a^-1//2*x^3*(c+d*x^6)^-1//2*(b*c+-1*a*d)^(1/2))+-1//3*a^-1*c^-1*x^-3*(c+d*x^6)^(1/2))
@test integrate(x^-10*(a+b*x^6)^-1*(c+d*x^6)^-1//2, x) == :(-1//9*a^-1*c^-1*x^-9*(c+d*x^6)^(1/2)+1//3*a^-5//2*b^2*(b*c+-1*a*d)^-1//2*arctan(a^-1//2*x^3*(c+d*x^6)^-1//2*(b*c+-1*a*d)^(1/2))+1//9*a^-2*c^-2*x^-3*(c+d*x^6)^(1/2)*(2*a*d+3*b*c))
@test integrate(x^17*(a+b*x^6)^-2*(c+d*x^6)^-1//2, x) == :(1//3*b^-2*d^-1*(c+d*x^6)^(1/2)+-1//6*a^2*b^-2*(a+b*x^6)^-1*(c+d*x^6)^(1/2)*(b*c+-1*a*d)^-1+1//6*a*b^-5//2*(b*c+-1*a*d)^-3//2*(-3*a*d+4*b*c)*arctanh(b^(1/2)*(c+d*x^6)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^11*(a+b*x^6)^-2*(c+d*x^6)^-1//2, x) == :(-1//6*b^-3//2*(b*c+-1*a*d)^-3//2*(-1*a*d+2*b*c)*arctanh(b^(1/2)*(c+d*x^6)^(1/2)*(b*c+-1*a*d)^-1//2)+1//6*a*b^-1*(a+b*x^6)^-1*(c+d*x^6)^(1/2)*(b*c+-1*a*d)^-1)
@test integrate(x^5*(a+b*x^6)^-2*(c+d*x^6)^-1//2, x) == :(-1*(a+b*x^6)^-1*(c+d*x^6)^(1/2)*(-6*a*d+6*b*c)^-1+1//6*d*b^-1//2*(b*c+-1*a*d)^-3//2*arctanh(b^(1/2)*(c+d*x^6)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-1*(a+b*x^6)^-2*(c+d*x^6)^-1//2, x) == :(-1//3*a^-2*c^-1//2*arctanh(c^-1//2*(c+d*x^6)^(1/2))+1//6*b*a^-1*(a+b*x^6)^-1*(c+d*x^6)^(1/2)*(b*c+-1*a*d)^-1+1//6*a^-2*b^(1/2)*(b*c+-1*a*d)^-3//2*(-3*a*d+2*b*c)*arctanh(b^(1/2)*(c+d*x^6)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-7*(a+b*x^6)^-2*(c+d*x^6)^-1//2, x) == :(1//6*a^-3*c^-3//2*(a*d+4*b*c)*arctanh(c^-1//2*(c+d*x^6)^(1/2))+-1//6*a^-1*c^-1*x^-6*(a+b*x^6)^-1*(c+d*x^6)^(1/2)+-1//6*a^-3*b^3//2*(b*c+-1*a*d)^-3//2*(-5*a*d+4*b*c)*arctanh(b^(1/2)*(c+d*x^6)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//6*b*a^-2*c^-1*(a+b*x^6)^-1*(c+d*x^6)^(1/2)*(b*c+-1*a*d)^-1*(-1*a*d+2*b*c))
@test integrate(x^14*(a+b*x^6)^-2*(c+d*x^6)^-1//2, x) == :(1//3*b^-2*d^-1//2*arctanh(d^(1/2)*x^3*(c+d*x^6)^-1//2)+-1//6*a^(1/2)*b^-2*(b*c+-1*a*d)^-3//2*(-2*a*d+3*b*c)*arctan(a^-1//2*x^3*(c+d*x^6)^-1//2*(b*c+-1*a*d)^(1/2))+1//6*a*b^-1*x^3*(a+b*x^6)^-1*(c+d*x^6)^(1/2)*(b*c+-1*a*d)^-1)
@test integrate(x^8*(a+b*x^6)^-2*(c+d*x^6)^-1//2, x) == :(-1*x^3*(a+b*x^6)^-1*(c+d*x^6)^(1/2)*(-6*a*d+6*b*c)^-1+1//6*c*a^-1//2*(b*c+-1*a*d)^-3//2*arctan(a^-1//2*x^3*(c+d*x^6)^-1//2*(b*c+-1*a*d)^(1/2)))
@test integrate(x^2*(a+b*x^6)^-2*(c+d*x^6)^-1//2, x) == :(1//6*a^-3//2*(b*c+-1*a*d)^-3//2*(b*c+-2*a*d)*arctan(a^-1//2*x^3*(c+d*x^6)^-1//2*(b*c+-1*a*d)^(1/2))+1//6*b*a^-1*x^3*(a+b*x^6)^-1*(c+d*x^6)^(1/2)*(b*c+-1*a*d)^-1)
@test integrate(x^-4*(a+b*x^6)^-2*(c+d*x^6)^-1//2, x) == :(-1//6*b*a^-5//2*(b*c+-1*a*d)^-3//2*(-4*a*d+3*b*c)*arctan(a^-1//2*x^3*(c+d*x^6)^-1//2*(b*c+-1*a*d)^(1/2))+-1//6*a^-2*c^-1*x^-3*(c+d*x^6)^(1/2)*(b*c+-1*a*d)^-1*(-2*a*d+3*b*c)+1//6*b*a^-1*x^-3*(a+b*x^6)^-1*(c+d*x^6)^(1/2)*(b*c+-1*a*d)^-1)
@test integrate(x^-10*(a+b*x^6)^-2*(c+d*x^6)^-1//2, x) == :(1//6*a^-7//2*b^2*(b*c+-1*a*d)^-3//2*(-6*a*d+5*b*c)*arctan(a^-1//2*x^3*(c+d*x^6)^-1//2*(b*c+-1*a*d)^(1/2))+-1//18*a^-2*c^-1*x^-9*(c+d*x^6)^(1/2)*(b*c+-1*a*d)^-1*(-2*a*d+5*b*c)+1//6*b*a^-1*x^-9*(a+b*x^6)^-1*(c+d*x^6)^(1/2)*(b*c+-1*a*d)^-1+1//18*a^-3*c^-2*x^-3*(c+d*x^6)^(1/2)*(b*c+-1*a*d)^-1*(-4*a^2*d^2+15*b^2*c^2+-8*a*b*c*d))
@test integrate(x^23*(a+b*x^8)^-1*(c+d*x^8)^-1//2, x) == :(1//12*b^-1*d^-2*(c+d*x^8)^3//2+-1//4*a^2*b^-5//2*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x^8)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//4*b^-2*d^-2*(c+d*x^8)^(1/2)*(a*d+b*c))
@test integrate(x^15*(a+b*x^8)^-1*(c+d*x^8)^-1//2, x) == :(1//4*b^-1*d^-1*(c+d*x^8)^(1/2)+1//4*a*b^-3//2*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x^8)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^7*(a+b*x^8)^-1*(c+d*x^8)^-1//2, x) == :(-1//4*b^-1//2*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x^8)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-1*(a+b*x^8)^-1*(c+d*x^8)^-1//2, x) == :(-1//4*a^-1*c^-1//2*arctanh(c^-1//2*(c+d*x^8)^(1/2))+1//4*a^-1*b^(1/2)*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x^8)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-9*(a+b*x^8)^-1*(c+d*x^8)^-1//2, x) == :(-1//4*a^-2*b^3//2*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*x^8)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//8*a^-1*c^-1*x^-8*(c+d*x^8)^(1/2)+1//8*a^-2*c^-3//2*(a*d+2*b*c)*arctanh(c^-1//2*(c+d*x^8)^(1/2)))
@test integrate(x^19*(a+b*x^8)^-1*(c+d*x^8)^-1//2, x) == :(-1//8*b^-2*d^-3//2*(b*c+2*a*d)*arctanh(d^(1/2)*x^4*(c+d*x^8)^-1//2)+1//4*a^3//2*b^-2*(b*c+-1*a*d)^-1//2*arctan(a^-1//2*x^4*(c+d*x^8)^-1//2*(b*c+-1*a*d)^(1/2))+1//8*b^-1*d^-1*x^4*(c+d*x^8)^(1/2))
@test integrate(x^11*(a+b*x^8)^-1*(c+d*x^8)^-1//2, x) == :(1//4*b^-1*d^-1//2*arctanh(d^(1/2)*x^4*(c+d*x^8)^-1//2)+-1//4*a^(1/2)*b^-1*(b*c+-1*a*d)^-1//2*arctan(a^-1//2*x^4*(c+d*x^8)^-1//2*(b*c+-1*a*d)^(1/2)))
@test integrate(x^3*(a+b*x^8)^-1*(c+d*x^8)^-1//2, x) == :(1//4*a^-1//2*(b*c+-1*a*d)^-1//2*arctan(a^-1//2*x^4*(c+d*x^8)^-1//2*(b*c+-1*a*d)^(1/2)))
@test integrate(x^-5*(a+b*x^8)^-1*(c+d*x^8)^-1//2, x) == :(-1//4*b*a^-3//2*(b*c+-1*a*d)^-1//2*arctan(a^-1//2*x^4*(c+d*x^8)^-1//2*(b*c+-1*a*d)^(1/2))+-1//4*a^-1*c^-1*x^-4*(c+d*x^8)^(1/2))
@test integrate(x^-13*(a+b*x^8)^-1*(c+d*x^8)^-1//2, x) == :(-1//12*a^-1*c^-1*x^-12*(c+d*x^8)^(1/2)+1//4*a^-5//2*b^2*(b*c+-1*a*d)^-1//2*arctan(a^-1//2*x^4*(c+d*x^8)^-1//2*(b*c+-1*a*d)^(1/2))+1//12*a^-2*c^-2*x^-4*(c+d*x^8)^(1/2)*(2*a*d+3*b*c))
@test integrate(x^23*(a+b*x^8)^-2*(c+d*x^8)^-1//2, x) == :(1//4*b^-2*d^-1*(c+d*x^8)^(1/2)+-1//8*a^2*b^-2*(a+b*x^8)^-1*(c+d*x^8)^(1/2)*(b*c+-1*a*d)^-1+1//8*a*b^-5//2*(b*c+-1*a*d)^-3//2*(-3*a*d+4*b*c)*arctanh(b^(1/2)*(c+d*x^8)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^15*(a+b*x^8)^-2*(c+d*x^8)^-1//2, x) == :(-1//8*b^-3//2*(b*c+-1*a*d)^-3//2*(-1*a*d+2*b*c)*arctanh(b^(1/2)*(c+d*x^8)^(1/2)*(b*c+-1*a*d)^-1//2)+1//8*a*b^-1*(a+b*x^8)^-1*(c+d*x^8)^(1/2)*(b*c+-1*a*d)^-1)
@test integrate(x^7*(a+b*x^8)^-2*(c+d*x^8)^-1//2, x) == :(-1*(a+b*x^8)^-1*(c+d*x^8)^(1/2)*(-8*a*d+8*b*c)^-1+1//8*d*b^-1//2*(b*c+-1*a*d)^-3//2*arctanh(b^(1/2)*(c+d*x^8)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-1*(a+b*x^8)^-2*(c+d*x^8)^-1//2, x) == :(-1//4*a^-2*c^-1//2*arctanh(c^-1//2*(c+d*x^8)^(1/2))+1//8*b*a^-1*(a+b*x^8)^-1*(c+d*x^8)^(1/2)*(b*c+-1*a*d)^-1+1//8*a^-2*b^(1/2)*(b*c+-1*a*d)^-3//2*(-3*a*d+2*b*c)*arctanh(b^(1/2)*(c+d*x^8)^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate(x^-9*(a+b*x^8)^-2*(c+d*x^8)^-1//2, x) == :(1//8*a^-3*c^-3//2*(a*d+4*b*c)*arctanh(c^-1//2*(c+d*x^8)^(1/2))+-1//8*a^-1*c^-1*x^-8*(a+b*x^8)^-1*(c+d*x^8)^(1/2)+-1//8*a^-3*b^3//2*(b*c+-1*a*d)^-3//2*(-5*a*d+4*b*c)*arctanh(b^(1/2)*(c+d*x^8)^(1/2)*(b*c+-1*a*d)^-1//2)+-1//8*b*a^-2*c^-1*(a+b*x^8)^-1*(c+d*x^8)^(1/2)*(b*c+-1*a*d)^-1*(-1*a*d+2*b*c))
@test integrate(x^19*(a+b*x^8)^-2*(c+d*x^8)^-1//2, x) == :(1//4*b^-2*d^-1//2*arctanh(d^(1/2)*x^4*(c+d*x^8)^-1//2)+-1//8*a^(1/2)*b^-2*(b*c+-1*a*d)^-3//2*(-2*a*d+3*b*c)*arctan(a^-1//2*x^4*(c+d*x^8)^-1//2*(b*c+-1*a*d)^(1/2))+1//8*a*b^-1*x^4*(a+b*x^8)^-1*(c+d*x^8)^(1/2)*(b*c+-1*a*d)^-1)
@test integrate(x^11*(a+b*x^8)^-2*(c+d*x^8)^-1//2, x) == :(-1*x^4*(a+b*x^8)^-1*(c+d*x^8)^(1/2)*(-8*a*d+8*b*c)^-1+1//8*c*a^-1//2*(b*c+-1*a*d)^-3//2*arctan(a^-1//2*x^4*(c+d*x^8)^-1//2*(b*c+-1*a*d)^(1/2)))
@test integrate(x^3*(a+b*x^8)^-2*(c+d*x^8)^-1//2, x) == :(1//8*a^-3//2*(b*c+-1*a*d)^-3//2*(b*c+-2*a*d)*arctan(a^-1//2*x^4*(c+d*x^8)^-1//2*(b*c+-1*a*d)^(1/2))+1//8*b*a^-1*x^4*(a+b*x^8)^-1*(c+d*x^8)^(1/2)*(b*c+-1*a*d)^-1)
@test integrate(x^-5*(a+b*x^8)^-2*(c+d*x^8)^-1//2, x) == :(-1//8*b*a^-5//2*(b*c+-1*a*d)^-3//2*(-4*a*d+3*b*c)*arctan(a^-1//2*x^4*(c+d*x^8)^-1//2*(b*c+-1*a*d)^(1/2))+-1//8*a^-2*c^-1*x^-4*(c+d*x^8)^(1/2)*(b*c+-1*a*d)^-1*(-2*a*d+3*b*c)+1//8*b*a^-1*x^-4*(a+b*x^8)^-1*(c+d*x^8)^(1/2)*(b*c+-1*a*d)^-1)
@test integrate(x^-13*(a+b*x^8)^-2*(c+d*x^8)^-1//2, x) == :(1//8*a^-7//2*b^2*(b*c+-1*a*d)^-3//2*(-6*a*d+5*b*c)*arctan(a^-1//2*x^4*(c+d*x^8)^-1//2*(b*c+-1*a*d)^(1/2))+-1//24*a^-2*c^-1*x^-12*(c+d*x^8)^(1/2)*(b*c+-1*a*d)^-1*(-2*a*d+5*b*c)+1//8*b*a^-1*x^-12*(a+b*x^8)^-1*(c+d*x^8)^(1/2)*(b*c+-1*a*d)^-1+1//24*a^-3*c^-2*x^-4*(c+d*x^8)^(1/2)*(b*c+-1*a*d)^-1*(-4*a^2*d^2+15*b^2*c^2+-8*a*b*c*d))
@test integrate(x^5*(c+d*x^-2)^(1/2)*(a+b*x^-2), x) == :(-1//16*c^-5//2*d^2*(-1*a*d+2*b*c)*arctanh(c^-1//2*(c+d*x^-2)^(1/2))+1//6*a*c^-1*x^6*(c+d*x^-2)^3//2+1//8*c^-1*x^4*(c+d*x^-2)^(1/2)*(-1*a*d+2*b*c)+1//16*d*c^-2*x^2*(c+d*x^-2)^(1/2)*(-1*a*d+2*b*c))
@test integrate(x^3*(c+d*x^-2)^(1/2)*(a+b*x^-2), x) == :(1//4*a*c^-1*x^4*(c+d*x^-2)^3//2+1//8*d*c^-3//2*(-1*a*d+4*b*c)*arctanh(c^-1//2*(c+d*x^-2)^(1/2))+1//8*c^-1*x^2*(c+d*x^-2)^(1/2)*(-1*a*d+4*b*c))
@test integrate(x*(c+d*x^-2)^(1/2)*(a+b*x^-2), x) == :((1/2)*c^-1//2*(a*d+2*b*c)*arctanh(c^-1//2*(c+d*x^-2)^(1/2))+-1//2*c^-1*(c+d*x^-2)^(1/2)*(a*d+2*b*c)+(1/2)*a*c^-1*x^2*(c+d*x^-2)^3//2)
@test integrate(x^-1*(c+d*x^-2)^(1/2)*(a+b*x^-2), x) == :(-1*a*(c+d*x^-2)^(1/2)+a*c^(1/2)*arctanh(c^-1//2*(c+d*x^-2)^(1/2))+-1//3*b*d^-1*(c+d*x^-2)^3//2)
@test integrate(x^-3*(c+d*x^-2)^(1/2)*(a+b*x^-2), x) == :(-1//5*b*d^-2*(c+d*x^-2)^5//2+1//3*d^-2*(c+d*x^-2)^3//2*(b*c+-1*a*d))
@test integrate(x^-5*(c+d*x^-2)^(1/2)*(a+b*x^-2), x) == :(-1//7*b*d^-3*(c+d*x^-2)^7//2+1//5*d^-3*(c+d*x^-2)^5//2*(-1*a*d+2*b*c)+-1//3*c*d^-3*(c+d*x^-2)^3//2*(b*c+-1*a*d))
@test integrate(x^-7*(c+d*x^-2)^(1/2)*(a+b*x^-2), x) == :(-1//9*b*d^-4*(c+d*x^-2)^9//2+1//7*d^-4*(c+d*x^-2)^7//2*(-1*a*d+3*b*c)+-1//5*c*d^-4*(c+d*x^-2)^5//2*(-2*a*d+3*b*c)+1//3*c^2*d^-4*(c+d*x^-2)^3//2*(b*c+-1*a*d))
@test integrate(x^-9*(c+d*x^-2)^(1/2)*(a+b*x^-2), x) == :(-1//11*b*d^-5*(c+d*x^-2)^11//2+1//9*d^-5*(c+d*x^-2)^9//2*(-1*a*d+4*b*c)+-3//7*c*d^-5*(c+d*x^-2)^7//2*(-1*a*d+2*b*c)+-1//3*c^3*d^-5*(c+d*x^-2)^3//2*(b*c+-1*a*d)+1//5*c^2*d^-5*(c+d*x^-2)^5//2*(-3*a*d+4*b*c))
@test integrate(x^10*(c+d*x^-2)^(1/2)*(a+b*x^-2), x) == :(1//11*a*c^-1*x^11*(c+d*x^-2)^3//2+1//99*c^-2*x^9*(c+d*x^-2)^3//2*(-8*a*d+11*b*c)+-16//3465*c^-5*d^3*x^3*(c+d*x^-2)^3//2*(-8*a*d+11*b*c)+-2//231*d*c^-3*x^7*(c+d*x^-2)^3//2*(-8*a*d+11*b*c)+8//1155*c^-4*d^2*x^5*(c+d*x^-2)^3//2*(-8*a*d+11*b*c))
@test integrate(x^8*(c+d*x^-2)^(1/2)*(a+b*x^-2), x) == :(1//9*a*c^-1*x^9*(c+d*x^-2)^3//2+1//21*c^-2*x^7*(c+d*x^-2)^3//2*(-2*a*d+3*b*c)+-4//105*d*c^-3*x^5*(c+d*x^-2)^3//2*(-2*a*d+3*b*c)+8//315*c^-4*d^2*x^3*(c+d*x^-2)^3//2*(-2*a*d+3*b*c))
@test integrate(x^6*(c+d*x^-2)^(1/2)*(a+b*x^-2), x) == :(1//7*a*c^-1*x^7*(c+d*x^-2)^3//2+1//35*c^-2*x^5*(c+d*x^-2)^3//2*(-4*a*d+7*b*c)+-2//105*d*c^-3*x^3*(c+d*x^-2)^3//2*(-4*a*d+7*b*c))
@test integrate(x^4*(c+d*x^-2)^(1/2)*(a+b*x^-2), x) == :(1//5*a*c^-1*x^5*(c+d*x^-2)^3//2+1//15*c^-2*x^3*(c+d*x^-2)^3//2*(-2*a*d+5*b*c))
@test integrate(x^2*(c+d*x^-2)^(1/2)*(a+b*x^-2), x) == :(b*x*(c+d*x^-2)^(1/2)+-1*b*d^(1/2)*arctanh(d^(1/2)*x^-1*(c+d*x^-2)^-1//2)+1//3*a*c^-1*x^3*(c+d*x^-2)^3//2)
@test integrate((c+d*x^-2)^(1/2)*(a+b*x^-2), x) == :(-1//2*d^-1//2*(b*c+2*a*d)*arctanh(d^(1/2)*x^-1*(c+d*x^-2)^-1//2)+a*x*c^-1*(c+d*x^-2)^3//2+-1//2*c^-1*x^-1*(c+d*x^-2)^(1/2)*(b*c+2*a*d))
@test integrate(x^-2*(c+d*x^-2)^(1/2)*(a+b*x^-2), x) == :(-1//4*b*d^-1*x^-1*(c+d*x^-2)^3//2+1//8*c*d^-3//2*(b*c+-4*a*d)*arctanh(d^(1/2)*x^-1*(c+d*x^-2)^-1//2)+1//8*d^-1*x^-1*(c+d*x^-2)^(1/2)*(b*c+-4*a*d))
@test integrate(x^-4*(c+d*x^-2)^(1/2)*(a+b*x^-2), x) == :(-1//6*b*d^-1*x^-3*(c+d*x^-2)^3//2+-1//16*c^2*d^-5//2*(b*c+-2*a*d)*arctanh(d^(1/2)*x^-1*(c+d*x^-2)^-1//2)+1//8*d^-1*x^-3*(c+d*x^-2)^(1/2)*(b*c+-2*a*d)+1//16*c*d^-2*x^-1*(c+d*x^-2)^(1/2)*(b*c+-2*a*d))
@test integrate(x^5*(c+d*x^-2)^3//2*(a+b*x^-2), x) == :(1//6*a*c^-1*x^6*(c+d*x^-2)^5//2+1//16*c^-3//2*d^2*(-1*a*d+6*b*c)*arctanh(c^-1//2*(c+d*x^-2)^(1/2))+1//24*c^-1*x^4*(c+d*x^-2)^3//2*(-1*a*d+6*b*c)+1//16*d*c^-1*x^2*(c+d*x^-2)^(1/2)*(-1*a*d+6*b*c))
@test integrate(x^3*(c+d*x^-2)^3//2*(a+b*x^-2), x) == :(-3//8*d*c^-1*(c+d*x^-2)^(1/2)*(a*d+4*b*c)+1//4*a*c^-1*x^4*(c+d*x^-2)^5//2+1//8*c^-1*x^2*(c+d*x^-2)^3//2*(a*d+4*b*c)+3//8*d*c^-1//2*(a*d+4*b*c)*arctanh(c^-1//2*(c+d*x^-2)^(1/2)))
@test integrate(x*(c+d*x^-2)^3//2*(a+b*x^-2), x) == :((c+d*x^-2)^(1/2)*(-1*b*c+-3//2*a*d)+(1/2)*c^(1/2)*(2*b*c+3*a*d)*arctanh(c^-1//2*(c+d*x^-2)^(1/2))+-1//6*c^-1*(c+d*x^-2)^3//2*(2*b*c+3*a*d)+(1/2)*a*c^-1*x^2*(c+d*x^-2)^5//2)
@test integrate(x^-1*(c+d*x^-2)^3//2*(a+b*x^-2), x) == :(-1//3*a*(c+d*x^-2)^3//2+a*c^3//2*arctanh(c^-1//2*(c+d*x^-2)^(1/2))+-1*a*c*(c+d*x^-2)^(1/2)+-1//5*b*d^-1*(c+d*x^-2)^5//2)
@test integrate(x^-3*(c+d*x^-2)^3//2*(a+b*x^-2), x) == :(-1//7*b*d^-2*(c+d*x^-2)^7//2+1//5*d^-2*(c+d*x^-2)^5//2*(b*c+-1*a*d))
@test integrate(x^-5*(c+d*x^-2)^3//2*(a+b*x^-2), x) == :(-1//9*b*d^-3*(c+d*x^-2)^9//2+1//7*d^-3*(c+d*x^-2)^7//2*(-1*a*d+2*b*c)+-1//5*c*d^-3*(c+d*x^-2)^5//2*(b*c+-1*a*d))
@test integrate(x^-7*(c+d*x^-2)^3//2*(a+b*x^-2), x) == :(-1//11*b*d^-4*(c+d*x^-2)^11//2+1//9*d^-4*(c+d*x^-2)^9//2*(-1*a*d+3*b*c)+-1//7*c*d^-4*(c+d*x^-2)^7//2*(-2*a*d+3*b*c)+1//5*c^2*d^-4*(c+d*x^-2)^5//2*(b*c+-1*a*d))
@test integrate(x^-9*(c+d*x^-2)^3//2*(a+b*x^-2), x) == :(-1//13*b*d^-5*(c+d*x^-2)^13//2+1//11*d^-5*(c+d*x^-2)^11//2*(-1*a*d+4*b*c)+-1//3*c*d^-5*(c+d*x^-2)^9//2*(-1*a*d+2*b*c)+-1//5*c^3*d^-5*(c+d*x^-2)^5//2*(b*c+-1*a*d)+1//7*c^2*d^-5*(c+d*x^-2)^7//2*(-3*a*d+4*b*c))
@test integrate(x^12*(c+d*x^-2)^3//2*(a+b*x^-2), x) == :(1//13*a*c^-1*x^13*(c+d*x^-2)^5//2+1//143*c^-2*x^11*(c+d*x^-2)^5//2*(-8*a*d+13*b*c)+-16//15015*c^-5*d^3*x^5*(c+d*x^-2)^5//2*(-8*a*d+13*b*c)+-2//429*d*c^-3*x^9*(c+d*x^-2)^5//2*(-8*a*d+13*b*c)+8//3003*c^-4*d^2*x^7*(c+d*x^-2)^5//2*(-8*a*d+13*b*c))
@test integrate(x^10*(c+d*x^-2)^3//2*(a+b*x^-2), x) == :(1//11*a*c^-1*x^11*(c+d*x^-2)^5//2+1//99*c^-2*x^9*(c+d*x^-2)^5//2*(-6*a*d+11*b*c)+-4//693*d*c^-3*x^7*(c+d*x^-2)^5//2*(-6*a*d+11*b*c)+8//3465*c^-4*d^2*x^5*(c+d*x^-2)^5//2*(-6*a*d+11*b*c))
@test integrate(x^8*(c+d*x^-2)^3//2*(a+b*x^-2), x) == :(1//9*a*c^-1*x^9*(c+d*x^-2)^5//2+1//63*c^-2*x^7*(c+d*x^-2)^5//2*(-4*a*d+9*b*c)+-2//315*d*c^-3*x^5*(c+d*x^-2)^5//2*(-4*a*d+9*b*c))
@test integrate(x^6*(c+d*x^-2)^3//2*(a+b*x^-2), x) == :(1//7*a*c^-1*x^7*(c+d*x^-2)^5//2+1//35*c^-2*x^5*(c+d*x^-2)^5//2*(-2*a*d+7*b*c))
@test integrate(x^4*(c+d*x^-2)^3//2*(a+b*x^-2), x) == :(-1*b*d^3//2*arctanh(d^(1/2)*x^-1*(c+d*x^-2)^-1//2)+1//3*b*x^3*(c+d*x^-2)^3//2+b*d*x*(c+d*x^-2)^(1/2)+1//5*a*c^-1*x^5*(c+d*x^-2)^5//2)
@test integrate(x^2*(c+d*x^-2)^3//2*(a+b*x^-2), x) == :(-1//2*d^(1/2)*(2*a*d+3*b*c)*arctanh(d^(1/2)*x^-1*(c+d*x^-2)^-1//2)+1//3*a*c^-1*x^3*(c+d*x^-2)^5//2+1//3*x*c^-1*(c+d*x^-2)^3//2*(2*a*d+3*b*c)+-1//2*d*c^-1*x^-1*(c+d*x^-2)^(1/2)*(2*a*d+3*b*c))
@test integrate((c+d*x^-2)^3//2*(a+b*x^-2), x) == :(-1//8*x^-1*(c+d*x^-2)^(1/2)*(3*b*c+12*a*d)+a*x*c^-1*(c+d*x^-2)^5//2+-3//8*c*d^-1//2*(b*c+4*a*d)*arctanh(d^(1/2)*x^-1*(c+d*x^-2)^-1//2)+-1//4*c^-1*x^-1*(c+d*x^-2)^3//2*(b*c+4*a*d))
@test integrate(x^-2*(c+d*x^-2)^3//2*(a+b*x^-2), x) == :(-1//6*b*d^-1*x^-1*(c+d*x^-2)^5//2+1//16*c^2*d^-3//2*(b*c+-6*a*d)*arctanh(d^(1/2)*x^-1*(c+d*x^-2)^-1//2)+1//24*d^-1*x^-1*(c+d*x^-2)^3//2*(b*c+-6*a*d)+1//16*c*d^-1*x^-1*(c+d*x^-2)^(1/2)*(b*c+-6*a*d))
@test integrate(x^-4*(c+d*x^-2)^3//2*(a+b*x^-2), x) == :(-1//8*b*d^-1*x^-3*(c+d*x^-2)^5//2+-1//128*c^3*d^-5//2*(-8*a*d+3*b*c)*arctanh(d^(1/2)*x^-1*(c+d*x^-2)^-1//2)+1//48*d^-1*x^-3*(c+d*x^-2)^3//2*(-8*a*d+3*b*c)+1//64*c*d^-1*x^-3*(c+d*x^-2)^(1/2)*(-8*a*d+3*b*c)+1//128*c^2*d^-2*x^-1*(c+d*x^-2)^(1/2)*(-8*a*d+3*b*c))
@test integrate(x^3*(c+d*x^-2)^-1//2*(a+b*x^-2), x) == :(-1//8*d*c^-5//2*(-3*a*d+4*b*c)*arctanh(c^-1//2*(c+d*x^-2)^(1/2))+1//4*a*c^-1*x^4*(c+d*x^-2)^(1/2)+1//8*c^-2*x^2*(c+d*x^-2)^(1/2)*(-3*a*d+4*b*c))
@test integrate(x*(c+d*x^-2)^-1//2*(a+b*x^-2), x) == :((1/2)*c^-3//2*(-1*a*d+2*b*c)*arctanh(c^-1//2*(c+d*x^-2)^(1/2))+(1/2)*a*c^-1*x^2*(c+d*x^-2)^(1/2))
@test integrate(x^-1*(c+d*x^-2)^-1//2*(a+b*x^-2), x) == :(a*c^-1//2*arctanh(c^-1//2*(c+d*x^-2)^(1/2))+-1*b*d^-1*(c+d*x^-2)^(1/2))
@test integrate(x^-3*(c+d*x^-2)^-1//2*(a+b*x^-2), x) == :(d^-2*(c+d*x^-2)^(1/2)*(b*c+-1*a*d)+-1//3*b*d^-2*(c+d*x^-2)^3//2)
@test integrate(x^-5*(c+d*x^-2)^-1//2*(a+b*x^-2), x) == :(-1//5*b*d^-3*(c+d*x^-2)^5//2+1//3*d^-3*(c+d*x^-2)^3//2*(-1*a*d+2*b*c)+-1*c*d^-3*(c+d*x^-2)^(1/2)*(b*c+-1*a*d))
@test integrate(x^-7*(c+d*x^-2)^-1//2*(a+b*x^-2), x) == :(-1//7*b*d^-4*(c+d*x^-2)^7//2+1//5*d^-4*(c+d*x^-2)^5//2*(-1*a*d+3*b*c)+c^2*d^-4*(c+d*x^-2)^(1/2)*(b*c+-1*a*d)+-1//3*c*d^-4*(c+d*x^-2)^3//2*(-2*a*d+3*b*c))
@test integrate(x^4*(c+d*x^-2)^-1//2*(a+b*x^-2), x) == :(1//5*a*c^-1*x^5*(c+d*x^-2)^(1/2)+1//15*c^-2*x^3*(c+d*x^-2)^(1/2)*(-4*a*d+5*b*c)+-2//15*d*x*c^-3*(c+d*x^-2)^(1/2)*(-4*a*d+5*b*c))
@test integrate(x^2*(c+d*x^-2)^-1//2*(a+b*x^-2), x) == :(1//3*a*c^-1*x^3*(c+d*x^-2)^(1/2)+1//3*x*c^-2*(c+d*x^-2)^(1/2)*(-2*a*d+3*b*c))
@test integrate((c+d*x^-2)^-1//2*(a+b*x^-2), x) == :(-1*b*d^-1//2*arctanh(d^(1/2)*x^-1*(c+d*x^-2)^-1//2)+a*x*c^-1*(c+d*x^-2)^(1/2))
@test integrate(x^-2*(c+d*x^-2)^-1//2*(a+b*x^-2), x) == :((1/2)*d^-3//2*(b*c+-2*a*d)*arctanh(d^(1/2)*x^-1*(c+d*x^-2)^-1//2)+-1//2*b*d^-1*x^-1*(c+d*x^-2)^(1/2))
@test integrate(x^-4*(c+d*x^-2)^-1//2*(a+b*x^-2), x) == :(-1//4*b*d^-1*x^-3*(c+d*x^-2)^(1/2)+-1//8*c*d^-5//2*(-4*a*d+3*b*c)*arctanh(d^(1/2)*x^-1*(c+d*x^-2)^-1//2)+1//8*d^-2*x^-1*(c+d*x^-2)^(1/2)*(-4*a*d+3*b*c))
@test integrate(x^3*(c+d*x^-2)^-3//2*(a+b*x^-2), x) == :(-3//8*d*c^-7//2*(-5*a*d+4*b*c)*arctanh(c^-1//2*(c+d*x^-2)^(1/2))+1//4*a*c^-1*x^4*(c+d*x^-2)^-1//2+1//8*c^-2*x^2*(c+d*x^-2)^-1//2*(-5*a*d+4*b*c)+3//8*d*c^-3*(c+d*x^-2)^-1//2*(-5*a*d+4*b*c))
@test integrate(x*(c+d*x^-2)^-3//2*(a+b*x^-2), x) == :((1/2)*c^-5//2*(-3*a*d+2*b*c)*arctanh(c^-1//2*(c+d*x^-2)^(1/2))+-1//2*c^-2*(c+d*x^-2)^-1//2*(-3*a*d+2*b*c)+(1/2)*a*c^-1*x^2*(c+d*x^-2)^-1//2)
@test integrate(x^-1*(c+d*x^-2)^-3//2*(a+b*x^-2), x) == :(a*c^-3//2*arctanh(c^-1//2*(c+d*x^-2)^(1/2))+c^-1*d^-1*(c+d*x^-2)^-1//2*(b*c+-1*a*d))
@test integrate(x^-3*(c+d*x^-2)^-3//2*(a+b*x^-2), x) == :(-1*b*d^-2*(c+d*x^-2)^(1/2)+-1*d^-2*(c+d*x^-2)^-1//2*(b*c+-1*a*d))
@test integrate(x^-5*(c+d*x^-2)^-3//2*(a+b*x^-2), x) == :(d^-3*(c+d*x^-2)^(1/2)*(-1*a*d+2*b*c)+-1//3*b*d^-3*(c+d*x^-2)^3//2+c*d^-3*(c+d*x^-2)^-1//2*(b*c+-1*a*d))
@test integrate(x^-7*(c+d*x^-2)^-3//2*(a+b*x^-2), x) == :(-1//5*b*d^-4*(c+d*x^-2)^5//2+1//3*d^-4*(c+d*x^-2)^3//2*(-1*a*d+3*b*c)+-1*c*d^-4*(c+d*x^-2)^(1/2)*(-2*a*d+3*b*c)+-1*c^2*d^-4*(c+d*x^-2)^-1//2*(b*c+-1*a*d))
@test integrate(x^-9*(c+d*x^-2)^-3//2*(a+b*x^-2), x) == :(-1//7*b*d^-5*(c+d*x^-2)^7//2+1//5*d^-5*(c+d*x^-2)^5//2*(-1*a*d+4*b*c)+c^2*d^-5*(c+d*x^-2)^(1/2)*(-3*a*d+4*b*c)+c^3*d^-5*(c+d*x^-2)^-1//2*(b*c+-1*a*d)+-1*c*d^-5*(c+d*x^-2)^3//2*(-1*a*d+2*b*c))
@test integrate(x^4*(c+d*x^-2)^-3//2*(a+b*x^-2), x) == :(1//5*a*c^-1*x^5*(c+d*x^-2)^-1//2+1//15*c^-2*x^3*(c+d*x^-2)^-1//2*(-6*a*d+5*b*c)+-8//15*d*x*c^-4*(c+d*x^-2)^(1/2)*(-6*a*d+5*b*c)+4//15*d*x*c^-3*(c+d*x^-2)^-1//2*(-6*a*d+5*b*c))
@test integrate(x^2*(c+d*x^-2)^-3//2*(a+b*x^-2), x) == :(-1//3*x*c^-2*(c+d*x^-2)^-1//2*(-4*a*d+3*b*c)+1//3*a*c^-1*x^3*(c+d*x^-2)^-1//2+1//3*x*c^-3*(c+d*x^-2)^(1/2)*(-8*a*d+6*b*c))
@test integrate((c+d*x^-2)^-3//2*(a+b*x^-2), x) == :(a*x*c^-1*(c+d*x^-2)^-1//2+-1*c^-2*x^-1*(c+d*x^-2)^-1//2*(b*c+-2*a*d))
@test integrate(x^-2*(c+d*x^-2)^-3//2*(a+b*x^-2), x) == :(-1*b*d^-3//2*arctanh(d^(1/2)*x^-1*(c+d*x^-2)^-1//2)+c^-1*d^-1*x^-1*(c+d*x^-2)^-1//2*(b*c+-1*a*d))
@test integrate(x^-4*(c+d*x^-2)^-3//2*(a+b*x^-2), x) == :((1/2)*d^-5//2*(-2*a*d+3*b*c)*arctanh(d^(1/2)*x^-1*(c+d*x^-2)^-1//2)+-1//2*b*d^-1*x^-3*(c+d*x^-2)^-1//2+-1//2*d^-2*x^-1*(c+d*x^-2)^-1//2*(-2*a*d+3*b*c))
@test integrate(x^-6*(c+d*x^-2)^-3//2*(a+b*x^-2), x) == :(-3//8*c*d^-7//2*(-4*a*d+5*b*c)*arctanh(d^(1/2)*x^-1*(c+d*x^-2)^-1//2)+-1//4*b*d^-1*x^-5*(c+d*x^-2)^-1//2+-1//4*d^-2*x^-3*(c+d*x^-2)^-1//2*(-4*a*d+5*b*c)+1//8*d^-3*x^-1*(c+d*x^-2)^(1/2)*(-12*a*d+15*b*c))
@test integrate(x^5//2*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2), x) == :(-5//64*arccosh(x^(1/2))+-5//64*x^(1/2)*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2)+-5//96*x^3//2*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2)+-1//24*x^5//2*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2)+1//4*x^7//2*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2))
@test integrate(x^3//2*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2), x) == :(-1//8*arccosh(x^(1/2))+-1//8*x^(1/2)*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2)+-1//12*x^3//2*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2)+1//3*x^5//2*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2))
@test integrate(x^(1/2)*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2), x) == :(-1//4*arccosh(x^(1/2))+(1/2)*x^3//2*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2)+-1//4*x^(1/2)*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2))
@test integrate(x^-1//2*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2), x) == :(-1*arccosh(x^(1/2))+x^(1/2)*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2))
@test integrate(x^-3//2*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2), x) == :(2*arccosh(x^(1/2))+-2*x^(1/2)*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2)+2*x^-1//2*(1+x^(1/2))^3//2*(-1+x^(1/2))^3//2)
@test integrate(x^-5//2*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2), x) == :(2//3*x^-3//2*(1+x^(1/2))^3//2*(-1+x^(1/2))^3//2)
@test integrate(x^-7//2*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2), x) == :(2//5*x^-5//2*(1+x^(1/2))^3//2*(-1+x^(1/2))^3//2+4//15*x^-3//2*(1+x^(1/2))^3//2*(-1+x^(1/2))^3//2)
@test integrate(x^-9//2*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2), x) == :(2//7*x^-7//2*(1+x^(1/2))^3//2*(-1+x^(1/2))^3//2+8//35*x^-5//2*(1+x^(1/2))^3//2*(-1+x^(1/2))^3//2+16//105*x^-3//2*(1+x^(1/2))^3//2*(-1+x^(1/2))^3//2)
@test integrate(x^-11//2*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2), x) == :(2//9*x^-9//2*(1+x^(1/2))^3//2*(-1+x^(1/2))^3//2+4//21*x^-7//2*(1+x^(1/2))^3//2*(-1+x^(1/2))^3//2+16//105*x^-5//2*(1+x^(1/2))^3//2*(-1+x^(1/2))^3//2+32//315*x^-3//2*(1+x^(1/2))^3//2*(-1+x^(1/2))^3//2)
@test integrate(x^5//2*(1+x^(1/2))^-1//2*(-1+x^(1/2))^-1//2, x) == :(5//8*arccosh(x^(1/2))+1//3*x^5//2*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2)+5//8*x^(1/2)*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2)+5//12*x^3//2*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2))
@test integrate(x^3//2*(1+x^(1/2))^-1//2*(-1+x^(1/2))^-1//2, x) == :(3//4*arccosh(x^(1/2))+(1/2)*x^3//2*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2)+3//4*x^(1/2)*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2))
@test integrate(x^(1/2)*(1+x^(1/2))^-1//2*(-1+x^(1/2))^-1//2, x) == :(x^(1/2)*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2)+arccosh(x^(1/2)))
@test integrate(x^-1//2*(1+x^(1/2))^-1//2*(-1+x^(1/2))^-1//2, x) == :(2*arccosh(x^(1/2)))
@test integrate(x^-3//2*(1+x^(1/2))^-1//2*(-1+x^(1/2))^-1//2, x) == :(2*x^-1//2*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2))
@test integrate(x^-5//2*(1+x^(1/2))^-1//2*(-1+x^(1/2))^-1//2, x) == :(2//3*x^-3//2*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2)+4//3*x^-1//2*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2))
@test integrate(x^-7//2*(1+x^(1/2))^-1//2*(-1+x^(1/2))^-1//2, x) == :(2//5*x^-5//2*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2)+8//15*x^-3//2*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2)+16//15*x^-1//2*(1+x^(1/2))^(1/2)*(-1+x^(1/2))^(1/2))
@test integrate(x^-1*(1+-1*x^6)^-1*(1+x^6), x) == :(-1//3*log(1+-1*x^6)+log(x))
@test integrate((e*x)^m*(a+b*x^n)^p*(a*(1+m)+b*x^n*(1+m+n+n*p)), x) == :(e^-1*(e*x)^(1+m)*(a+b*x^n)^(1+p))
@test integrate(x^-1*(a+b*x^n)^-1*(c+d*x^n)^-1, x) == :(a^-1*c^-1*log(x)+d*c^-1*n^-1*(b*c+-1*a*d)^-1*log(c+d*x^n)+-1*b*a^-1*n^-1*(b*c+-1*a*d)^-1*log(a+b*x^n))
@test integrate(x^-1*(a+b*x^n)^-2*(c+d*x^n)^-1, x) == :(a^-2*c^-1*log(x)+b*a^-1*n^-1*(a+b*x^n)^-1*(b*c+-1*a*d)^-1+-1*c^-1*d^2*n^-1*(b*c+-1*a*d)^-2*log(c+d*x^n)+-1*b*a^-2*n^-1*(b*c+-1*a*d)^-2*(b*c+-2*a*d)*log(a+b*x^n))
@test integrate(x^(-1+2n)*(a+b*x^n)^3*(c+d*x^n)^-1, x) == :(-1*d^-4*n^-1*x^n*(b*c+-1*a*d)^3+1//4*b^3*d^-1*n^-1*x^(4n)+c*d^-5*n^-1*(b*c+-1*a*d)^3*log(c+d*x^n)+(1/2)*b*d^-3*n^-1*x^(2n)*(b^2*c^2+3*a^2*d^2+-3*a*b*c*d)+-1//3*b^2*d^-2*n^-1*x^(3n)*(b*c+-3*a*d))
@test integrate(x^(-1+2n)*(a+b*x^n)^2*(c+d*x^n)^-1, x) == :(d^-3*n^-1*x^n*(b*c+-1*a*d)^2+1//3*b^2*d^-1*n^-1*x^(3n)+-1*c*d^-4*n^-1*(b*c+-1*a*d)^2*log(c+d*x^n)+-1//2*b*d^-2*n^-1*x^(2n)*(b*c+-2*a*d))
@test integrate(x^(-1+2n)*(c+d*x^n)^-1*(a+b*x^n), x) == :((1/2)*b*d^-1*n^-1*x^(2n)+-1*d^-2*n^-1*x^n*(b*c+-1*a*d)+c*d^-3*n^-1*(b*c+-1*a*d)*log(c+d*x^n))
@test integrate(x^(-1+2n)*(a+b*x^n)^-1*(c+d*x^n)^-1, x) == :(c*d^-1*n^-1*(b*c+-1*a*d)^-1*log(c+d*x^n)+-1*a*b^-1*n^-1*(b*c+-1*a*d)^-1*log(a+b*x^n))
@test integrate(x^(-1+2n)*(a+b*x^n)^-2*(c+d*x^n)^-1, x) == :(c*n^-1*(b*c+-1*a*d)^-2*log(a+b*x^n)+-1*c*n^-1*(b*c+-1*a*d)^-2*log(c+d*x^n)+a*b^-1*n^-1*(a+b*x^n)^-1*(b*c+-1*a*d)^-1)
@test integrate(x^(-1+2n)*(a+b*x^n)^-3*(c+d*x^n)^-1, x) == :(-1*c*n^-1*(a+b*x^n)^-1*(b*c+-1*a*d)^-2+c*d*n^-1*(b*c+-1*a*d)^-3*log(c+d*x^n)+(1/2)*a*b^-1*n^-1*(a+b*x^n)^-2*(b*c+-1*a*d)^-1+-1*c*d*n^-1*(b*c+-1*a*d)^-3*log(a+b*x^n))
@test integrate(x^(-1+3n)*(a+b*x^n)^3*(c+d*x^n)^-1, x) == :(-1//2*d^-4*n^-1*x^(2n)*(b*c+-1*a*d)^3+1//5*b^3*d^-1*n^-1*x^(5n)+c*d^-5*n^-1*x^n*(b*c+-1*a*d)^3+-1*c^2*d^-6*n^-1*(b*c+-1*a*d)^3*log(c+d*x^n)+-1//4*b^2*d^-2*n^-1*x^(4n)*(b*c+-3*a*d)+1//3*b*d^-3*n^-1*x^(3n)*(b^2*c^2+3*a^2*d^2+-3*a*b*c*d))
@test integrate(x^(-1+3n)*(a+b*x^n)^2*(c+d*x^n)^-1, x) == :((1/2)*d^-3*n^-1*x^(2n)*(b*c+-1*a*d)^2+1//4*b^2*d^-1*n^-1*x^(4n)+c^2*d^-5*n^-1*(b*c+-1*a*d)^2*log(c+d*x^n)+-1*c*d^-4*n^-1*x^n*(b*c+-1*a*d)^2+-1//3*b*d^-2*n^-1*x^(3n)*(b*c+-2*a*d))
@test integrate(x^(-1+3n)*(c+d*x^n)^-1*(a+b*x^n), x) == :(-1//2*d^-2*n^-1*x^(2n)*(b*c+-1*a*d)+1//3*b*d^-1*n^-1*x^(3n)+c*d^-3*n^-1*x^n*(b*c+-1*a*d)+-1*c^2*d^-4*n^-1*(b*c+-1*a*d)*log(c+d*x^n))
@test integrate(x^(-1+3n)*(a+b*x^n)^-1*(c+d*x^n)^-1, x) == :(b^-1*d^-1*n^-1*x^n+a^2*b^-2*n^-1*(b*c+-1*a*d)^-1*log(a+b*x^n)+-1*c^2*d^-2*n^-1*(b*c+-1*a*d)^-1*log(c+d*x^n))
@test integrate(x^(-1+3n)*(a+b*x^n)^-2*(c+d*x^n)^-1, x) == :(c^2*d^-1*n^-1*(b*c+-1*a*d)^-2*log(c+d*x^n)+-1*a^2*b^-2*n^-1*(a+b*x^n)^-1*(b*c+-1*a*d)^-1+-1*a*b^-2*n^-1*(b*c+-1*a*d)^-2*(-1*a*d+2*b*c)*log(a+b*x^n))
@test integrate(x^(-1+3n)*(a+b*x^n)^-3*(c+d*x^n)^-1, x) == :(c^2*n^-1*(b*c+-1*a*d)^-3*log(a+b*x^n)+-1*c^2*n^-1*(b*c+-1*a*d)^-3*log(c+d*x^n)+-1//2*a^2*b^-2*n^-1*(a+b*x^n)^-2*(b*c+-1*a*d)^-1+a*b^-2*n^-1*(a+b*x^n)^-1*(b*c+-1*a*d)^-2*(-1*a*d+2*b*c))
@test integrate(x^13*(b+c*x)^13*(b+2*c*x), x) == :(1//14*x^14*(b+c*x)^14)
@test integrate(x^27*(b+c*x^2)^13*(b+2*c*x^2), x) == :(1//28*x^28*(b+c*x^2)^14)
@test integrate(x^41*(b+c*x^3)^13*(b+2*c*x^3), x) == :(1//42*x^42*(b+c*x^3)^14)
@test integrate(x^(-1+14n)*(b+c*x^n)^13*(b+2*c*x^n), x) == :(1//14*n^-1*x^(14n)*(b+c*x^n)^14)
@test integrate(x^(-1+m)*(a+b*x^n)^(-1+p)*(a*m+b*x^n*(m+n*p)), x) == :(x^m*(a+b*x^n)^p)
@test integrate(x^-1*(b+c*x^2)^-1*(b+2*c*x^2), x) == :((1/2)*log(b+c*x^2)+log(x))
@test integrate(x^-1*(b+c*x^3)^-1*(b+2*c*x^3), x) == :(1//3*log(b+c*x^3)+log(x))
@test integrate(x^-1*(b+c*x^n)^-1*(b+2*c*x^n), x) == :(n^-1*log(b+c*x^n)+log(x))
@test integrate(x^-8*(b+c*x)^-8*(b+2*c*x), x) == :(-1//7*x^-7*(b+c*x)^-7)
@test integrate(x^-15*(b+c*x^2)^-8*(b+2*c*x^2), x) == :(-1//14*x^-14*(b+c*x^2)^-7)
@test integrate(x^-22*(b+c*x^3)^-8*(b+2*c*x^3), x) == :(-1//21*x^-21*(b+c*x^3)^-7)
@test integrate(x^(-1+-7n)*(b+c*x^n)^-8*(b+2*c*x^n), x) == :(-1//7*n^-1*x^(-7n)*(b+c*x^n)^-7)
@test integrate(x^31*(1+x^16)^(1/2)*(1+-1*x^16)^-1, x) == :(-1//8*(1+x^16)^(1/2)+-1//24*(1+x^16)^3//2+1//8*2^(1/2)*arctanh((1/2)*2^(1/2)*(1+x^16)^(1/2)))
@test integrate(x^-1*(a+b*x^-1)^-1//2*(c+d*x^-1)^(1/2), x) == :(-2*b^-1//2*d^(1/2)*arctanh(b^-1//2*d^(1/2)*(a+b*x^-1)^(1/2)*(c+d*x^-1)^-1//2)+2*a^-1//2*c^(1/2)*arctanh(a^-1//2*c^(1/2)*(a+b*x^-1)^(1/2)*(c+d*x^-1)^-1//2))
@test integrate(x^(-1+2n)*(a+b*x^n)^5//2*(c+d*x^n)^-1//2, x) == :(1//4*b^-1*d^-1*n^-1*(a+b*x^n)^7//2*(c+d*x^n)^(1/2)+-1//24*b^-1*d^-2*n^-1*(a+b*x^n)^5//2*(c+d*x^n)^(1/2)*(a*d+7*b*c)+5//64*b^-3//2*d^-9//2*n^-1*(b*c+-1*a*d)^3*(a*d+7*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x^n)^(1/2)*(c+d*x^n)^-1//2)+-5//64*b^-1*d^-4*n^-1*(a+b*x^n)^(1/2)*(c+d*x^n)^(1/2)*(b*c+-1*a*d)^2*(a*d+7*b*c)+1//96*b^-1*d^-3*n^-1*(a+b*x^n)^3//2*(c+d*x^n)^(1/2)*(a*d+7*b*c)*(-5*a*d+5*b*c))
@test integrate(x^(-1+2n)*(a+b*x^n)^3//2*(c+d*x^n)^-1//2, x) == :(1//3*b^-1*d^-1*n^-1*(a+b*x^n)^5//2*(c+d*x^n)^(1/2)+-1//8*b^-3//2*d^-7//2*n^-1*(b*c+-1*a*d)^2*(a*d+5*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x^n)^(1/2)*(c+d*x^n)^-1//2)+-1//12*b^-1*d^-2*n^-1*(a+b*x^n)^3//2*(c+d*x^n)^(1/2)*(a*d+5*b*c)+1//8*b^-1*d^-3*n^-1*(a+b*x^n)^(1/2)*(c+d*x^n)^(1/2)*(a*d+5*b*c)*(b*c+-1*a*d))
@test integrate(x^(-1+2n)*(a+b*x^n)^(1/2)*(c+d*x^n)^-1//2, x) == :((1/2)*b^-1*d^-1*n^-1*(a+b*x^n)^3//2*(c+d*x^n)^(1/2)+-1//4*b^-1*d^-2*n^-1*(a+b*x^n)^(1/2)*(c+d*x^n)^(1/2)*(a*d+3*b*c)+1//4*b^-3//2*d^-5//2*n^-1*(a*d+3*b*c)*(b*c+-1*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x^n)^(1/2)*(c+d*x^n)^-1//2))
@test integrate(x^(-1+2n)*(a+b*x^n)^-1//2*(c+d*x^n)^-1//2, x) == :(b^-1*d^-1*n^-1*(a+b*x^n)^(1/2)*(c+d*x^n)^(1/2)+-1*b^-3//2*d^-3//2*n^-1*(a*d+b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*x^n)^(1/2)*(c+d*x^n)^-1//2))
@test integrate(x^(-1+2n)*(a+b*x^n)^-3//2*(c+d*x^n)^-1//2, x) == :(2*b^-3//2*d^-1//2*n^-1*arctanh(b^-1//2*d^(1/2)*(a+b*x^n)^(1/2)*(c+d*x^n)^-1//2)+2*a*b^-1*n^-1*(a+b*x^n)^-1//2*(c+d*x^n)^(1/2)*(b*c+-1*a*d)^-1)
@test integrate(x^(-1+2n)*(a+b*x^n)^-5//2*(c+d*x^n)^-1//2, x) == :(-1//3*b^-1*n^-1*(a+b*x^n)^-1//2*(c+d*x^n)^(1/2)*(b*c+-1*a*d)^-2*(-2*a*d+6*b*c)+2//3*a*b^-1*n^-1*(a+b*x^n)^-3//2*(c+d*x^n)^(1/2)*(b*c+-1*a*d)^-1)
@test integrate(x^(-1+3n)*(a+b*x^n)^5//2*(c+d*x^n)^-1//2, x) == :(-1//40*b^-2*d^-2*n^-1*(a+b*x^n)^7//2*(c+d*x^n)^(1/2)*(3*a*d+9*b*c)+-1//128*b^-5//2*d^-11//2*n^-1*(b*c+-1*a*d)^3*(3*a^2*d^2+63*b^2*c^2+14*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x^n)^(1/2)*(c+d*x^n)^-1//2)+1//5*b^-1*d^-1*n^-1*x^n*(a+b*x^n)^7//2*(c+d*x^n)^(1/2)+1//240*b^-2*d^-3*n^-1*(a+b*x^n)^5//2*(c+d*x^n)^(1/2)*(3*a^2*d^2+63*b^2*c^2+14*a*b*c*d)+-1//192*b^-2*d^-4*n^-1*(a+b*x^n)^3//2*(c+d*x^n)^(1/2)*(b*c+-1*a*d)*(3*a^2*d^2+63*b^2*c^2+14*a*b*c*d)+1//128*b^-2*d^-5*n^-1*(a+b*x^n)^(1/2)*(c+d*x^n)^(1/2)*(b*c+-1*a*d)^2*(3*a^2*d^2+63*b^2*c^2+14*a*b*c*d))
@test integrate(x^(-1+3n)*(a+b*x^n)^3//2*(c+d*x^n)^-1//2, x) == :(-1//24*b^-2*d^-2*n^-1*(a+b*x^n)^5//2*(c+d*x^n)^(1/2)*(3*a*d+7*b*c)+1//4*b^-1*d^-1*n^-1*x^n*(a+b*x^n)^5//2*(c+d*x^n)^(1/2)+1//64*b^-5//2*d^-9//2*n^-1*(b*c+-1*a*d)^2*(3*a^2*d^2+35*b^2*c^2+10*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x^n)^(1/2)*(c+d*x^n)^-1//2)+1//96*b^-2*d^-3*n^-1*(a+b*x^n)^3//2*(c+d*x^n)^(1/2)*(3*a^2*d^2+35*b^2*c^2+10*a*b*c*d)+-1//64*b^-2*d^-4*n^-1*(a+b*x^n)^(1/2)*(c+d*x^n)^(1/2)*(b*c+-1*a*d)*(3*a^2*d^2+35*b^2*c^2+10*a*b*c*d))
@test integrate(x^(-1+3n)*(a+b*x^n)^(1/2)*(c+d*x^n)^-1//2, x) == :(-1//8*b^-5//2*d^-7//2*n^-1*(b*c+-1*a*d)*(a^2*d^2+5*b^2*c^2+2*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x^n)^(1/2)*(c+d*x^n)^-1//2)+-1//12*b^-2*d^-2*n^-1*(a+b*x^n)^3//2*(c+d*x^n)^(1/2)*(3*a*d+5*b*c)+1//3*b^-1*d^-1*n^-1*x^n*(a+b*x^n)^3//2*(c+d*x^n)^(1/2)+1//8*b^-2*d^-3*n^-1*(a+b*x^n)^(1/2)*(c+d*x^n)^(1/2)*(a^2*d^2+5*b^2*c^2+2*a*b*c*d))
@test integrate(x^(-1+3n)*(a+b*x^n)^-1//2*(c+d*x^n)^-1//2, x) == :(-1//4*b^-5//2*d^-5//2*n^-1*(-3*(a*d+b*c)^2+4*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x^n)^(1/2)*(c+d*x^n)^-1//2)+(1/2)*b^-1*d^-1*n^-1*x^n*(a+b*x^n)^(1/2)*(c+d*x^n)^(1/2)+-1//4*b^-2*d^-2*n^-1*(a+b*x^n)^(1/2)*(c+d*x^n)^(1/2)*(3*a*d+3*b*c))
@test integrate(x^(-1+3n)*(a+b*x^n)^-3//2*(c+d*x^n)^-1//2, x) == :(b^-2*d^-1*n^-1*(a+b*x^n)^(1/2)*(c+d*x^n)^(1/2)+-1*b^-5//2*d^-3//2*n^-1*(b*c+3*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*x^n)^(1/2)*(c+d*x^n)^-1//2)+-2*a^2*b^-2*n^-1*(a+b*x^n)^-1//2*(c+d*x^n)^(1/2)*(b*c+-1*a*d)^-1)
@test integrate(x^(-1+3n)*(a+b*x^n)^-5//2*(c+d*x^n)^-1//2, x) == :(2*b^-5//2*d^-1//2*n^-1*arctanh(b^-1//2*d^(1/2)*(a+b*x^n)^(1/2)*(c+d*x^n)^-1//2)+-2//3*a^2*b^-2*n^-1*(a+b*x^n)^-3//2*(c+d*x^n)^(1/2)*(b*c+-1*a*d)^-1+4//3*a*b^-2*n^-1*(a+b*x^n)^-1//2*(c+d*x^n)^(1/2)*(b*c+-1*a*d)^-2*(-2*a*d+3*b*c))
@test integrate(x^p*(b+c*x)^p*(b+2*c*x), x) == :(x^(1+p)*(1+p)^-1*(b+c*x)^(1+p))
@test integrate(x^(1+2p)*(b+c*x^2)^p*(b+2*c*x^2), x) == :(x^(2+2p)*(2+2p)^-1*(b+c*x^2)^(1+p))
@test integrate(x^(2+3p)*(b+c*x^3)^p*(b+2*c*x^3), x) == :(x^(3+3p)*(3+3p)^-1*(b+c*x^3)^(1+p))
@test integrate(x^(-1+n*(1+p))*(b+c*x^n)^p*(b+2*c*x^n), x) == :(n^-1*x^(n*(1+p))*(1+p)^-1*(b+c*x^n)^(1+p))

max_stars_repo_path: test/1 Algebraic functions/1.1 Binomial products/1.1.3 General/1.1.3.4 (e x)^m (a+b x^n)^p (c+d x^n)^q.jl