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

@test integrate((a*x^3+b*x^6)^5//3, x) == :(1//11*b^-1*x^-5*(a*x^3+b*x^6)^8//3+-3//88*a*b^-2*x^-8*(a*x^3+b*x^6)^8//3)
@test integrate((a*x^3+b*x^6)^2//3, x) == :(1//5*b^-1*x^-5*(a*x^3+b*x^6)^5//3)
@test integrate((a*x^3+b*x^6)^-2//3, x) == :(-1*a^-1*x^-2*(a*x^3+b*x^6)^1//3)
@test integrate((a*x^3+b*x^6)^-5//3, x) == :((1/2)*a^-1*x^-2*(a*x^3+b*x^6)^-2//3+-3//4*a^-2*x^-5*(a*x^3+b*x^6)^1//3+9//4*b*a^-3*x^-2*(a*x^3+b*x^6)^1//3)
@test integrate((x^6+-1*x^3)^-1, x) == :((1/2)*x^-2+-1//6*log(1+x+x^2)+1//3*log(1+-1x)+-1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+2x)))
@test integrate(x^5*(a^2+b^2*x^6+2*a*b*x^3)^(1/2), x) == :(a*x^6*(6a+6*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+b*x^9*(9a+9*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^4*(a^2+b^2*x^6+2*a*b*x^3)^(1/2), x) == :(a*x^5*(5a+5*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+b*x^8*(8a+8*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^3*(a^2+b^2*x^6+2*a*b*x^3)^(1/2), x) == :(a*x^4*(4a+4*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+b*x^7*(7a+7*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^2*(a^2+b^2*x^6+2*a*b*x^3)^(1/2), x) == :(1//6*b^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)*(a+b*x^3))
@test integrate(x*(a^2+b^2*x^6+2*a*b*x^3)^(1/2), x) == :(a*x^2*(2a+2*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+b*x^5*(5a+5*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate((a^2+b^2*x^6+2*a*b*x^3)^(1/2), x) == :(a*x*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+b*x^4*(4a+4*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2), x) == :(a*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)*log(x)+b*x^3*(3a+3*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-2*(a^2+b^2*x^6+2*a*b*x^3)^(1/2), x) == :(b*x^2*(2a+2*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1*a*x^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-3*(a^2+b^2*x^6+2*a*b*x^3)^(1/2), x) == :(b*x*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//2*a*x^-2*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-4*(a^2+b^2*x^6+2*a*b*x^3)^(1/2), x) == :(b*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)*log(x)+-1//3*a*x^-3*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-5*(a^2+b^2*x^6+2*a*b*x^3)^(1/2), x) == :(-1*b*x^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//4*a*x^-4*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-6*(a^2+b^2*x^6+2*a*b*x^3)^(1/2), x) == :(-1//2*b*x^-2*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//5*a*x^-5*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-7*(a^2+b^2*x^6+2*a*b*x^3)^(1/2), x) == :(-1//3*b*x^-3*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//6*a*x^-6*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-8*(a^2+b^2*x^6+2*a*b*x^3)^(1/2), x) == :(-1//4*b*x^-4*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//7*a*x^-7*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-9*(a^2+b^2*x^6+2*a*b*x^3)^(1/2), x) == :(-1//5*b*x^-5*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//8*a*x^-8*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-10*(a^2+b^2*x^6+2*a*b*x^3)^(1/2), x) == :(-1//6*b*x^-6*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//9*a*x^-9*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-11*(a^2+b^2*x^6+2*a*b*x^3)^(1/2), x) == :(-1//7*b*x^-7*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//10*a*x^-10*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^9*(a^2+b^2*x^6+2*a*b*x^3)^3//2, x) == :(a^3*x^10*(10a+10*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+b^3*x^19*(19a+19*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+3*a*b^2*x^16*(16a+16*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+3*b*a^2*x^13*(13a+13*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^8*(a^2+b^2*x^6+2*a*b*x^3)^3//2, x) == :(1//18*b^-3*(a+b*x^3)^5*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-2//15*a*b^-3*(a+b*x^3)^4*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+1//12*a^2*b^-3*(a+b*x^3)^3*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^7*(a^2+b^2*x^6+2*a*b*x^3)^3//2, x) == :(a^3*x^8*(8a+8*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+b^3*x^17*(17a+17*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+3*a*b^2*x^14*(14a+14*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+3*b*a^2*x^11*(11a+11*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^6*(a^2+b^2*x^6+2*a*b*x^3)^3//2, x) == :(a^3*x^7*(7a+7*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+b^3*x^16*(16a+16*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+3*a*b^2*x^13*(13a+13*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+3*b*a^2*x^10*(10a+10*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^5*(a^2+b^2*x^6+2*a*b*x^3)^3//2, x) == :(1//15*b^-2*(a+b*x^3)^4*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//12*a*b^-2*(a+b*x^3)^3*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^4*(a^2+b^2*x^6+2*a*b*x^3)^3//2, x) == :(a^3*x^5*(5a+5*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+b^3*x^14*(14a+14*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+3*a*b^2*x^11*(11a+11*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+3*b*a^2*x^8*(8a+8*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^3*(a^2+b^2*x^6+2*a*b*x^3)^3//2, x) == :(a^3*x^4*(4a+4*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+b^3*x^13*(13a+13*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+3*a*b^2*x^10*(10a+10*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+3*b*a^2*x^7*(7a+7*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^2*(a^2+b^2*x^6+2*a*b*x^3)^3//2, x) == :(1//12*b^-1*(a^2+b^2*x^6+2*a*b*x^3)^3//2*(a+b*x^3))
@test integrate(x*(a^2+b^2*x^6+2*a*b*x^3)^3//2, x) == :(a^3*x^2*(2a+2*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+b^3*x^11*(11a+11*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+3*a*b^2*x^8*(8a+8*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+3*b*a^2*x^5*(5a+5*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate((a^2+b^2*x^6+2*a*b*x^3)^3//2, x) == :(x*a^3*(a+b*x^3)^-3*(a^2+b^2*x^6+2*a*b*x^3)^3//2+1//10*b^3*x^10*(a+b*x^3)^-3*(a^2+b^2*x^6+2*a*b*x^3)^3//2+3//4*b*a^2*x^4*(a+b*x^3)^-3*(a^2+b^2*x^6+2*a*b*x^3)^3//2+3//7*a*b^2*x^7*(a+b*x^3)^-3*(a^2+b^2*x^6+2*a*b*x^3)^3//2)
@test integrate(x^-1*(a^2+b^2*x^6+2*a*b*x^3)^3//2, x) == :(a^3*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)*log(x)+b^3*x^9*(9a+9*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+a*b^2*x^6*(2a+2*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+b*a^2*x^3*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-2*(a^2+b^2*x^6+2*a*b*x^3)^3//2, x) == :(b^3*x^8*(8a+8*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1*a^3*x^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+3*a*b^2*x^5*(5a+5*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+3*b*a^2*x^2*(2a+2*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-3*(a^2+b^2*x^6+2*a*b*x^3)^3//2, x) == :(b^3*x^7*(7a+7*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//2*a^3*x^-2*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+3*a*b^2*x^4*(4a+4*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+3*b*x*a^2*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-4*(a^2+b^2*x^6+2*a*b*x^3)^3//2, x) == :(b^3*x^6*(6a+6*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//3*a^3*x^-3*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+a*b^2*x^3*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+3*b*a^2*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)*log(x))
@test integrate(x^-5*(a^2+b^2*x^6+2*a*b*x^3)^3//2, x) == :(b^3*x^5*(5a+5*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//4*a^3*x^-4*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-3*b*a^2*x^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+3*a*b^2*x^2*(2a+2*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-6*(a^2+b^2*x^6+2*a*b*x^3)^3//2, x) == :(b^3*x^4*(4a+4*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//5*a^3*x^-5*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+3*a*x*b^2*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-3//2*b*a^2*x^-2*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-7*(a^2+b^2*x^6+2*a*b*x^3)^3//2, x) == :(b^3*x^3*(3a+3*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//6*a^3*x^-6*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1*b*a^2*x^-3*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+3*a*b^2*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)*log(x))
@test integrate(x^-8*(a^2+b^2*x^6+2*a*b*x^3)^3//2, x) == :(b^3*x^2*(2a+2*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//7*a^3*x^-7*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-3*a*b^2*x^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-3//4*b*a^2*x^-4*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-9*(a^2+b^2*x^6+2*a*b*x^3)^3//2, x) == :(x*b^3*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//8*a^3*x^-8*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-3//2*a*b^2*x^-2*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-3//5*b*a^2*x^-5*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-10*(a^2+b^2*x^6+2*a*b*x^3)^3//2, x) == :(b^3*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)*log(x)+-1//9*a^3*x^-9*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1*a*b^2*x^-3*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//2*b*a^2*x^-6*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-11*(a^2+b^2*x^6+2*a*b*x^3)^3//2, x) == :(-1*b^3*x^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//10*a^3*x^-10*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-3//4*a*b^2*x^-4*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-3//7*b*a^2*x^-7*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-12*(a^2+b^2*x^6+2*a*b*x^3)^3//2, x) == :(-1//2*b^3*x^-2*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//11*a^3*x^-11*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-3//5*a*b^2*x^-5*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-3//8*b*a^2*x^-8*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-13*(a^2+b^2*x^6+2*a*b*x^3)^3//2, x) == :(-1//12*a^-1*x^-12*(a+b*x^3)^3*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-14*(a^2+b^2*x^6+2*a*b*x^3)^3//2, x) == :(-1//4*b^3*x^-4*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//13*a^3*x^-13*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-3//7*a*b^2*x^-7*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-3//10*b*a^2*x^-10*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-15*(a^2+b^2*x^6+2*a*b*x^3)^3//2, x) == :(-1//5*b^3*x^-5*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//14*a^3*x^-14*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-3//8*a*b^2*x^-8*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-3//11*b*a^2*x^-11*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-16*(a^2+b^2*x^6+2*a*b*x^3)^3//2, x) == :(-1//15*a^-1*x^-15*(a+b*x^3)^3*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+1//60*b*a^-2*x^-12*(a+b*x^3)^3*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-17*(a^2+b^2*x^6+2*a*b*x^3)^3//2, x) == :(-1//7*b^3*x^-7*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//16*a^3*x^-16*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-3//10*a*b^2*x^-10*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-3//13*b*a^2*x^-13*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^13*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(a^5*x^14*(14a+14*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+b^5*x^29*(29a+29*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+a^3*b^2*x^20*(2a+2*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a*b^4*x^26*(26a+26*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*b*a^4*x^17*(17a+17*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+10*a^2*b^3*x^23*(23a+23*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^12*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(a^5*x^13*(13a+13*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+b^5*x^28*(28a+28*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+a*b^4*x^25*(5a+5*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*b*a^4*x^16*(16a+16*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a^2*b^3*x^22*(11a+11*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+10*a^3*b^2*x^19*(19a+19*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^11*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(1//27*b^-4*(a+b*x^3)^8*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//8*a*b^-4*(a+b*x^3)^7*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//18*a^3*b^-4*(a+b*x^3)^5*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+1//7*a^2*b^-4*(a+b*x^3)^6*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^10*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(a^5*x^11*(11a+11*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+b^5*x^26*(26a+26*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+a^2*b^3*x^20*(2a+2*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a*b^4*x^23*(23a+23*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*b*a^4*x^14*(14a+14*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+10*a^3*b^2*x^17*(17a+17*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^9*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(a^5*x^10*(10a+10*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+b^5*x^25*(25a+25*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a*b^4*x^22*(22a+22*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*b*a^4*x^13*(13a+13*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a^3*b^2*x^16*(8a+8*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+10*a^2*b^3*x^19*(19a+19*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^8*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(1//24*b^-3*(a+b*x^3)^7*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-2//21*a*b^-3*(a+b*x^3)^6*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+1//18*a^2*b^-3*(a+b*x^3)^5*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^7*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(a^5*x^8*(8a+8*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+b^5*x^23*(23a+23*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+a*b^4*x^20*(4a+4*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*b*a^4*x^11*(11a+11*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a^3*b^2*x^14*(7a+7*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+10*a^2*b^3*x^17*(17a+17*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^6*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(a^5*x^7*(7a+7*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+b^5*x^22*(22a+22*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+b*a^4*x^10*(2a+2*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a*b^4*x^19*(19a+19*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a^2*b^3*x^16*(8a+8*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+10*a^3*b^2*x^13*(13a+13*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^5*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(1//21*b^-2*(a+b*x^3)^6*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//18*a*b^-2*(a+b*x^3)^5*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^4*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(a^5*x^5*(5a+5*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+b^5*x^20*(20a+20*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a*b^4*x^17*(17a+17*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*b*a^4*x^8*(8a+8*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a^2*b^3*x^14*(7a+7*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+10*a^3*b^2*x^11*(11a+11*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^3*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(a^5*x^4*(4a+4*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+b^5*x^19*(19a+19*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+a^3*b^2*x^10*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a*b^4*x^16*(16a+16*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*b*a^4*x^7*(7a+7*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+10*a^2*b^3*x^13*(13a+13*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^2*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(1//18*b^-1*(a^2+b^2*x^6+2*a*b*x^3)^5//2*(a+b*x^3))
@test integrate(x*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(a^5*x^2*(2a+2*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+b^5*x^17*(17a+17*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+b*a^4*x^5*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a*b^4*x^14*(14a+14*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a^3*b^2*x^8*(4a+4*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+10*a^2*b^3*x^11*(11a+11*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate((a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(x*a^5*(a+b*x^3)^-5*(a^2+b^2*x^6+2*a*b*x^3)^5//2+1//16*b^5*x^16*(a+b*x^3)^-5*(a^2+b^2*x^6+2*a*b*x^3)^5//2+a^2*b^3*x^10*(a+b*x^3)^-5*(a^2+b^2*x^6+2*a*b*x^3)^5//2+5//4*b*a^4*x^4*(a+b*x^3)^-5*(a^2+b^2*x^6+2*a*b*x^3)^5//2+5//13*a*b^4*x^13*(a+b*x^3)^-5*(a^2+b^2*x^6+2*a*b*x^3)^5//2+10//7*a^3*b^2*x^7*(a+b*x^3)^-5*(a^2+b^2*x^6+2*a*b*x^3)^5//2)
@test integrate(x^-1*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(a^5*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)*log(x)+b^5*x^15*(15a+15*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a*b^4*x^12*(12a+12*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*b*a^4*x^3*(3a+3*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a^3*b^2*x^6*(3a+3*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+10*a^2*b^3*x^9*(9a+9*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-2*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(b^5*x^14*(14a+14*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1*a^5*x^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+2*a^3*b^2*x^5*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a*b^4*x^11*(11a+11*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*b*a^4*x^2*(2a+2*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a^2*b^3*x^8*(4a+4*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-3*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(b^5*x^13*(13a+13*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//2*a^5*x^-2*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+a*b^4*x^10*(2a+2*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*b*x*a^4*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a^3*b^2*x^4*(2a+2*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+10*a^2*b^3*x^7*(7a+7*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-4*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(b^5*x^12*(12a+12*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//3*a^5*x^-3*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a*b^4*x^9*(9a+9*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*b*a^4*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)*log(x)+5*a^2*b^3*x^6*(3a+3*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+10*a^3*b^2*x^3*(3a+3*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-5*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(b^5*x^11*(11a+11*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//4*a^5*x^-4*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5*b*a^4*x^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+2*a^2*b^3*x^5*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a*b^4*x^8*(8a+8*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a^3*b^2*x^2*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-6*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(b^5*x^10*(10a+10*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//5*a^5*x^-5*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a*b^4*x^7*(7a+7*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a^2*b^3*x^4*(2a+2*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+10*x*a^3*b^2*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5//2*b*a^4*x^-2*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-7*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(b^5*x^9*(9a+9*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//6*a^5*x^-6*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a*b^4*x^6*(6a+6*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+10*a^2*b^3*x^3*(3a+3*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+10*a^3*b^2*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)*log(x)+-5//3*b*a^4*x^-3*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-8*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(b^5*x^8*(8a+8*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//7*a^5*x^-7*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+a*b^4*x^5*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-10*a^3*b^2*x^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a^2*b^3*x^2*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5//4*b*a^4*x^-4*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-9*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(b^5*x^7*(7a+7*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//8*a^5*x^-8*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1*b*a^4*x^-5*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5*a^3*b^2*x^-2*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a*b^4*x^4*(4a+4*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+10*x*a^2*b^3*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-10*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(b^5*x^6*(6a+6*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//9*a^5*x^-9*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a*b^4*x^3*(3a+3*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+10*a^2*b^3*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)*log(x)+-10//3*a^3*b^2*x^-3*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5//6*b*a^4*x^-6*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-11*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(b^5*x^5*(5a+5*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//10*a^5*x^-10*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-10*a^2*b^3*x^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a*b^4*x^2*(2a+2*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5//2*a^3*b^2*x^-4*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5//7*b*a^4*x^-7*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-12*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(b^5*x^4*(4a+4*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//11*a^5*x^-11*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5*a^2*b^3*x^-2*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-2*a^3*b^2*x^-5*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a*x*b^4*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5//8*b*a^4*x^-8*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-13*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(b^5*x^3*(3a+3*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//12*a^5*x^-12*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a*b^4*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)*log(x)+-10//3*a^2*b^3*x^-3*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5//3*a^3*b^2*x^-6*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5//9*b*a^4*x^-9*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-14*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(b^5*x^2*(2a+2*b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//13*a^5*x^-13*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5*a*b^4*x^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-10//7*a^3*b^2*x^-7*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5//2*a^2*b^3*x^-4*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//2*b*a^4*x^-10*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-15*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(x*b^5*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//14*a^5*x^-14*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-2*a^2*b^3*x^-5*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5//2*a*b^4*x^-2*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5//4*a^3*b^2*x^-8*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5//11*b*a^4*x^-11*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-16*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(b^5*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)*log(x)+-1//15*a^5*x^-15*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-10//9*a^3*b^2*x^-9*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5//3*a*b^4*x^-3*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5//3*a^2*b^3*x^-6*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5//12*b*a^4*x^-12*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-17*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(-1*b^5*x^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//16*a^5*x^-16*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1*a^3*b^2*x^-10*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-10//7*a^2*b^3*x^-7*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5//4*a*b^4*x^-4*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5//13*b*a^4*x^-13*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-18*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(-1//2*b^5*x^-2*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//17*a^5*x^-17*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1*a*b^4*x^-5*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-10//11*a^3*b^2*x^-11*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5//4*a^2*b^3*x^-8*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5//14*b*a^4*x^-14*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-19*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(-1//18*a^-1*x^-18*(a+b*x^3)^5*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-20*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(-1//4*b^5*x^-4*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//19*a^5*x^-19*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1*a^2*b^3*x^-10*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-10//13*a^3*b^2*x^-13*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5//7*a*b^4*x^-7*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5//16*b*a^4*x^-16*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-21*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(-1//5*b^5*x^-5*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//20*a^5*x^-20*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-10//11*a^2*b^3*x^-11*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5//7*a^3*b^2*x^-14*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5//8*a*b^4*x^-8*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5//17*b*a^4*x^-17*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-22*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(-1//21*a^-1*x^-21*(a+b*x^3)^5*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+1//126*b*a^-2*x^-18*(a+b*x^3)^5*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-23*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(-1//7*b^5*x^-7*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//22*a^5*x^-22*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-10//13*a^2*b^3*x^-13*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5//8*a^3*b^2*x^-16*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5//19*b*a^4*x^-19*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//2*a*b^4*x^-10*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-24*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(-1//8*b^5*x^-8*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//23*a^5*x^-23*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-10//17*a^3*b^2*x^-17*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5//7*a^2*b^3*x^-14*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-5//11*a*b^4*x^-11*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//4*b*a^4*x^-20*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^-25*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(-1//24*a^-1*x^-24*(a+b*x^3)^5*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+-1//504*a^-3*b^2*x^-18*(a+b*x^3)^5*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+1//84*b*a^-2*x^-21*(a+b*x^3)^5*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^4*(a^2+b^2*x^6+2*a*b*x^3)^-1//2, x) == :((1/2)*b^-1*x^2*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)+-1//6*a^2//3*b^-5//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^2//3*b^-5//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(a^1//3+x*b^1//3)+1//3*3^(1/2)*a^2//3*b^-5//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2, x) == :(x*b^-1*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)+-1//3*a^1//3*b^-4//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(a^1//3+x*b^1//3)+1//6*a^1//3*b^-4//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*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^-4//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^2*(a^2+b^2*x^6+2*a*b*x^3)^-1//2, x) == :(1//3*b^-1*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(a+b*x^3))
@test integrate(x*(a^2+b^2*x^6+2*a*b*x^3)^-1//2, x) == :(-1//3*a^-1//3*b^-2//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(a^1//3+x*b^1//3)+1//6*a^-1//3*b^-2//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*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^-2//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate((a^2+b^2*x^6+2*a*b*x^3)^-1//2, x) == :(-1//6*a^-2//3*b^-1//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-2//3*b^-1//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(a^1//3+x*b^1//3)+-1//3*3^(1/2)*a^-2//3*b^-1//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-1*(a^2+b^2*x^6+2*a*b*x^3)^-1//2, x) == :(a^-1*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(x)+-1//3*a^-1*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(a+b*x^3))
@test integrate(x^-2*(a^2+b^2*x^6+2*a*b*x^3)^-1//2, x) == :(-1*a^-1*x^-1*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)+-1//6*a^-4//3*b^1//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-4//3*b^1//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(a^1//3+x*b^1//3)+1//3*3^(1/2)*a^-4//3*b^1//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2, x) == :((1/2)*a^-1*x^-2*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(-1a+-1*b*x^3)+-1//3*a^-5//3*b^2//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(a^1//3+x*b^1//3)+1//6*a^-5//3*b^2//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*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^2//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-4*(a^2+b^2*x^6+2*a*b*x^3)^-1//2, x) == :(1//3*a^-1*x^-3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(-1a+-1*b*x^3)+-1*b*a^-2*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(x)+1//3*b*a^-2*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(a+b*x^3))
@test integrate(x^4*(a^2+b^2*x^6+2*a*b*x^3)^-3//2, x) == :(-1//6*b^-1*x^2*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+1//9*a^-1*b^-1*x^2*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+-1//27*a^-4//3*b^-5//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(a^1//3+x*b^1//3)+1//54*a^-4//3*b^-5//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//27*3^(1/2)*a^-4//3*b^-5//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^3*(a^2+b^2*x^6+2*a*b*x^3)^-3//2, x) == :(-1//6*x*b^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+1//18*x*a^-1*b^-1*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+-1//54*a^-5//3*b^-4//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//27*a^-5//3*b^-4//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(a^1//3+x*b^1//3)+-1//27*3^(1/2)*a^-5//3*b^-4//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^2*(a^2+b^2*x^6+2*a*b*x^3)^-3//2, x) == :(-1//6*b^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^-1//2)
@test integrate(x*(a^2+b^2*x^6+2*a*b*x^3)^-3//2, x) == :(2//9*a^-2*x^2*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+1//6*a^-1*x^2*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+-1//27*a^-7//3*b^-2//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(2a+2*b*x^3)*log(a^1//3+x*b^1//3)+1//27*a^-7//3*b^-2//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*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^-2//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(2a+2*b*x^3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate((a^2+b^2*x^6+2*a*b*x^3)^-3//2, x) == :(1//6*x*a^-1*(a^2+b^2*x^6+2*a*b*x^3)^-3//2*(a+b*x^3)+5//18*x*a^-2*(a+b*x^3)^2*(a^2+b^2*x^6+2*a*b*x^3)^-3//2+-5//54*a^-8//3*b^-1//3*(a+b*x^3)^3*(a^2+b^2*x^6+2*a*b*x^3)^-3//2*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+5//27*a^-8//3*b^-1//3*(a+b*x^3)^3*(a^2+b^2*x^6+2*a*b*x^3)^-3//2*log(a^1//3+x*b^1//3)+-5//27*3^(1/2)*a^-8//3*b^-1//3*(a+b*x^3)^3*(a^2+b^2*x^6+2*a*b*x^3)^-3//2*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-1*(a^2+b^2*x^6+2*a*b*x^3)^-3//2, x) == :(1//3*a^-2*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+1//6*a^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+a^-3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(x)+-1//3*a^-3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(a+b*x^3))
@test integrate(x^-2*(a^2+b^2*x^6+2*a*b*x^3)^-3//2, x) == :(7//18*a^-2*x^-1*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+-1//9*a^-3*x^-1*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(14a+14*b*x^3)+1//6*a^-1*x^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+-7//27*a^-10//3*b^1//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+14//27*a^-10//3*b^1//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(a^1//3+x*b^1//3)+14//27*3^(1/2)*a^-10//3*b^1//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-3*(a^2+b^2*x^6+2*a*b*x^3)^-3//2, x) == :(4//9*a^-2*x^-2*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+-1//9*a^-3*x^-2*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(10a+10*b*x^3)+1//6*a^-1*x^-2*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+-20//27*a^-11//3*b^2//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(a^1//3+x*b^1//3)+10//27*a^-11//3*b^2//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+20//27*3^(1/2)*a^-11//3*b^2//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-4*(a^2+b^2*x^6+2*a*b*x^3)^-3//2, x) == :(-2//3*b*a^-3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+-1//3*a^-3*x^-3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)+-1//6*b*a^-2*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+b*a^-4*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(a+b*x^3)+-3*b*a^-4*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(x))
@test integrate(x^6*(a^2+b^2*x^6+2*a*b*x^3)^-5//2, x) == :(-1//12*b^-1*x^4*(a+b*x^3)^-3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+-1//27*x*b^-2*(a+b*x^3)^-2*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+5//486*x*a^-2*b^-2*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+-1//1458*a^-8//3*b^-7//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(5a+5*b*x^3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//162*x*a^-1*b^-2*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+1//729*a^-8//3*b^-7//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(5a+5*b*x^3)*log(a^1//3+x*b^1//3)+-1//729*3^(1/2)*a^-8//3*b^-7//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(5a+5*b*x^3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^5*(a^2+b^2*x^6+2*a*b*x^3)^-5//2, x) == :(-1//9*b^-2*(a+b*x^3)^-2*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+1//12*a*b^-2*(a+b*x^3)^-3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2)
@test integrate(x^4*(a^2+b^2*x^6+2*a*b*x^3)^-5//2, x) == :(-1//12*b^-1*x^2*(a+b*x^3)^-3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+7//243*a^-3*b^-1*x^2*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+-1//729*a^-10//3*b^-5//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(7a+7*b*x^3)*log(a^1//3+x*b^1//3)+1//54*a^-1*b^-1*x^2*(a+b*x^3)^-2*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+1//1458*a^-10//3*b^-5//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(7a+7*b*x^3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+7//324*a^-2*b^-1*x^2*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+-1//729*3^(1/2)*a^-10//3*b^-5//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(7a+7*b*x^3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^3*(a^2+b^2*x^6+2*a*b*x^3)^-5//2, x) == :(-1//12*x*b^-1*(a+b*x^3)^-3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+5//243*x*a^-3*b^-1*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+-1//729*a^-11//3*b^-4//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(5a+5*b*x^3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//81*x*a^-2*b^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+1//108*x*a^-1*b^-1*(a+b*x^3)^-2*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+1//729*a^-11//3*b^-4//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(10a+10*b*x^3)*log(a^1//3+x*b^1//3)+-1//729*3^(1/2)*a^-11//3*b^-4//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(10a+10*b*x^3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^2*(a^2+b^2*x^6+2*a*b*x^3)^-5//2, x) == :(-1//12*b^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^-3//2)
@test integrate(x*(a^2+b^2*x^6+2*a*b*x^3)^-5//2, x) == :(35//243*a^-4*x^2*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+1//12*a^-1*x^2*(a+b*x^3)^-3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+5//54*a^-2*x^2*(a+b*x^3)^-2*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+35//324*a^-3*x^2*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+-1//729*a^-13//3*b^-2//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(35a+35*b*x^3)*log(a^1//3+x*b^1//3)+1//1458*a^-13//3*b^-2//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(35a+35*b*x^3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//729*3^(1/2)*a^-13//3*b^-2//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(35a+35*b*x^3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate((a^2+b^2*x^6+2*a*b*x^3)^-5//2, x) == :(1//12*x*a^-1*(a^2+b^2*x^6+2*a*b*x^3)^-5//2*(a+b*x^3)+11//81*x*a^-3*(a+b*x^3)^3*(a^2+b^2*x^6+2*a*b*x^3)^-5//2+11//108*x*a^-2*(a+b*x^3)^2*(a^2+b^2*x^6+2*a*b*x^3)^-5//2+55//243*x*a^-4*(a+b*x^3)^4*(a^2+b^2*x^6+2*a*b*x^3)^-5//2+-55//729*a^-14//3*b^-1//3*(a+b*x^3)^5*(a^2+b^2*x^6+2*a*b*x^3)^-5//2*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+110//729*a^-14//3*b^-1//3*(a+b*x^3)^5*(a^2+b^2*x^6+2*a*b*x^3)^-5//2*log(a^1//3+x*b^1//3)+-110//729*3^(1/2)*a^-14//3*b^-1//3*(a+b*x^3)^5*(a^2+b^2*x^6+2*a*b*x^3)^-5//2*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-1*(a^2+b^2*x^6+2*a*b*x^3)^-5//2, x) == :(1//3*a^-4*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+1//6*a^-3*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+1//9*a^-2*(a+b*x^3)^-2*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+1//12*a^-1*(a+b*x^3)^-3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+a^-5*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(x)+-1//3*a^-5*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(a+b*x^3))
@test integrate(x^-2*(a^2+b^2*x^6+2*a*b*x^3)^-5//2, x) == :(455//972*a^-4*x^-1*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+-1//243*a^-5*x^-1*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(455a+455*b*x^3)+1//12*a^-1*x^-1*(a+b*x^3)^-3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+13//108*a^-2*x^-1*(a+b*x^3)^-2*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+65//324*a^-3*x^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+-455//1458*a^-16//3*b^1//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+455//729*a^-16//3*b^1//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(a^1//3+x*b^1//3)+455//729*3^(1/2)*a^-16//3*b^1//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-3*(a^2+b^2*x^6+2*a*b*x^3)^-5//2, x) == :(154//243*a^-4*x^-2*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+-1//243*a^-5*x^-2*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(385a+385*b*x^3)+1//12*a^-1*x^-2*(a+b*x^3)^-3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+7//54*a^-2*x^-2*(a+b*x^3)^-2*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+77//324*a^-3*x^-2*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+-770//729*a^-17//3*b^2//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(a^1//3+x*b^1//3)+385//729*a^-17//3*b^2//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+770//729*3^(1/2)*a^-17//3*b^2//3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-4*(a^2+b^2*x^6+2*a*b*x^3)^-5//2, x) == :(-4//3*b*a^-5*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+-2//9*b*a^-3*(a+b*x^3)^-2*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+-1//2*b*a^-4*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+-1//3*a^-5*x^-3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)+-1//12*b*a^-2*(a+b*x^3)^-3*(a^2+b^2*x^6+2*a*b*x^3)^-1//2+-5*b*a^-6*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(x)+5//3*b*a^-6*(a^2+b^2*x^6+2*a*b*x^3)^-1//2*(a+b*x^3)*log(a+b*x^3))
@test integrate((d*x)^m*(a^2+b^2*x^6+2*a*b*x^3)^5//2, x) == :(a^5*d^-1*(d*x)^(1+m)*(1+m)^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+b^5*d^-16*(d*x)^(16+m)*(16+m)^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*a*b^4*d^-13*(d*x)^(13+m)*(13+m)^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+5*b*a^4*d^-4*(d*x)^(4+m)*(4+m)^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+10*a^2*b^3*d^-10*(d*x)^(10+m)*(10+m)^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+10*a^3*b^2*d^-7*(d*x)^(7+m)*(7+m)^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate((d*x)^m*(a^2+b^2*x^6+2*a*b*x^3)^3//2, x) == :(a^3*d^-1*(d*x)^(1+m)*(1+m)^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+b^3*d^-10*(d*x)^(10+m)*(10+m)^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+3*a*b^2*d^-7*(d*x)^(7+m)*(7+m)^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+3*b*a^2*d^-4*(d*x)^(4+m)*(4+m)^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate((d*x)^m*(a^2+b^2*x^6+2*a*b*x^3)^(1/2), x) == :(a*d^-1*(d*x)^(1+m)*(1+m)^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2)+b*d^-4*(d*x)^(4+m)*(4+m)^-1*(a+b*x^3)^-1*(a^2+b^2*x^6+2*a*b*x^3)^(1/2))
@test integrate(x^11*(a^2+b^2*x^6+2*a*b*x^3)^p, x) == :(1//6*b^-4*(2+p)^-1*(a+b*x^3)^4*(a^2+b^2*x^6+2*a*b*x^3)^p+(1/2)*a^2*b^-4*(1+p)^-1*(a+b*x^3)^2*(a^2+b^2*x^6+2*a*b*x^3)^p+-1*a*b^-4*(3+2p)^-1*(a+b*x^3)^3*(a^2+b^2*x^6+2*a*b*x^3)^p+-1//3*a^3*b^-4*(1+2p)^-1*(a^2+b^2*x^6+2*a*b*x^3)^p*(a+b*x^3))
@test integrate(x^8*(a^2+b^2*x^6+2*a*b*x^3)^p, x) == :(1//3*b^-3*(3+2p)^-1*(a+b*x^3)^3*(a^2+b^2*x^6+2*a*b*x^3)^p+-1//3*a*b^-3*(1+p)^-1*(a+b*x^3)^2*(a^2+b^2*x^6+2*a*b*x^3)^p+1//3*a^2*b^-3*(1+2p)^-1*(a^2+b^2*x^6+2*a*b*x^3)^p*(a+b*x^3))
@test integrate(x^5*(a^2+b^2*x^6+2*a*b*x^3)^p, x) == :(1//6*b^-2*(1+p)^-1*(a+b*x^3)^2*(a^2+b^2*x^6+2*a*b*x^3)^p+-1//3*a*b^-2*(1+2p)^-1*(a^2+b^2*x^6+2*a*b*x^3)^p*(a+b*x^3))
@test integrate(x^2*(a^2+b^2*x^6+2*a*b*x^3)^p, x) == :(1//3*b^-1*(1+2p)^-1*(a^2+b^2*x^6+2*a*b*x^3)^p*(a+b*x^3))
@test integrate(x^8*(a+b*x^3+c*x^6)^-1, x) == :(1//3*c^-1*x^3+-1//6*b*c^-2*log(a+b*x^3+c*x^6)+-1//3*c^-2*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^3)))
@test integrate(x^5*(a+b*x^3+c*x^6)^-1, x) == :(1//6*c^-1*log(a+b*x^3+c*x^6)+1//3*b*c^-1*(b^2+-4*a*c)^-1//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^3)))
@test integrate(x^2*(a+b*x^3+c*x^6)^-1, x) == :(-2//3*(b^2+-4*a*c)^-1//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^3)))
@test integrate(x^-1*(a+b*x^3+c*x^6)^-1, x) == :(a^-1*log(x)+-1//6*a^-1*log(a+b*x^3+c*x^6)+1//3*b*a^-1*(b^2+-4*a*c)^-1//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^3)))
@test integrate(x^-4*(a+b*x^3+c*x^6)^-1, x) == :(-1//3*a^-1*x^-3+-1*b*a^-2*log(x)+1//6*b*a^-2*log(a+b*x^3+c*x^6)+-1//3*a^-2*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^3)))
@test integrate(x^7*(a+b*x^3+c*x^6)^-1, x) == :((1/2)*c^-1*x^2+-1//12*2^1//3*c^-5//3*(b+(b^2+-4*a*c)^(1/2))^-1//3*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*log((b+(b^2+-4*a*c)^(1/2))^2//3+2^2//3*c^2//3*x^2+-1*x*2^1//3*c^1//3*(b+(b^2+-4*a*c)^(1/2))^1//3)+-1//12*2^1//3*c^-5//3*(b+-1*(b^2+-4*a*c)^(1/2))^-1//3*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*log((b+-1*(b^2+-4*a*c)^(1/2))^2//3+2^2//3*c^2//3*x^2+-1*x*2^1//3*c^1//3*(b+-1*(b^2+-4*a*c)^(1/2))^1//3)+1//6*2^1//3*c^-5//3*(b+(b^2+-4*a*c)^(1/2))^-1//3*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*log((b+(b^2+-4*a*c)^(1/2))^1//3+x*2^1//3*c^1//3)+1//6*2^1//3*c^-5//3*(b+-1*(b^2+-4*a*c)^(1/2))^-1//3*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*log((b+-1*(b^2+-4*a*c)^(1/2))^1//3+x*2^1//3*c^1//3)+1//6*2^1//3*3^(1/2)*c^-5//3*(b+(b^2+-4*a*c)^(1/2))^-1//3*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(1//3*3^(1/2)*(1+-2*x*2^1//3*c^1//3*(b+(b^2+-4*a*c)^(1/2))^-1//3))+1//6*2^1//3*3^(1/2)*c^-5//3*(b+-1*(b^2+-4*a*c)^(1/2))^-1//3*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(1//3*3^(1/2)*(1+-2*x*2^1//3*c^1//3*(b+-1*(b^2+-4*a*c)^(1/2))^-1//3)))
@test integrate(x^6*(a+b*x^3+c*x^6)^-1, x) == :(x*c^-1+-1//6*2^2//3*c^-4//3*(b+(b^2+-4*a*c)^(1/2))^-2//3*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*log((b+(b^2+-4*a*c)^(1/2))^1//3+x*2^1//3*c^1//3)+-1//6*2^2//3*c^-4//3*(b+-1*(b^2+-4*a*c)^(1/2))^-2//3*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*log((b+-1*(b^2+-4*a*c)^(1/2))^1//3+x*2^1//3*c^1//3)+1//12*2^2//3*c^-4//3*(b+(b^2+-4*a*c)^(1/2))^-2//3*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*log((b+(b^2+-4*a*c)^(1/2))^2//3+2^2//3*c^2//3*x^2+-1*x*2^1//3*c^1//3*(b+(b^2+-4*a*c)^(1/2))^1//3)+1//12*2^2//3*c^-4//3*(b+-1*(b^2+-4*a*c)^(1/2))^-2//3*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*log((b+-1*(b^2+-4*a*c)^(1/2))^2//3+2^2//3*c^2//3*x^2+-1*x*2^1//3*c^1//3*(b+-1*(b^2+-4*a*c)^(1/2))^1//3)+1//6*2^2//3*3^(1/2)*c^-4//3*(b+(b^2+-4*a*c)^(1/2))^-2//3*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(1//3*3^(1/2)*(1+-2*x*2^1//3*c^1//3*(b+(b^2+-4*a*c)^(1/2))^-1//3))+1//6*2^2//3*3^(1/2)*c^-4//3*(b+-1*(b^2+-4*a*c)^(1/2))^-2//3*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(1//3*3^(1/2)*(1+-2*x*2^1//3*c^1//3*(b+-1*(b^2+-4*a*c)^(1/2))^-1//3)))
@test integrate(x^4*(a+b*x^3+c*x^6)^-1, x) == :(-1//6*2^1//3*c^-2//3*(b+(b^2+-4*a*c)^(1/2))^2//3*(b^2+-4*a*c)^-1//2*log((b+(b^2+-4*a*c)^(1/2))^1//3+x*2^1//3*c^1//3)+-1//12*2^1//3*c^-2//3*(b+-1*(b^2+-4*a*c)^(1/2))^2//3*(b^2+-4*a*c)^-1//2*log((b+-1*(b^2+-4*a*c)^(1/2))^2//3+2^2//3*c^2//3*x^2+-1*x*2^1//3*c^1//3*(b+-1*(b^2+-4*a*c)^(1/2))^1//3)+1//6*2^1//3*c^-2//3*(b+-1*(b^2+-4*a*c)^(1/2))^2//3*(b^2+-4*a*c)^-1//2*log((b+-1*(b^2+-4*a*c)^(1/2))^1//3+x*2^1//3*c^1//3)+1//12*2^1//3*c^-2//3*(b+(b^2+-4*a*c)^(1/2))^2//3*(b^2+-4*a*c)^-1//2*log((b+(b^2+-4*a*c)^(1/2))^2//3+2^2//3*c^2//3*x^2+-1*x*2^1//3*c^1//3*(b+(b^2+-4*a*c)^(1/2))^1//3)+-1//6*2^1//3*3^(1/2)*c^-2//3*(b+(b^2+-4*a*c)^(1/2))^2//3*(b^2+-4*a*c)^-1//2*arctan(1//3*3^(1/2)*(1+-2*x*2^1//3*c^1//3*(b+(b^2+-4*a*c)^(1/2))^-1//3))+1//6*2^1//3*3^(1/2)*c^-2//3*(b+-1*(b^2+-4*a*c)^(1/2))^2//3*(b^2+-4*a*c)^-1//2*arctan(1//3*3^(1/2)*(1+-2*x*2^1//3*c^1//3*(b+-1*(b^2+-4*a*c)^(1/2))^-1//3)))
@test integrate(x^3*(a+b*x^3+c*x^6)^-1, x) == :(-1//6*2^2//3*c^-1//3*(b+-1*(b^2+-4*a*c)^(1/2))^1//3*(b^2+-4*a*c)^-1//2*log((b+-1*(b^2+-4*a*c)^(1/2))^1//3+x*2^1//3*c^1//3)+-1//12*2^2//3*c^-1//3*(b+(b^2+-4*a*c)^(1/2))^1//3*(b^2+-4*a*c)^-1//2*log((b+(b^2+-4*a*c)^(1/2))^2//3+2^2//3*c^2//3*x^2+-1*x*2^1//3*c^1//3*(b+(b^2+-4*a*c)^(1/2))^1//3)+1//6*2^2//3*c^-1//3*(b+(b^2+-4*a*c)^(1/2))^1//3*(b^2+-4*a*c)^-1//2*log((b+(b^2+-4*a*c)^(1/2))^1//3+x*2^1//3*c^1//3)+1//12*2^2//3*c^-1//3*(b+-1*(b^2+-4*a*c)^(1/2))^1//3*(b^2+-4*a*c)^-1//2*log((b+-1*(b^2+-4*a*c)^(1/2))^2//3+2^2//3*c^2//3*x^2+-1*x*2^1//3*c^1//3*(b+-1*(b^2+-4*a*c)^(1/2))^1//3)+-1//6*2^2//3*3^(1/2)*c^-1//3*(b+(b^2+-4*a*c)^(1/2))^1//3*(b^2+-4*a*c)^-1//2*arctan(1//3*3^(1/2)*(1+-2*x*2^1//3*c^1//3*(b+(b^2+-4*a*c)^(1/2))^-1//3))+1//6*2^2//3*3^(1/2)*c^-1//3*(b+-1*(b^2+-4*a*c)^(1/2))^1//3*(b^2+-4*a*c)^-1//2*arctan(1//3*3^(1/2)*(1+-2*x*2^1//3*c^1//3*(b+-1*(b^2+-4*a*c)^(1/2))^-1//3)))
@test integrate(x*(a+b*x^3+c*x^6)^-1, x) == :(-1//3*2^1//3*c^1//3*(b+-1*(b^2+-4*a*c)^(1/2))^-1//3*(b^2+-4*a*c)^-1//2*log((b+-1*(b^2+-4*a*c)^(1/2))^1//3+x*2^1//3*c^1//3)+-1//6*2^1//3*c^1//3*(b+(b^2+-4*a*c)^(1/2))^-1//3*(b^2+-4*a*c)^-1//2*log((b+(b^2+-4*a*c)^(1/2))^2//3+2^2//3*c^2//3*x^2+-1*x*2^1//3*c^1//3*(b+(b^2+-4*a*c)^(1/2))^1//3)+1//3*2^1//3*c^1//3*(b+(b^2+-4*a*c)^(1/2))^-1//3*(b^2+-4*a*c)^-1//2*log((b+(b^2+-4*a*c)^(1/2))^1//3+x*2^1//3*c^1//3)+1//6*2^1//3*c^1//3*(b+-1*(b^2+-4*a*c)^(1/2))^-1//3*(b^2+-4*a*c)^-1//2*log((b+-1*(b^2+-4*a*c)^(1/2))^2//3+2^2//3*c^2//3*x^2+-1*x*2^1//3*c^1//3*(b+-1*(b^2+-4*a*c)^(1/2))^1//3)+-1//3*2^1//3*3^(1/2)*c^1//3*(b+-1*(b^2+-4*a*c)^(1/2))^-1//3*(b^2+-4*a*c)^-1//2*arctan(1//3*3^(1/2)*(1+-2*x*2^1//3*c^1//3*(b+-1*(b^2+-4*a*c)^(1/2))^-1//3))+1//3*2^1//3*3^(1/2)*c^1//3*(b+(b^2+-4*a*c)^(1/2))^-1//3*(b^2+-4*a*c)^-1//2*arctan(1//3*3^(1/2)*(1+-2*x*2^1//3*c^1//3*(b+(b^2+-4*a*c)^(1/2))^-1//3)))
@test integrate((a+b*x^3+c*x^6)^-1, x) == :(-1//3*2^2//3*c^2//3*(b+(b^2+-4*a*c)^(1/2))^-2//3*(b^2+-4*a*c)^-1//2*log((b+(b^2+-4*a*c)^(1/2))^1//3+x*2^1//3*c^1//3)+-1//6*2^2//3*c^2//3*(b+-1*(b^2+-4*a*c)^(1/2))^-2//3*(b^2+-4*a*c)^-1//2*log((b+-1*(b^2+-4*a*c)^(1/2))^2//3+2^2//3*c^2//3*x^2+-1*x*2^1//3*c^1//3*(b+-1*(b^2+-4*a*c)^(1/2))^1//3)+1//3*2^2//3*c^2//3*(b+-1*(b^2+-4*a*c)^(1/2))^-2//3*(b^2+-4*a*c)^-1//2*log((b+-1*(b^2+-4*a*c)^(1/2))^1//3+x*2^1//3*c^1//3)+1//6*2^2//3*c^2//3*(b+(b^2+-4*a*c)^(1/2))^-2//3*(b^2+-4*a*c)^-1//2*log((b+(b^2+-4*a*c)^(1/2))^2//3+2^2//3*c^2//3*x^2+-1*x*2^1//3*c^1//3*(b+(b^2+-4*a*c)^(1/2))^1//3)+-1//3*2^2//3*3^(1/2)*c^2//3*(b+-1*(b^2+-4*a*c)^(1/2))^-2//3*(b^2+-4*a*c)^-1//2*arctan(1//3*3^(1/2)*(1+-2*x*2^1//3*c^1//3*(b+-1*(b^2+-4*a*c)^(1/2))^-1//3))+1//3*2^2//3*3^(1/2)*c^2//3*(b+(b^2+-4*a*c)^(1/2))^-2//3*(b^2+-4*a*c)^-1//2*arctan(1//3*3^(1/2)*(1+-2*x*2^1//3*c^1//3*(b+(b^2+-4*a*c)^(1/2))^-1//3)))
@test integrate(x^-2*(a+b*x^3+c*x^6)^-1, x) == :(-1*a^-1*x^-1+-1//12*2^1//3*a^-1*c^1//3*(b+(b^2+-4*a*c)^(1/2))^-1//3*(1+-1*b*(b^2+-4*a*c)^-1//2)*log((b+(b^2+-4*a*c)^(1/2))^2//3+2^2//3*c^2//3*x^2+-1*x*2^1//3*c^1//3*(b+(b^2+-4*a*c)^(1/2))^1//3)+-1//12*2^1//3*a^-1*c^1//3*(b+-1*(b^2+-4*a*c)^(1/2))^-1//3*(1+b*(b^2+-4*a*c)^-1//2)*log((b+-1*(b^2+-4*a*c)^(1/2))^2//3+2^2//3*c^2//3*x^2+-1*x*2^1//3*c^1//3*(b+-1*(b^2+-4*a*c)^(1/2))^1//3)+1//6*2^1//3*a^-1*c^1//3*(b+(b^2+-4*a*c)^(1/2))^-1//3*(1+-1*b*(b^2+-4*a*c)^-1//2)*log((b+(b^2+-4*a*c)^(1/2))^1//3+x*2^1//3*c^1//3)+1//6*2^1//3*a^-1*c^1//3*(b+-1*(b^2+-4*a*c)^(1/2))^-1//3*(1+b*(b^2+-4*a*c)^-1//2)*log((b+-1*(b^2+-4*a*c)^(1/2))^1//3+x*2^1//3*c^1//3)+1//6*2^1//3*3^(1/2)*a^-1*c^1//3*(b+(b^2+-4*a*c)^(1/2))^-1//3*(1+-1*b*(b^2+-4*a*c)^-1//2)*arctan(1//3*3^(1/2)*(1+-2*x*2^1//3*c^1//3*(b+(b^2+-4*a*c)^(1/2))^-1//3))+1//6*2^1//3*3^(1/2)*a^-1*c^1//3*(b+-1*(b^2+-4*a*c)^(1/2))^-1//3*(1+b*(b^2+-4*a*c)^-1//2)*arctan(1//3*3^(1/2)*(1+-2*x*2^1//3*c^1//3*(b+-1*(b^2+-4*a*c)^(1/2))^-1//3)))
@test integrate(x^-3*(a+b*x^3+c*x^6)^-1, x) == :(-1//2*a^-1*x^-2+-1//6*2^2//3*a^-1*c^2//3*(b+(b^2+-4*a*c)^(1/2))^-2//3*(1+-1*b*(b^2+-4*a*c)^-1//2)*log((b+(b^2+-4*a*c)^(1/2))^1//3+x*2^1//3*c^1//3)+-1//6*2^2//3*a^-1*c^2//3*(b+-1*(b^2+-4*a*c)^(1/2))^-2//3*(1+b*(b^2+-4*a*c)^-1//2)*log((b+-1*(b^2+-4*a*c)^(1/2))^1//3+x*2^1//3*c^1//3)+1//12*2^2//3*a^-1*c^2//3*(b+(b^2+-4*a*c)^(1/2))^-2//3*(1+-1*b*(b^2+-4*a*c)^-1//2)*log((b+(b^2+-4*a*c)^(1/2))^2//3+2^2//3*c^2//3*x^2+-1*x*2^1//3*c^1//3*(b+(b^2+-4*a*c)^(1/2))^1//3)+1//12*2^2//3*a^-1*c^2//3*(b+-1*(b^2+-4*a*c)^(1/2))^-2//3*(1+b*(b^2+-4*a*c)^-1//2)*log((b+-1*(b^2+-4*a*c)^(1/2))^2//3+2^2//3*c^2//3*x^2+-1*x*2^1//3*c^1//3*(b+-1*(b^2+-4*a*c)^(1/2))^1//3)+1//6*2^2//3*3^(1/2)*a^-1*c^2//3*(b+(b^2+-4*a*c)^(1/2))^-2//3*(1+-1*b*(b^2+-4*a*c)^-1//2)*arctan(1//3*3^(1/2)*(1+-2*x*2^1//3*c^1//3*(b+(b^2+-4*a*c)^(1/2))^-1//3))+1//6*2^2//3*3^(1/2)*a^-1*c^2//3*(b+-1*(b^2+-4*a*c)^(1/2))^-2//3*(1+b*(b^2+-4*a*c)^-1//2)*arctan(1//3*3^(1/2)*(1+-2*x*2^1//3*c^1//3*(b+-1*(b^2+-4*a*c)^(1/2))^-1//3)))
@test integrate(x^11*(3+x^6+4*x^3)^-1, x) == :(-4//3*x^3+-1//6*log(1+x^3)+1//6*x^6+9//2*log(3+x^3))
@test integrate(x^8*(3+x^6+4*x^3)^-1, x) == :(-3//2*log(3+x^3)+1//3*x^3+1//6*log(1+x^3))
@test integrate(x^5*(3+x^6+4*x^3)^-1, x) == :((1/2)*log(3+x^3)+-1//6*log(1+x^3))
@test integrate(x^-1*(3+x^6+4*x^3)^-1, x) == :(-1//6*log(1+x^3)+1//3*log(x)+1//18*log(3+x^3))
@test integrate(x^-4*(3+x^6+4*x^3)^-1, x) == :(-4//9*log(x)+-1//9*x^-3+-1//54*log(3+x^3)+1//6*log(1+x^3))
@test integrate(x^-7*(3+x^6+4*x^3)^-1, x) == :(-1//6*log(1+x^3)+-1//18*x^-6+1//162*log(3+x^3)+4//27*x^-3+13//27*log(x))
@test integrate(x^10*(3+x^6+4*x^3)^-1, x) == :(-2*x^2+-1//12*log(1+x^2+-1x)+1//5*x^5+1//6*log(1+x)+-9//2*3^1//6*arctan(1//3*3^1//6*(3^1//3+-2x))+-3//2*3^2//3*log(x+3^1//3)+1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x))+3//4*3^2//3*log(3^2//3+x^2+-1*x*3^1//3))
@test integrate(x^9*(3+x^6+4*x^3)^-1, x) == :(-4x+-1//6*log(1+x)+1//4*x^4+1//12*log(1+x^2+-1x)+-3//2*3^5//6*arctan(1//3*3^1//6*(3^1//3+-2x))+-3//4*3^1//3*log(3^2//3+x^2+-1*x*3^1//3)+1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x))+3//2*3^1//3*log(x+3^1//3))
@test integrate(x^7*(3+x^6+4*x^3)^-1, x) == :((1/2)*x^2+-1//6*log(1+x)+1//12*log(1+x^2+-1x)+(1/2)*3^2//3*log(x+3^1//3)+-1//4*3^2//3*log(3^2//3+x^2+-1*x*3^1//3)+-1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x))+3//2*3^1//6*arctan(1//3*3^1//6*(3^1//3+-2x)))
@test integrate(x^6*(3+x^6+4*x^3)^-1, x) == :(x+-1//12*log(1+x^2+-1x)+1//6*log(1+x)+(1/2)*3^5//6*arctan(1//3*3^1//6*(3^1//3+-2x))+-1//2*3^1//3*log(x+3^1//3)+-1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x))+1//4*3^1//3*log(3^2//3+x^2+-1*x*3^1//3))
@test integrate(x^4*(3+x^6+4*x^3)^-1, x) == :(-1//12*log(1+x^2+-1x)+1//6*log(1+x)+-1//2*3^1//6*arctan(1//3*3^1//6*(3^1//3+-2x))+-1//6*3^2//3*log(x+3^1//3)+1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x))+1//12*3^2//3*log(3^2//3+x^2+-1*x*3^1//3))
@test integrate(x^3*(3+x^6+4*x^3)^-1, x) == :(-1//6*log(1+x)+1//12*log(1+x^2+-1x)+-1//6*3^5//6*arctan(1//3*3^1//6*(3^1//3+-2x))+-1//12*3^1//3*log(3^2//3+x^2+-1*x*3^1//3)+1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x))+1//6*3^1//3*log(x+3^1//3))
@test integrate(x*(3+x^6+4*x^3)^-1, x) == :(-1//6*log(1+x)+1//12*log(1+x^2+-1x)+-1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x))+-1//36*3^2//3*log(3^2//3+x^2+-1*x*3^1//3)+1//6*3^1//6*arctan(1//3*3^1//6*(3^1//3+-2x))+1//18*3^2//3*log(x+3^1//3))
@test integrate((3+x^6+4*x^3)^-1, x) == :(-1//12*log(1+x^2+-1x)+1//6*log(1+x)+-1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x))+-1//18*3^1//3*log(x+3^1//3)+1//18*3^5//6*arctan(1//3*3^1//6*(3^1//3+-2x))+1//36*3^1//3*log(3^2//3+x^2+-1*x*3^1//3))
@test integrate(x^-2*(3+x^6+4*x^3)^-1, x) == :(-1//3*x^-1+-1//12*log(1+x^2+-1x)+1//6*log(1+x)+-1//18*3^1//6*arctan(1//3*3^1//6*(3^1//3+-2x))+-1//54*3^2//3*log(x+3^1//3)+1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x))+1//108*3^2//3*log(3^2//3+x^2+-1*x*3^1//3))
@test integrate(x^-3*(3+x^6+4*x^3)^-1, x) == :(-1//6*x^-2+-1//6*log(1+x)+1//12*log(1+x^2+-1x)+-1//54*3^5//6*arctan(1//3*3^1//6*(3^1//3+-2x))+-1//108*3^1//3*log(3^2//3+x^2+-1*x*3^1//3)+1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x))+1//54*3^1//3*log(x+3^1//3))
@test integrate(x^-5*(3+x^6+4*x^3)^-1, x) == :(-1//6*log(1+x)+-1//12*x^-4+1//12*log(1+x^2+-1x)+4//9*x^-1+-1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x))+-1//324*3^2//3*log(3^2//3+x^2+-1*x*3^1//3)+1//54*3^1//6*arctan(1//3*3^1//6*(3^1//3+-2x))+1//162*3^2//3*log(x+3^1//3))
@test integrate(x^-6*(3+x^6+4*x^3)^-1, x) == :(-1//12*log(1+x^2+-1x)+-1//15*x^-5+1//6*log(1+x)+2//9*x^-2+-1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x))+-1//162*3^1//3*log(x+3^1//3)+1//162*3^5//6*arctan(1//3*3^1//6*(3^1//3+-2x))+1//324*3^1//3*log(3^2//3+x^2+-1*x*3^1//3))
@test integrate(x^6*(1+x^6+-1*x^3)^-1, x) == :(x+-1//6*2^2//3*(1+im*3^(1/2))^-2//3*(im+3^(1/2))*arctan(1//3*3^(1/2)*(1+2*x*(1/2+(1/2)*im*3^(1/2))^-1//3))+-1//36*2^2//3*(1+im*3^(1/2))^-2//3*(3+im*3^(1/2))*log((1+im*3^(1/2))^2//3+x*(2+2*im*3^(1/2))^1//3+2^2//3*x^2)+-1//36*2^2//3*(1+-1*im*3^(1/2))^-2//3*(3+-1*im*3^(1/2))*log((1+-1*im*3^(1/2))^2//3+x*(2+-2*im*3^(1/2))^1//3+2^2//3*x^2)+1//6*2^2//3*(1+-1*im*3^(1/2))^-2//3*(im+-1*3^(1/2))*arctan(1//3*3^(1/2)*(1+2*x*(1/2+-1//2*im*3^(1/2))^-1//3))+1//18*2^2//3*(1+im*3^(1/2))^-2//3*(3+im*3^(1/2))*log((1+im*3^(1/2))^1//3+-1*x*2^1//3)+1//18*2^2//3*(1+-1*im*3^(1/2))^-2//3*(3+-1*im*3^(1/2))*log((1+-1*im*3^(1/2))^1//3+-1*x*2^1//3))
@test integrate(x^5*(1+x^6+-1*x^3)^-1, x) == :(1//6*log(1+x^6+-1*x^3)+-1//9*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x^3)))
@test integrate(x^4*(1+x^6+-1*x^3)^-1, x) == :(-1//6*2^1//3*(1+im*3^(1/2))^-1//3*(im+-1*3^(1/2))*arctan(1//3*3^(1/2)*(1+2*x*(1/2+(1/2)*im*3^(1/2))^-1//3))+-1//36*2^1//3*(1+im*3^(1/2))^-1//3*(3+-1*im*3^(1/2))*log((1+im*3^(1/2))^2//3+x*(2+2*im*3^(1/2))^1//3+2^2//3*x^2)+-1//36*2^1//3*(1+-1*im*3^(1/2))^-1//3*(3+im*3^(1/2))*log((1+-1*im*3^(1/2))^2//3+x*(2+-2*im*3^(1/2))^1//3+2^2//3*x^2)+1//6*2^1//3*(1+-1*im*3^(1/2))^-1//3*(im+3^(1/2))*arctan(1//3*3^(1/2)*(1+2*x*(1/2+-1//2*im*3^(1/2))^-1//3))+1//18*2^1//3*(1+im*3^(1/2))^-1//3*(3+-1*im*3^(1/2))*log((1+im*3^(1/2))^1//3+-1*x*2^1//3)+1//18*2^1//3*(1+-1*im*3^(1/2))^-1//3*(3+im*3^(1/2))*log((1+-1*im*3^(1/2))^1//3+-1*x*2^1//3))
@test integrate(x^3*(1+x^6+-1*x^3)^-1, x) == :(-1//6*2^2//3*(1+-1*im*3^(1/2))^-2//3*(im+3^(1/2))*arctan(1//3*3^(1/2)*(1+2*x*(1/2+-1//2*im*3^(1/2))^-1//3))+-1//36*2^2//3*(1+im*3^(1/2))^-2//3*(3+-1*im*3^(1/2))*log((1+im*3^(1/2))^2//3+x*(2+2*im*3^(1/2))^1//3+2^2//3*x^2)+-1//36*2^2//3*(1+-1*im*3^(1/2))^-2//3*(3+im*3^(1/2))*log((1+-1*im*3^(1/2))^2//3+x*(2+-2*im*3^(1/2))^1//3+2^2//3*x^2)+1//6*2^2//3*(1+im*3^(1/2))^-2//3*(im+-1*3^(1/2))*arctan(1//3*3^(1/2)*(1+2*x*(1/2+(1/2)*im*3^(1/2))^-1//3))+1//18*2^2//3*(1+im*3^(1/2))^-2//3*(3+-1*im*3^(1/2))*log((1+im*3^(1/2))^1//3+-1*x*2^1//3)+1//18*2^2//3*(1+-1*im*3^(1/2))^-2//3*(3+im*3^(1/2))*log((1+-1*im*3^(1/2))^1//3+-1*x*2^1//3))
@test integrate(x^2*(1+x^6+-1*x^3)^-1, x) == :(-2//9*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x^3)))
@test integrate(x*(1+x^6+-1*x^3)^-1, x) == :(-1//3*im*(1/2+(1/2)*im*3^(1/2))^-1//3*arctan(1//3*3^(1/2)*(1+2*x*(1/2+(1/2)*im*3^(1/2))^-1//3))+1//3*im*(1/2+-1//2*im*3^(1/2))^-1//3*arctan(1//3*3^(1/2)*(1+2*x*(1/2+-1//2*im*3^(1/2))^-1//3))+-1//9*im*3^(1/2)*(1/2+(1/2)*im*3^(1/2))^-1//3*log((1+im*3^(1/2))^1//3+-1*x*2^1//3)+1//9*im*3^(1/2)*(1/2+-1//2*im*3^(1/2))^-1//3*log((1+-1*im*3^(1/2))^1//3+-1*x*2^1//3)+-1//18*im*2^1//3*3^(1/2)*(1+-1*im*3^(1/2))^-1//3*log((1+-1*im*3^(1/2))^2//3+x*(2+-2*im*3^(1/2))^1//3+2^2//3*x^2)+1//18*im*2^1//3*3^(1/2)*(1+im*3^(1/2))^-1//3*log((1+im*3^(1/2))^2//3+x*(2+2*im*3^(1/2))^1//3+2^2//3*x^2))
@test integrate(x^-1*(1+x^6+-1*x^3)^-1, x) == :(-1//6*log(1+x^6+-1*x^3)+-1//9*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x^3))+log(x))
@test integrate(x^-2*(1+x^6+-1*x^3)^-1, x) == :(-1*x^-1+-1//6*2^1//3*(1+im*3^(1/2))^-1//3*(im+3^(1/2))*arctan(1//3*3^(1/2)*(1+2*x*(1/2+(1/2)*im*3^(1/2))^-1//3))+-1//18*2^1//3*(1+im*3^(1/2))^-1//3*(3+im*3^(1/2))*log((1+im*3^(1/2))^1//3+-1*x*2^1//3)+-1//18*2^1//3*(1+-1*im*3^(1/2))^-1//3*(3+-1*im*3^(1/2))*log((1+-1*im*3^(1/2))^1//3+-1*x*2^1//3)+1//6*2^1//3*(1+-1*im*3^(1/2))^-1//3*(im+-1*3^(1/2))*arctan(1//3*3^(1/2)*(1+2*x*(1/2+-1//2*im*3^(1/2))^-1//3))+1//36*2^1//3*(1+im*3^(1/2))^-1//3*(3+im*3^(1/2))*log((1+im*3^(1/2))^2//3+x*(2+2*im*3^(1/2))^1//3+2^2//3*x^2)+1//36*2^1//3*(1+-1*im*3^(1/2))^-1//3*(3+-1*im*3^(1/2))*log((1+-1*im*3^(1/2))^2//3+x*(2+-2*im*3^(1/2))^1//3+2^2//3*x^2))
@test integrate(x^-3*(1+x^6+-1*x^3)^-1, x) == :(-1//2*x^-2+-1//6*2^2//3*(1+-1*im*3^(1/2))^-2//3*(im+-1*3^(1/2))*arctan(1//3*3^(1/2)*(1+2*x*(1/2+-1//2*im*3^(1/2))^-1//3))+-1//18*2^2//3*(1+im*3^(1/2))^-2//3*(3+im*3^(1/2))*log((1+im*3^(1/2))^1//3+-1*x*2^1//3)+-1//18*2^2//3*(1+-1*im*3^(1/2))^-2//3*(3+-1*im*3^(1/2))*log((1+-1*im*3^(1/2))^1//3+-1*x*2^1//3)+1//6*2^2//3*(1+im*3^(1/2))^-2//3*(im+3^(1/2))*arctan(1//3*3^(1/2)*(1+2*x*(1/2+(1/2)*im*3^(1/2))^-1//3))+1//36*2^2//3*(1+im*3^(1/2))^-2//3*(3+im*3^(1/2))*log((1+im*3^(1/2))^2//3+x*(2+2*im*3^(1/2))^1//3+2^2//3*x^2)+1//36*2^2//3*(1+-1*im*3^(1/2))^-2//3*(3+-1*im*3^(1/2))*log((1+-1*im*3^(1/2))^2//3+x*(2+-2*im*3^(1/2))^1//3+2^2//3*x^2))
@test integrate(x^-4*(1+x^6+-1*x^3)^-1, x) == :(-1//3*x^-3+-1//6*log(1+x^6+-1*x^3)+1//9*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x^3))+log(x))
@test integrate(x^-5*(1+x^6+-1*x^3)^-1, x) == :(-1*x^-1+-1//4*x^-4+-1//6*2^1//3*(1+-1*im*3^(1/2))^-1//3*(im+3^(1/2))*arctan(1//3*3^(1/2)*(1+2*x*(1/2+-1//2*im*3^(1/2))^-1//3))+-1//18*2^1//3*(1+im*3^(1/2))^-1//3*(3+-1*im*3^(1/2))*log((1+im*3^(1/2))^1//3+-1*x*2^1//3)+-1//18*2^1//3*(1+-1*im*3^(1/2))^-1//3*(3+im*3^(1/2))*log((1+-1*im*3^(1/2))^1//3+-1*x*2^1//3)+1//6*2^1//3*(1+im*3^(1/2))^-1//3*(im+-1*3^(1/2))*arctan(1//3*3^(1/2)*(1+2*x*(1/2+(1/2)*im*3^(1/2))^-1//3))+1//36*2^1//3*(1+im*3^(1/2))^-1//3*(3+-1*im*3^(1/2))*log((1+im*3^(1/2))^2//3+x*(2+2*im*3^(1/2))^1//3+2^2//3*x^2)+1//36*2^1//3*(1+-1*im*3^(1/2))^-1//3*(3+im*3^(1/2))*log((1+-1*im*3^(1/2))^2//3+x*(2+-2*im*3^(1/2))^1//3+2^2//3*x^2))
@test integrate((2+x^3+x^6)^-1, x) == :(-1//21*im*7^(1/2)*(1/2+-1//2*im*7^(1/2))^-2//3*log((1+-1*im*7^(1/2))^1//3+x*2^1//3)+-1//21*im*21^(1/2)*(1/2+(1/2)*im*7^(1/2))^-2//3*arctan(1//3*3^(1/2)*(1+-2*x*(1/2+(1/2)*im*7^(1/2))^-1//3))+1//21*im*7^(1/2)*(1/2+(1/2)*im*7^(1/2))^-2//3*log((1+im*7^(1/2))^1//3+x*2^1//3)+1//21*im*21^(1/2)*(1/2+-1//2*im*7^(1/2))^-2//3*arctan(1//3*3^(1/2)*(1+-2*x*(1/2+-1//2*im*7^(1/2))^-1//3))+-1//42*im*2^2//3*7^(1/2)*(1+im*7^(1/2))^-2//3*log((1+im*7^(1/2))^2//3+2^2//3*x^2+-1*x*(2+2*im*7^(1/2))^1//3)+1//42*im*2^2//3*7^(1/2)*(1+-1*im*7^(1/2))^-2//3*log((1+-1*im*7^(1/2))^2//3+2^2//3*x^2+-1*x*(2+-2*im*7^(1/2))^1//3))
@test integrate(x^2*(2+x^3+x^6)^-1, x) == :(2//21*7^(1/2)*arctan(1//7*7^(1/2)*(1+2*x^3)))
@test integrate(x^3*(2+x^3+x^6)^-1, x) == :(-1//21*im*21^(1/2)*(1/2+-1//2*im*7^(1/2))^1//3*arctan(1//3*3^(1/2)*(1+-2*x*(1/2+-1//2*im*7^(1/2))^-1//3))+-1//84*2^2//3*(1+im*7^(1/2))^-2//3*(7+-1*im*7^(1/2))*log((1+im*7^(1/2))^2//3+2^2//3*x^2+-1*x*(2+2*im*7^(1/2))^1//3)+-1//84*2^2//3*(1+-1*im*7^(1/2))^-2//3*(7+im*7^(1/2))*log((1+-1*im*7^(1/2))^2//3+2^2//3*x^2+-1*x*(2+-2*im*7^(1/2))^1//3)+1//21*im*21^(1/2)*(1/2+(1/2)*im*7^(1/2))^1//3*arctan(1//3*3^(1/2)*(1+-2*x*(1/2+(1/2)*im*7^(1/2))^-1//3))+1//42*2^2//3*(1+im*7^(1/2))^-2//3*(7+-1*im*7^(1/2))*log((1+im*7^(1/2))^1//3+x*2^1//3)+1//42*2^2//3*(1+-1*im*7^(1/2))^-2//3*(7+im*7^(1/2))*log((1+-1*im*7^(1/2))^1//3+x*2^1//3))
@test integrate(x^14*(a+b*x^3+c*x^6)^(1/2), x) == :(-1//2880*c^-4*(a+b*x^3+c*x^6)^3//2*(7*b*(15*b^2+-28*a*c)+-6*c*x^3*(21*b^2+-20*a*c))+1//18*c^-1*x^9*(a+b*x^3+c*x^6)^3//2+-1//20*b*c^-2*x^6*(a+b*x^3+c*x^6)^3//2+-1//3072*c^-11//2*(b^2+-4*a*c)*(21*b^4+16*a^2*c^2+-56*a*c*b^2)*arctanh((1/2)*c^-1//2*(a+b*x^3+c*x^6)^-1//2*(b+2*c*x^3))+1//1536*c^-5*(a+b*x^3+c*x^6)^(1/2)*(b+2*c*x^3)*(21*b^4+16*a^2*c^2+-56*a*c*b^2))
@test integrate(x^11*(a+b*x^3+c*x^6)^(1/2), x) == :(1//15*c^-1*x^6*(a+b*x^3+c*x^6)^3//2+1//720*c^-3*(a+b*x^3+c*x^6)^3//2*(35*b^2+-32*a*c+-42*b*c*x^3)+-1//384*b*c^-4*(a+b*x^3+c*x^6)^(1/2)*(b+2*c*x^3)*(7*b^2+-12*a*c)+1//768*b*c^-9//2*(b^2+-4*a*c)*(7*b^2+-12*a*c)*arctanh((1/2)*c^-1//2*(a+b*x^3+c*x^6)^-1//2*(b+2*c*x^3)))
@test integrate(x^8*(a+b*x^3+c*x^6)^(1/2), x) == :(-5//72*b*c^-2*(a+b*x^3+c*x^6)^3//2+1//12*c^-1*x^3*(a+b*x^3+c*x^6)^3//2+-1//384*c^-7//2*(b^2+-4*a*c)*(5*b^2+-4*a*c)*arctanh((1/2)*c^-1//2*(a+b*x^3+c*x^6)^-1//2*(b+2*c*x^3))+1//192*c^-3*(a+b*x^3+c*x^6)^(1/2)*(b+2*c*x^3)*(5*b^2+-4*a*c))
@test integrate(x^5*(a+b*x^3+c*x^6)^(1/2), x) == :(1//9*c^-1*(a+b*x^3+c*x^6)^3//2+-1//24*b*c^-2*(a+b*x^3+c*x^6)^(1/2)*(b+2*c*x^3)+1//48*b*c^-5//2*(b^2+-4*a*c)*arctanh((1/2)*c^-1//2*(a+b*x^3+c*x^6)^-1//2*(b+2*c*x^3)))
@test integrate(x^2*(a+b*x^3+c*x^6)^(1/2), x) == :(-1//24*c^-3//2*(b^2+-4*a*c)*arctanh((1/2)*c^-1//2*(a+b*x^3+c*x^6)^-1//2*(b+2*c*x^3))+1//12*c^-1*(a+b*x^3+c*x^6)^(1/2)*(b+2*c*x^3))
@test integrate(x^-1*(a+b*x^3+c*x^6)^(1/2), x) == :(1//3*(a+b*x^3+c*x^6)^(1/2)+-1//3*a^(1/2)*arctanh((1/2)*a^-1//2*(a+b*x^3+c*x^6)^-1//2*(2a+b*x^3))+1//6*b*c^-1//2*arctanh((1/2)*c^-1//2*(a+b*x^3+c*x^6)^-1//2*(b+2*c*x^3)))
@test integrate(x^-4*(a+b*x^3+c*x^6)^(1/2), x) == :(-1//3*x^-3*(a+b*x^3+c*x^6)^(1/2)+1//3*c^(1/2)*arctanh((1/2)*c^-1//2*(a+b*x^3+c*x^6)^-1//2*(b+2*c*x^3))+-1//6*b*a^-1//2*arctanh((1/2)*a^-1//2*(a+b*x^3+c*x^6)^-1//2*(2a+b*x^3)))
@test integrate(x^-7*(a+b*x^3+c*x^6)^(1/2), x) == :(1//24*a^-3//2*(b^2+-4*a*c)*arctanh((1/2)*a^-1//2*(a+b*x^3+c*x^6)^-1//2*(2a+b*x^3))+-1//12*a^-1*x^-6*(a+b*x^3+c*x^6)^(1/2)*(2a+b*x^3))
@test integrate(x^-10*(a+b*x^3+c*x^6)^(1/2), x) == :(-1//9*a^-1*x^-9*(a+b*x^3+c*x^6)^3//2+-1//48*b*a^-5//2*(b^2+-4*a*c)*arctanh((1/2)*a^-1//2*(a+b*x^3+c*x^6)^-1//2*(2a+b*x^3))+1//24*b*a^-2*x^-6*(a+b*x^3+c*x^6)^(1/2)*(2a+b*x^3))
@test integrate(x^-13*(a+b*x^3+c*x^6)^(1/2), x) == :(-1//12*a^-1*x^-12*(a+b*x^3+c*x^6)^3//2+1//384*a^-7//2*(b^2+-4*a*c)*(5*b^2+-4*a*c)*arctanh((1/2)*a^-1//2*(a+b*x^3+c*x^6)^-1//2*(2a+b*x^3))+5//72*b*a^-2*x^-9*(a+b*x^3+c*x^6)^3//2+-1//192*a^-3*x^-6*(a+b*x^3+c*x^6)^(1/2)*(2a+b*x^3)*(5*b^2+-4*a*c))
@test integrate(x^-16*(a+b*x^3+c*x^6)^(1/2), x) == :(-1//15*a^-1*x^-15*(a+b*x^3+c*x^6)^3//2+-1//720*a^-3*x^-9*(a+b*x^3+c*x^6)^3//2*(35*b^2+-32*a*c)+7//120*b*a^-2*x^-12*(a+b*x^3+c*x^6)^3//2+-1//768*b*a^-9//2*(b^2+-4*a*c)*(7*b^2+-12*a*c)*arctanh((1/2)*a^-1//2*(a+b*x^3+c*x^6)^-1//2*(2a+b*x^3))+1//384*b*a^-4*x^-6*(a+b*x^3+c*x^6)^(1/2)*(2a+b*x^3)*(7*b^2+-12*a*c))
@test integrate(x^14*(a+b*x^3+c*x^6)^3//2, x) == :(-1//13440*c^-4*(a+b*x^3+c*x^6)^5//2*(3*b*(77*b^2+-124*a*c)+-10*c*x^3*(33*b^2+-28*a*c))+1//24*c^-1*x^9*(a+b*x^3+c*x^6)^5//2+-11//336*b*c^-2*x^6*(a+b*x^3+c*x^6)^5//2+1//6144*c^-5*(a+b*x^3+c*x^6)^3//2*(b+2*c*x^3)*(33*b^4+16*a^2*c^2+-72*a*c*b^2)+1//32768*c^-13//2*(b^2+-4*a*c)^2*(33*b^4+16*a^2*c^2+-72*a*c*b^2)*arctanh((1/2)*c^-1//2*(a+b*x^3+c*x^6)^-1//2*(b+2*c*x^3))+-1//16384*c^-6*(a+b*x^3+c*x^6)^(1/2)*(b+2*c*x^3)*(b^2+-4*a*c)*(33*b^4+16*a^2*c^2+-72*a*c*b^2))
@test integrate(x^11*(a+b*x^3+c*x^6)^3//2, x) == :(1//21*c^-1*x^6*(a+b*x^3+c*x^6)^5//2+1//840*c^-3*(a+b*x^3+c*x^6)^5//2*(21*b^2+-16*a*c+-30*b*c*x^3)+-1//384*b*c^-4*(a+b*x^3+c*x^6)^3//2*(b+2*c*x^3)*(3*b^2+-4*a*c)+-1//2048*b*c^-11//2*(b^2+-4*a*c)^2*(3*b^2+-4*a*c)*arctanh((1/2)*c^-1//2*(a+b*x^3+c*x^6)^-1//2*(b+2*c*x^3))+1//1024*b*c^-5*(a+b*x^3+c*x^6)^(1/2)*(b+2*c*x^3)*(b^2+-4*a*c)*(3*b^2+-4*a*c))
@test integrate(x^8*(a+b*x^3+c*x^6)^3//2, x) == :(-7//180*b*c^-2*(a+b*x^3+c*x^6)^5//2+1//18*c^-1*x^3*(a+b*x^3+c*x^6)^5//2+1//576*c^-3*(a+b*x^3+c*x^6)^3//2*(b+2*c*x^3)*(7*b^2+-4*a*c)+1//3072*c^-9//2*(b^2+-4*a*c)^2*(7*b^2+-4*a*c)*arctanh((1/2)*c^-1//2*(a+b*x^3+c*x^6)^-1//2*(b+2*c*x^3))+-1//1536*c^-4*(a+b*x^3+c*x^6)^(1/2)*(b+2*c*x^3)*(b^2+-4*a*c)*(7*b^2+-4*a*c))
@test integrate(x^5*(a+b*x^3+c*x^6)^3//2, x) == :(1//15*c^-1*(a+b*x^3+c*x^6)^5//2+-1//48*b*c^-2*(a+b*x^3+c*x^6)^3//2*(b+2*c*x^3)+-1//256*b*c^-7//2*(b^2+-4*a*c)^2*arctanh((1/2)*c^-1//2*(a+b*x^3+c*x^6)^-1//2*(b+2*c*x^3))+1//128*b*c^-3*(a+b*x^3+c*x^6)^(1/2)*(b+2*c*x^3)*(b^2+-4*a*c))
@test integrate(x^2*(a+b*x^3+c*x^6)^3//2, x) == :(1//24*c^-1*(a+b*x^3+c*x^6)^3//2*(b+2*c*x^3)+1//128*c^-5//2*(b^2+-4*a*c)^2*arctanh((1/2)*c^-1//2*(a+b*x^3+c*x^6)^-1//2*(b+2*c*x^3))+-1//64*c^-2*(a+b*x^3+c*x^6)^(1/2)*(b+2*c*x^3)*(b^2+-4*a*c))
@test integrate(x^-1*(a+b*x^3+c*x^6)^3//2, x) == :(1//9*(a+b*x^3+c*x^6)^3//2+-1//3*a^3//2*arctanh((1/2)*a^-1//2*(a+b*x^3+c*x^6)^-1//2*(2a+b*x^3))+1//24*c^-1*(a+b*x^3+c*x^6)^(1/2)*(b^2+8*a*c+2*b*c*x^3)+-1//48*b*c^-3//2*(b^2+-12*a*c)*arctanh((1/2)*c^-1//2*(a+b*x^3+c*x^6)^-1//2*(b+2*c*x^3)))
@test integrate(x^-4*(a+b*x^3+c*x^6)^3//2, x) == :((a+b*x^3+c*x^6)^(1/2)*(3//4*b+(1/2)*c*x^3)+-1//3*x^-3*(a+b*x^3+c*x^6)^3//2+-1//2*b*a^(1/2)*arctanh((1/2)*a^-1//2*(a+b*x^3+c*x^6)^-1//2*(2a+b*x^3))+1//8*c^-1//2*(b^2+4*a*c)*arctanh((1/2)*c^-1//2*(a+b*x^3+c*x^6)^-1//2*(b+2*c*x^3)))
@test integrate(x^-7*(a+b*x^3+c*x^6)^3//2, x) == :(-1//6*x^-6*(a+b*x^3+c*x^6)^3//2+(1/2)*b*c^(1/2)*arctanh((1/2)*c^-1//2*(a+b*x^3+c*x^6)^-1//2*(b+2*c*x^3))+-1//4*x^-3*(a+b*x^3+c*x^6)^(1/2)*(b+-2*c*x^3)+-1//8*a^-1//2*(b^2+4*a*c)*arctanh((1/2)*a^-1//2*(a+b*x^3+c*x^6)^-1//2*(2a+b*x^3)))
@test integrate(x^-10*(a+b*x^3+c*x^6)^3//2, x) == :(-1//9*x^-9*(a+b*x^3+c*x^6)^3//2+1//3*c^3//2*arctanh((1/2)*c^-1//2*(a+b*x^3+c*x^6)^-1//2*(b+2*c*x^3))+-1//24*a^-1*x^-6*(a+b*x^3+c*x^6)^(1/2)*(x^3*(b^2+8*a*c)+2*a*b)+1//48*b*a^-3//2*(b^2+-12*a*c)*arctanh((1/2)*a^-1//2*(a+b*x^3+c*x^6)^-1//2*(2a+b*x^3)))
@test integrate(x^-13*(a+b*x^3+c*x^6)^3//2, x) == :(-1//128*a^-5//2*(b^2+-4*a*c)^2*arctanh((1/2)*a^-1//2*(a+b*x^3+c*x^6)^-1//2*(2a+b*x^3))+-1//24*a^-1*x^-12*(a+b*x^3+c*x^6)^3//2*(2a+b*x^3)+1//64*a^-2*x^-6*(a+b*x^3+c*x^6)^(1/2)*(b^2+-4*a*c)*(2a+b*x^3))
@test integrate(x^-16*(a+b*x^3+c*x^6)^3//2, x) == :(-1//15*a^-1*x^-15*(a+b*x^3+c*x^6)^5//2+1//256*b*a^-7//2*(b^2+-4*a*c)^2*arctanh((1/2)*a^-1//2*(a+b*x^3+c*x^6)^-1//2*(2a+b*x^3))+1//48*b*a^-2*x^-12*(a+b*x^3+c*x^6)^3//2*(2a+b*x^3)+-1//128*b*a^-3*x^-6*(a+b*x^3+c*x^6)^(1/2)*(b^2+-4*a*c)*(2a+b*x^3))
@test integrate(x^-19*(a+b*x^3+c*x^6)^3//2, x) == :(-1//18*a^-1*x^-18*(a+b*x^3+c*x^6)^5//2+-1//3072*a^-9//2*(b^2+-4*a*c)^2*(7*b^2+-4*a*c)*arctanh((1/2)*a^-1//2*(a+b*x^3+c*x^6)^-1//2*(2a+b*x^3))+7//180*b*a^-2*x^-15*(a+b*x^3+c*x^6)^5//2+-1//576*a^-3*x^-12*(a+b*x^3+c*x^6)^3//2*(2a+b*x^3)*(7*b^2+-4*a*c)+1//1536*a^-4*x^-6*(a+b*x^3+c*x^6)^(1/2)*(b^2+-4*a*c)*(2a+b*x^3)*(7*b^2+-4*a*c))
@test integrate(x^-22*(a+b*x^3+c*x^6)^3//2, x) == :(-1//21*a^-1*x^-21*(a+b*x^3+c*x^6)^5//2+-1//840*a^-3*x^-15*(a+b*x^3+c*x^6)^5//2*(21*b^2+-16*a*c)+1//28*b*a^-2*x^-18*(a+b*x^3+c*x^6)^5//2+1//2048*b*a^-11//2*(b^2+-4*a*c)^2*(3*b^2+-4*a*c)*arctanh((1/2)*a^-1//2*(a+b*x^3+c*x^6)^-1//2*(2a+b*x^3))+1//384*b*a^-4*x^-12*(a+b*x^3+c*x^6)^3//2*(2a+b*x^3)*(3*b^2+-4*a*c)+-1//1024*b*a^-5*x^-6*(a+b*x^3+c*x^6)^(1/2)*(b^2+-4*a*c)*(2a+b*x^3)*(3*b^2+-4*a*c))
@test integrate(x^14*(a+b*x^3+c*x^6)^-1//2, x) == :(-1//576*c^-4*(a+b*x^3+c*x^6)^(1/2)*(5*b*(21*b^2+-44*a*c)+-2*c*x^3*(35*b^2+-36*a*c))+1//12*c^-1*x^9*(a+b*x^3+c*x^6)^(1/2)+1//384*c^-9//2*(35*b^4+48*a^2*c^2+-120*a*c*b^2)*arctanh((1/2)*c^-1//2*(a+b*x^3+c*x^6)^-1//2*(b+2*c*x^3))+-7//72*b*c^-2*x^6*(a+b*x^3+c*x^6)^(1/2))
@test integrate(x^11*(a+b*x^3+c*x^6)^-1//2, x) == :(1//9*c^-1*x^6*(a+b*x^3+c*x^6)^(1/2)+1//72*c^-3*(a+b*x^3+c*x^6)^(1/2)*(15*b^2+-16*a*c+-10*b*c*x^3)+-1//48*b*c^-7//2*(5*b^2+-12*a*c)*arctanh((1/2)*c^-1//2*(a+b*x^3+c*x^6)^-1//2*(b+2*c*x^3)))
@test integrate(x^8*(a+b*x^3+c*x^6)^-1//2, x) == :(-1//4*b*c^-2*(a+b*x^3+c*x^6)^(1/2)+1//6*c^-1*x^3*(a+b*x^3+c*x^6)^(1/2)+1//24*c^-5//2*(3*b^2+-4*a*c)*arctanh((1/2)*c^-1//2*(a+b*x^3+c*x^6)^-1//2*(b+2*c*x^3)))
@test integrate(x^5*(a+b*x^3+c*x^6)^-1//2, x) == :(1//3*c^-1*(a+b*x^3+c*x^6)^(1/2)+-1//6*b*c^-3//2*arctanh((1/2)*c^-1//2*(a+b*x^3+c*x^6)^-1//2*(b+2*c*x^3)))
@test integrate(x^2*(a+b*x^3+c*x^6)^-1//2, x) == :(1//3*c^-1//2*arctanh((1/2)*c^-1//2*(a+b*x^3+c*x^6)^-1//2*(b+2*c*x^3)))
@test integrate(x^-1*(a+b*x^3+c*x^6)^-1//2, x) == :(-1//3*a^-1//2*arctanh((1/2)*a^-1//2*(a+b*x^3+c*x^6)^-1//2*(2a+b*x^3)))
@test integrate(x^-4*(a+b*x^3+c*x^6)^-1//2, x) == :(-1//3*a^-1*x^-3*(a+b*x^3+c*x^6)^(1/2)+1//6*b*a^-3//2*arctanh((1/2)*a^-1//2*(a+b*x^3+c*x^6)^-1//2*(2a+b*x^3)))
@test integrate(x^-7*(a+b*x^3+c*x^6)^-1//2, x) == :(-1//6*a^-1*x^-6*(a+b*x^3+c*x^6)^(1/2)+-1//24*a^-5//2*(3*b^2+-4*a*c)*arctanh((1/2)*a^-1//2*(a+b*x^3+c*x^6)^-1//2*(2a+b*x^3))+1//4*b*a^-2*x^-3*(a+b*x^3+c*x^6)^(1/2))
@test integrate(x^-10*(a+b*x^3+c*x^6)^-1//2, x) == :(-1//9*a^-1*x^-9*(a+b*x^3+c*x^6)^(1/2)+-1//72*a^-3*x^-3*(a+b*x^3+c*x^6)^(1/2)*(15*b^2+-16*a*c)+1//48*b*a^-7//2*(5*b^2+-12*a*c)*arctanh((1/2)*a^-1//2*(a+b*x^3+c*x^6)^-1//2*(2a+b*x^3))+5//36*b*a^-2*x^-6*(a+b*x^3+c*x^6)^(1/2))
@test integrate(x^-13*(a+b*x^3+c*x^6)^-1//2, x) == :(-1//12*a^-1*x^-12*(a+b*x^3+c*x^6)^(1/2)+-1//384*a^-9//2*(35*b^4+48*a^2*c^2+-120*a*c*b^2)*arctanh((1/2)*a^-1//2*(a+b*x^3+c*x^6)^-1//2*(2a+b*x^3))+-1//288*a^-3*x^-6*(a+b*x^3+c*x^6)^(1/2)*(35*b^2+-36*a*c)+7//72*b*a^-2*x^-9*(a+b*x^3+c*x^6)^(1/2)+5//576*b*a^-4*x^-3*(a+b*x^3+c*x^6)^(1/2)*(21*b^2+-44*a*c))
@test integrate(x^14*(a+b*x^3+c*x^6)^-3//2, x) == :(1//8*c^-7//2*(5*b^2+-4*a*c)*arctanh((1/2)*c^-1//2*(a+b*x^3+c*x^6)^-1//2*(b+2*c*x^3))+2*x^9*(3*b^2+-12*a*c)^-1*(a+b*x^3+c*x^6)^-1//2*(2a+b*x^3)+-1//12*c^-3*(b^2+-4*a*c)^-1*(a+b*x^3+c*x^6)^(1/2)*(b*(15*b^2+-52*a*c)+-2*c*x^3*(5*b^2+-12*a*c))+-2//3*b*c^-1*x^6*(b^2+-4*a*c)^-1*(a+b*x^3+c*x^6)^(1/2))
@test integrate(x^11*(a+b*x^3+c*x^6)^-3//2, x) == :(-1//2*b*c^-5//2*arctanh((1/2)*c^-1//2*(a+b*x^3+c*x^6)^-1//2*(b+2*c*x^3))+2*x^6*(3*b^2+-12*a*c)^-1*(a+b*x^3+c*x^6)^-1//2*(2a+b*x^3)+1//3*c^-2*(b^2+-4*a*c)^-1*(a+b*x^3+c*x^6)^(1/2)*(3*b^2+-8*a*c+-2*b*c*x^3))
@test integrate(x^8*(a+b*x^3+c*x^6)^-3//2, x) == :(1//3*c^-3//2*arctanh((1/2)*c^-1//2*(a+b*x^3+c*x^6)^-1//2*(b+2*c*x^3))+2*x^3*(3*b^2+-12*a*c)^-1*(a+b*x^3+c*x^6)^-1//2*(2a+b*x^3)+-2//3*b*c^-1*(b^2+-4*a*c)^-1*(a+b*x^3+c*x^6)^(1/2))
@test integrate(x^5*(a+b*x^3+c*x^6)^-3//2, x) == :((3*b^2+-12*a*c)^-1*(a+b*x^3+c*x^6)^-1//2*(4a+2*b*x^3))
@test integrate(x^2*(a+b*x^3+c*x^6)^-3//2, x) == :(-1*(3*b^2+-12*a*c)^-1*(a+b*x^3+c*x^6)^-1//2*(2b+4*c*x^3))
@test integrate(x^-1*(a+b*x^3+c*x^6)^-3//2, x) == :(-1//3*a^-3//2*arctanh((1/2)*a^-1//2*(a+b*x^3+c*x^6)^-1//2*(2a+b*x^3))+1//3*a^-1*(b^2+-4*a*c)^-1*(a+b*x^3+c*x^6)^-1//2*(2*b^2+-4*a*c+2*b*c*x^3))
@test integrate(x^-4*(a+b*x^3+c*x^6)^-3//2, x) == :((1/2)*b*a^-5//2*arctanh((1/2)*a^-1//2*(a+b*x^3+c*x^6)^-1//2*(2a+b*x^3))+-1//3*a^-2*x^-3*(b^2+-4*a*c)^-1*(a+b*x^3+c*x^6)^(1/2)*(3*b^2+-8*a*c)+1//3*a^-1*x^-3*(b^2+-4*a*c)^-1*(a+b*x^3+c*x^6)^-1//2*(2*b^2+-4*a*c+2*b*c*x^3))
@test integrate(x^-7*(a+b*x^3+c*x^6)^-3//2, x) == :(-1//8*a^-7//2*(5*b^2+-4*a*c)*arctanh((1/2)*a^-1//2*(a+b*x^3+c*x^6)^-1//2*(2a+b*x^3))+-1//6*a^-2*x^-6*(b^2+-4*a*c)^-1*(a+b*x^3+c*x^6)^(1/2)*(5*b^2+-12*a*c)+1//3*a^-1*x^-6*(b^2+-4*a*c)^-1*(a+b*x^3+c*x^6)^-1//2*(2*b^2+-4*a*c+2*b*c*x^3)+1//12*b*a^-3*x^-3*(b^2+-4*a*c)^-1*(a+b*x^3+c*x^6)^(1/2)*(15*b^2+-52*a*c))
@test integrate(x^-10*(a+b*x^3+c*x^6)^-3//2, x) == :(5//48*b*a^-9//2*(7*b^2+-12*a*c)*arctanh((1/2)*a^-1//2*(a+b*x^3+c*x^6)^-1//2*(2a+b*x^3))+-1//9*a^-2*x^-9*(b^2+-4*a*c)^-1*(a+b*x^3+c*x^6)^(1/2)*(7*b^2+-16*a*c)+-1//72*a^-4*x^-3*(b^2+-4*a*c)^-1*(a+b*x^3+c*x^6)^(1/2)*(105*b^4+256*a^2*c^2+-460*a*c*b^2)+1//3*a^-1*x^-9*(b^2+-4*a*c)^-1*(a+b*x^3+c*x^6)^-1//2*(2*b^2+-4*a*c+2*b*c*x^3)+1//36*b*a^-3*x^-6*(b^2+-4*a*c)^-1*(a+b*x^3+c*x^6)^(1/2)*(35*b^2+-116*a*c))
@test integrate((d*x)^m*(a+b*x^3+c*x^6)^2, x) == :(a^2*d^-1*(d*x)^(1+m)*(1+m)^-1+c^2*d^-13*(d*x)^(13+m)*(13+m)^-1+d^-7*(d*x)^(7+m)*(7+m)^-1*(b^2+2*a*c)+2*a*b*d^-4*(d*x)^(4+m)*(4+m)^-1+2*b*c*d^-10*(d*x)^(10+m)*(10+m)^-1)
@test integrate((d*x)^m*(a+b*x^3+c*x^6), x) == :(a*d^-1*(d*x)^(1+m)*(1+m)^-1+b*d^-4*(d*x)^(4+m)*(4+m)^-1+c*d^-7*(d*x)^(7+m)*(7+m)^-1)
@test integrate(x^9*(1+x^8+2*x^4)^-1, x) == :(-3//4*arctan(x^2)+3//4*x^2+-1*x^6*(4+4*x^4)^-1)
@test integrate(x^7*(1+x^8+2*x^4)^-1, x) == :((4+4*x^4)^-1+1//4*log(1+x^4))
@test integrate(x^5*(1+x^8+2*x^4)^-1, x) == :(1//4*arctan(x^2)+-1*x^2*(4+4*x^4)^-1)
@test integrate(x^3*(1+x^8+2*x^4)^-1, x) == :(-1*(4+4*x^4)^-1)
@test integrate(x*(1+x^8+2*x^4)^-1, x) == :(1//4*arctan(x^2)+x^2*(4+4*x^4)^-1)
@test integrate(x^-1*(1+x^8+2*x^4)^-1, x) == :((4+4*x^4)^-1+-1//4*log(1+x^4)+log(x))
@test integrate(x^-3*(1+x^8+2*x^4)^-1, x) == :(-3//4*x^-2+-3//4*arctan(x^2)+1//4*x^-2*(1+x^4)^-1)
@test integrate(x^-5*(1+x^8+2*x^4)^-1, x) == :((1/2)*log(1+x^4)+-1*(4+4*x^4)^-1+-2*log(x)+-1//4*x^-4)
@test integrate(x^-7*(1+x^8+2*x^4)^-1, x) == :(-5//12*x^-6+5//4*x^-2+5//4*arctan(x^2)+1//4*x^-6*(1+x^4)^-1)
@test integrate(x^8*(1+x^8+2*x^4)^-1, x) == :(5//4*x+-1*x^5*(4+4*x^4)^-1+-5//16*2^(1/2)*arctan(1+x*2^(1/2))+-5//32*2^(1/2)*log(1+x^2+x*2^(1/2))+5//16*2^(1/2)*arctan(1+-1*x*2^(1/2))+5//32*2^(1/2)*log(1+x^2+-1*x*2^(1/2)))
@test integrate(x^6*(1+x^8+2*x^4)^-1, x) == :(-1*x^3*(4+4*x^4)^-1+-3//16*2^(1/2)*arctan(1+-1*x*2^(1/2))+-3//32*2^(1/2)*log(1+x^2+x*2^(1/2))+3//16*2^(1/2)*arctan(1+x*2^(1/2))+3//32*2^(1/2)*log(1+x^2+-1*x*2^(1/2)))
@test integrate(x^4*(1+x^8+2*x^4)^-1, x) == :(-1*x*(4+4*x^4)^-1+-1//16*2^(1/2)*arctan(1+-1*x*2^(1/2))+-1//32*2^(1/2)*log(1+x^2+-1*x*2^(1/2))+1//16*2^(1/2)*arctan(1+x*2^(1/2))+1//32*2^(1/2)*log(1+x^2+x*2^(1/2)))
@test integrate(x^2*(1+x^8+2*x^4)^-1, x) == :(x^3*(4+4*x^4)^-1+-1//16*2^(1/2)*arctan(1+-1*x*2^(1/2))+-1//32*2^(1/2)*log(1+x^2+x*2^(1/2))+1//16*2^(1/2)*arctan(1+x*2^(1/2))+1//32*2^(1/2)*log(1+x^2+-1*x*2^(1/2)))
@test integrate((1+x^8+2*x^4)^-1, x) == :(x*(4+4*x^4)^-1+-3//16*2^(1/2)*arctan(1+-1*x*2^(1/2))+-3//32*2^(1/2)*log(1+x^2+-1*x*2^(1/2))+3//16*2^(1/2)*arctan(1+x*2^(1/2))+3//32*2^(1/2)*log(1+x^2+x*2^(1/2)))
@test integrate(x^-2*(1+x^8+2*x^4)^-1, x) == :(-5//4*x^-1+-5//16*2^(1/2)*arctan(1+x*2^(1/2))+-5//32*2^(1/2)*log(1+x^2+-1*x*2^(1/2))+1//4*x^-1*(1+x^4)^-1+5//16*2^(1/2)*arctan(1+-1*x*2^(1/2))+5//32*2^(1/2)*log(1+x^2+x*2^(1/2)))
@test integrate(x^-4*(1+x^8+2*x^4)^-1, x) == :(-7//12*x^-3+-7//16*2^(1/2)*arctan(1+x*2^(1/2))+-7//32*2^(1/2)*log(1+x^2+x*2^(1/2))+1//4*x^-3*(1+x^4)^-1+7//16*2^(1/2)*arctan(1+-1*x*2^(1/2))+7//32*2^(1/2)*log(1+x^2+-1*x*2^(1/2)))
@test integrate(x^-6*(1+x^8+2*x^4)^-1, x) == :(-9//20*x^-5+9//4*x^-1+-9//16*2^(1/2)*arctan(1+-1*x*2^(1/2))+-9//32*2^(1/2)*log(1+x^2+x*2^(1/2))+1//4*x^-5*(1+x^4)^-1+9//16*2^(1/2)*arctan(1+x*2^(1/2))+9//32*2^(1/2)*log(1+x^2+-1*x*2^(1/2)))
@test integrate(x^-8*(1+x^8+2*x^4)^-1, x) == :(-11//28*x^-7+11//12*x^-3+-11//16*2^(1/2)*arctan(1+-1*x*2^(1/2))+-11//32*2^(1/2)*log(1+x^2+-1*x*2^(1/2))+1//4*x^-7*(1+x^4)^-1+11//16*2^(1/2)*arctan(1+x*2^(1/2))+11//32*2^(1/2)*log(1+x^2+x*2^(1/2)))
@test integrate(x^9*(1+x^8+-2*x^4)^-1, x) == :(-3//4*arctanh(x^2)+3//4*x^2+x^6*(4+-4*x^4)^-1)
@test integrate(x^7*(1+x^8+-2*x^4)^-1, x) == :((4+-4*x^4)^-1+1//4*log(1+-1*x^4))
@test integrate(x^5*(1+x^8+-2*x^4)^-1, x) == :(-1//4*arctanh(x^2)+x^2*(4+-4*x^4)^-1)
@test integrate(x^3*(1+x^8+-2*x^4)^-1, x) == :((4+-4*x^4)^-1)
@test integrate(x*(1+x^8+-2*x^4)^-1, x) == :(1//4*arctanh(x^2)+x^2*(4+-4*x^4)^-1)
@test integrate(x^-1*(1+x^8+-2*x^4)^-1, x) == :((4+-4*x^4)^-1+-1//4*log(1+-1*x^4)+log(x))
@test integrate(x^-3*(1+x^8+-2*x^4)^-1, x) == :(-3//4*x^-2+3//4*arctanh(x^2)+1//4*x^-2*(1+-1*x^4)^-1)
@test integrate(x^-5*(1+x^8+-2*x^4)^-1, x) == :((4+-4*x^4)^-1+2*log(x)+-1//2*log(1+-1*x^4)+-1//4*x^-4)
@test integrate(x^-7*(1+x^8+-2*x^4)^-1, x) == :(-5//4*x^-2+-5//12*x^-6+5//4*arctanh(x^2)+1//4*x^-6*(1+-1*x^4)^-1)
@test integrate(x^8*(1+x^8+-2*x^4)^-1, x) == :(-5//8*arctan(x)+-5//8*arctanh(x)+5//4*x+x^5*(4+-4*x^4)^-1)
@test integrate(x^6*(1+x^8+-2*x^4)^-1, x) == :(-3//8*arctanh(x)+3//8*arctan(x)+x^3*(4+-4*x^4)^-1)
@test integrate(x^4*(1+x^8+-2*x^4)^-1, x) == :(-1//8*arctan(x)+-1//8*arctanh(x)+x*(4+-4*x^4)^-1)
@test integrate(x^2*(1+x^8+-2*x^4)^-1, x) == :(-1//8*arctan(x)+1//8*arctanh(x)+x^3*(4+-4*x^4)^-1)
@test integrate((1+x^8+-2*x^4)^-1, x) == :(3//8*arctan(x)+3//8*arctanh(x)+x*(4+-4*x^4)^-1)
@test integrate(x^-2*(1+x^8+-2*x^4)^-1, x) == :(-5//4*x^-1+-5//8*arctan(x)+5//8*arctanh(x)+1//4*x^-1*(1+-1*x^4)^-1)
@test integrate(x^-4*(1+x^8+-2*x^4)^-1, x) == :(-7//12*x^-3+7//8*arctan(x)+7//8*arctanh(x)+1//4*x^-3*(1+-1*x^4)^-1)
@test integrate(x^-6*(1+x^8+-2*x^4)^-1, x) == :(-9//4*x^-1+-9//8*arctan(x)+-9//20*x^-5+9//8*arctanh(x)+1//4*x^-5*(1+-1*x^4)^-1)
@test integrate(x^-8*(1+x^8+-2*x^4)^-1, x) == :(-11//12*x^-3+-11//28*x^-7+11//8*arctan(x)+11//8*arctanh(x)+1//4*x^-7*(1+-1*x^4)^-1)
@test integrate(x^11*(a+b*x^4+c*x^8)^-1, x) == :(1//4*c^-1*x^4+-1//8*b*c^-2*log(a+b*x^4+c*x^8)+-1//4*c^-2*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^4)))
@test integrate(x^9*(a+b*x^4+c*x^8)^-1, x) == :((1/2)*c^-1*x^2+-1//4*2^(1/2)*c^-3//2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(2^(1/2)*c^(1/2)*x^2*(b+(b^2+-4*a*c)^(1/2))^-1//2)+-1//4*2^(1/2)*c^-3//2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(2^(1/2)*c^(1/2)*x^2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^7*(a+b*x^4+c*x^8)^-1, x) == :(1//8*c^-1*log(a+b*x^4+c*x^8)+1//4*b*c^-1*(b^2+-4*a*c)^-1//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^4)))
@test integrate(x^5*(a+b*x^4+c*x^8)^-1, x) == :(-1//4*2^(1/2)*c^-1//2*(b+-1*(b^2+-4*a*c)^(1/2))^(1/2)*(b^2+-4*a*c)^-1//2*arctan(2^(1/2)*c^(1/2)*x^2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2)+1//4*2^(1/2)*c^-1//2*(b+(b^2+-4*a*c)^(1/2))^(1/2)*(b^2+-4*a*c)^-1//2*arctan(2^(1/2)*c^(1/2)*x^2*(b+(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^3*(a+b*x^4+c*x^8)^-1, x) == :(-1//2*(b^2+-4*a*c)^-1//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^4)))
@test integrate(x*(a+b*x^4+c*x^8)^-1, x) == :((1/2)*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1//2*arctan(2^(1/2)*c^(1/2)*x^2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2)+-1//2*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1//2*arctan(2^(1/2)*c^(1/2)*x^2*(b+(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^-1*(a+b*x^4+c*x^8)^-1, x) == :(a^-1*log(x)+-1//8*a^-1*log(a+b*x^4+c*x^8)+1//4*b*a^-1*(b^2+-4*a*c)^-1//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^4)))
@test integrate(x^-3*(a+b*x^4+c*x^8)^-1, x) == :(-1//2*a^-1*x^-2+-1//4*2^(1/2)*a^-1*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(1+-1*b*(b^2+-4*a*c)^-1//2)*arctan(2^(1/2)*c^(1/2)*x^2*(b+(b^2+-4*a*c)^(1/2))^-1//2)+-1//4*2^(1/2)*a^-1*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(1+b*(b^2+-4*a*c)^-1//2)*arctan(2^(1/2)*c^(1/2)*x^2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^-5*(a+b*x^4+c*x^8)^-1, x) == :(-1//4*a^-1*x^-4+-1*b*a^-2*log(x)+1//8*b*a^-2*log(a+b*x^4+c*x^8)+-1//4*a^-2*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^4)))
@test integrate(x^10*(a+b*x^4+c*x^8)^-1, x) == :(1//3*c^-1*x^3+-1//4*2^1//4*c^-7//4*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(x*2^1//4*c^1//4*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1//4*2^1//4*c^-7//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(x*2^1//4*c^1//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+1//4*2^1//4*c^-7//4*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctanh(x*2^1//4*c^1//4*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+1//4*2^1//4*c^-7//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctanh(x*2^1//4*c^1//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate(x^8*(a+b*x^4+c*x^8)^-1, x) == :(x*c^-1+1//4*2^3//4*c^-5//4*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(x*2^1//4*c^1//4*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+1//4*2^3//4*c^-5//4*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctanh(x*2^1//4*c^1//4*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+1//4*2^3//4*c^-5//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(x*2^1//4*c^1//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+1//4*2^3//4*c^-5//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctanh(x*2^1//4*c^1//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate(x^6*(a+b*x^4+c*x^8)^-1, x) == :(-1//4*2^1//4*c^-3//4*(b^2+-4*a*c)^-1//2*((b^2+-4*a*c)^(1/2)+-1b)^3//4*arctanh(x*2^1//4*c^1//4*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1//4*2^1//4*c^-3//4*(b^2+-4*a*c)^-1//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^3//4*arctan(x*2^1//4*c^1//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+1//4*2^1//4*c^-3//4*(b^2+-4*a*c)^-1//2*((b^2+-4*a*c)^(1/2)+-1b)^3//4*arctan(x*2^1//4*c^1//4*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+1//4*2^1//4*c^-3//4*(b^2+-4*a*c)^-1//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^3//4*arctanh(x*2^1//4*c^1//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate(x^4*(a+b*x^4+c*x^8)^-1, x) == :(-1//4*2^3//4*c^-1//4*(b^2+-4*a*c)^-1//2*((b^2+-4*a*c)^(1/2)+-1b)^1//4*arctan(x*2^1//4*c^1//4*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1//4*2^3//4*c^-1//4*(b^2+-4*a*c)^-1//2*((b^2+-4*a*c)^(1/2)+-1b)^1//4*arctanh(x*2^1//4*c^1//4*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+1//4*2^3//4*c^-1//4*(b^2+-4*a*c)^-1//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^1//4*arctan(x*2^1//4*c^1//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+1//4*2^3//4*c^-1//4*(b^2+-4*a*c)^-1//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^1//4*arctanh(x*2^1//4*c^1//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate(x^2*(a+b*x^4+c*x^8)^-1, x) == :((1/2)*2^1//4*c^1//4*(b^2+-4*a*c)^-1//2*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*arctan(x*2^1//4*c^1//4*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+(1/2)*2^1//4*c^1//4*(b^2+-4*a*c)^-1//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*arctanh(x*2^1//4*c^1//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+-1//2*2^1//4*c^1//4*(b^2+-4*a*c)^-1//2*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*arctanh(x*2^1//4*c^1//4*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1//2*2^1//4*c^1//4*(b^2+-4*a*c)^-1//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*arctan(x*2^1//4*c^1//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate((a+b*x^4+c*x^8)^-1, x) == :((1/2)*2^3//4*c^3//4*(b^2+-4*a*c)^-1//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*arctan(x*2^1//4*c^1//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+(1/2)*2^3//4*c^3//4*(b^2+-4*a*c)^-1//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*arctanh(x*2^1//4*c^1//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+-1//2*2^3//4*c^3//4*(b^2+-4*a*c)^-1//2*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*arctan(x*2^1//4*c^1//4*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1//2*2^3//4*c^3//4*(b^2+-4*a*c)^-1//2*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*arctanh(x*2^1//4*c^1//4*((b^2+-4*a*c)^(1/2)+-1b)^-1//4))
@test integrate(x^-2*(a+b*x^4+c*x^8)^-1, x) == :(-1*a^-1*x^-1+-1//4*2^1//4*a^-1*c^1//4*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*(1+b*(b^2+-4*a*c)^-1//2)*arctan(x*2^1//4*c^1//4*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1//4*2^1//4*a^-1*c^1//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*(1+-1*b*(b^2+-4*a*c)^-1//2)*arctan(x*2^1//4*c^1//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+1//4*2^1//4*a^-1*c^1//4*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*(1+b*(b^2+-4*a*c)^-1//2)*arctanh(x*2^1//4*c^1//4*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+1//4*2^1//4*a^-1*c^1//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*(1+-1*b*(b^2+-4*a*c)^-1//2)*arctanh(x*2^1//4*c^1//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate(x^-4*(a+b*x^4+c*x^8)^-1, x) == :(-1//3*a^-1*x^-3+1//4*2^3//4*a^-1*c^3//4*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(1+b*(b^2+-4*a*c)^-1//2)*arctan(x*2^1//4*c^1//4*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+1//4*2^3//4*a^-1*c^3//4*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(1+b*(b^2+-4*a*c)^-1//2)*arctanh(x*2^1//4*c^1//4*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+1//4*2^3//4*a^-1*c^3//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(1+-1*b*(b^2+-4*a*c)^-1//2)*arctan(x*2^1//4*c^1//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+1//4*2^3//4*a^-1*c^3//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(1+-1*b*(b^2+-4*a*c)^-1//2)*arctanh(x*2^1//4*c^1//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate(x^11*(1+x^4+x^8)^-1, x) == :(-1//8*log(1+x^4+x^8)+1//4*x^4+-1//12*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*x^4)))
@test integrate(x^9*(1+x^4+x^8)^-1, x) == :((1/2)*x^2+-1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*x^2))+1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x^2)))
@test integrate(x^7*(1+x^4+x^8)^-1, x) == :(1//8*log(1+x^4+x^8)+-1//12*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*x^4)))
@test integrate(x^5*(1+x^4+x^8)^-1, x) == :(-1//8*log(1+x^2+x^4)+1//8*log(1+x^4+-1*x^2)+-1//12*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x^2))+1//12*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*x^2)))
@test integrate(x^3*(1+x^4+x^8)^-1, x) == :(1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*x^4)))
@test integrate(x*(1+x^4+x^8)^-1, x) == :(-1//8*log(1+x^4+-1*x^2)+1//8*log(1+x^2+x^4)+-1//12*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x^2))+1//12*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*x^2)))
@test integrate(x^-1*(1+x^4+x^8)^-1, x) == :(-1//8*log(1+x^4+x^8)+-1//12*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*x^4))+log(x))
@test integrate(x^-3*(1+x^4+x^8)^-1, x) == :(-1//2*x^-2+-1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*x^2))+1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x^2)))
@test integrate(x^-5*(1+x^4+x^8)^-1, x) == :(-1*log(x)+-1//4*x^-4+1//8*log(1+x^4+x^8)+-1//12*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*x^4)))
@test integrate(x^-7*(1+x^4+x^8)^-1, x) == :((1/2)*x^-2+-1//6*x^-6+-1//8*log(1+x^2+x^4)+1//8*log(1+x^4+-1*x^2)+-1//12*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x^2))+1//12*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*x^2)))
@test integrate(x^8*(1+x^4+x^8)^-1, x) == :(x+-1//4*arctan(3^(1/2)+2x)+-1//8*log(1+x+x^2)+1//4*arctan(3^(1/2)+-2x)+1//8*log(1+x^2+-1x)+-1//12*3^(1/2)*arctan(1//3*3^(1/2)*(1+2x))+-1//24*3^(1/2)*log(1+x^2+x*3^(1/2))+1//12*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x))+1//24*3^(1/2)*log(1+x^2+-1*x*3^(1/2)))
@test integrate(x^6*(1+x^4+x^8)^-1, x) == :(-1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x))+-1//12*3^(1/2)*log(1+x^2+x*3^(1/2))+1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+2x))+1//12*3^(1/2)*log(1+x^2+-1*x*3^(1/2)))
@test integrate(x^4*(1+x^4+x^8)^-1, x) == :(-1//4*arctan(3^(1/2)+-2x)+-1//8*log(1+x^2+-1x)+1//4*arctan(3^(1/2)+2x)+1//8*log(1+x+x^2)+-1//12*3^(1/2)*arctan(1//3*3^(1/2)*(1+2x))+-1//24*3^(1/2)*log(1+x^2+x*3^(1/2))+1//12*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x))+1//24*3^(1/2)*log(1+x^2+-1*x*3^(1/2)))
@test integrate(x^2*(1+x^4+x^8)^-1, x) == :(-1//4*arctan(3^(1/2)+-2x)+-1//8*log(1+x+x^2)+1//4*arctan(3^(1/2)+2x)+1//8*log(1+x^2+-1x)+-1//12*3^(1/2)*arctan(1//3*3^(1/2)*(1+2x))+-1//24*3^(1/2)*log(1+x^2+-1*x*3^(1/2))+1//12*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x))+1//24*3^(1/2)*log(1+x^2+x*3^(1/2)))
@test integrate((1+x^4+x^8)^-1, x) == :(-1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x))+-1//12*3^(1/2)*log(1+x^2+-1*x*3^(1/2))+1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+2x))+1//12*3^(1/2)*log(1+x^2+x*3^(1/2)))
@test integrate(x^-2*(1+x^4+x^8)^-1, x) == :(-1*x^-1+-1//4*arctan(3^(1/2)+2x)+-1//8*log(1+x^2+-1x)+1//4*arctan(3^(1/2)+-2x)+1//8*log(1+x+x^2)+-1//12*3^(1/2)*arctan(1//3*3^(1/2)*(1+2x))+-1//24*3^(1/2)*log(1+x^2+-1*x*3^(1/2))+1//12*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x))+1//24*3^(1/2)*log(1+x^2+x*3^(1/2)))
@test integrate(x^-4*(1+x^4+x^8)^-1, x) == :(-1//3*x^-3+-1//4*arctan(3^(1/2)+2x)+-1//8*log(1+x+x^2)+1//4*arctan(3^(1/2)+-2x)+1//8*log(1+x^2+-1x)+-1//12*3^(1/2)*arctan(1//3*3^(1/2)*(1+2x))+-1//24*3^(1/2)*log(1+x^2+x*3^(1/2))+1//12*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x))+1//24*3^(1/2)*log(1+x^2+-1*x*3^(1/2)))
@test integrate(x^-6*(1+x^4+x^8)^-1, x) == :(x^-1+-1//5*x^-5+-1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x))+-1//12*3^(1/2)*log(1+x^2+x*3^(1/2))+1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+2x))+1//12*3^(1/2)*log(1+x^2+-1*x*3^(1/2)))
@test integrate(x^-8*(1+x^4+x^8)^-1, x) == :(-1//4*arctan(3^(1/2)+-2x)+-1//7*x^-7+-1//8*log(1+x^2+-1x)+1//3*x^-3+1//4*arctan(3^(1/2)+2x)+1//8*log(1+x+x^2)+-1//12*3^(1/2)*arctan(1//3*3^(1/2)*(1+2x))+-1//24*3^(1/2)*log(1+x^2+x*3^(1/2))+1//12*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x))+1//24*3^(1/2)*log(1+x^2+-1*x*3^(1/2)))
@test integrate(x^11*(1+x^8+-1*x^4)^-1, x) == :(1//4*x^4+1//8*log(1+x^8+-1*x^4)+1//12*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x^4)))
@test integrate(x^9*(1+x^8+-1*x^4)^-1, x) == :((1/2)*x^2+-1//12*3^(1/2)*log(1+x^4+3^(1/2)*x^2)+1//12*3^(1/2)*log(1+x^4+-1*3^(1/2)*x^2))
@test integrate(x^7*(1+x^8+-1*x^4)^-1, x) == :(1//8*log(1+x^8+-1*x^4)+-1//12*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x^4)))
@test integrate(x^5*(1+x^8+-1*x^4)^-1, x) == :(-1//4*arctan(3^(1/2)+-2*x^2)+1//4*arctan(3^(1/2)+2*x^2)+-1//24*3^(1/2)*log(1+x^4+3^(1/2)*x^2)+1//24*3^(1/2)*log(1+x^4+-1*3^(1/2)*x^2))
@test integrate(x^3*(1+x^8+-1*x^4)^-1, x) == :(-1//6*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x^4)))
@test integrate(x*(1+x^8+-1*x^4)^-1, x) == :(-1//4*arctan(3^(1/2)+-2*x^2)+1//4*arctan(3^(1/2)+2*x^2)+-1//24*3^(1/2)*log(1+x^4+-1*3^(1/2)*x^2)+1//24*3^(1/2)*log(1+x^4+3^(1/2)*x^2))
@test integrate(x^-1*(1+x^8+-1*x^4)^-1, x) == :(-1//8*log(1+x^8+-1*x^4)+-1//12*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x^4))+log(x))
@test integrate(x^-3*(1+x^8+-1*x^4)^-1, x) == :(-1//2*x^-2+-1//12*3^(1/2)*log(1+x^4+-1*3^(1/2)*x^2)+1//12*3^(1/2)*log(1+x^4+3^(1/2)*x^2))
@test integrate(x^-5*(1+x^8+-1*x^4)^-1, x) == :(-1//4*x^-4+-1//8*log(1+x^8+-1*x^4)+1//12*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x^4))+log(x))
@test integrate(x^-7*(1+x^8+-1*x^4)^-1, x) == :(-1//2*x^-2+-1//4*arctan(3^(1/2)+2*x^2)+-1//6*x^-6+1//4*arctan(3^(1/2)+-2*x^2)+-1//24*3^(1/2)*log(1+x^4+-1*3^(1/2)*x^2)+1//24*3^(1/2)*log(1+x^4+3^(1/2)*x^2))
@test integrate(x^8*(1+x^8+-1*x^4)^-1, x) == :(x+-1//4*(6+-3*3^(1/2))^-1//2*arctan((2+3^(1/2))^-1//2*((2+-1*3^(1/2))^(1/2)+2x))+-1//4*(6+3*3^(1/2))^-1//2*arctan((2+-1*3^(1/2))^-1//2*((2+3^(1/2))^(1/2)+-2x))+-1//8*(2//3+-1//3*3^(1/2))^(1/2)*log(1+x^2+-1*x*(2+-1*3^(1/2))^(1/2))+-1//8*(2//3+1//3*3^(1/2))^(1/2)*log(1+x^2+x*(2+3^(1/2))^(1/2))+1//4*(6+-3*3^(1/2))^-1//2*arctan((2+3^(1/2))^-1//2*((2+-1*3^(1/2))^(1/2)+-2x))+1//4*(6+3*3^(1/2))^-1//2*arctan((2+-1*3^(1/2))^-1//2*((2+3^(1/2))^(1/2)+2x))+1//8*(2//3+-1//3*3^(1/2))^(1/2)*log(1+x^2+x*(2+-1*3^(1/2))^(1/2))+1//8*(2//3+1//3*3^(1/2))^(1/2)*log(1+x^2+-1*x*(2+3^(1/2))^(1/2)))
@test integrate(x^6*(1+x^8+-1*x^4)^-1, x) == :(-1//12*6^(1/2)*arctan((2+3^(1/2))^-1//2*((2+-1*3^(1/2))^(1/2)+-2x))+-1//12*6^(1/2)*arctan((2+-1*3^(1/2))^-1//2*((2+3^(1/2))^(1/2)+-2x))+-1//24*6^(1/2)*log(1+x^2+x*(2+3^(1/2))^(1/2))+-1//24*6^(1/2)*log(1+x^2+x*(2+-1*3^(1/2))^(1/2))+1//12*6^(1/2)*arctan((2+3^(1/2))^-1//2*((2+-1*3^(1/2))^(1/2)+2x))+1//12*6^(1/2)*arctan((2+-1*3^(1/2))^-1//2*((2+3^(1/2))^(1/2)+2x))+1//24*6^(1/2)*log(1+x^2+-1*x*(2+3^(1/2))^(1/2))+1//24*6^(1/2)*log(1+x^2+-1*x*(2+-1*3^(1/2))^(1/2)))
@test integrate(x^4*(1+x^8+-1*x^4)^-1, x) == :(-1//4*(6+-3*3^(1/2))^-1//2*arctan((2+-1*3^(1/2))^-1//2*((2+3^(1/2))^(1/2)+-2x))+-1//4*(6+3*3^(1/2))^-1//2*arctan((2+3^(1/2))^-1//2*((2+-1*3^(1/2))^(1/2)+2x))+-1//8*(6+-3*3^(1/2))^-1//2*log(1+x^2+-1*x*(2+-1*3^(1/2))^(1/2))+-1//8*(6+3*3^(1/2))^-1//2*log(1+x^2+x*(2+3^(1/2))^(1/2))+1//4*(6+-3*3^(1/2))^-1//2*arctan((2+-1*3^(1/2))^-1//2*((2+3^(1/2))^(1/2)+2x))+1//4*(6+3*3^(1/2))^-1//2*arctan((2+3^(1/2))^-1//2*((2+-1*3^(1/2))^(1/2)+-2x))+1//8*(6+-3*3^(1/2))^-1//2*log(1+x^2+x*(2+-1*3^(1/2))^(1/2))+1//8*(6+3*3^(1/2))^-1//2*log(1+x^2+-1*x*(2+3^(1/2))^(1/2)))
@test integrate(x^2*(1+x^8+-1*x^4)^-1, x) == :(-1//4*(2//3+-1//3*3^(1/2))^(1/2)*arctan((2+3^(1/2))^-1//2*((2+-1*3^(1/2))^(1/2)+2x))+-1//4*(2//3+1//3*3^(1/2))^(1/2)*arctan((2+-1*3^(1/2))^-1//2*((2+3^(1/2))^(1/2)+-2x))+-1//8*(6+-3*3^(1/2))^-1//2*log(1+x^2+x*(2+-1*3^(1/2))^(1/2))+-1//8*(6+3*3^(1/2))^-1//2*log(1+x^2+-1*x*(2+3^(1/2))^(1/2))+1//4*(2//3+-1//3*3^(1/2))^(1/2)*arctan((2+3^(1/2))^-1//2*((2+-1*3^(1/2))^(1/2)+-2x))+1//4*(2//3+1//3*3^(1/2))^(1/2)*arctan((2+-1*3^(1/2))^-1//2*((2+3^(1/2))^(1/2)+2x))+1//8*(6+-3*3^(1/2))^-1//2*log(1+x^2+-1*x*(2+-1*3^(1/2))^(1/2))+1//8*(6+3*3^(1/2))^-1//2*log(1+x^2+x*(2+3^(1/2))^(1/2)))
@test integrate((1+x^8+-1*x^4)^-1, x) == :(-1//12*6^(1/2)*arctan((2+3^(1/2))^-1//2*((2+-1*3^(1/2))^(1/2)+-2x))+-1//12*6^(1/2)*arctan((2+-1*3^(1/2))^-1//2*((2+3^(1/2))^(1/2)+-2x))+-1//24*6^(1/2)*log(1+x^2+-1*x*(2+3^(1/2))^(1/2))+-1//24*6^(1/2)*log(1+x^2+-1*x*(2+-1*3^(1/2))^(1/2))+1//12*6^(1/2)*arctan((2+3^(1/2))^-1//2*((2+-1*3^(1/2))^(1/2)+2x))+1//12*6^(1/2)*arctan((2+-1*3^(1/2))^-1//2*((2+3^(1/2))^(1/2)+2x))+1//24*6^(1/2)*log(1+x^2+x*(2+3^(1/2))^(1/2))+1//24*6^(1/2)*log(1+x^2+x*(2+-1*3^(1/2))^(1/2)))
@test integrate(x^-2*(1+x^8+-1*x^4)^-1, x) == :(-1*x^-1+-1//4*(6+-3*3^(1/2))^-1//2*arctan((2+3^(1/2))^-1//2*((2+-1*3^(1/2))^(1/2)+2x))+-1//4*(6+3*3^(1/2))^-1//2*arctan((2+-1*3^(1/2))^-1//2*((2+3^(1/2))^(1/2)+-2x))+-1//8*(2//3+-1//3*3^(1/2))^(1/2)*log(1+x^2+x*(2+-1*3^(1/2))^(1/2))+-1//8*(2//3+1//3*3^(1/2))^(1/2)*log(1+x^2+-1*x*(2+3^(1/2))^(1/2))+1//4*(6+-3*3^(1/2))^-1//2*arctan((2+3^(1/2))^-1//2*((2+-1*3^(1/2))^(1/2)+-2x))+1//4*(6+3*3^(1/2))^-1//2*arctan((2+-1*3^(1/2))^-1//2*((2+3^(1/2))^(1/2)+2x))+1//8*(2//3+-1//3*3^(1/2))^(1/2)*log(1+x^2+-1*x*(2+-1*3^(1/2))^(1/2))+1//8*(2//3+1//3*3^(1/2))^(1/2)*log(1+x^2+x*(2+3^(1/2))^(1/2)))
@test integrate(x^-4*(1+x^8+-1*x^4)^-1, x) == :(-1//3*x^-3+-1//4*(2//3+-1//3*3^(1/2))^(1/2)*arctan((2+-1*3^(1/2))^-1//2*((2+3^(1/2))^(1/2)+2x))+-1//4*(2//3+1//3*3^(1/2))^(1/2)*arctan((2+3^(1/2))^-1//2*((2+-1*3^(1/2))^(1/2)+-2x))+-1//8*(2//3+-1//3*3^(1/2))^(1/2)*log(1+x^2+x*(2+-1*3^(1/2))^(1/2))+-1//8*(2//3+1//3*3^(1/2))^(1/2)*log(1+x^2+-1*x*(2+3^(1/2))^(1/2))+1//4*(2//3+-1//3*3^(1/2))^(1/2)*arctan((2+-1*3^(1/2))^-1//2*((2+3^(1/2))^(1/2)+-2x))+1//4*(2//3+1//3*3^(1/2))^(1/2)*arctan((2+3^(1/2))^-1//2*((2+-1*3^(1/2))^(1/2)+2x))+1//8*(2//3+-1//3*3^(1/2))^(1/2)*log(1+x^2+-1*x*(2+-1*3^(1/2))^(1/2))+1//8*(2//3+1//3*3^(1/2))^(1/2)*log(1+x^2+x*(2+3^(1/2))^(1/2)))
@test integrate(x^-6*(1+x^8+-1*x^4)^-1, x) == :(-1*x^-1+-1//5*x^-5+-1//12*6^(1/2)*arctan((2+3^(1/2))^-1//2*((2+-1*3^(1/2))^(1/2)+2x))+-1//12*6^(1/2)*arctan((2+-1*3^(1/2))^-1//2*((2+3^(1/2))^(1/2)+2x))+-1//24*6^(1/2)*log(1+x^2+-1*x*(2+3^(1/2))^(1/2))+-1//24*6^(1/2)*log(1+x^2+-1*x*(2+-1*3^(1/2))^(1/2))+1//12*6^(1/2)*arctan((2+3^(1/2))^-1//2*((2+-1*3^(1/2))^(1/2)+-2x))+1//12*6^(1/2)*arctan((2+-1*3^(1/2))^-1//2*((2+3^(1/2))^(1/2)+-2x))+1//24*6^(1/2)*log(1+x^2+x*(2+3^(1/2))^(1/2))+1//24*6^(1/2)*log(1+x^2+x*(2+-1*3^(1/2))^(1/2)))
@test integrate(x^-8*(1+x^8+-1*x^4)^-1, x) == :(-1//3*x^-3+-1//7*x^-7+-1//4*(2//3+-1//3*3^(1/2))^(1/2)*arctan((2+3^(1/2))^-1//2*((2+-1*3^(1/2))^(1/2)+-2x))+-1//4*(2//3+1//3*3^(1/2))^(1/2)*arctan((2+-1*3^(1/2))^-1//2*((2+3^(1/2))^(1/2)+2x))+-1//8*(2//3+-1//3*3^(1/2))^(1/2)*log(1+x^2+-1*x*(2+3^(1/2))^(1/2))+-1//8*(2//3+1//3*3^(1/2))^(1/2)*log(1+x^2+x*(2+-1*3^(1/2))^(1/2))+1//4*(2//3+-1//3*3^(1/2))^(1/2)*arctan((2+3^(1/2))^-1//2*((2+-1*3^(1/2))^(1/2)+2x))+1//4*(2//3+1//3*3^(1/2))^(1/2)*arctan((2+-1*3^(1/2))^-1//2*((2+3^(1/2))^(1/2)+-2x))+1//8*(2//3+-1//3*3^(1/2))^(1/2)*log(1+x^2+x*(2+3^(1/2))^(1/2))+1//8*(2//3+1//3*3^(1/2))^(1/2)*log(1+x^2+-1*x*(2+-1*3^(1/2))^(1/2)))
@test integrate(x^11*(1+x^8+3*x^4)^-1, x) == :(1//4*x^4+-1*(3//8+-7//40*5^(1/2))*log(3+-1*5^(1/2)+2*x^4)+-1*(3//8+7//40*5^(1/2))*log(3+5^(1/2)+2*x^4))
@test integrate(x^9*(1+x^8+3*x^4)^-1, x) == :((1/2)*x^2+(1/2)*(9//5+-4//5*5^(1/2))^(1/2)*arctan(x^2*(3//2+(1/2)*5^(1/2))^(1/2))+-1//2*(9//5+4//5*5^(1/2))^(1/2)*arctan(2^(1/2)*x^2*(3+5^(1/2))^-1//2))
@test integrate(x^7*(1+x^8+3*x^4)^-1, x) == :((1//8+-3//40*5^(1/2))*log(3+-1*5^(1/2)+2*x^4)+(1//8+3//40*5^(1/2))*log(3+5^(1/2)+2*x^4))
@test integrate(x^5*(1+x^8+3*x^4)^-1, x) == :((1/2)*(3//10+1//10*5^(1/2))^(1/2)*arctan(2^(1/2)*x^2*(3+5^(1/2))^-1//2)+-1//2*(3//10+-1//10*5^(1/2))^(1/2)*arctan(x^2*(3//2+(1/2)*5^(1/2))^(1/2)))
@test integrate(x^3*(1+x^8+3*x^4)^-1, x) == :(-1//10*5^(1/2)*arctanh(1//5*5^(1/2)*(3+2*x^4)))
@test integrate(x*(1+x^8+3*x^4)^-1, x) == :((1/2)*(3//10+1//10*5^(1/2))^(1/2)*arctan(x^2*(3//2+(1/2)*5^(1/2))^(1/2))+-1*(30+10*5^(1/2))^-1//2*arctan(2^(1/2)*x^2*(3+5^(1/2))^-1//2))
@test integrate(x^-1*(1+x^8+3*x^4)^-1, x) == :(-1*(1//8+-3//40*5^(1/2))*log(3+5^(1/2)+2*x^4)+-1*(1//8+3//40*5^(1/2))*log(3+-1*5^(1/2)+2*x^4)+log(x))
@test integrate(x^-3*(1+x^8+3*x^4)^-1, x) == :(-1//2*x^-2+(1/2)*(9//5+-4//5*5^(1/2))^(1/2)*arctan(2^(1/2)*x^2*(3+5^(1/2))^-1//2)+-1//40*10^(1/2)*(3+5^(1/2))^3//2*arctan(x^2*(3//2+(1/2)*5^(1/2))^(1/2)))
@test integrate(x^-5*(1+x^8+3*x^4)^-1, x) == :(-3*log(x)+-1//4*x^-4+(3//8+-7//40*5^(1/2))*log(3+5^(1/2)+2*x^4)+(3//8+7//40*5^(1/2))*log(3+-1*5^(1/2)+2*x^4))
@test integrate(x^-7*(1+x^8+3*x^4)^-1, x) == :(-1//6*x^-6+3//2*x^-2+(1/2)*(123//10+11//2*5^(1/2))^(1/2)*arctan(x^2*(3//2+(1/2)*5^(1/2))^(1/2))+-1//2*(123//10+-11//2*5^(1/2))^(1/2)*arctan(2^(1/2)*x^2*(3+5^(1/2))^-1//2))
@test integrate(x^8*(1+x^8+3*x^4)^-1, x) == :(x+-1//20*2^1//4*5^(1/2)*(123+-55*5^(1/2))^1//4*arctan(1+-1*x*2^3//4*(3+-1*5^(1/2))^-1//4)+-1//20*2^1//4*5^(1/2)*(123+55*5^(1/2))^1//4*arctan(1+x*2^3//4*(3+5^(1/2))^-1//4)+-1//40*2^1//4*5^(1/2)*(123+-55*5^(1/2))^1//4*log((6+-2*5^(1/2))^(1/2)+2*x^2+-2*x*(6+-2*5^(1/2))^1//4)+-1//40*2^1//4*5^(1/2)*(123+55*5^(1/2))^1//4*log((6+2*5^(1/2))^(1/2)+2*x^2+2*x*(6+2*5^(1/2))^1//4)+1//20*2^1//4*5^(1/2)*(123+-55*5^(1/2))^1//4*arctan(1+x*2^3//4*(3+-1*5^(1/2))^-1//4)+1//20*2^1//4*5^(1/2)*(123+55*5^(1/2))^1//4*arctan(1+-1*x*2^3//4*(3+5^(1/2))^-1//4)+1//40*2^1//4*5^(1/2)*(123+-55*5^(1/2))^1//4*log((6+-2*5^(1/2))^(1/2)+2*x^2+2*x*(6+-2*5^(1/2))^1//4)+1//40*2^1//4*5^(1/2)*(123+55*5^(1/2))^1//4*log((6+2*5^(1/2))^(1/2)+2*x^2+-2*x*(6+2*5^(1/2))^1//4))
@test integrate(x^4*(1+x^8+3*x^4)^-1, x) == :(-1//20*2^1//4*5^(1/2)*(3+5^(1/2))^1//4*arctan(1+-1*x*2^3//4*(3+5^(1/2))^-1//4)+-1//20*2^1//4*5^(1/2)*(3+-1*5^(1/2))^1//4*arctan(1+x*2^3//4*(3+-1*5^(1/2))^-1//4)+-1//40*2^1//4*5^(1/2)*(3+5^(1/2))^1//4*log((6+2*5^(1/2))^(1/2)+2*x^2+-2*x*(6+2*5^(1/2))^1//4)+-1//40*2^1//4*5^(1/2)*(3+-1*5^(1/2))^1//4*log((6+-2*5^(1/2))^(1/2)+2*x^2+2*x*(6+-2*5^(1/2))^1//4)+1//20*2^1//4*5^(1/2)*(3+5^(1/2))^1//4*arctan(1+x*2^3//4*(3+5^(1/2))^-1//4)+1//20*2^1//4*5^(1/2)*(3+-1*5^(1/2))^1//4*arctan(1+-1*x*2^3//4*(3+-1*5^(1/2))^-1//4)+1//40*2^1//4*5^(1/2)*(3+5^(1/2))^1//4*log((6+2*5^(1/2))^(1/2)+2*x^2+2*x*(6+2*5^(1/2))^1//4)+1//40*2^1//4*5^(1/2)*(3+-1*5^(1/2))^1//4*log((6+-2*5^(1/2))^(1/2)+2*x^2+-2*x*(6+-2*5^(1/2))^1//4))
@test integrate(x^2*(1+x^8+3*x^4)^-1, x) == :(-1//10*5^(1/2)*(6+-2*5^(1/2))^-1//4*arctan(1+-1*x*2^3//4*(3+-1*5^(1/2))^-1//4)+-1//10*5^(1/2)*(6+2*5^(1/2))^-1//4*arctan(1+x*2^3//4*(3+5^(1/2))^-1//4)+-1//20*5^(1/2)*(6+-2*5^(1/2))^-1//4*log((6+-2*5^(1/2))^(1/2)+2*x^2+2*x*(6+-2*5^(1/2))^1//4)+-1//20*5^(1/2)*(6+2*5^(1/2))^-1//4*log((6+2*5^(1/2))^(1/2)+2*x^2+-2*x*(6+2*5^(1/2))^1//4)+1//10*5^(1/2)*(6+-2*5^(1/2))^-1//4*arctan(1+x*2^3//4*(3+-1*5^(1/2))^-1//4)+1//10*5^(1/2)*(6+2*5^(1/2))^-1//4*arctan(1+-1*x*2^3//4*(3+5^(1/2))^-1//4)+1//20*5^(1/2)*(6+-2*5^(1/2))^-1//4*log((6+-2*5^(1/2))^(1/2)+2*x^2+-2*x*(6+-2*5^(1/2))^1//4)+1//20*5^(1/2)*(6+2*5^(1/2))^-1//4*log((6+2*5^(1/2))^(1/2)+2*x^2+2*x*(6+2*5^(1/2))^1//4))
@test integrate(x^-4*(1+x^8+3*x^4)^-1, x) == :(-1//3*x^-3+-1//20*2^1//4*5^(1/2)*(843+-377*5^(1/2))^1//4*arctan(1+-1*x*2^3//4*(3+5^(1/2))^-1//4)+-1//20*2^1//4*5^(1/2)*(843+377*5^(1/2))^1//4*arctan(1+x*2^3//4*(3+-1*5^(1/2))^-1//4)+-1//40*2^1//4*5^(1/2)*(843+-377*5^(1/2))^1//4*log((6+2*5^(1/2))^(1/2)+2*x^2+-2*x*(6+2*5^(1/2))^1//4)+-1//40*2^1//4*5^(1/2)*(843+377*5^(1/2))^1//4*log((6+-2*5^(1/2))^(1/2)+2*x^2+2*x*(6+-2*5^(1/2))^1//4)+1//20*2^1//4*5^(1/2)*(843+-377*5^(1/2))^1//4*arctan(1+x*2^3//4*(3+5^(1/2))^-1//4)+1//20*2^1//4*5^(1/2)*(843+377*5^(1/2))^1//4*arctan(1+-1*x*2^3//4*(3+-1*5^(1/2))^-1//4)+1//40*2^1//4*5^(1/2)*(843+-377*5^(1/2))^1//4*log((6+2*5^(1/2))^(1/2)+2*x^2+2*x*(6+2*5^(1/2))^1//4)+1//40*2^1//4*5^(1/2)*(843+377*5^(1/2))^1//4*log((6+-2*5^(1/2))^(1/2)+2*x^2+-2*x*(6+-2*5^(1/2))^1//4))
@test integrate(x^11*(1+x^8+-3*x^4)^-1, x) == :(1//4*x^4+(3//8+-7//40*5^(1/2))*log(3+-1*5^(1/2)+-2*x^4)+(3//8+7//40*5^(1/2))*log(3+5^(1/2)+-2*x^4))
@test integrate(x^9*(1+x^8+-3*x^4)^-1, x) == :((1/2)*x^2+(1/2)*(9//5+-4//5*5^(1/2))^(1/2)*arctanh(x^2*(3//2+(1/2)*5^(1/2))^(1/2))+-1//2*(9//5+4//5*5^(1/2))^(1/2)*arctanh(2^(1/2)*x^2*(3+5^(1/2))^-1//2))
@test integrate(x^7*(1+x^8+-3*x^4)^-1, x) == :((1//8+-3//40*5^(1/2))*log(3+-1*5^(1/2)+-2*x^4)+(1//8+3//40*5^(1/2))*log(3+5^(1/2)+-2*x^4))
@test integrate(x^5*(1+x^8+-3*x^4)^-1, x) == :((1/2)*(3//10+-1//10*5^(1/2))^(1/2)*arctanh(x^2*(3//2+(1/2)*5^(1/2))^(1/2))+-1//2*(3//10+1//10*5^(1/2))^(1/2)*arctanh(2^(1/2)*x^2*(3+5^(1/2))^-1//2))
@test integrate(x^3*(1+x^8+-3*x^4)^-1, x) == :(1//10*5^(1/2)*arctanh(1//5*5^(1/2)*(3+-2*x^4)))
@test integrate(x*(1+x^8+-3*x^4)^-1, x) == :((1/2)*(3//10+1//10*5^(1/2))^(1/2)*arctanh(x^2*(3//2+(1/2)*5^(1/2))^(1/2))+-1*(30+10*5^(1/2))^-1//2*arctanh(2^(1/2)*x^2*(3+5^(1/2))^-1//2))
@test integrate(x^-1*(1+x^8+-3*x^4)^-1, x) == :(-1*(1//8+-3//40*5^(1/2))*log(3+5^(1/2)+-2*x^4)+-1*(1//8+3//40*5^(1/2))*log(3+-1*5^(1/2)+-2*x^4)+log(x))
@test integrate(x^-3*(1+x^8+-3*x^4)^-1, x) == :(-1//2*x^-2+-1//2*(9//5+-4//5*5^(1/2))^(1/2)*arctanh(2^(1/2)*x^2*(3+5^(1/2))^-1//2)+1//40*10^(1/2)*(3+5^(1/2))^3//2*arctanh(x^2*(3//2+(1/2)*5^(1/2))^(1/2)))
@test integrate(x^-5*(1+x^8+-3*x^4)^-1, x) == :(3*log(x)+-1//4*x^-4+-1*(3//8+-7//40*5^(1/2))*log(3+5^(1/2)+-2*x^4)+-1*(3//8+7//40*5^(1/2))*log(3+-1*5^(1/2)+-2*x^4))
@test integrate(x^-7*(1+x^8+-3*x^4)^-1, x) == :(-3//2*x^-2+-1//6*x^-6+(1/2)*(123//10+11//2*5^(1/2))^(1/2)*arctanh(x^2*(3//2+(1/2)*5^(1/2))^(1/2))+-1//2*(123//10+-11//2*5^(1/2))^(1/2)*arctanh(2^(1/2)*x^2*(3+5^(1/2))^-1//2))
@test integrate(x^8*(1+x^8+-3*x^4)^-1, x) == :(x+-1//10*5^(1/2)*(123//2+55//2*5^(1/2))^1//4*arctan(x*2^1//4*(3+5^(1/2))^-1//4)+-1//10*5^(1/2)*(123//2+55//2*5^(1/2))^1//4*arctanh(x*2^1//4*(3+5^(1/2))^-1//4)+1//20*5^(1/2)*(984+-440*5^(1/2))^1//4*arctan(x*(3//2+(1/2)*5^(1/2))^1//4)+1//20*5^(1/2)*(984+-440*5^(1/2))^1//4*arctanh(x*(3//2+(1/2)*5^(1/2))^1//4))
@test integrate(x^6*(1+x^8+-3*x^4)^-1, x) == :(-1//20*5^(1/2)*(144+-64*5^(1/2))^1//4*arctan(x*(3//2+(1/2)*5^(1/2))^1//4)+1//20*5^(1/2)*(144+-64*5^(1/2))^1//4*arctanh(x*(3//2+(1/2)*5^(1/2))^1//4)+-1//20*2^1//4*5^(1/2)*(3+5^(1/2))^3//4*arctanh(x*2^1//4*(3+5^(1/2))^-1//4)+1//20*2^1//4*5^(1/2)*(3+5^(1/2))^3//4*arctan(x*2^1//4*(3+5^(1/2))^-1//4))
@test integrate(x^4*(1+x^8+-3*x^4)^-1, x) == :(-1//10*5^(1/2)*(3//2+(1/2)*5^(1/2))^1//4*arctan(x*2^1//4*(3+5^(1/2))^-1//4)+-1//10*5^(1/2)*(3//2+(1/2)*5^(1/2))^1//4*arctanh(x*2^1//4*(3+5^(1/2))^-1//4)+1//10*5^(1/2)*(3//2+-1//2*5^(1/2))^1//4*arctan(x*(3//2+(1/2)*5^(1/2))^1//4)+1//10*5^(1/2)*(3//2+-1//2*5^(1/2))^1//4*arctanh(x*(3//2+(1/2)*5^(1/2))^1//4))
@test integrate(x^-2*(1+x^8+-3*x^4)^-1, x) == :(-1*x^-1+-1//20*5^(1/2)*(984+-440*5^(1/2))^1//4*arctanh(x*2^1//4*(3+5^(1/2))^-1//4)+1//20*5^(1/2)*(984+-440*5^(1/2))^1//4*arctan(x*2^1//4*(3+5^(1/2))^-1//4)+-1//40*2^3//4*5^(1/2)*(3+5^(1/2))^5//4*arctan(x*(3//2+(1/2)*5^(1/2))^1//4)+1//40*2^3//4*5^(1/2)*(3+5^(1/2))^5//4*arctanh(x*(3//2+(1/2)*5^(1/2))^1//4))
@test integrate(x^-6*(1+x^8+-3*x^4)^-1, x) == :(-3*x^-1+-1//5*x^-5+-1//10*5^(1/2)*(2889+-1292*5^(1/2))^1//4*arctanh(x*2^1//4*(3+5^(1/2))^-1//4)+-1//10*5^(1/2)*(2889+1292*5^(1/2))^1//4*arctan(x*(3//2+(1/2)*5^(1/2))^1//4)+1//10*5^(1/2)*(2889+-1292*5^(1/2))^1//4*arctan(x*2^1//4*(3+5^(1/2))^-1//4)+1//10*5^(1/2)*(2889+1292*5^(1/2))^1//4*arctanh(x*(3//2+(1/2)*5^(1/2))^1//4))
@test integrate(x^-8*(1+x^8+-3*x^4)^-1, x) == :(-1*x^-3+-1//7*x^-7+-1//10*5^(1/2)*(39603//2+-17711//2*5^(1/2))^1//4*arctan(x*2^1//4*(3+5^(1/2))^-1//4)+-1//10*5^(1/2)*(39603//2+-17711//2*5^(1/2))^1//4*arctanh(x*2^1//4*(3+5^(1/2))^-1//4)+1//10*5^(1/2)*(39603//2+17711//2*5^(1/2))^1//4*arctan(x*(3//2+(1/2)*5^(1/2))^1//4)+1//10*5^(1/2)*(39603//2+17711//2*5^(1/2))^1//4*arctanh(x*(3//2+(1/2)*5^(1/2))^1//4))
@test integrate(x^3*(2+x^8+3*x^4)^-1, x) == :(-1//4*log(2+x^4)+1//4*log(1+x^4))
@test integrate(x^11*(2+x^8+3*x^4)^-1, x) == :(-1*log(2+x^4)+1//4*x^4+1//4*log(1+x^4))
@test integrate(x^9*(2+x^5+x^10)^-1, x) == :(1//10*log(2+x^5+x^10)+-1//35*7^(1/2)*arctan(1//7*7^(1/2)*(1+2*x^5)))
@test integrate(x^4*(2+x^5+x^10)^-1, x) == :(2//35*7^(1/2)*arctan(1//7*7^(1/2)*(1+2*x^5)))
@test integrate(x^-1*(1+x^5+x^10)^-1, x) == :(-1//10*log(1+x^5+x^10)+-1//15*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*x^5))+log(x))
@test integrate(x^-6*(1+x^5+x^10)^-1, x) == :(-1*log(x)+-1//5*x^-5+1//10*log(1+x^5+x^10)+-1//15*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*x^5)))
@test integrate((x+x^6+x^11)^-1, x) == :(-1//10*log(1+x^5+x^10)+-1//15*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*x^5))+log(x))
@test integrate(x^3*(c+a*x^-2+b*x^-1)^-1, x) == :(1//4*c^-1*x^4+(1/2)*c^-5*(b^4+a^2*c^2+-3*a*c*b^2)*log(a+b*x+c*x^2)+(1/2)*c^-3*x^2*(b^2+-1*a*c)+-1//3*b*c^-2*x^3+-1*b*x*c^-4*(b^2+-2*a*c)+b*c^-5*(b^2+-4*a*c)^-1//2*(b^4+5*a^2*c^2+-5*a*c*b^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x)))
@test integrate(x^2*(c+a*x^-2+b*x^-1)^-1, x) == :(1//3*c^-1*x^3+x*c^-3*(b^2+-1*a*c)+-1//2*b*c^-2*x^2+-1*c^-4*(b^2+-4*a*c)^-1//2*(b^4+2*a^2*c^2+-4*a*c*b^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x))+-1//2*b*c^-4*(b^2+-2*a*c)*log(a+b*x+c*x^2))
@test integrate(x*(c+a*x^-2+b*x^-1)^-1, x) == :((1/2)*c^-1*x^2+(1/2)*c^-3*(b^2+-1*a*c)*log(a+b*x+c*x^2)+-1*b*x*c^-2+b*c^-3*(b^2+-4*a*c)^-1//2*(b^2+-3*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x)))
@test integrate((c+a*x^-2+b*x^-1)^-1, x) == :(x*c^-1+-1//2*b*c^-2*log(a+b*x+c*x^2)+-1*c^-2*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x)))
@test integrate(x^-1*(c+a*x^-2+b*x^-1)^-1, x) == :((1/2)*c^-1*log(a+b*x+c*x^2)+b*c^-1*(b^2+-4*a*c)^-1//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x)))
@test integrate(x^-2*(c+a*x^-2+b*x^-1)^-1, x) == :(2*(b^2+-4*a*c)^-1//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*a*x^-1)))
@test integrate(x^-3*(c+a*x^-2+b*x^-1)^-1, x) == :(a^-1*log(x)+-1//2*a^-1*log(a+b*x+c*x^2)+b*a^-1*(b^2+-4*a*c)^-1//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x)))
@test integrate(x^-4*(c+a*x^-2+b*x^-1)^-1, x) == :(-1*a^-1*x^-1+(1/2)*b*a^-2*log(a+b*x+c*x^2)+-1*b*a^-2*log(x)+-1*a^-2*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x)))
@test integrate(x^-5*(c+a*x^-2+b*x^-1)^-1, x) == :(-1//2*a^-1*x^-2+b*a^-2*x^-1+a^-3*(b^2+-1*a*c)*log(x)+-1//2*a^-3*(b^2+-1*a*c)*log(a+b*x+c*x^2)+b*a^-3*(b^2+-4*a*c)^-1//2*(b^2+-3*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x)))
@test integrate(x^-6*(c+a*x^-2+b*x^-1)^-1, x) == :(-1//3*a^-1*x^-3+(1/2)*b*a^-2*x^-2+-1*a^-3*x^-1*(b^2+-1*a*c)+(1/2)*b*a^-4*(b^2+-2*a*c)*log(a+b*x+c*x^2)+-1*b*a^-4*(b^2+-2*a*c)*log(x)+-1*a^-4*(b^2+-4*a*c)^-1//2*(b^4+2*a^2*c^2+-4*a*c*b^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x)))
@test integrate(x*(c+a*x^-2+b*x^-1)^-2, x) == :((1/2)*c^-4*(3*b^2+-2*a*c)*log(a+b*x+c*x^2)+x^4*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-1*(2a+b*x)+(1/2)*c^-2*x^2*(b^2+-4*a*c)^-1*(3*b^2+-8*a*c)+-1*b*c^-1*x^3*(b^2+-4*a*c)^-1+b*c^-4*(b^2+-4*a*c)^-3//2*(3*b^4+30*a^2*c^2+-20*a*c*b^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x))+-1*b*x*c^-3*(b^2+-4*a*c)^-1*(3*b^2+-11*a*c))
@test integrate((c+a*x^-2+b*x^-1)^-2, x) == :(-1*b*c^-3*log(a+b*x+c*x^2)+x*c^-2*(b^2+-4*a*c)^-1*(2*b^2+-6*a*c)+x^3*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-1*(2a+b*x)+-1*b*c^-1*x^2*(b^2+-4*a*c)^-1+-1*c^-3*(b^2+-4*a*c)^-3//2*(2*b^4+12*a^2*c^2+-12*a*c*b^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x)))
@test integrate(x^-1*(c+a*x^-2+b*x^-1)^-2, x) == :((1/2)*c^-2*log(a+b*x+c*x^2)+x^2*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-1*(2a+b*x)+-1*b*x*c^-1*(b^2+-4*a*c)^-1+b*c^-2*(b^2+-4*a*c)^-3//2*(b^2+-6*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x)))
@test integrate(x^-2*(c+a*x^-2+b*x^-1)^-2, x) == :((b^2+-4*a*c)^-1*(c+a*x^-2+b*x^-1)^-1*(b+2*a*x^-1)+-4*a*(b^2+-4*a*c)^-3//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*a*x^-1)))
@test integrate(x^-3*(c+a*x^-2+b*x^-1)^-2, x) == :((b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-1*(2a+b*x)+-2*b*(b^2+-4*a*c)^-3//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x)))
@test integrate(x^-4*(c+a*x^-2+b*x^-1)^-2, x) == :(-1*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-1*(b+2*c*x)+4*c*(b^2+-4*a*c)^-3//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x)))
@test integrate(x^-5*(c+a*x^-2+b*x^-1)^-2, x) == :(a^-2*log(x)+-1//2*a^-2*log(a+b*x+c*x^2)+a^-1*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-1*(b^2+-2*a*c+b*c*x)+b*a^-2*(b^2+-4*a*c)^-3//2*(b^2+-6*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x)))
@test integrate(x^-6*(c+a*x^-2+b*x^-1)^-2, x) == :(b*a^-3*log(a+b*x+c*x^2)+-2*b*a^-3*log(x)+a^-2*x^-1*(b^2+-4*a*c)^-1*(-2*b^2+6*a*c)+-1*a^-3*(b^2+-4*a*c)^-3//2*(2*b^4+12*a^2*c^2+-12*a*c*b^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x))+a^-1*x^-1*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-1*(b^2+-2*a*c+b*c*x))
@test integrate(x^-7*(c+a*x^-2+b*x^-1)^-2, x) == :(a^-4*(3*b^2+-2*a*c)*log(x)+-1//2*a^-4*(3*b^2+-2*a*c)*log(a+b*x+c*x^2)+-1//2*a^-2*x^-2*(b^2+-4*a*c)^-1*(3*b^2+-8*a*c)+b*a^-4*(b^2+-4*a*c)^-3//2*(3*b^4+30*a^2*c^2+-20*a*c*b^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x))+b*a^-3*x^-1*(b^2+-4*a*c)^-1*(3*b^2+-11*a*c)+a^-1*x^-2*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-1*(b^2+-2*a*c+b*c*x))
@test integrate((c+a*x^-2+b*x^-1)^-3, x) == :(-3//2*b*c^-4*log(a+b*x+c*x^2)+x*c^-3*(b^2+-4*a*c)^-2*(3*b^4+30*a^2*c^2+-21*a*c*b^2)+x^5*(2*b^2+-8*a*c)^-1*(a+b*x+c*x^2)^-2*(2a+b*x)+-1*c^-4*(b^2+-4*a*c)^-5//2*(3*b^6+-60*a^3*c^3+-30*a*c*b^4+90*a^2*b^2*c^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x))+c^-1*x^3*(b^2+-4*a*c)^-2*(a+b*x+c*x^2)^-1*(a*(b^2+-10*a*c)+b*x*(b^2+-7*a*c))+-3//2*b*c^-2*x^2*(b^2+-4*a*c)^-2*(b^2+-6*a*c))
@test integrate(x^-1*(c+a*x^-2+b*x^-1)^-3, x) == :((1/2)*c^-3*log(a+b*x+c*x^2)+x^4*(2*b^2+-8*a*c)^-1*(a+b*x+c*x^2)^-2*(2a+b*x)+b*c^-3*(b^2+-4*a*c)^-5//2*(b^4+30*a^2*c^2+-10*a*c*b^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x))+(1/2)*c^-1*x^2*(b^2+-4*a*c)^-2*(a+b*x+c*x^2)^-1*(a*(b^2+-16*a*c)+b*x*(b^2+-10*a*c))+-1*b*x*c^-2*(b^2+-4*a*c)^-2*(b^2+-7*a*c))
@test integrate(x^-2*(c+a*x^-2+b*x^-1)^-3, x) == :((2*b^2+-8*a*c)^-1*(c+a*x^-2+b*x^-1)^-2*(b+2*a*x^-1)+12*a^2*(b^2+-4*a*c)^-5//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*a*x^-1))+-3*a*(b^2+-4*a*c)^-2*(c+a*x^-2+b*x^-1)^-1*(b+2*a*x^-1))
@test integrate(x^-3*(c+a*x^-2+b*x^-1)^-3, x) == :(-1*x^3*(2*b^2+-8*a*c)^-1*(a+b*x+c*x^2)^-2*(b+2*c*x)+6*a*b*(b^2+-4*a*c)^-5//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x))+3//2*b*x*(b^2+-4*a*c)^-2*(a+b*x+c*x^2)^-1*(2a+b*x))
@test integrate(x^-4*(c+a*x^-2+b*x^-1)^-3, x) == :((b^2+-4*a*c)^-2*(a+b*x+c*x^2)^-1*(x*(b^2+2*a*c)+3*a*b)+-1*(b^2+-4*a*c)^-5//2*(2*b^2+4*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x))+x*(2*b^2+-8*a*c)^-1*(a+b*x+c*x^2)^-2*(2a+b*x))
@test integrate(x^-5*(c+a*x^-2+b*x^-1)^-3, x) == :((2*b^2+-8*a*c)^-1*(a+b*x+c*x^2)^-2*(2a+b*x)+6*b*c*(b^2+-4*a*c)^-5//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x))+-3//2*b*(b^2+-4*a*c)^-2*(a+b*x+c*x^2)^-1*(b+2*c*x))
@test integrate(x^-6*(c+a*x^-2+b*x^-1)^-3, x) == :((2*b^2+-8*a*c)^-1*(a+b*x+c*x^2)^-2*(-1b+-2*c*x)+-12*c^2*(b^2+-4*a*c)^-5//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x))+3*c*(b^2+-4*a*c)^-2*(a+b*x+c*x^2)^-1*(b+2*c*x))
@test integrate(x^-7*(c+a*x^-2+b*x^-1)^-3, x) == :(a^-3*log(x)+-1//2*a^-3*log(a+b*x+c*x^2)+(1/2)*a^-1*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-2*(b^2+-2*a*c+b*c*x)+(1/2)*a^-2*(b^2+-4*a*c)^-2*(a+b*x+c*x^2)^-1*(2*b^4+16*a^2*c^2+-15*a*c*b^2+2*b*c*x*(b^2+-7*a*c))+b*a^-3*(b^2+-4*a*c)^-5//2*(b^4+30*a^2*c^2+-10*a*c*b^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x)))
@test integrate(x^-8*(c+a*x^-2+b*x^-1)^-3, x) == :(-3*b*a^-4*log(x)+3//2*b*a^-4*log(a+b*x+c*x^2)+-1*a^-4*(b^2+-4*a*c)^-5//2*(3*b^6+-60*a^3*c^3+-30*a*c*b^4+90*a^2*b^2*c^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x))+(1/2)*a^-1*x^-1*(b^2+-4*a*c)^-1*(a+b*x+c*x^2)^-2*(b^2+-2*a*c+b*c*x)+(1/2)*a^-2*x^-1*(b^2+-4*a*c)^-2*(a+b*x+c*x^2)^-1*(3*b^4+20*a^2*c^2+-20*a*c*b^2+3*b*c*x*(b^2+-6*a*c))+-1*a^-3*x^-1*(b^2+-4*a*c)^-2*(b^2+-2*a*c)*(3*b^2+-15*a*c))
@test integrate(x^2*(15+2*x^-2+13*x^-1)^-1, x) == :(-16//567*log(2+3x)+-13//450*x^2+1//45*x^3+1//4375*log(1+5x)+139//3375*x)
@test integrate(x*(15+2*x^-2+13*x^-1)^-1, x) == :(-13//225*x+-1//875*log(1+5x)+1//30*x^2+8//189*log(2+3x))
@test integrate((15+2*x^-2+13*x^-1)^-1, x) == :(-4//63*log(2+3x)+1//15*x+1//175*log(1+5x))
@test integrate(x^-1*(15+2*x^-2+13*x^-1)^-1, x) == :(-1//35*log(1+5x)+2//21*log(2+3x))
@test integrate(x^-2*(15+2*x^-2+13*x^-1)^-1, x) == :(-1//7*log(3+2*x^-1)+1//7*log(5+x^-1))
@test integrate(x^-3*(15+2*x^-2+13*x^-1)^-1, x) == :((1/2)*log(x)+-5//7*log(1+5x)+3//14*log(2+3x))
@test integrate(x^-4*(15+2*x^-2+13*x^-1)^-1, x) == :(-13//4*log(x)+-9//28*log(2+3x)+-1//2*x^-1+25//7*log(1+5x))
@test integrate(x^-5*(15+2*x^-2+13*x^-1)^-1, x) == :(-125//7*log(1+5x)+-1//4*x^-2+13//4*x^-1+27//56*log(2+3x)+139//8*log(x))
@test integrate(x^-6*(15+2*x^-2+13*x^-1)^-1, x) == :(-1417//16*log(x)+-139//8*x^-1+-81//112*log(2+3x)+-1//6*x^-3+13//8*x^-2+625//7*log(1+5x))
@test integrate((a+b*x^-1+c*x^-2)^5//2, x) == :(x*(a+b*x^-1+c*x^-2)^5//2+-5//24*(a+b*x^-1+c*x^-2)^3//2*(7b+6*c*x^-1)+-5//64*c^-1*(a+b*x^-1+c*x^-2)^(1/2)*(b*(b^2+44*a*c)+2*c*x^-1*(b^2+12*a*c))+1//128*c^-3//2*(5*b^4+-240*a^2*c^2+-120*a*c*b^2)*arctanh((1/2)*c^-1//2*(a+b*x^-1+c*x^-2)^-1//2*(b+2*c*x^-1))+5//2*b*a^3//2*arctanh((1/2)*a^-1//2*(a+b*x^-1+c*x^-2)^-1//2*(2a+b*x^-1)))
@test integrate((a+b*x^-1+c*x^-2)^3//2, x) == :(x*(a+b*x^-1+c*x^-2)^3//2+-3//4*(a+b*x^-1+c*x^-2)^(1/2)*(3b+2*c*x^-1)+-1//8*c^-1//2*(3*b^2+12*a*c)*arctanh((1/2)*c^-1//2*(a+b*x^-1+c*x^-2)^-1//2*(b+2*c*x^-1))+3//2*b*a^(1/2)*arctanh((1/2)*a^-1//2*(a+b*x^-1+c*x^-2)^-1//2*(2a+b*x^-1)))
@test integrate((a+b*x^-1+c*x^-2)^(1/2), x) == :(x*(a+b*x^-1+c*x^-2)^(1/2)+-1*c^(1/2)*arctanh((1/2)*c^-1//2*(a+b*x^-1+c*x^-2)^-1//2*(b+2*c*x^-1))+(1/2)*b*a^-1//2*arctanh((1/2)*a^-1//2*(a+b*x^-1+c*x^-2)^-1//2*(2a+b*x^-1)))
@test integrate((a+b*x^-1+c*x^-2)^-1//2, x) == :(x*a^-1*(a+b*x^-1+c*x^-2)^(1/2)+-1//2*b*a^-3//2*arctanh((1/2)*a^-1//2*(a+b*x^-1+c*x^-2)^-1//2*(2a+b*x^-1)))
@test integrate((a+b*x^-1+c*x^-2)^-3//2, x) == :(-3//2*b*a^-5//2*arctanh((1/2)*a^-1//2*(a+b*x^-1+c*x^-2)^-1//2*(2a+b*x^-1))+x*a^-2*(b^2+-4*a*c)^-1*(a+b*x^-1+c*x^-2)^(1/2)*(3*b^2+-8*a*c)+-1*x*a^-1*(b^2+-4*a*c)^-1*(a+b*x^-1+c*x^-2)^-1//2*(2*b^2+-4*a*c+2*b*c*x^-1))
@test integrate((a+b*x^-1+c*x^-2)^-5//2, x) == :(-5//2*b*a^-7//2*arctanh((1/2)*a^-1//2*(a+b*x^-1+c*x^-2)^-1//2*(2a+b*x^-1))+-1//3*x*a^-1*(b^2+-4*a*c)^-1*(a+b*x^-1+c*x^-2)^-3//2*(2*b^2+-4*a*c+2*b*c*x^-1)+-1//3*x*a^-2*(b^2+-4*a*c)^-2*(a+b*x^-1+c*x^-2)^-1//2*(10*b^4+64*a^2*c^2+-64*a*c*b^2+2*b*c*x^-1*(5*b^2+-28*a*c))+1//3*x*a^-3*(b^2+-4*a*c)^-2*(a+b*x^-1+c*x^-2)^(1/2)*(15*b^4+128*a^2*c^2+-100*a*c*b^2))
@test integrate((a^2+b^2*x^-2+2*a*b*x^-1)^(1/2), x) == :(a*x*(a+b*x^-1)^-1*(a^2+b^2*x^-2+2*a*b*x^-1)^(1/2)+-1*b*(a+b*x^-1)^-1*(a^2+b^2*x^-2+2*a*b*x^-1)^(1/2)*log(x^-1))
@test integrate((c+a*x^-4+b*x^-2)^-1, x) == :(x*c^-1+-1//2*2^(1/2)*c^-3//2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+-1//2*2^(1/2)*c^-3//2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate((c+a*x^-6+b*x^-3)^-1, x) == :(x*c^-1+-1//6*2^2//3*c^-4//3*(b+(b^2+-4*a*c)^(1/2))^-2//3*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*log((b+(b^2+-4*a*c)^(1/2))^1//3+x*2^1//3*c^1//3)+-1//6*2^2//3*c^-4//3*(b+-1*(b^2+-4*a*c)^(1/2))^-2//3*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*log((b+-1*(b^2+-4*a*c)^(1/2))^1//3+x*2^1//3*c^1//3)+1//12*2^2//3*c^-4//3*(b+(b^2+-4*a*c)^(1/2))^-2//3*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*log((b+(b^2+-4*a*c)^(1/2))^2//3+2^2//3*c^2//3*x^2+-1*x*2^1//3*c^1//3*(b+(b^2+-4*a*c)^(1/2))^1//3)+1//12*2^2//3*c^-4//3*(b+-1*(b^2+-4*a*c)^(1/2))^-2//3*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*log((b+-1*(b^2+-4*a*c)^(1/2))^2//3+2^2//3*c^2//3*x^2+-1*x*2^1//3*c^1//3*(b+-1*(b^2+-4*a*c)^(1/2))^1//3)+1//6*2^2//3*3^(1/2)*c^-4//3*(b+(b^2+-4*a*c)^(1/2))^-2//3*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(1//3*3^(1/2)*(1+-2*x*2^1//3*c^1//3*(b+(b^2+-4*a*c)^(1/2))^-1//3))+1//6*2^2//3*3^(1/2)*c^-4//3*(b+-1*(b^2+-4*a*c)^(1/2))^-2//3*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(1//3*3^(1/2)*(1+-2*x*2^1//3*c^1//3*(b+-1*(b^2+-4*a*c)^(1/2))^-1//3)))
@test integrate((c+a*x^-8+b*x^-4)^-1, x) == :(x*c^-1+1//4*2^3//4*c^-5//4*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(x*2^1//4*c^1//4*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+1//4*2^3//4*c^-5//4*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctanh(x*2^1//4*c^1//4*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+1//4*2^3//4*c^-5//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(x*2^1//4*c^1//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+1//4*2^3//4*c^-5//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctanh(x*2^1//4*c^1//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate(x^-1*(a+b*x^(1/2)+c*x)^(1/2), x) == :(2*(a+b*x^(1/2)+c*x)^(1/2)+-2*a^(1/2)*arctanh((1/2)*a^-1//2*(a+b*x^(1/2)+c*x)^-1//2*(2a+b*x^(1/2)))+b*c^-1//2*arctanh((1/2)*c^-1//2*(a+b*x^(1/2)+c*x)^-1//2*(b+2*c*x^(1/2))))
@test integrate((b*x^(1/2)+c*x+1//4*b^2*c^-1)^2, x) == :(1//192*c^-4*(b+2*c*x^(1/2))^6+-1//160*b*c^-4*(b+2*c*x^(1/2))^5)
@test integrate((a^2+x*b^2+2*a*b*x^(1/2))^-1//2, x) == :(2*b^-2*(a^2+x*b^2+2*a*b*x^(1/2))^(1/2)+-2*a*b^-2*(a^2+x*b^2+2*a*b*x^(1/2))^-1//2*(a+b*x^(1/2))*log(a+b*x^(1/2)))
@test integrate((a^2+b^2*x^2//3+2*a*b*x^1//3)^7//2, x) == :(3//10*b^-3*(a+b*x^1//3)^9*(a^2+b^2*x^2//3+2*a*b*x^1//3)^(1/2)+-2//3*a*b^-3*(a+b*x^1//3)^8*(a^2+b^2*x^2//3+2*a*b*x^1//3)^(1/2)+3//8*a^2*b^-3*(a+b*x^1//3)^7*(a^2+b^2*x^2//3+2*a*b*x^1//3)^(1/2))
@test integrate((a^2+b^2*x^2//3+2*a*b*x^1//3)^5//2, x) == :(3//8*b^-3*(a+b*x^1//3)^7*(a^2+b^2*x^2//3+2*a*b*x^1//3)^(1/2)+(1/2)*a^2*b^-3*(a+b*x^1//3)^5*(a^2+b^2*x^2//3+2*a*b*x^1//3)^(1/2)+-6//7*a*b^-3*(a+b*x^1//3)^6*(a^2+b^2*x^2//3+2*a*b*x^1//3)^(1/2))
@test integrate((a^2+b^2*x^2//3+2*a*b*x^1//3)^3//2, x) == :((1/2)*b^-3*(a+b*x^1//3)^5*(a^2+b^2*x^2//3+2*a*b*x^1//3)^(1/2)+-6//5*a*b^-3*(a+b*x^1//3)^4*(a^2+b^2*x^2//3+2*a*b*x^1//3)^(1/2)+3//4*a^2*b^-3*(a+b*x^1//3)^3*(a^2+b^2*x^2//3+2*a*b*x^1//3)^(1/2))
@test integrate((a^2+b^2*x^2//3+2*a*b*x^1//3)^(1/2), x) == :(a*x*(a+b*x^1//3)^-1*(a^2+b^2*x^2//3+2*a*b*x^1//3)^(1/2)+3*b*x^4//3*(4a+4*b*x^1//3)^-1*(a^2+b^2*x^2//3+2*a*b*x^1//3)^(1/2))
@test integrate((a^2+b^2*x^2//3+2*a*b*x^1//3)^-1//2, x) == :((1/2)*b^-1*x^2//3*(a^2+b^2*x^2//3+2*a*b*x^1//3)^-1//2*(3a+3*b*x^1//3)+-3*a*b^-2*x^1//3*(a^2+b^2*x^2//3+2*a*b*x^1//3)^-1//2*(a+b*x^1//3)+3*a^2*b^-3*(a^2+b^2*x^2//3+2*a*b*x^1//3)^-1//2*(a+b*x^1//3)*log(a+b*x^1//3))
@test integrate((a^2+b^2*x^2//3+2*a*b*x^1//3)^-3//2, x) == :(6*a*b^-3*(a^2+b^2*x^2//3+2*a*b*x^1//3)^-1//2+b^-3*(a^2+b^2*x^2//3+2*a*b*x^1//3)^-1//2*(3a+3*b*x^1//3)*log(a+b*x^1//3)+-3//2*a^2*b^-3*(a+b*x^1//3)^-1*(a^2+b^2*x^2//3+2*a*b*x^1//3)^-1//2)
@test integrate((a^2+b^2*x^2//3+2*a*b*x^1//3)^-5//2, x) == :(-3//2*b^-3*(a+b*x^1//3)^-1*(a^2+b^2*x^2//3+2*a*b*x^1//3)^-1//2+2*a*b^-3*(a+b*x^1//3)^-2*(a^2+b^2*x^2//3+2*a*b*x^1//3)^-1//2+-3//4*a^2*b^-3*(a+b*x^1//3)^-3*(a^2+b^2*x^2//3+2*a*b*x^1//3)^-1//2)
@test integrate((a^2+b^2*x^2//3+2*a*b*x^1//3)^-7//2, x) == :(-3//4*b^-3*(a+b*x^1//3)^-3*(a^2+b^2*x^2//3+2*a*b*x^1//3)^-1//2+-1//2*a^2*b^-3*(a+b*x^1//3)^-5*(a^2+b^2*x^2//3+2*a*b*x^1//3)^-1//2+6//5*a*b^-3*(a+b*x^1//3)^-4*(a^2+b^2*x^2//3+2*a*b*x^1//3)^-1//2)
@test integrate((a^2+b^2*x^2//3+2*a*b*x^1//3)^-9//2, x) == :(-1//2*b^-3*(a+b*x^1//3)^-5*(a^2+b^2*x^2//3+2*a*b*x^1//3)^-1//2+-3//8*a^2*b^-3*(a+b*x^1//3)^-7*(a^2+b^2*x^2//3+2*a*b*x^1//3)^-1//2+6//7*a*b^-3*(a+b*x^1//3)^-6*(a^2+b^2*x^2//3+2*a*b*x^1//3)^-1//2)
@test integrate((a^2+b^2*x^2//3+2*a*b*x^1//3)^-11//2, x) == :(-3//8*b^-3*(a+b*x^1//3)^-7*(a^2+b^2*x^2//3+2*a*b*x^1//3)^-1//2+-3//10*a^2*b^-3*(a+b*x^1//3)^-9*(a^2+b^2*x^2//3+2*a*b*x^1//3)^-1//2+2//3*a*b^-3*(a+b*x^1//3)^-8*(a^2+b^2*x^2//3+2*a*b*x^1//3)^-1//2)
@test integrate(x^2*(a^2+b^2*x^2//3+2*a*b*x^1//3)^p, x) == :(-84*a^9*b^-9*(1+b*a^-1*x^1//3)^4*(2+p)^-1*(a^2+b^2*x^2//3+2*a*b*x^1//3)^p+-84*a^9*b^-9*(1+b*a^-1*x^1//3)^6*(3+p)^-1*(a^2+b^2*x^2//3+2*a*b*x^1//3)^p+-12*a^9*b^-9*(1+p)^-1*(1+b*a^-1*x^1//3)^2*(a^2+b^2*x^2//3+2*a*b*x^1//3)^p+-12*a^9*b^-9*(1+b*a^-1*x^1//3)^8*(4+p)^-1*(a^2+b^2*x^2//3+2*a*b*x^1//3)^p+3*a^9*b^-9*(1+2p)^-1*(a^2+b^2*x^2//3+2*a*b*x^1//3)^p*(1+b*a^-1*x^1//3)+3*a^9*b^-9*(1+b*a^-1*x^1//3)^9*(9+2p)^-1*(a^2+b^2*x^2//3+2*a*b*x^1//3)^p+84*a^9*b^-9*(1+b*a^-1*x^1//3)^3*(3+2p)^-1*(a^2+b^2*x^2//3+2*a*b*x^1//3)^p+84*a^9*b^-9*(1+b*a^-1*x^1//3)^7*(7+2p)^-1*(a^2+b^2*x^2//3+2*a*b*x^1//3)^p+210*a^9*b^-9*(1+b*a^-1*x^1//3)^5*(5+2p)^-1*(a^2+b^2*x^2//3+2*a*b*x^1//3)^p)
@test integrate(x*(a^2+b^2*x^2//3+2*a*b*x^1//3)^p, x) == :(-30*a^6*b^-6*(1+b*a^-1*x^1//3)^3*(3+2p)^-1*(a^2+b^2*x^2//3+2*a*b*x^1//3)^p+-15*a^6*b^-6*(1+b*a^-1*x^1//3)^5*(5+2p)^-1*(a^2+b^2*x^2//3+2*a*b*x^1//3)^p+-3*a^6*b^-6*(1+2p)^-1*(a^2+b^2*x^2//3+2*a*b*x^1//3)^p*(1+b*a^-1*x^1//3)+15*a^6*b^-6*(1+b*a^-1*x^1//3)^4*(2+p)^-1*(a^2+b^2*x^2//3+2*a*b*x^1//3)^p+3//2*a^6*b^-6*(1+b*a^-1*x^1//3)^6*(3+p)^-1*(a^2+b^2*x^2//3+2*a*b*x^1//3)^p+15//2*a^6*b^-6*(1+p)^-1*(1+b*a^-1*x^1//3)^2*(a^2+b^2*x^2//3+2*a*b*x^1//3)^p)
@test integrate((a^2+b^2*x^2//3+2*a*b*x^1//3)^p, x) == :(3*b^-3*(3+2p)^-1*(a+b*x^1//3)^3*(a^2+b^2*x^2//3+2*a*b*x^1//3)^p+-3*a*b^-3*(1+p)^-1*(a+b*x^1//3)^2*(a^2+b^2*x^2//3+2*a*b*x^1//3)^p+3*a^2*b^-3*(1+2p)^-1*(a^2+b^2*x^2//3+2*a*b*x^1//3)^p*(a+b*x^1//3))
@test integrate(x^-2*(a^2+b^2*x^2//3+2*a*b*x^1//3)^p+-2//3*p*a^-3*b^3*x^-1*(a^2+b^2*x^2//3+2*a*b*x^1//3)^p*(1+-1p)*(1+-2p), x) == :(-1*a^-1*x^-1*(a^2+b^2*x^2//3+2*a*b*x^1//3)^p*(a+b*x^1//3)+b*a^-2*x^-2//3*(a^2+b^2*x^2//3+2*a*b*x^1//3)^p*(1+-1p)*(a+b*x^1//3)+-1*a^-3*b^2*x^-1//3*(a^2+b^2*x^2//3+2*a*b*x^1//3)^p*(1+-1p)*(1+-2p)*(a+b*x^1//3))
@test integrate((a^2+b^2*x^(1/2)+2*a*b*x^1//4)^-3//2, x) == :(-12*a^2*b^-4*(a^2+b^2*x^(1/2)+2*a*b*x^1//4)^-1//2+b^-3*x^1//4*(a^2+b^2*x^(1/2)+2*a*b*x^1//4)^-1//2*(4a+4*b*x^1//4)+2*a^3*b^-4*(a+b*x^1//4)^-1*(a^2+b^2*x^(1/2)+2*a*b*x^1//4)^-1//2+-12*a*b^-4*(a^2+b^2*x^(1/2)+2*a*b*x^1//4)^-1//2*(a+b*x^1//4)*log(a+b*x^1//4))
@test integrate((a^2+b^2*x^1//3+2*a*b*x^1//6)^-5//2, x) == :(-60*a^2*b^-6*(a^2+b^2*x^1//3+2*a*b*x^1//6)^-1//2+b^-5*x^1//6*(a^2+b^2*x^1//3+2*a*b*x^1//6)^-1//2*(6a+6*b*x^1//6)+-10*a^4*b^-6*(a+b*x^1//6)^-2*(a^2+b^2*x^1//3+2*a*b*x^1//6)^-1//2+30*a^3*b^-6*(a+b*x^1//6)^-1*(a^2+b^2*x^1//3+2*a*b*x^1//6)^-1//2+3//2*a^5*b^-6*(a+b*x^1//6)^-3*(a^2+b^2*x^1//3+2*a*b*x^1//6)^-1//2+-30*a*b^-6*(a^2+b^2*x^1//3+2*a*b*x^1//6)^-1//2*(a+b*x^1//6)*log(a+b*x^1//6))
@test integrate((a^2+b^2*x^-1+2*a*b*x^-1//2)^3//2, x) == :(x*a^3*(a+b*x^-1//2)^-1*(a^2+b^2*x^-1+2*a*b*x^-1//2)^(1/2)+-2*b^3*x^-1//2*(a+b*x^-1//2)^-1*(a^2+b^2*x^-1+2*a*b*x^-1//2)^(1/2)+6*a*b^2*(a+b*x^-1//2)^-1*(a^2+b^2*x^-1+2*a*b*x^-1//2)^(1/2)*log(x^(1/2))+6*b*a^2*x^(1/2)*(a+b*x^-1//2)^-1*(a^2+b^2*x^-1+2*a*b*x^-1//2)^(1/2))
@test integrate((a^2+b^2*x^-2//3+2*a*b*x^-1//3)^7//2, x) == :(x*a^7*(a+b*x^-1//3)^-1*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^(1/2)+-3*b^7*x^-4//3*(4a+4*b*x^-1//3)^-1*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^(1/2)+-105*a^3*b^4*x^-1//3*(a+b*x^-1//3)^-1*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^(1/2)+-63*a^2*b^5*x^-2//3*(2a+2*b*x^-1//3)^-1*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^(1/2)+-7*a*b^6*x^-1*(a+b*x^-1//3)^-1*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^(1/2)+21*b*a^6*x^2//3*(2a+2*b*x^-1//3)^-1*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^(1/2)+63*a^5*b^2*x^1//3*(a+b*x^-1//3)^-1*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^(1/2)+105*a^4*b^3*(a+b*x^-1//3)^-1*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^(1/2)*log(x^1//3))
@test integrate((a^2+b^2*x^-2//3+2*a*b*x^-1//3)^5//2, x) == :(x*a^5*(a+b*x^-1//3)^-1*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^(1/2)+-3*b^5*x^-2//3*(2a+2*b*x^-1//3)^-1*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^(1/2)+-15*a*b^4*x^-1//3*(a+b*x^-1//3)^-1*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^(1/2)+15*b*a^4*x^2//3*(2a+2*b*x^-1//3)^-1*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^(1/2)+30*a^2*b^3*(a+b*x^-1//3)^-1*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^(1/2)*log(x^1//3)+30*a^3*b^2*x^1//3*(a+b*x^-1//3)^-1*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^(1/2))
@test integrate((a^2+b^2*x^-2//3+2*a*b*x^-1//3)^3//2, x) == :(x*a^3*(a+b*x^-1//3)^-1*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^(1/2)+3*b^3*(a+b*x^-1//3)^-1*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^(1/2)*log(x^1//3)+9*a*b^2*x^1//3*(a+b*x^-1//3)^-1*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^(1/2)+9*b*a^2*x^2//3*(2a+2*b*x^-1//3)^-1*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^(1/2))
@test integrate((a^2+b^2*x^-2//3+2*a*b*x^-1//3)^(1/2), x) == :(a*x*(a+b*x^-1//3)^-1*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^(1/2)+3*b*x^2//3*(2a+2*b*x^-1//3)^-1*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^(1/2))
@test integrate((a^2+b^2*x^-2//3+2*a*b*x^-1//3)^-1//2, x) == :(x*a^-1*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^-1//2*(a+b*x^-1//3)+-3*a^-4*b^3*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^-1//2*(a+b*x^-1//3)*log(b+a*x^1//3)+3*a^-3*b^2*x^1//3*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^-1//2*(a+b*x^-1//3)+-3//2*b*a^-2*x^2//3*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^-1//2*(a+b*x^-1//3))
@test integrate((a^2+b^2*x^-2//3+2*a*b*x^-1//3)^-3//2, x) == :(x*a^-3*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^-1//2*(a+b*x^-1//3)+-30*a^-6*b^3*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^-1//2*(a+b*x^-1//3)*log(b+a*x^1//3)+-15*a^-6*b^4*(b+a*x^1//3)^-1*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^-1//2*(a+b*x^-1//3)+18*a^-5*b^2*x^1//3*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^-1//2*(a+b*x^-1//3)+-9//2*b*a^-4*x^2//3*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^-1//2*(a+b*x^-1//3)+3//2*a^-6*b^5*(b+a*x^1//3)^-2*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^-1//2*(a+b*x^-1//3))
@test integrate((a^2+b^2*x^-2//3+2*a*b*x^-1//3)^-5//2, x) == :(x*a^-5*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^-1//2*(a+b*x^-1//3)+-105*a^-8*b^3*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^-1//2*(a+b*x^-1//3)*log(b+a*x^1//3)+-105*a^-8*b^4*(b+a*x^1//3)^-1*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^-1//2*(a+b*x^-1//3)+-7*a^-8*b^6*(b+a*x^1//3)^-3*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^-1//2*(a+b*x^-1//3)+45*a^-7*b^2*x^1//3*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^-1//2*(a+b*x^-1//3)+-15//2*b*a^-6*x^2//3*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^-1//2*(a+b*x^-1//3)+3//4*a^-8*b^7*(b+a*x^1//3)^-4*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^-1//2*(a+b*x^-1//3)+63//2*a^-8*b^5*(b+a*x^1//3)^-2*(a^2+b^2*x^-2//3+2*a*b*x^-1//3)^-1//2*(a+b*x^-1//3))
@test integrate((a^2+b^2*x^-1//2+2*a*b*x^-1//4)^5//2, x) == :(x*a^5*(a+b*x^-1//4)^-1*(a^2+b^2*x^-1//2+2*a*b*x^-1//4)^(1/2)+-4*b^5*x^-1//4*(a+b*x^-1//4)^-1*(a^2+b^2*x^-1//2+2*a*b*x^-1//4)^(1/2)+20*a*b^4*(a+b*x^-1//4)^-1*(a^2+b^2*x^-1//2+2*a*b*x^-1//4)^(1/2)*log(x^1//4)+20*b*a^4*x^3//4*(3a+3*b*x^-1//4)^-1*(a^2+b^2*x^-1//2+2*a*b*x^-1//4)^(1/2)+20*a^3*b^2*x^(1/2)*(a+b*x^-1//4)^-1*(a^2+b^2*x^-1//2+2*a*b*x^-1//4)^(1/2)+40*a^2*b^3*x^1//4*(a+b*x^-1//4)^-1*(a^2+b^2*x^-1//2+2*a*b*x^-1//4)^(1/2))
@test integrate((a^2+b^2*x^-2//5+2*a*b*x^-1//5)^5//2, x) == :(x*a^5*(a+b*x^-1//5)^-1*(a^2+b^2*x^-2//5+2*a*b*x^-1//5)^(1/2)+5*b^5*(a+b*x^-1//5)^-1*(a^2+b^2*x^-2//5+2*a*b*x^-1//5)^(1/2)*log(x^1//5)+25*a*b^4*x^1//5*(a+b*x^-1//5)^-1*(a^2+b^2*x^-2//5+2*a*b*x^-1//5)^(1/2)+25*b*a^4*x^4//5*(4a+4*b*x^-1//5)^-1*(a^2+b^2*x^-2//5+2*a*b*x^-1//5)^(1/2)+25*a^2*b^3*x^2//5*(a+b*x^-1//5)^-1*(a^2+b^2*x^-2//5+2*a*b*x^-1//5)^(1/2)+50*a^3*b^2*x^3//5*(3a+3*b*x^-1//5)^-1*(a^2+b^2*x^-2//5+2*a*b*x^-1//5)^(1/2))
@test integrate((a^2+b^2*x^2//5+2*a*b*x^1//5)^-5//2, x) == :(20*a*b^-5*(a^2+b^2*x^2//5+2*a*b*x^1//5)^-1//2+b^-5*(a^2+b^2*x^2//5+2*a*b*x^1//5)^-1//2*(5a+5*b*x^1//5)*log(a+b*x^1//5)+-15*a^2*b^-5*(a+b*x^1//5)^-1*(a^2+b^2*x^2//5+2*a*b*x^1//5)^-1//2+-5//4*a^4*b^-5*(a+b*x^1//5)^-3*(a^2+b^2*x^2//5+2*a*b*x^1//5)^-1//2+20//3*a^3*b^-5*(a+b*x^1//5)^-2*(a^2+b^2*x^2//5+2*a*b*x^1//5)^-1//2)
@test integrate((a^2+b^2*x^-1//3+2*a*b*x^-1//6)^7//2, x) == :(x*a^7*(a+b*x^-1//6)^-1*(a^2+b^2*x^-1//3+2*a*b*x^-1//6)^(1/2)+-6*b^7*x^-1//6*(a+b*x^-1//6)^-1*(a^2+b^2*x^-1//3+2*a*b*x^-1//6)^(1/2)+42*a*b^6*(a+b*x^-1//6)^-1*(a^2+b^2*x^-1//3+2*a*b*x^-1//6)^(1/2)*log(x^1//6)+42*b*a^6*x^5//6*(5a+5*b*x^-1//6)^-1*(a^2+b^2*x^-1//3+2*a*b*x^-1//6)^(1/2)+63*a^5*b^2*x^2//3*(2a+2*b*x^-1//6)^-1*(a^2+b^2*x^-1//3+2*a*b*x^-1//6)^(1/2)+70*a^4*b^3*x^(1/2)*(a+b*x^-1//6)^-1*(a^2+b^2*x^-1//3+2*a*b*x^-1//6)^(1/2)+105*a^3*b^4*x^1//3*(a+b*x^-1//6)^-1*(a^2+b^2*x^-1//3+2*a*b*x^-1//6)^(1/2)+126*a^2*b^5*x^1//6*(a+b*x^-1//6)^-1*(a^2+b^2*x^-1//3+2*a*b*x^-1//6)^(1/2))
@test integrate(x^(-1+4n)*(b*x^n+c*x^(2n))^-1, x) == :((1/2)*c^-1*n^-1*x^(2n)+b^2*c^-3*n^-1*log(b+c*x^n)+-1*b*c^-2*n^-1*x^n)
@test integrate(x^(-1+3n)*(b*x^n+c*x^(2n))^-1, x) == :(c^-1*n^-1*x^n+-1*b*c^-2*n^-1*log(b+c*x^n))
@test integrate(x^(-1+2n)*(b*x^n+c*x^(2n))^-1, x) == :(c^-1*n^-1*log(b+c*x^n))
@test integrate(x^(-1+n)*(b*x^n+c*x^(2n))^-1, x) == :(b^-1*log(x)+-1*b^-1*n^-1*log(b+c*x^n))
@test integrate(x^(-1+-1n)*(b*x^n+c*x^(2n))^-1, x) == :(b^-3*c^2*log(x)+-1//2*b^-1*n^-1*x^(-2n)+c*b^-2*n^-1*x^(-1n)+-1*b^-3*c^2*n^-1*log(b+c*x^n))
@test integrate(x^(-1+-2n)*(b*x^n+c*x^(2n))^-1, x) == :(-1*b^-4*c^3*log(x)+-1//3*b^-1*n^-1*x^(-3n)+b^-4*c^3*n^-1*log(b+c*x^n)+(1/2)*c*b^-2*n^-1*x^(-2n)+-1*b^-3*c^2*n^-1*x^(-1n))
@test integrate(x^(-1+-3n)*(b*x^n+c*x^(2n))^-1, x) == :(b^-5*c^4*log(x)+-1//4*b^-1*n^-1*x^(-4n)+b^-4*c^3*n^-1*x^(-1n)+-1*b^-5*c^4*n^-1*log(b+c*x^n)+-1//2*b^-3*c^2*n^-1*x^(-2n)+1//3*c*b^-2*n^-1*x^(-3n))
@test integrate(x^(-1+1//4*n)*(b*x^n+c*x^(2n))^-1, x) == :(-4//3*b^-1*n^-1*x^(-3//4*n)+2^(1/2)*b^-7//4*c^3//4*n^-1*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1//4*n))+(1/2)*2^(1/2)*b^-7//4*c^3//4*n^-1*log(b^(1/2)+c^(1/2)*x^((1/2)*n)+-1*2^(1/2)*b^1//4*c^1//4*x^(1//4*n))+-1*2^(1/2)*b^-7//4*c^3//4*n^-1*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1//4*n))+-1//2*2^(1/2)*b^-7//4*c^3//4*n^-1*log(b^(1/2)+c^(1/2)*x^((1/2)*n)+2^(1/2)*b^1//4*c^1//4*x^(1//4*n)))
@test integrate(x^(-1+1//3*n)*(b*x^n+c*x^(2n))^-1, x) == :(-3//2*b^-1*n^-1*x^(-2//3*n)+(1/2)*b^-5//3*c^2//3*n^-1*log(b^2//3+c^2//3*x^(2//3*n)+-1*b^1//3*c^1//3*x^(1//3*n))+-1*b^-5//3*c^2//3*n^-1*log(b^1//3+c^1//3*x^(1//3*n))+3^(1/2)*b^-5//3*c^2//3*n^-1*arctan(1//3*3^(1/2)*b^-1//3*(b^1//3+-2*c^1//3*x^(1//3*n))))
@test integrate(x^(-1+(1/2)*n)*(b*x^n+c*x^(2n))^-1, x) == :(-2*b^-1*n^-1*x^(-1//2*n)+2*b^-3//2*c^(1/2)*n^-1*arctan(b^(1/2)*c^-1//2*x^(-1//2*n)))
@test integrate(x^(-1+-1//2*n)*(b*x^n+c*x^(2n))^-1, x) == :(-2//3*b^-1*n^-1*x^(-3//2*n)+-2*b^-5//2*c^3//2*n^-1*arctan(b^(1/2)*c^-1//2*x^(-1//2*n))+2*c*b^-2*n^-1*x^(-1//2*n))
@test integrate(x^(-1+-1//4*n)*(b*x^n+c*x^(2n))^-1, x) == :(-4//5*b^-1*n^-1*x^(-5//4*n)+4*c*b^-2*n^-1*x^(-1//4*n)+2^(1/2)*b^-9//4*c^5//4*n^-1*arctan(1+-1*2^(1/2)*b^1//4*c^-1//4*x^(-1//4*n))+(1/2)*2^(1/2)*b^-9//4*c^5//4*n^-1*log(c^(1/2)+b^(1/2)*x^(-1//2*n)+-1*2^(1/2)*b^1//4*c^1//4*x^(-1//4*n))+-1*2^(1/2)*b^-9//4*c^5//4*n^-1*arctan(1+2^(1/2)*b^1//4*c^-1//4*x^(-1//4*n))+-1//2*2^(1/2)*b^-9//4*c^5//4*n^-1*log(c^(1/2)+b^(1/2)*x^(-1//2*n)+2^(1/2)*b^1//4*c^1//4*x^(-1//4*n)))
@test integrate(x^(-1+-1*n*(-1+p))*(b*x^n+c*x^(2n))^p, x) == :(c^-1*n^-1*x^(-1*n*(1+p))*(1+p)^-1*(b*x^n+c*x^(2n))^(1+p))
@test integrate(x^(-1+-1*n*(1+2p))*(b*x^n+c*x^(2n))^p, x) == :(-1*b^-1*n^-1*x^(-2*n*(1+p))*(1+p)^-1*(b*x^n+c*x^(2n))^(1+p))
@test integrate(x^(-1+2n)*(a^2+b^2*x^(2n)+2*a*b*x^n)^5//2, x) == :(1//7*n^-1*(a+b*x^n)^7*(a*b^2+b^3*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2)+-1//6*a*n^-1*(a+b*x^n)^6*(a*b^2+b^3*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2))
@test integrate(x^(-1+2n)*(a^2+b^2*x^(2n)+2*a*b*x^n)^3//2, x) == :(1//5*n^-1*(a+b*x^n)^5*(a*b^2+b^3*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2)+-1//4*a*n^-1*(a+b*x^n)^4*(a*b^2+b^3*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2))
@test integrate(x^(-1+2n)*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2), x) == :((1/2)*a*n^-1*x^(2n)*(a+b*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2)+1//3*b^2*n^-1*x^(3n)*(a*b+b^2*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2))
@test integrate(x^(-1+2n)*(a^2+b^2*x^(2n)+2*a*b*x^n)^-1//2, x) == :(b^-1*n^-1*x^n*(a^2+b^2*x^(2n)+2*a*b*x^n)^-1//2*(a+b*x^n)+-1*a*b^-2*n^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^-1//2*(a+b*x^n)*log(a+b*x^n))
@test integrate(x^(-1+2n)*(a^2+b^2*x^(2n)+2*a*b*x^n)^-3//2, x) == :((1/2)*a^-1*n^-1*x^(2n)*(a+b*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^-1//2)
@test integrate(x^(-1+2n)*(a^2+b^2*x^(2n)+2*a*b*x^n)^-5//2, x) == :(-1//3*b^-2*n^-1*(a+b*x^n)^-2*(a^2+b^2*x^(2n)+2*a*b*x^n)^-1//2+1//4*a*b^-2*n^-1*(a+b*x^n)^-3*(a^2+b^2*x^(2n)+2*a*b*x^n)^-1//2)
@test integrate(x^(-1+2n)*(a^2+b^2*x^(2n)+2*a*b*x^n)^-7//2, x) == :(-1//5*b^-2*n^-1*(a+b*x^n)^-4*(a^2+b^2*x^(2n)+2*a*b*x^n)^-1//2+1//6*a*b^-2*n^-1*(a+b*x^n)^-5*(a^2+b^2*x^(2n)+2*a*b*x^n)^-1//2)
@test integrate((d*x)^m*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2), x) == :(a*d^-1*(d*x)^(1+m)*(1+m)^-1*(a+b*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2)+b^2*x^(1+n)*(d*x)^m*(a*b+b^2*x^n)^-1*(1+m+n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2))
@test integrate(x^2*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2), x) == :(a*x^3*(3a+3*b*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2)+b^2*x^(3+n)*(3+n)^-1*(a*b+b^2*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2))
@test integrate(x*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2), x) == :(a*x^2*(2a+2*b*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2)+b^2*x^(2+n)*(2+n)^-1*(a*b+b^2*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2))
@test integrate((a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2), x) == :(a*x*(a+b*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2)+b^2*x^(1+n)*(1+n)^-1*(a*b+b^2*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2))
@test integrate(x^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2), x) == :(a*(a+b*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2)*log(x)+b^2*n^-1*x^n*(a*b+b^2*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2))
@test integrate(x^-2*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2), x) == :(-1*a*x^-1*(a+b*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2)+-1*b^2*x^(-1+n)*(1+-1n)^-1*(a*b+b^2*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2))
@test integrate(x^-3*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2), x) == :(-1//2*a*x^-2*(a+b*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2)+-1*b^2*x^(-2+n)*(2+-1n)^-1*(a*b+b^2*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2))
@test integrate((d*x)^m*(a^2+b^2*x^(2n)+2*a*b*x^n)^3//2, x) == :(a^3*d^-1*(d*x)^(1+m)*(1+m)^-1*(a+b*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2)+b^4*x^(1+3n)*(d*x)^m*(a*b+b^2*x^n)^-1*(1+m+3n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2)+3*a*b^3*x^(1+2n)*(d*x)^m*(a*b+b^2*x^n)^-1*(1+m+2n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2)+3*a^2*b^2*x^(1+n)*(d*x)^m*(a*b+b^2*x^n)^-1*(1+m+n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2))
@test integrate(x^2*(a^2+b^2*x^(2n)+2*a*b*x^n)^3//2, x) == :(a^3*x^3*(3a+3*b*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2)+b^4*x^(3+3n)*(3+3n)^-1*(a*b+b^2*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2)+3*a*b^3*x^(3+2n)*(3+2n)^-1*(a*b+b^2*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2)+3*a^2*b^2*x^(3+n)*(3+n)^-1*(a*b+b^2*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2))
@test integrate(x*(a^2+b^2*x^(2n)+2*a*b*x^n)^3//2, x) == :(a^3*x^2*(2a+2*b*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2)+b^4*x^(2+3n)*(2+3n)^-1*(a*b+b^2*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2)+3*a*b^3*x^(2+2n)*(2+2n)^-1*(a*b+b^2*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2)+3*a^2*b^2*x^(2+n)*(2+n)^-1*(a*b+b^2*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2))
@test integrate((a^2+b^2*x^(2n)+2*a*b*x^n)^3//2, x) == :(x*a^3*(a+b*x^n)^-3*(a^2+b^2*x^(2n)+2*a*b*x^n)^3//2+b^6*x^(1+3n)*(1+3n)^-1*(a*b+b^2*x^n)^-3*(a^2+b^2*x^(2n)+2*a*b*x^n)^3//2+3*a*b^5*x^(1+2n)*(1+2n)^-1*(a*b+b^2*x^n)^-3*(a^2+b^2*x^(2n)+2*a*b*x^n)^3//2+3*a^2*b^4*x^(1+n)*(1+n)^-1*(a*b+b^2*x^n)^-3*(a^2+b^2*x^(2n)+2*a*b*x^n)^3//2)
@test integrate(x^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^3//2, x) == :(a^3*(a+b*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2)*log(x)+1//3*b^4*n^-1*x^(3n)*(a*b+b^2*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2)+3*a^2*b^2*n^-1*x^n*(a*b+b^2*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2)+3//2*a*b^3*n^-1*x^(2n)*(a*b+b^2*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2))
@test integrate(x^-2*(a^2+b^2*x^(2n)+2*a*b*x^n)^3//2, x) == :(-1*a^3*x^-1*(a+b*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2)+-1*b^4*x^(-1+3n)*(1+-3n)^-1*(a*b+b^2*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2)+-3*a*b^3*x^(-1+2n)*(1+-2n)^-1*(a*b+b^2*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2)+-3*a^2*b^2*x^(-1+n)*(1+-1n)^-1*(a*b+b^2*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2))
@test integrate(x^-3*(a^2+b^2*x^(2n)+2*a*b*x^n)^3//2, x) == :(-1//2*a^3*x^-2*(a+b*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2)+-1*b^4*x^(-2+3n)*(2+-3n)^-1*(a*b+b^2*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2)+-3*a*b^3*x^(-2+2n)*(2+-2n)^-1*(a*b+b^2*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2)+-3*a^2*b^2*x^(-2+n)*(2+-1n)^-1*(a*b+b^2*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(1/2))
@test integrate(x^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^-1//2, x) == :(a^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^-1//2*(a+b*x^n)*log(x)+-1*a^-1*n^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^-1//2*(a+b*x^n)*log(a+b*x^n))
@test integrate(x^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^-3//2, x) == :(a^-2*n^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^-1//2+a^-3*(a^2+b^2*x^(2n)+2*a*b*x^n)^-1//2*(a+b*x^n)*log(x)+(1/2)*a^-1*n^-1*(a+b*x^n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^-1//2+-1*a^-3*n^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^-1//2*(a+b*x^n)*log(a+b*x^n))
@test integrate((a^2+b^2*x^(-2*(1+2p)^-1)+2*a*b*x^(-1*(1+2p)^-1))^p, x) == :(x*a^-1*(a^2+b^2*x^(-2*(1+2p)^-1)+2*a*b*x^((-1+-2p)^-1))^p*(a+b*x^((-1+-2p)^-1)))
@test integrate((a^2+b^2*x^(2n)+2*a*b*x^n)^((1/2)*n^-1*(-1+-1n)), x) == :(x*a^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(-1//2*n^-1*(1+n))*(a+b*x^n))
@test integrate((a^2+b^2*x^(-1*(1+p)^-1)+2*a*b*x^(-1*(2+2p)^-1))^p, x) == :(-1*x*a^-2*(1+2p)^-1*(a+b*x^(-1*(2+2p)^-1))^2*(a^2+b^2*x^(-1*(1+p)^-1)+2*a*b*x^(-1*(2+2p)^-1))^p+x*a^-1*(1+2p)^-1*(a^2+b^2*x^(-1*(1+p)^-1)+2*a*b*x^(-1*(2+2p)^-1))^p*(2+2p)*(a+b*x^(-1*(2+2p)^-1)))
@test integrate((a^2+b^2*x^(2n)+2*a*b*x^n)^((1/2)*n^-1*(-1+-2n)), x) == :(x*a^-1*(1+n)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^(-1+-1//2*n^-1)*(a+b*x^n)+n*x*a^-2*(1+n)^-1*(a+b*x^n)^2*(a^2+b^2*x^(2n)+2*a*b*x^n)^(-1+-1//2*n^-1))
@test integrate(x^(-1+2n)*(a^2+b^2*x^(2n)+2*a*b*x^n)^p, x) == :((1/2)*a^2*b^-2*n^-1*(1+p)^-1*(1+b*a^-1*x^n)^2*(a^2+b^2*x^(2n)+2*a*b*x^n)^p+-1*a^2*b^-2*n^-1*(1+2p)^-1*(a^2+b^2*x^(2n)+2*a*b*x^n)^p*(1+b*a^-1*x^n))
@test integrate(x^(-1+4n)*(a+b*x^n+c*x^(2n))^-1, x) == :((1/2)*c^-1*n^-1*x^(2n)+(1/2)*c^-3*n^-1*(b^2+-1*a*c)*log(a+b*x^n+c*x^(2n))+-1*b*c^-2*n^-1*x^n+b*c^-3*n^-1*(b^2+-4*a*c)^-1//2*(b^2+-3*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^n)))
@test integrate(x^(-1+3n)*(a+b*x^n+c*x^(2n))^-1, x) == :(c^-1*n^-1*x^n+-1//2*b*c^-2*n^-1*log(a+b*x^n+c*x^(2n))+-1*c^-2*n^-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^n)))
@test integrate(x^(-1+2n)*(a+b*x^n+c*x^(2n))^-1, x) == :((1/2)*c^-1*n^-1*log(a+b*x^n+c*x^(2n))+b*c^-1*n^-1*(b^2+-4*a*c)^-1//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^n)))
@test integrate(x^(-1+n)*(a+b*x^n+c*x^(2n))^-1, x) == :(-2*n^-1*(b^2+-4*a*c)^-1//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^n)))
@test integrate(x^(-1+-1n)*(a+b*x^n+c*x^(2n))^-1, x) == :(-1*b*a^-2*log(x)+-1*a^-1*n^-1*x^(-1n)+(1/2)*b*a^-2*n^-1*log(a+b*x^n+c*x^(2n))+-1*a^-2*n^-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^n)))
@test integrate(x^(-1+-2n)*(a+b*x^n+c*x^(2n))^-1, x) == :(a^-3*(b^2+-1*a*c)*log(x)+-1//2*a^-1*n^-1*x^(-2n)+b*a^-2*n^-1*x^(-1n)+-1//2*a^-3*n^-1*(b^2+-1*a*c)*log(a+b*x^n+c*x^(2n))+b*a^-3*n^-1*(b^2+-4*a*c)^-1//2*(b^2+-3*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^n)))
@test integrate(x^(-1+-3n)*(a+b*x^n+c*x^(2n))^-1, x) == :(-1//3*a^-1*n^-1*x^(-3n)+(1/2)*b*a^-2*n^-1*x^(-2n)+-1*b*a^-4*(b^2+-2*a*c)*log(x)+-1*a^-3*n^-1*x^(-1n)*(b^2+-1*a*c)+(1/2)*b*a^-4*n^-1*(b^2+-2*a*c)*log(a+b*x^n+c*x^(2n))+-1*a^-4*n^-1*(b^2+-4*a*c)^-1//2*(b^4+2*a^2*c^2+-4*a*c*b^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^n)))
@test integrate(x^(-1+1//4*n)*(a+b*x^n+c*x^(2n))^-1, x) == :(-2*2^3//4*c^3//4*n^-1*(b^2+-4*a*c)^-1//2*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*arctan(2^1//4*c^1//4*x^(1//4*n)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-2*2^3//4*c^3//4*n^-1*(b^2+-4*a*c)^-1//2*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*arctanh(2^1//4*c^1//4*x^(1//4*n)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+2*2^3//4*c^3//4*n^-1*(b^2+-4*a*c)^-1//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*arctan(2^1//4*c^1//4*x^(1//4*n)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+2*2^3//4*c^3//4*n^-1*(b^2+-4*a*c)^-1//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*arctanh(2^1//4*c^1//4*x^(1//4*n)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate(x^(-1+1//3*n)*(a+b*x^n+c*x^(2n))^-1, x) == :(2^2//3*c^2//3*n^-1*(b+-1*(b^2+-4*a*c)^(1/2))^-2//3*(b^2+-4*a*c)^-1//2*log((b+-1*(b^2+-4*a*c)^(1/2))^1//3+2^1//3*c^1//3*x^(1//3*n))+(1/2)*2^2//3*c^2//3*n^-1*(b+(b^2+-4*a*c)^(1/2))^-2//3*(b^2+-4*a*c)^-1//2*log((b+(b^2+-4*a*c)^(1/2))^2//3+2^2//3*c^2//3*x^(2//3*n)+-1*2^1//3*c^1//3*x^(1//3*n)*(b+(b^2+-4*a*c)^(1/2))^1//3)+-1*2^2//3*c^2//3*n^-1*(b+(b^2+-4*a*c)^(1/2))^-2//3*(b^2+-4*a*c)^-1//2*log((b+(b^2+-4*a*c)^(1/2))^1//3+2^1//3*c^1//3*x^(1//3*n))+-1//2*2^2//3*c^2//3*n^-1*(b+-1*(b^2+-4*a*c)^(1/2))^-2//3*(b^2+-4*a*c)^-1//2*log((b+-1*(b^2+-4*a*c)^(1/2))^2//3+2^2//3*c^2//3*x^(2//3*n)+-1*2^1//3*c^1//3*x^(1//3*n)*(b+-1*(b^2+-4*a*c)^(1/2))^1//3)+2^2//3*3^(1/2)*c^2//3*n^-1*(b+(b^2+-4*a*c)^(1/2))^-2//3*(b^2+-4*a*c)^-1//2*arctan(1//3*3^(1/2)*(1+-2*2^1//3*c^1//3*x^(1//3*n)*(b+(b^2+-4*a*c)^(1/2))^-1//3))+-1*2^2//3*3^(1/2)*c^2//3*n^-1*(b+-1*(b^2+-4*a*c)^(1/2))^-2//3*(b^2+-4*a*c)^-1//2*arctan(1//3*3^(1/2)*(1+-2*2^1//3*c^1//3*x^(1//3*n)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//3)))
@test integrate(x^(-1+(1/2)*n)*(a+b*x^n+c*x^(2n))^-1, x) == :(-2*2^(1/2)*c^(1/2)*n^-1*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1//2*arctan(2^(1/2)*c^(1/2)*x^((1/2)*n)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+2*2^(1/2)*c^(1/2)*n^-1*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1//2*arctan(2^(1/2)*c^(1/2)*x^((1/2)*n)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^(-1+-1//2*n)*(a+b*x^n+c*x^(2n))^-1, x) == :(-2*a^-1*n^-1*x^(-1//2*n)+2^(1/2)*a^-3//2*n^-1*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(2^(1/2)*a^(1/2)*x^(-1//2*n)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+2^(1/2)*a^-3//2*n^-1*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(2^(1/2)*a^(1/2)*x^(-1//2*n)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^(-1+-1//3*n)*(a+b*x^n+c*x^(2n))^-1, x) == :(-3*a^-1*n^-1*x^(-1//3*n)+(1/2)*2^2//3*a^-4//3*n^-1*(b+(b^2+-4*a*c)^(1/2))^-2//3*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*log((b+(b^2+-4*a*c)^(1/2))^1//3+2^1//3*a^1//3*x^(-1//3*n))+(1/2)*2^2//3*a^-4//3*n^-1*(b+-1*(b^2+-4*a*c)^(1/2))^-2//3*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*log((b+-1*(b^2+-4*a*c)^(1/2))^1//3+2^1//3*a^1//3*x^(-1//3*n))+-1//4*2^2//3*a^-4//3*n^-1*(b+(b^2+-4*a*c)^(1/2))^-2//3*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*log((b+(b^2+-4*a*c)^(1/2))^2//3+2^2//3*a^2//3*x^(-2//3*n)+-1*2^1//3*a^1//3*x^(-1//3*n)*(b+(b^2+-4*a*c)^(1/2))^1//3)+-1//4*2^2//3*a^-4//3*n^-1*(b+-1*(b^2+-4*a*c)^(1/2))^-2//3*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*log((b+-1*(b^2+-4*a*c)^(1/2))^2//3+2^2//3*a^2//3*x^(-2//3*n)+-1*2^1//3*a^1//3*x^(-1//3*n)*(b+-1*(b^2+-4*a*c)^(1/2))^1//3)+-1//2*2^2//3*3^(1/2)*a^-4//3*n^-1*(b+(b^2+-4*a*c)^(1/2))^-2//3*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(1//3*3^(1/2)*(1+-2*2^1//3*a^1//3*x^(-1//3*n)*(b+(b^2+-4*a*c)^(1/2))^-1//3))+-1//2*2^2//3*3^(1/2)*a^-4//3*n^-1*(b+-1*(b^2+-4*a*c)^(1/2))^-2//3*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(1//3*3^(1/2)*(1+-2*2^1//3*a^1//3*x^(-1//3*n)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//3)))
@test integrate(x^(-1+-1//4*n)*(a+b*x^n+c*x^(2n))^-1, x) == :(-4*a^-1*n^-1*x^(-1//4*n)+-1*2^3//4*a^-5//4*n^-1*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(2^1//4*a^1//4*x^(-1//4*n)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1*2^3//4*a^-5//4*n^-1*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctanh(2^1//4*a^1//4*x^(-1//4*n)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1*2^3//4*a^-5//4*n^-1*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(2^1//4*a^1//4*x^(-1//4*n)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+-1*2^3//4*a^-5//4*n^-1*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctanh(2^1//4*a^1//4*x^(-1//4*n)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate(x^-1*(a+b*x^n+c*x^(2n))^-1, x) == :(a^-1*log(x)+-1//2*a^-1*n^-1*log(a+b*x^n+c*x^(2n))+b*a^-1*n^-1*(b^2+-4*a*c)^-1//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^n)))
@test integrate(x^-1*(a+b*x^n+c*x^(2n))^(1/2), x) == :(n^-1*(a+b*x^n+c*x^(2n))^(1/2)+-1*a^(1/2)*n^-1*arctanh((1/2)*a^-1//2*(a+b*x^n+c*x^(2n))^-1//2*(2a+b*x^n))+(1/2)*b*c^-1//2*n^-1*arctanh((1/2)*c^-1//2*(a+b*x^n+c*x^(2n))^-1//2*(b+2*c*x^n)))
@test integrate(x^-1*(a+b*x^n+c*x^(2n))^3//2, x) == :(1//3*n^-1*(a+b*x^n+c*x^(2n))^3//2+-1*a^3//2*n^-1*arctanh((1/2)*a^-1//2*(a+b*x^n+c*x^(2n))^-1//2*(2a+b*x^n))+1//8*c^-1*n^-1*(a+b*x^n+c*x^(2n))^(1/2)*(b^2+8*a*c+2*b*c*x^n)+-1//16*b*c^-3//2*n^-1*(b^2+-12*a*c)*arctanh((1/2)*c^-1//2*(a+b*x^n+c*x^(2n))^-1//2*(b+2*c*x^n)))
@test integrate(x^-1*(a+b*x^n+c*x^(2n))^-1//2, x) == :(-1*a^-1//2*n^-1*arctanh((1/2)*a^-1//2*(a+b*x^n+c*x^(2n))^-1//2*(2a+b*x^n)))
@test integrate(x^-1*(a+b*x^n+c*x^(2n))^-3//2, x) == :(-1*a^-3//2*n^-1*arctanh((1/2)*a^-1//2*(a+b*x^n+c*x^(2n))^-1//2*(2a+b*x^n))+a^-1*n^-1*(b^2+-4*a*c)^-1*(a+b*x^n+c*x^(2n))^-1//2*(2*b^2+-4*a*c+2*b*c*x^n))
@test integrate((d*x)^m*(a+b*x^n+c*x^(2n))^3, x) == :(a^3*d^-1*(d*x)^(1+m)*(1+m)^-1+c^3*x^(1+6n)*(d*x)^m*(1+m+6n)^-1+b*x^(1+3n)*(d*x)^m*(1+m+3n)^-1*(b^2+6*a*c)+3*a*x^(1+2n)*(d*x)^m*(1+m+2n)^-1*(b^2+a*c)+3*b*a^2*x^(1+n)*(d*x)^m*(1+m+n)^-1+3*b*c^2*x^(1+5n)*(d*x)^m*(1+m+5n)^-1+3*c*x^(1+4n)*(d*x)^m*(1+m+4n)^-1*(b^2+a*c))
@test integrate((d*x)^m*(a+b*x^n+c*x^(2n))^2, x) == :(a^2*d^-1*(d*x)^(1+m)*(1+m)^-1+c^2*x^(1+4n)*(d*x)^m*(1+m+4n)^-1+x^(1+2n)*(d*x)^m*(1+m+2n)^-1*(b^2+2*a*c)+2*a*b*x^(1+n)*(d*x)^m*(1+m+n)^-1+2*b*c*x^(1+3n)*(d*x)^m*(1+m+3n)^-1)
@test integrate((d*x)^m*(a+b*x^n+c*x^(2n)), x) == :(a*d^-1*(d*x)^(1+m)*(1+m)^-1+b*x^(1+n)*(d*x)^m*(1+m+n)^-1+c*x^(1+2n)*(d*x)^m*(1+m+2n)^-1)
@test integrate((d+e*x)^3*(a+b*(d+e*x)^2+c*(d+e*x)^4), x) == :(1//4*a*e^-1*(d+e*x)^4+1//6*b*e^-1*(d+e*x)^6+1//8*c*e^-1*(d+e*x)^8)
@test integrate((d+e*x)^3*(a+b*(d+e*x)^2+c*(d+e*x)^4)^2, x) == :(1//4*a^2*e^-1*(d+e*x)^4+1//8*e^-1*(d+e*x)^8*(b^2+2*a*c)+1//12*c^2*e^-1*(d+e*x)^12+1//3*a*b*e^-1*(d+e*x)^6+1//5*b*c*e^-1*(d+e*x)^10)
@test integrate((d+e*x)^3*(a+b*(d+e*x)^2+c*(d+e*x)^4)^3, x) == :(1//4*a^3*e^-1*(d+e*x)^4+1//16*c^3*e^-1*(d+e*x)^16+(1/2)*b*a^2*e^-1*(d+e*x)^6+1//4*c*e^-1*(d+e*x)^12*(b^2+a*c)+1//10*b*e^-1*(d+e*x)^10*(b^2+6*a*c)+3//8*a*e^-1*(d+e*x)^8*(b^2+a*c)+3//14*b*c^2*e^-1*(d+e*x)^14)
@test integrate((d*f+e*f*x)^3*(a+b*(d+e*x)^2+c*(d+e*x)^4), x) == :(1//4*a*e^-1*f^3*(d+e*x)^4+1//6*b*e^-1*f^3*(d+e*x)^6+1//8*c*e^-1*f^3*(d+e*x)^8)
@test integrate((d*f+e*f*x)^3*(a+b*(d+e*x)^2+c*(d+e*x)^4)^2, x) == :(1//4*a^2*e^-1*f^3*(d+e*x)^4+1//8*e^-1*f^3*(d+e*x)^8*(b^2+2*a*c)+1//12*c^2*e^-1*f^3*(d+e*x)^12+1//3*a*b*e^-1*f^3*(d+e*x)^6+1//5*b*c*e^-1*f^3*(d+e*x)^10)
@test integrate((d*f+e*f*x)^3*(a+b*(d+e*x)^2+c*(d+e*x)^4)^3, x) == :(1//4*a^3*e^-1*f^3*(d+e*x)^4+1//16*c^3*e^-1*f^3*(d+e*x)^16+(1/2)*b*a^2*e^-1*f^3*(d+e*x)^6+1//4*c*e^-1*f^3*(d+e*x)^12*(b^2+a*c)+1//10*b*e^-1*f^3*(d+e*x)^10*(b^2+6*a*c)+3//8*a*e^-1*f^3*(d+e*x)^8*(b^2+a*c)+3//14*b*c^2*e^-1*f^3*(d+e*x)^14)
@test integrate((d+e*x)^4*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1, x) == :(x*c^-1+-1//2*2^(1/2)*c^-3//2*e^-1*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x))+-1//2*2^(1/2)*c^-3//2*e^-1*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x)))
@test integrate((d+e*x)^3*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1, x) == :(1//4*c^-1*e^-1*log(a+b*(d+e*x)^2+c*(d+e*x)^4)+(1/2)*b*c^-1*e^-1*(b^2+-4*a*c)^-1//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*(d+e*x)^2)))
@test integrate((d+e*x)^2*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1, x) == :((1/2)*2^(1/2)*c^-1//2*e^-1*(b+(b^2+-4*a*c)^(1/2))^(1/2)*(b^2+-4*a*c)^-1//2*arctan(2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x))+-1//2*2^(1/2)*c^-1//2*e^-1*(b+-1*(b^2+-4*a*c)^(1/2))^(1/2)*(b^2+-4*a*c)^-1//2*arctan(2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x)))
@test integrate((a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(d+e*x), x) == :(-1*e^-1*(b^2+-4*a*c)^-1//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*(d+e*x)^2)))
@test integrate((d+e*x)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1, x) == :(a^-1*e^-1*log(d+e*x)+-1//4*a^-1*e^-1*log(a+b*(d+e*x)^2+c*(d+e*x)^4)+(1/2)*b*a^-1*e^-1*(b^2+-4*a*c)^-1//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*(d+e*x)^2)))
@test integrate((d+e*x)^-2*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1, x) == :(-1*a^-1*e^-1*(d+e*x)^-1+-1//2*2^(1/2)*a^-1*c^(1/2)*e^-1*(b+(b^2+-4*a*c)^(1/2))^-1//2*(1+-1*b*(b^2+-4*a*c)^-1//2)*arctan(2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x))+-1//2*2^(1/2)*a^-1*c^(1/2)*e^-1*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(1+b*(b^2+-4*a*c)^-1//2)*arctan(2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x)))
@test integrate((d+e*x)^-3*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1, x) == :(-1//2*a^-1*e^-1*(d+e*x)^-2+-1*b*a^-2*e^-1*log(d+e*x)+1//4*b*a^-2*e^-1*log(a+b*(d+e*x)^2+c*(d+e*x)^4)+-1//2*a^-2*e^-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*(d+e*x)^2)))
@test integrate((d+e*x)^-4*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1, x) == :(-1//3*a^-1*e^-1*(d+e*x)^-3+b*a^-2*e^-1*(d+e*x)^-1+(1/2)*2^(1/2)*a^-2*c^(1/2)*e^-1*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x))+(1/2)*2^(1/2)*a^-2*c^(1/2)*e^-1*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x)))
@test integrate((d+e*x)^4*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-2, x) == :(e^-1*(2*b^2+-8*a*c)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(d+e*x)*(2a+b*(d+e*x)^2)+1//4*2^(1/2)*c^-1//2*e^-1*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-3//2*(b^2+b*(b^2+-4*a*c)^(1/2)+4*a*c)*arctan(2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x))+1//4*2^(1/2)*c^-1//2*e^-1*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+4*a*c))*arctan(2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x)))
@test integrate((d+e*x)^3*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-2, x) == :(e^-1*(2*b^2+-8*a*c)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(2a+b*(d+e*x)^2)+-1*b*e^-1*(b^2+-4*a*c)^-3//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*(d+e*x)^2)))
@test integrate((d+e*x)^2*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-2, x) == :(-1*e^-1*(2*b^2+-8*a*c)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(b+2*c*(d+e*x)^2)*(d+e*x)+(1/2)*2^(1/2)*c^(1/2)*e^-1*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-3//2*(-1*(b^2+-4*a*c)^(1/2)+2b)*arctan(2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x))+-1//2*2^(1/2)*c^(1/2)*e^-1*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-3//2*((b^2+-4*a*c)^(1/2)+2b)*arctan(2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x)))
@test integrate((a+b*(d+e*x)^2+c*(d+e*x)^4)^-2*(d+e*x), x) == :(e^-1*(2*b^2+-8*a*c)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(-1b+-2*c*(d+e*x)^2)+2*c*e^-1*(b^2+-4*a*c)^-3//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*(d+e*x)^2)))
@test integrate((a+b*(d+e*x)^2+c*(d+e*x)^4)^-2, x) == :((1/2)*a^-1*(b^2+-4*a*c)^-1*(a+b*e^2*(x+d*e^-1)^2+c*e^4*(x+d*e^-1)^4)^-1*(x+d*e^-1)*(b^2+-2*a*c+b*c*e^2*(x+d*e^-1)^2)+-1//4*2^(1/2)*a^-1*c^(1/2)*e^-1*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-3//2*(b^2+-1*b*(b^2+-4*a*c)^(1/2)+-12*a*c)*arctan(2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x))+1//4*2^(1/2)*a^-1*c^(1/2)*e^-1*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-3//2*(b^2+b*(b^2+-4*a*c)^(1/2)+-12*a*c)*arctan(2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x)))
@test integrate((d+e*x)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-2, x) == :(a^-2*e^-1*log(d+e*x)+-1//4*a^-2*e^-1*log(a+b*(d+e*x)^2+c*(d+e*x)^4)+(1/2)*a^-1*e^-1*(b^2+-4*a*c)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(b^2+-2*a*c+b*c*(d+e*x)^2)+(1/2)*b*a^-2*e^-1*(b^2+-4*a*c)^-3//2*(b^2+-6*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*(d+e*x)^2)))
@test integrate((d+e*x)^-2*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-2, x) == :(-1//2*a^-2*e^-1*(d+e*x)^-1*(b^2+-4*a*c)^-1*(3*b^2+-10*a*c)+(1/2)*a^-1*e^-1*(d+e*x)^-1*(b^2+-4*a*c)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(b^2+-2*a*c+b*c*(d+e*x)^2)+-1//4*2^(1/2)*a^-2*c^(1/2)*e^-1*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-3//2*(3*b^3+(b^2+-4*a*c)^(1/2)*(3*b^2+-10*a*c)+-16*a*b*c)*arctan(2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x))+1//4*2^(1/2)*a^-2*c^(1/2)*e^-1*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-3//2*(3*b^3+-1*(b^2+-4*a*c)^(1/2)*(3*b^2+-10*a*c)+-16*a*b*c)*arctan(2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x)))
@test integrate((d+e*x)^-3*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-2, x) == :((1/2)*b*a^-3*e^-1*log(a+b*(d+e*x)^2+c*(d+e*x)^4)+-2*b*a^-3*e^-1*log(d+e*x)+-1*a^-3*e^-1*(b^2+-4*a*c)^-3//2*(b^4+6*a^2*c^2+-6*a*c*b^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*(d+e*x)^2))+-1*a^-2*e^-1*(d+e*x)^-2*(b^2+-4*a*c)^-1*(b^2+-3*a*c)+(1/2)*a^-1*e^-1*(d+e*x)^-2*(b^2+-4*a*c)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(b^2+-2*a*c+b*c*(d+e*x)^2))
@test integrate((d+e*x)^-4*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-2, x) == :(-1//6*a^-2*e^-1*(d+e*x)^-3*(b^2+-4*a*c)^-1*(5*b^2+-14*a*c)+(1/2)*b*a^-3*e^-1*(d+e*x)^-1*(b^2+-4*a*c)^-1*(5*b^2+-19*a*c)+(1/2)*a^-1*e^-1*(d+e*x)^-3*(b^2+-4*a*c)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(b^2+-2*a*c+b*c*(d+e*x)^2)+-1//4*2^(1/2)*a^-3*c^(1/2)*e^-1*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-3//2*(5*b^4+28*a^2*c^2+-1*b*(b^2+-4*a*c)^(1/2)*(5*b^2+-19*a*c)+-29*a*c*b^2)*arctan(2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x))+1//4*2^(1/2)*a^-3*c^(1/2)*e^-1*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-3//2*(5*b^4+28*a^2*c^2+b*(b^2+-4*a*c)^(1/2)*(5*b^2+-19*a*c)+-29*a*c*b^2)*arctan(2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x)))
@test integrate((d+e*x)^4*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-3, x) == :(e^-1*(4*b^2+-16*a*c)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-2*(d+e*x)*(2a+b*(d+e*x)^2)+-1//8*e^-1*(b^2+-4*a*c)^-2*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(d+e*x)*(7*b^2+-4*a*c+12*b*c*(d+e*x)^2)+-3//8*2^(1/2)*c^(1/2)*e^-1*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-5//2*(3*b^2+2*b*(b^2+-4*a*c)^(1/2)+4*a*c)*arctan(2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x))+3//8*2^(1/2)*c^(1/2)*e^-1*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-5//2*(3*b^2+-2*b*(b^2+-4*a*c)^(1/2)+4*a*c)*arctan(2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x)))
@test integrate((d+e*x)^3*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-3, x) == :(e^-1*(4*b^2+-16*a*c)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-2*(2a+b*(d+e*x)^2)+3*b*c*e^-1*(b^2+-4*a*c)^-5//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*(d+e*x)^2))+-3//4*b*e^-1*(b^2+-4*a*c)^-2*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(b+2*c*(d+e*x)^2))
@test integrate((d+e*x)^2*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-3, x) == :(-1*e^-1*(4*b^2+-16*a*c)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-2*(b+2*c*(d+e*x)^2)*(d+e*x)+1//8*a^-1*e^-1*(b^2+-4*a*c)^-2*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(d+e*x)*(b*(b^2+8*a*c)+c*(d+e*x)^2*(b^2+20*a*c))+1//16*2^(1/2)*a^-1*c^(1/2)*e^-1*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-2*(b^2+20*a*c+-1*b*(b^2+-4*a*c)^-1//2*(b^2+-52*a*c))*arctan(2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x))+1//16*2^(1/2)*a^-1*c^(1/2)*e^-1*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-2*(b^2+20*a*c+b*(b^2+-4*a*c)^-1//2*(b^2+-52*a*c))*arctan(2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x)))
@test integrate((a+b*(d+e*x)^2+c*(d+e*x)^4)^-3*(d+e*x), x) == :(e^-1*(4*b^2+-16*a*c)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-2*(-1b+-2*c*(d+e*x)^2)+-6*c^2*e^-1*(b^2+-4*a*c)^-5//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*(d+e*x)^2))+3//2*c*e^-1*(b^2+-4*a*c)^-2*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(b+2*c*(d+e*x)^2))
@test integrate((a+b*(d+e*x)^2+c*(d+e*x)^4)^-3, x) == :(1//4*a^-1*(b^2+-4*a*c)^-1*(a+b*e^2*(x+d*e^-1)^2+c*e^4*(x+d*e^-1)^4)^-2*(x+d*e^-1)*(b^2+-2*a*c+b*c*e^2*(x+d*e^-1)^2)+1//8*a^-2*(b^2+-4*a*c)^-2*(a+b*e^2*(x+d*e^-1)^2+c*e^4*(x+d*e^-1)^4)^-1*(x+d*e^-1)*((b^2+-7*a*c)*(3*b^2+-4*a*c)+3*b*c*e^2*(x+d*e^-1)^2*(b^2+-8*a*c))+-3//16*2^(1/2)*a^-2*c^(1/2)*e^-1*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-5//2*(b^4+56*a^2*c^2+-1*b*(b^2+-4*a*c)^(1/2)*(b^2+-8*a*c)+-10*a*c*b^2)*arctan(2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x))+3//16*2^(1/2)*a^-2*c^(1/2)*e^-1*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-5//2*(b^4+56*a^2*c^2+b*(b^2+-4*a*c)^(1/2)*(b^2+-8*a*c)+-10*a*c*b^2)*arctan(2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x)))
@test integrate((d+e*x)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-3, x) == :(a^-3*e^-1*log(d+e*x)+-1//4*a^-3*e^-1*log(a+b*(d+e*x)^2+c*(d+e*x)^4)+1//4*a^-1*e^-1*(b^2+-4*a*c)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-2*(b^2+-2*a*c+b*c*(d+e*x)^2)+1//4*a^-2*e^-1*(b^2+-4*a*c)^-2*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(2*b^4+16*a^2*c^2+-15*a*c*b^2+2*b*c*(d+e*x)^2*(b^2+-7*a*c))+(1/2)*b*a^-3*e^-1*(b^2+-4*a*c)^-5//2*(b^4+30*a^2*c^2+-10*a*c*b^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*(d+e*x)^2)))
@test integrate((d+e*x)^-2*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-3, x) == :(-1//8*a^-3*e^-1*(d+e*x)^-1*(b^2+-4*a*c)^-2*(b^2+-5*a*c)*(15*b^2+-36*a*c)+1//4*a^-1*e^-1*(d+e*x)^-1*(b^2+-4*a*c)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-2*(b^2+-2*a*c+b*c*(d+e*x)^2)+1//8*a^-2*e^-1*(d+e*x)^-1*(b^2+-4*a*c)^-2*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(5*b^4+36*a^2*c^2+-35*a*c*b^2+b*c*(d+e*x)^2*(5*b^2+-32*a*c))+-3//16*2^(1/2)*a^-3*c^(1/2)*e^-1*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-2*((b^2+-5*a*c)*(5*b^2+-12*a*c)+-1*(b^2+-4*a*c)^-1//2*(5*b^5+-47*a*c*b^3+124*b*a^2*c^2))*arctan(2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x))+-3//16*2^(1/2)*a^-3*c^(1/2)*e^-1*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-2*((b^2+-5*a*c)*(5*b^2+-12*a*c)+b*(b^2+-4*a*c)^-1//2*(5*b^4+124*a^2*c^2+-47*a*c*b^2))*arctan(2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x)))
@test integrate((d+e*x)^-3*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-3, x) == :(-3*b*a^-4*e^-1*log(d+e*x)+3//4*b*a^-4*e^-1*log(a+b*(d+e*x)^2+c*(d+e*x)^4)+-1//2*a^-4*e^-1*(b^2+-4*a*c)^-5//2*(3*b^6+-60*a^3*c^3+-30*a*c*b^4+90*a^2*b^2*c^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*(d+e*x)^2))+-1//2*a^-3*e^-1*(d+e*x)^-2*(b^2+-4*a*c)^-2*(b^2+-2*a*c)*(3*b^2+-15*a*c)+1//4*a^-1*e^-1*(d+e*x)^-2*(b^2+-4*a*c)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-2*(b^2+-2*a*c+b*c*(d+e*x)^2)+1//4*a^-2*e^-1*(d+e*x)^-2*(b^2+-4*a*c)^-2*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(3*b^4+20*a^2*c^2+-20*a*c*b^2+3*b*c*(d+e*x)^2*(b^2+-6*a*c)))
@test integrate((d*f+e*f*x)^4*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1, x) == :(x*c^-1*f^4+-1//2*2^(1/2)*c^-3//2*e^-1*f^4*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x))+-1//2*2^(1/2)*c^-3//2*e^-1*f^4*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x)))
@test integrate((d*f+e*f*x)^3*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1, x) == :(1//4*c^-1*e^-1*f^3*log(a+b*(d+e*x)^2+c*(d+e*x)^4)+(1/2)*b*c^-1*e^-1*f^3*(b^2+-4*a*c)^-1//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*(d+e*x)^2)))
@test integrate((d*f+e*f*x)^2*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1, x) == :((1/2)*2^(1/2)*c^-1//2*e^-1*f^2*(b+(b^2+-4*a*c)^(1/2))^(1/2)*(b^2+-4*a*c)^-1//2*arctan(2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x))+-1//2*2^(1/2)*c^-1//2*e^-1*f^2*(b+-1*(b^2+-4*a*c)^(1/2))^(1/2)*(b^2+-4*a*c)^-1//2*arctan(2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x)))
@test integrate((a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(d*f+e*f*x), x) == :(-1*f*e^-1*(b^2+-4*a*c)^-1//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*(d+e*x)^2)))
@test integrate((d*f+e*f*x)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1, x) == :(a^-1*e^-1*f^-1*log(d+e*x)+-1//4*a^-1*e^-1*f^-1*log(a+b*(d+e*x)^2+c*(d+e*x)^4)+(1/2)*b*a^-1*e^-1*f^-1*(b^2+-4*a*c)^-1//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*(d+e*x)^2)))
@test integrate((d*f+e*f*x)^-2*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1, x) == :(-1*a^-1*e^-1*f^-2*(d+e*x)^-1+-1//2*2^(1/2)*a^-1*c^(1/2)*e^-1*f^-2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(1+-1*b*(b^2+-4*a*c)^-1//2)*arctan(2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x))+-1//2*2^(1/2)*a^-1*c^(1/2)*e^-1*f^-2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(1+b*(b^2+-4*a*c)^-1//2)*arctan(2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x)))
@test integrate((d*f+e*f*x)^-3*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1, x) == :(-1//2*a^-1*e^-1*f^-3*(d+e*x)^-2+-1*b*a^-2*e^-1*f^-3*log(d+e*x)+1//4*b*a^-2*e^-1*f^-3*log(a+b*(d+e*x)^2+c*(d+e*x)^4)+-1//2*a^-2*e^-1*f^-3*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*(d+e*x)^2)))
@test integrate((d*f+e*f*x)^-4*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1, x) == :(-1//3*a^-1*e^-1*f^-4*(d+e*x)^-3+b*a^-2*e^-1*f^-4*(d+e*x)^-1+(1/2)*2^(1/2)*a^-2*c^(1/2)*e^-1*f^-4*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x))+(1/2)*2^(1/2)*a^-2*c^(1/2)*e^-1*f^-4*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x)))
@test integrate((d*f+e*f*x)^4*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-2, x) == :(e^-1*f^4*(2*b^2+-8*a*c)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(d+e*x)*(2a+b*(d+e*x)^2)+1//4*2^(1/2)*c^-1//2*e^-1*f^4*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-3//2*(b^2+b*(b^2+-4*a*c)^(1/2)+4*a*c)*arctan(2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x))+1//4*2^(1/2)*c^-1//2*e^-1*f^4*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+4*a*c))*arctan(2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x)))
@test integrate((d*f+e*f*x)^3*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-2, x) == :(e^-1*f^3*(2*b^2+-8*a*c)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(2a+b*(d+e*x)^2)+-1*b*e^-1*f^3*(b^2+-4*a*c)^-3//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*(d+e*x)^2)))
@test integrate((d*f+e*f*x)^2*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-2, x) == :(-1*e^-1*f^2*(2*b^2+-8*a*c)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(b+2*c*(d+e*x)^2)*(d+e*x)+(1/2)*2^(1/2)*c^(1/2)*e^-1*f^2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-3//2*(-1*(b^2+-4*a*c)^(1/2)+2b)*arctan(2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x))+-1//2*2^(1/2)*c^(1/2)*e^-1*f^2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-3//2*((b^2+-4*a*c)^(1/2)+2b)*arctan(2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x)))
@test integrate((a+b*(d+e*x)^2+c*(d+e*x)^4)^-2*(d*f+e*f*x), x) == :(-1*f*e^-1*(2*b^2+-8*a*c)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(b+2*c*(d+e*x)^2)+2*c*f*e^-1*(b^2+-4*a*c)^-3//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*(d+e*x)^2)))
@test integrate((d*f+e*f*x)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-2, x) == :(a^-2*e^-1*f^-1*log(d+e*x)+-1//4*a^-2*e^-1*f^-1*log(a+b*(d+e*x)^2+c*(d+e*x)^4)+(1/2)*a^-1*e^-1*f^-1*(b^2+-4*a*c)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(b^2+-2*a*c+b*c*(d+e*x)^2)+(1/2)*b*a^-2*e^-1*f^-1*(b^2+-4*a*c)^-3//2*(b^2+-6*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*(d+e*x)^2)))
@test integrate((d*f+e*f*x)^-2*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-2, x) == :(-1//2*a^-2*e^-1*f^-2*(d+e*x)^-1*(b^2+-4*a*c)^-1*(3*b^2+-10*a*c)+(1/2)*a^-1*e^-1*f^-2*(d+e*x)^-1*(b^2+-4*a*c)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(b^2+-2*a*c+b*c*(d+e*x)^2)+-1//4*2^(1/2)*a^-2*c^(1/2)*e^-1*f^-2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-3//2*(3*b^3+(b^2+-4*a*c)^(1/2)*(3*b^2+-10*a*c)+-16*a*b*c)*arctan(2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x))+1//4*2^(1/2)*a^-2*c^(1/2)*e^-1*f^-2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-3//2*(3*b^3+-1*(b^2+-4*a*c)^(1/2)*(3*b^2+-10*a*c)+-16*a*b*c)*arctan(2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x)))
@test integrate((d*f+e*f*x)^-3*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-2, x) == :((1/2)*b*a^-3*e^-1*f^-3*log(a+b*(d+e*x)^2+c*(d+e*x)^4)+-2*b*a^-3*e^-1*f^-3*log(d+e*x)+-1*a^-3*e^-1*f^-3*(b^2+-4*a*c)^-3//2*(b^4+6*a^2*c^2+-6*a*c*b^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*(d+e*x)^2))+-1*a^-2*e^-1*f^-3*(d+e*x)^-2*(b^2+-4*a*c)^-1*(b^2+-3*a*c)+(1/2)*a^-1*e^-1*f^-3*(d+e*x)^-2*(b^2+-4*a*c)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(b^2+-2*a*c+b*c*(d+e*x)^2))
@test integrate((d*f+e*f*x)^-4*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-2, x) == :(-1//6*a^-2*e^-1*f^-4*(d+e*x)^-3*(b^2+-4*a*c)^-1*(5*b^2+-14*a*c)+(1/2)*b*a^-3*e^-1*f^-4*(d+e*x)^-1*(b^2+-4*a*c)^-1*(5*b^2+-19*a*c)+(1/2)*a^-1*e^-1*f^-4*(d+e*x)^-3*(b^2+-4*a*c)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(b^2+-2*a*c+b*c*(d+e*x)^2)+-1//4*2^(1/2)*a^-3*c^(1/2)*e^-1*f^-4*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-3//2*(5*b^4+28*a^2*c^2+-1*b*(b^2+-4*a*c)^(1/2)*(5*b^2+-19*a*c)+-29*a*c*b^2)*arctan(2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x))+1//4*2^(1/2)*a^-3*c^(1/2)*e^-1*f^-4*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-3//2*(5*b^4+28*a^2*c^2+b*(b^2+-4*a*c)^(1/2)*(5*b^2+-19*a*c)+-29*a*c*b^2)*arctan(2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x)))
@test integrate((d*f+e*f*x)^4*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-3, x) == :(e^-1*f^4*(4*b^2+-16*a*c)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-2*(d+e*x)*(2a+b*(d+e*x)^2)+-1//8*e^-1*f^4*(b^2+-4*a*c)^-2*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(d+e*x)*(7*b^2+-4*a*c+12*b*c*(d+e*x)^2)+-3//8*2^(1/2)*c^(1/2)*e^-1*f^4*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-5//2*(3*b^2+2*b*(b^2+-4*a*c)^(1/2)+4*a*c)*arctan(2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x))+3//8*2^(1/2)*c^(1/2)*e^-1*f^4*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-5//2*(3*b^2+-2*b*(b^2+-4*a*c)^(1/2)+4*a*c)*arctan(2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x)))
@test integrate((d*f+e*f*x)^3*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-3, x) == :(e^-1*f^3*(4*b^2+-16*a*c)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-2*(2a+b*(d+e*x)^2)+3*b*c*e^-1*f^3*(b^2+-4*a*c)^-5//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*(d+e*x)^2))+-3//4*b*e^-1*f^3*(b^2+-4*a*c)^-2*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(b+2*c*(d+e*x)^2))
@test integrate((d*f+e*f*x)^2*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-3, x) == :(-1*e^-1*f^2*(4*b^2+-16*a*c)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-2*(b+2*c*(d+e*x)^2)*(d+e*x)+1//8*a^-1*e^-1*f^2*(b^2+-4*a*c)^-2*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(d+e*x)*(b*(b^2+8*a*c)+c*(d+e*x)^2*(b^2+20*a*c))+1//16*2^(1/2)*a^-1*c^(1/2)*e^-1*f^2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-2*(b^2+20*a*c+-1*b*(b^2+-4*a*c)^-1//2*(b^2+-52*a*c))*arctan(2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x))+1//16*2^(1/2)*a^-1*c^(1/2)*e^-1*f^2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-2*(b^2+20*a*c+b*(b^2+-4*a*c)^-1//2*(b^2+-52*a*c))*arctan(2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x)))
@test integrate((a+b*(d+e*x)^2+c*(d+e*x)^4)^-3*(d*f+e*f*x), x) == :(-1*f*e^-1*(4*b^2+-16*a*c)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-2*(b+2*c*(d+e*x)^2)+-6*f*c^2*e^-1*(b^2+-4*a*c)^-5//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*(d+e*x)^2))+3//2*c*f*e^-1*(b^2+-4*a*c)^-2*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(b+2*c*(d+e*x)^2))
@test integrate((d*f+e*f*x)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-3, x) == :(a^-3*e^-1*f^-1*log(d+e*x)+-1//4*a^-3*e^-1*f^-1*log(a+b*(d+e*x)^2+c*(d+e*x)^4)+1//4*a^-1*e^-1*f^-1*(b^2+-4*a*c)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-2*(b^2+-2*a*c+b*c*(d+e*x)^2)+1//4*a^-2*e^-1*f^-1*(b^2+-4*a*c)^-2*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(2*b^4+16*a^2*c^2+-15*a*c*b^2+2*b*c*(d+e*x)^2*(b^2+-7*a*c))+(1/2)*b*a^-3*e^-1*f^-1*(b^2+-4*a*c)^-5//2*(b^4+30*a^2*c^2+-10*a*c*b^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*(d+e*x)^2)))
@test integrate((d*f+e*f*x)^-2*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-3, x) == :(-1//8*a^-3*e^-1*f^-2*(d+e*x)^-1*(b^2+-4*a*c)^-2*(b^2+-5*a*c)*(15*b^2+-36*a*c)+1//4*a^-1*e^-1*f^-2*(d+e*x)^-1*(b^2+-4*a*c)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-2*(b^2+-2*a*c+b*c*(d+e*x)^2)+1//8*a^-2*e^-1*f^-2*(d+e*x)^-1*(b^2+-4*a*c)^-2*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(5*b^4+36*a^2*c^2+-35*a*c*b^2+b*c*(d+e*x)^2*(5*b^2+-32*a*c))+-3//16*2^(1/2)*a^-3*c^(1/2)*e^-1*f^-2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-2*((b^2+-5*a*c)*(5*b^2+-12*a*c)+-1*(b^2+-4*a*c)^-1//2*(5*b^5+-47*a*c*b^3+124*b*a^2*c^2))*arctan(2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x))+-3//16*2^(1/2)*a^-3*c^(1/2)*e^-1*f^-2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-2*((b^2+-5*a*c)*(5*b^2+-12*a*c)+b*(b^2+-4*a*c)^-1//2*(5*b^4+124*a^2*c^2+-47*a*c*b^2))*arctan(2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(d+e*x)))
@test integrate((d*f+e*f*x)^-3*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-3, x) == :(-3*b*a^-4*e^-1*f^-3*log(d+e*x)+3//4*b*a^-4*e^-1*f^-3*log(a+b*(d+e*x)^2+c*(d+e*x)^4)+-1//2*a^-4*e^-1*f^-3*(b^2+-4*a*c)^-5//2*(3*b^6+-60*a^3*c^3+-30*a*c*b^4+90*a^2*b^2*c^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*(d+e*x)^2))+-1//2*a^-3*e^-1*f^-3*(d+e*x)^-2*(b^2+-4*a*c)^-2*(b^2+-2*a*c)*(3*b^2+-15*a*c)+1//4*a^-1*e^-1*f^-3*(d+e*x)^-2*(b^2+-4*a*c)^-1*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-2*(b^2+-2*a*c+b*c*(d+e*x)^2)+1//4*a^-2*e^-1*f^-3*(d+e*x)^-2*(b^2+-4*a*c)^-2*(a+b*(d+e*x)^2+c*(d+e*x)^4)^-1*(3*b^4+20*a^2*c^2+-20*a*c*b^2+3*b*c*(d+e*x)^2*(b^2+-6*a*c)))
@test integrate((2+3x)^6*(1+(2+3x)^7+(2+3x)^14), x) == :(1//21*(2+3x)^7+1//42*(2+3x)^14+1//63*(2+3x)^21)
@test integrate((2+3x)^6*(1+(2+3x)^7+(2+3x)^14)^2, x) == :(1//21*(2+3x)^7+1//21*(2+3x)^14+1//21*(2+3x)^21+1//42*(2+3x)^28+1//105*(2+3x)^35)

max_stars_repo_path: test/1 Algebraic functions/1.2 Trinomial products/1.2.3 General/1.2.3.2 (d x)^m (a+b x^n+c x^(2 n))^p.jl