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

@test integrate((a+b*x)^-1//2*(c+d*x+e*x^2), x) == :(b^-3*(a+b*x)^(1/2)*(2*c*b^2+2*e*a^2+-2*a*b*d)+1//3*b^-3*(a+b*x)^3//2*(-4*a*e+2*b*d)+2//5*e*b^-3*(a+b*x)^5//2)
@test integrate((a+b*x)^-1//2*(c+d*x+e*x^2)^2, x) == :(2*b^-5*(a+b*x)^(1/2)*(c*b^2+e*a^2+-1*a*b*d)^2+-1//5*b^-5*(a+b*x)^5//2*(-12*a^2*e^2+-2*b^2*(d^2+2*c*e)+12*a*b*d*e)+2//9*b^-5*e^2*(a+b*x)^9//2+1//3*b^-5*(a+b*x)^3//2*(-8*a*e+4*b*d)*(c*b^2+e*a^2+-1*a*b*d)+4//7*e*b^-5*(a+b*x)^7//2*(b*d+-2*a*e))
@test integrate((a+b*x)^-1//2*(c+d*x+e*x^2)^3, x) == :(2*b^-7*(a+b*x)^(1/2)*(c*b^2+e*a^2+-1*a*b*d)^3+2//13*b^-7*e^3*(a+b*x)^13//2+b^-7*(a+b*x)^3//2*(c*b^2+e*a^2+-1*a*b*d)^2*(-4*a*e+2*b*d)+-2//3*e*b^-7*(a+b*x)^9//2*(-1*b^2*(d^2+c*e)+-5*a^2*e^2+5*a*b*d*e)+-1//5*b^-7*(a+b*x)^5//2*(-1*b^2*(d^2+c*e)+-5*a^2*e^2+5*a*b*d*e)*(6*c*b^2+6*e*a^2+-6*a*b*d)+-1//7*b^-7*(a+b*x)^7//2*(-4*a*e+2*b*d)*(-1*b^2*(d^2+6*c*e)+-10*a^2*e^2+10*a*b*d*e)+6//11*b^-7*e^2*(a+b*x)^11//2*(b*d+-2*a*e))
@test integrate((a+b*x)^-1//2*(c+d*x+e*x^2+f*x^3), x) == :(b^-4*(a+b*x)^(1/2)*(-2*f*a^3+2*c*b^3+-2*a*d*b^2+2*b*e*a^2)+1//3*b^-4*(a+b*x)^3//2*(2*d*b^2+6*f*a^2+-4*a*b*e)+1//5*b^-4*(a+b*x)^5//2*(-6*a*f+2*b*e)+2//7*f*b^-4*(a+b*x)^7//2)
@test integrate((a+b*x)^-1//2*(c+d*x+e*x^2+f*x^3)^2, x) == :(2*b^-7*(a+b*x)^(1/2)*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)^2+-1//9*b^-7*(a+b*x)^9//2*(-30*a^2*f^2+-2*b^2*(e^2+2*d*f)+20*a*b*e*f)+1//5*b^-7*(a+b*x)^5//2*(2*b^4*(d^2+2*c*e)+30*a^4*f^2+-12*a*b^3*(c*f+d*e)+12*a^2*b^2*(e^2+2*d*f)+-40*b*e*f*a^3)+1//7*b^-7*(a+b*x)^7//2*(-40*a^3*f^2+4*b^3*(c*f+d*e)+-8*a*b^2*(e^2+2*d*f)+40*b*e*f*a^2)+2//13*b^-7*f^2*(a+b*x)^13//2+1//3*b^-7*(a+b*x)^3//2*(4*d*b^2+12*f*a^2+-8*a*b*e)*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+4//11*f*b^-7*(a+b*x)^11//2*(b*e+-3*a*f))
@test integrate((a+b*x)^-1//2*(c+d*x+e*x^2+f*x^3)^3, x) == :(2*b^-10*(a+b*x)^(1/2)*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)^3+-1//7*b^-10*(a+b*x)^7//2*(-168*a^6*f^3+-2*b^6*(d^3+3*f*c^2+6*c*d*e)+-60*a^2*b^4*(d*e^2+f*d^2+2*c*e*f)+24*a*b^5*(c*e^2+e*d^2+2*c*d*f)+40*a^3*b^3*(e^3+3*c*f^2+6*d*e*f)+-210*f*a^4*b^2*(e^2+d*f)+336*b*e*a^5*f^2)+-1//11*b^-10*(a+b*x)^11//2*(-252*a^4*f^3+-6*b^4*(d*e^2+f*d^2+2*c*e*f)+12*a*b^3*(e^3+3*c*f^2+6*d*e*f)+-126*f*a^2*b^2*(e^2+d*f)+336*b*e*a^3*f^2)+1//3*b^-10*(a+b*x)^9//2*(-84*a^5*f^3+2*b^5*(c*e^2+e*d^2+2*c*d*f)+-10*a*b^4*(d*e^2+f*d^2+2*c*e*f)+10*a^2*b^3*(e^3+3*c*f^2+6*d*e*f)+-70*f*a^3*b^2*(e^2+d*f)+140*b*e*a^4*f^2)+1//13*b^-10*(a+b*x)^13//2*(-168*a^3*f^3+2*b^3*(e^3+3*c*f^2+6*d*e*f)+-42*a*f*b^2*(e^2+d*f)+168*b*e*a^2*f^2)+2//19*b^-10*f^3*(a+b*x)^19//2+b^-10*(a+b*x)^3//2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)^2*(2*d*b^2+6*f*a^2+-4*a*b*e)+-2//5*f*b^-10*(a+b*x)^15//2*(-1*b^2*(e^2+d*f)+-12*a^2*f^2+8*a*b*e*f)+1//5*b^-10*(a+b*x)^5//2*(-6*f*a^3+6*c*b^3+-6*a*d*b^2+6*b*e*a^2)*(b^4*(d^2+c*e)+12*a^4*f^2+a^2*b^2*(5*e^2+9*d*f)+-1*a*b^3*(3*c*f+5*d*e)+-16*b*e*f*a^3)+6//17*b^-10*f^2*(a+b*x)^17//2*(b*e+-3*a*f))
@test integrate((a+b*x^3)^-1*(c+d*x), x) == :(-1//6*a^-2//3*b^-1//3*(c+-1*d*a^1//3*b^-1//3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-2//3*b^-2//3*(c*b^1//3+-1*d*a^1//3)*log(a^1//3+x*b^1//3)+-1//3*3^(1/2)*a^-2//3*b^-2//3*(c*b^1//3+d*a^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate((a+b*x^3)^-2*(c+d*x), x) == :(-1//18*a^-5//3*b^-2//3*(-1*d*a^1//3+2*c*b^1//3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*x*a^-1*(a+b*x^3)^-1*(c+d*x)+1//9*a^-5//3*b^-2//3*(-1*d*a^1//3+2*c*b^1//3)*log(a^1//3+x*b^1//3)+-1//9*3^(1/2)*a^-5//3*b^-2//3*(d*a^1//3+2*c*b^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate((a+b*x^3)^-3*(c+d*x), x) == :(-1//54*a^-8//3*b^-2//3*(-2*d*a^1//3+5*c*b^1//3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//6*x*a^-1*(a+b*x^3)^-2*(c+d*x)+1//18*x*a^-2*(a+b*x^3)^-1*(5c+4*d*x)+1//27*a^-8//3*b^-2//3*(-2*d*a^1//3+5*c*b^1//3)*log(a^1//3+x*b^1//3)+-1//27*3^(1/2)*a^-8//3*b^-2//3*(2*d*a^1//3+5*c*b^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate((a+b*x^3)^-4*(c+d*x), x) == :(-1//243*a^-11//3*b^-2//3*(-7*d*a^1//3+20*c*b^1//3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*x*a^-1*(a+b*x^3)^-3*(c+d*x)+1//54*x*a^-2*(a+b*x^3)^-2*(8c+7*d*x)+1//243*a^-11//3*b^-2//3*(-14*d*a^1//3+40*c*b^1//3)*log(a^1//3+x*b^1//3)+2//81*x*a^-3*(a+b*x^3)^-1*(10c+7*d*x)+-1//243*3^(1/2)*a^-11//3*b^-2//3*(14*d*a^1//3+40*c*b^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate((d+e*x^3)^-1*(a+b*x), x) == :(-1//3*d^-2//3*e^-2//3*(b*d^1//3+-1*a*e^1//3)*log(d^1//3+x*e^1//3)+-1//6*d^-2//3*e^-1//3*(a+-1*b*d^1//3*e^-1//3)*log(d^2//3+e^2//3*x^2+-1*x*d^1//3*e^1//3)+-1//3*3^(1/2)*d^-2//3*e^-2//3*(a*e^1//3+b*d^1//3)*arctan(1//3*3^(1/2)*d^-1//3*(d^1//3+-2*x*e^1//3)))
@test integrate((d+-1*e*x^3)^-1*(a+b*x), x) == :(-1//3*d^-2//3*e^-2//3*(a*e^1//3+b*d^1//3)*log(d^1//3+-1*x*e^1//3)+1//6*d^-2//3*e^-2//3*(a*e^1//3+b*d^1//3)*log(d^2//3+e^2//3*x^2+x*d^1//3*e^1//3)+-1//3*3^(1/2)*d^-2//3*e^-2//3*(b*d^1//3+-1*a*e^1//3)*arctan(1//3*3^(1/2)*d^-1//3*(d^1//3+2*x*e^1//3)))
@test integrate((1+x^3)^-1*(1+x), x) == :(-2//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x)))
@test integrate((1+-1*x^3)^-1*(1+-1x), x) == :(2//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+2x)))
@test integrate((1+-1*x^3)^-1*(1+x), x) == :(-2//3*log(1+-1x)+1//3*log(1+x+x^2))
@test integrate((1+x^3)^-1*(1+-1x), x) == :(-1//3*log(1+x^2+-1x)+2//3*log(1+x))
@test integrate((1+-1*x^3)^-1*(3+-1x), x) == :(-2//3*log(1+-1x)+1//3*log(1+x+x^2)+4//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+2x)))
@test integrate((c^3+d^3*x^3)^-1*(c+d*x), x) == :(-2//3*3^(1/2)*c^-1*d^-1*arctan(1//3*3^(1/2)*c^-1*(c+-2*d*x)))
@test integrate((c^3+-1*d^3*x^3)^-1*(c+-1*d*x), x) == :(2//3*3^(1/2)*c^-1*d^-1*arctan(1//3*3^(1/2)*c^-1*(c+2*d*x)))
@test integrate((a+b*x^3)^-1*(B*x*b^2//3+B*a^1//3*b^1//3), x) == :(-2//3*B*3^(1/2)*a^-1//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate((a+b*x^3)^-1*(B*a^1//3*(-1b)^1//3+-1*B*x*(-1b)^2//3), x) == :(2//3*B*3^(1/2)*a^-1//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*x*(-1b)^1//3)))
@test integrate((a+b*x^3)^-1*(B*x+C*x^2)+-1*C*x^2*(a+b*x^3)^-1, x) == :(-1//3*B*a^-1//3*b^-2//3*log(a^1//3+x*b^1//3)+1//6*B*a^-1//3*b^-2//3*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//3*B*3^(1/2)*a^-1//3*b^-2//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate((a+b*x^3)^-1*(A+C*x^2)+-1*C*x^2*(a+b*x^3)^-1, x) == :(-1//6*A*a^-2//3*b^-1//3*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*A*a^-2//3*b^-1//3*log(a^1//3+x*b^1//3)+-1//3*A*3^(1/2)*a^-2//3*b^-1//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate((a+b*x^3)^-1*(A+B*x+C*x^2)+-1*C*x^2*(a+b*x^3)^-1, x) == :(-1//6*a^-2//3*b^-1//3*(A+-1*B*a^1//3*b^-1//3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-2//3*b^-2//3*(A*b^1//3+-1*B*a^1//3)*log(a^1//3+x*b^1//3)+-1//3*3^(1/2)*a^-2//3*b^-2//3*(A*b^1//3+B*a^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate((d+e*x^3)^-1*(b*x+c*x^2), x) == :(1//3*c*e^-1*log(d+e*x^3)+-1//3*b*d^-1//3*e^-2//3*log(d^1//3+x*e^1//3)+1//6*b*d^-1//3*e^-2//3*log(d^2//3+e^2//3*x^2+-1*x*d^1//3*e^1//3)+-1//3*b*3^(1/2)*d^-1//3*e^-2//3*arctan(1//3*3^(1/2)*d^-1//3*(d^1//3+-2*x*e^1//3)))
@test integrate((d+-1*e*x^3)^-1*(a+c*x^2), x) == :(-1//3*c*e^-1*log(d+-1*e*x^3)+-1//3*a*d^-2//3*e^-1//3*log(d^1//3+-1*x*e^1//3)+1//6*a*d^-2//3*e^-1//3*log(d^2//3+e^2//3*x^2+x*d^1//3*e^1//3)+1//3*a*3^(1/2)*d^-2//3*e^-1//3*arctan(1//3*3^(1/2)*d^-1//3*(d^1//3+2*x*e^1//3)))
@test integrate((a^3+b^3*x^3)^-1*(2*a^2+b^2*x^2), x) == :(b^-1*log(a+b*x)+-2//3*3^(1/2)*b^-1*arctan(1//3*3^(1/2)*a^-1*(a+-2*b*x)))
@test integrate((a^3+-1*b^3*x^3)^-1*(2*a^2+b^2*x^2), x) == :(-1*b^-1*log(a+-1*b*x)+2//3*3^(1/2)*b^-1*arctan(1//3*3^(1/2)*a^-1*(a+2*b*x)))
@test integrate((8+b*x^3)^-1*(8C+C*b^2//3*x^2), x) == :(C*b^-1//3*log(2+x*b^1//3)+-2//3*C*3^(1/2)*b^-1//3*arctan(1//3*3^(1/2)*(1+-1*x*b^1//3)))
@test integrate((a+8*x^3)^-1*(C*a^2//3+2*C*x^2), x) == :(1//4*C*log(a^1//3+2x)+-1//6*C*3^(1/2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-4x)))
@test integrate((-8+b*x^3)^-1*(8C+C*x^2*(-1b)^2//3), x) == :(-1*C*(-1b)^-1//3*log(2+x*(-1b)^1//3)+2//3*C*3^(1/2)*(-1b)^-1//3*arctan(1//3*3^(1/2)*(1+-1*x*(-1b)^1//3)))
@test integrate((a+-8*x^3)^-1*(C*(-1a)^2//3+2*C*x^2), x) == :(-1//4*C*log((-1a)^1//3+2x)+1//6*C*3^(1/2)*arctan(1//3*3^(1/2)*(1+-4*x*(-1a)^-1//3)))
@test integrate((a+b*x^3)^-1*(C*x^2+2*C*(a*b^-1)^2//3), x) == :(C*b^-1*log(x+(a*b^-1)^1//3)+-2//3*C*3^(1/2)*b^-1*arctan(1//3*3^(1/2)*(1+-2*x*(a*b^-1)^-1//3)))
@test integrate((a+-1*b*x^3)^-1*(C*x^2+2*C*(-1*a*b^-1)^2//3), x) == :(-1*C*b^-1*log(x+(-1*a*b^-1)^1//3)+2//3*C*3^(1/2)*b^-1*arctan(1//3*3^(1/2)*(1+-2*x*(-1*a*b^-1)^-1//3)))
@test integrate((a+b*x^3)^-1*(C*x^2+2*C*(-1*a*b^-1)^2//3), x) == :(C*b^-1*log((-1*a*b^-1)^1//3+-1x)+-2//3*C*3^(1/2)*b^-1*arctan(1//3*3^(1/2)*(1+2*x*(-1*a*b^-1)^-1//3)))
@test integrate((a+-1*b*x^3)^-1*(C*x^2+2*C*(a*b^-1)^2//3), x) == :(-1*C*b^-1*log((a*b^-1)^1//3+-1x)+2//3*C*3^(1/2)*b^-1*arctan(1//3*3^(1/2)*(1+2*x*(a*b^-1)^-1//3)))
@test integrate((a+b*x^3)^-1*(2*C*a^2//3+C*b^2//3*x^2), x) == :(C*b^-1//3*log(a^1//3+x*b^1//3)+-2//3*C*3^(1/2)*b^-1//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate((a+b*x^3)^-1*(-2*C*a^2//3+-1*C*x^2*(-1b)^2//3), x) == :(C*(-1b)^-1//3*log(a^1//3+-1*x*(-1b)^1//3)+-2//3*C*3^(1/2)*(-1b)^-1//3*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*x*(-1b)^1//3)))
@test integrate((-1+x^3)^-1*(-3+x^2), x) == :(-2//3*log(1+-1x)+5//6*log(1+x+x^2)+3^(1/2)*arctan(1//3*3^(1/2)*(1+2x)))
@test integrate((a+b*x^3)^-1*(2*C*a^2//3+B*x*b^2//3+B*a^1//3*b^1//3+C*b^2//3*x^2), x) == :(C*b^-1//3*log(a^1//3+x*b^1//3)+-1//3*3^(1/2)*(2*B*a^-1//3+2*C*b^-1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate((a+b*x^3)^-1*(-2*C*a^2//3+B*a^1//3*(-1b)^1//3+-1*B*x*(-1b)^2//3+-1*C*x^2*(-1b)^2//3), x) == :(C*(-1b)^-1//3*log(a^1//3+-1*x*(-1b)^1//3)+1//3*3^(1/2)*a^-1//3*b^-1*(2*B*b+2*C*a^1//3*(-1b)^2//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*x*(-1b)^1//3)))
@test integrate((-1*B^3+C^3*x^3)^-1*(B^2+C^2*x^2+B*C*x), x) == :(C^-1*log(B+-1*C*x))
@test integrate((a+b*x^3)^-1*(C*a^2//3+C*b^2//3*x^2+-1*C*x*a^1//3*b^1//3), x) == :(C*b^-1//3*log(a^1//3+x*b^1//3))
@test integrate((a+b*x^3)^-1*(B*x+B*(a*b^-1)^1//3+C*x^2+2*C*(a*b^-1)^2//3), x) == :(C*b^-1*log(x+(a*b^-1)^1//3)+-2//3*3^(1/2)*a^-1*(a*b^-1)^2//3*(B+C*(a*b^-1)^1//3)*arctan(1//3*3^(1/2)*(1+-2*x*(a*b^-1)^-1//3)))
@test integrate((a+-1*b*x^3)^-1*(B*x+B*(-1*a*b^-1)^1//3+C*x^2+2*C*(-1*a*b^-1)^2//3), x) == :(-1*C*b^-1*log(x+(-1*a*b^-1)^1//3)+1//3*3^(1/2)*b^-1*(-1*a*b^-1)^-1//3*(2B+2*C*(-1*a*b^-1)^1//3)*arctan(1//3*3^(1/2)*(1+-2*x*(-1*a*b^-1)^-1//3)))
@test integrate((a+b*x^3)^-1*(B*x+C*x^2+-1*B*(-1*a*b^-1)^1//3+2*C*(-1*a*b^-1)^2//3), x) == :(C*b^-1*log((-1*a*b^-1)^1//3+-1x)+1//3*3^(1/2)*b^-1*(-1*a*b^-1)^-1//3*(2B+-2*C*(-1*a*b^-1)^1//3)*arctan(1//3*3^(1/2)*(1+2*x*(-1*a*b^-1)^-1//3)))
@test integrate((a+-1*b*x^3)^-1*(B*x+C*x^2+-1*B*(a*b^-1)^1//3+2*C*(a*b^-1)^2//3), x) == :(-1*C*b^-1*log((a*b^-1)^1//3+-1x)+-2//3*3^(1/2)*a^-1*(a*b^-1)^2//3*(B+-1*C*(a*b^-1)^1//3)*arctan(1//3*3^(1/2)*(1+2*x*(a*b^-1)^-1//3)))
@test integrate((1+-1*x^3)^-1*(a+a*x+c*x^2), x) == :((-2//3*a+-1//3*c)*log(1+-1x)+(-1//3*c+1//3*a)*log(1+x+x^2))
@test integrate((1+-1*x^3)^-1*(a+b*x+c*x^2), x) == :((-1//3*c+1//6*a+1//6*b)*log(1+x+x^2)+-1*(1//3*a+1//3*b+1//3*c)*log(1+-1x)+1//3*3^(1/2)*(a+-1b)*arctan(1//3*3^(1/2)*(1+2x)))
@test integrate((1+-1*x^3)^-1*(1+x+x^2), x) == :(-1*log(1+-1x))
@test integrate((1+-1*x^3)^-1*(1+-1x+3*x^2), x) == :(-1*log(1+-1*x^3)+2//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+2x)))
@test integrate((1+-1*x^3)^-1*(1+x+4*x^2), x) == :(-1*log(1+x+x^2)+-2*log(1+-1x))
@test integrate((a+b*x^3)^3*(a*c+a*d*x+b*c*x^3+b*d*x^4), x) == :(c*x*a^4+(1/2)*d*a^4*x^2+1//13*c*b^4*x^13+1//14*d*b^4*x^14+b*c*a^3*x^4+2//5*a*c*b^3*x^10+3//4*d*a^2*b^2*x^8+4//5*b*d*a^3*x^5+4//11*a*d*b^3*x^11+6//7*c*a^2*b^2*x^7)
@test integrate((a+b*x^3)^2*(a*c+a*d*x+b*c*x^3+b*d*x^4), x) == :(c*x*a^3+(1/2)*d*a^3*x^2+1//10*c*b^3*x^10+1//11*d*b^3*x^11+3//4*b*c*a^2*x^4+3//5*b*d*a^2*x^5+3//7*a*c*b^2*x^7+3//8*a*d*b^2*x^8)
@test integrate((a+b*x^3)*(a*c+a*d*x+b*c*x^3+b*d*x^4), x) == :(c*x*a^2+(1/2)*d*a^2*x^2+1//7*c*b^2*x^7+1//8*d*b^2*x^8+(1/2)*a*b*c*x^4+2//5*a*b*d*x^5)
@test integrate((a+b*x^3)^-1*(a*c+a*d*x+b*c*x^3+b*d*x^4), x) == :(c*x+(1/2)*d*x^2)
@test integrate((a+b*x^3)^-2*(a*c+a*d*x+b*c*x^3+b*d*x^4), x) == :(-1//6*a^-2//3*b^-1//3*(c+-1*d*a^1//3*b^-1//3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-2//3*b^-2//3*(c*b^1//3+-1*d*a^1//3)*log(a^1//3+x*b^1//3)+-1//3*3^(1/2)*a^-2//3*b^-2//3*(c*b^1//3+d*a^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate((a+b*x^3)^-3*(a*c+a*d*x+b*c*x^3+b*d*x^4), x) == :(-1//18*a^-5//3*b^-2//3*(-1*d*a^1//3+2*c*b^1//3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*x*a^-1*(a+b*x^3)^-1*(c+d*x)+1//9*a^-5//3*b^-2//3*(-1*d*a^1//3+2*c*b^1//3)*log(a^1//3+x*b^1//3)+-1//9*3^(1/2)*a^-5//3*b^-2//3*(d*a^1//3+2*c*b^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate((a+b*x^3)^3//2*(a*c+a*d*x+b*c*x^3+b*d*x^4), x) == :((a+b*x^3)^5//2*(2//17*c*x+2//19*d*x^2)+30//46189*a*(a+b*x^3)^3//2*(187*d*x^2+247*c*x)+54//323323*a^2*(a+b*x^3)^(1/2)*(935*d*x^2+1729*c*x)+810//1729*d*a^3*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+-405//1729*d*3^1//4*a^10//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+54//323323*3^3//4*a^3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(1729*c*b^1//3+-1*d*a^1//3*(935+-935*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+b*x^3)^(1/2)*(a*c+a*d*x+b*c*x^3+b*d*x^4), x) == :((a+b*x^3)^3//2*(2//11*c*x+2//13*d*x^2)+18//5005*a*(a+b*x^3)^(1/2)*(55*d*x^2+91*c*x)+54//91*d*a^2*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+-27//91*d*3^1//4*a^7//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+18//5005*3^3//4*a^2*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(91*c*b^1//3+-1*d*a^1//3*(55+-55*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+b*x^3)^-1//2*(a*c+a*d*x+b*c*x^3+b*d*x^4), x) == :((a+b*x^3)^(1/2)*(2//5*c*x+2//7*d*x^2)+6//7*a*d*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+-3//7*d*3^1//4*a^4//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+2//35*a*3^3//4*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(7*c*b^1//3+-1*d*a^1//3*(5+-5*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+b*x^3)^-3//2*(a*c+a*d*x+b*c*x^3+b*d*x^4), x) == :(2*d*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+2//3*3^3//4*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(c*b^1//3+-1*d*a^1//3*(1+-1*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+-1*d*3^1//4*a^1//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+b*x^3)^-5//2*(a*c+a*d*x+b*c*x^3+b*d*x^4), x) == :(2//3*x*a^-1*(a+b*x^3)^-1//2*(c+d*x)+-2//3*d*a^-1*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+1//3*d*3^1//4*a^-2//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+2//9*3^3//4*a^-1*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(c*b^1//3+d*a^1//3*(1+-1*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+b*x^3)^-7//2*(a*c+a*d*x+b*c*x^3+b*d*x^4), x) == :(2//9*x*a^-1*(a+b*x^3)^-3//2*(c+d*x)+2//27*x*a^-2*(a+b*x^3)^-1//2*(7c+5*d*x)+-10//27*d*a^-2*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+2//81*3^3//4*a^-2*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(7*c*b^1//3+d*a^1//3*(5+-5*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+5//27*d*3^1//4*a^-5//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+b*x^3)^-9//2*(a*c+a*d*x+b*c*x^3+b*d*x^4), x) == :(2//15*x*a^-1*(a+b*x^3)^-5//2*(c+d*x)+2//135*x*a^-2*(a+b*x^3)^-3//2*(13c+11*d*x)+2//405*x*a^-3*(a+b*x^3)^-1//2*(91c+55*d*x)+-22//81*d*a^-3*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+2//1215*3^3//4*a^-3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(91*c*b^1//3+d*a^1//3*(55+-55*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+11//81*d*3^1//4*a^-8//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+b*x^3)^-1//2*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(2//3*e*b^-1*(a+b*x^3)^(1/2)+1//7*b^-5//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(-8*a*g+14*b*d)+2//5*f*x*b^-1*(a+b*x^3)^(1/2)+2//7*g*b^-1*x^2*(a+b*x^3)^(1/2)+2//105*3^3//4*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(7*b^1//3*(-2*a*f+5*b*c)+-1*a^1//3*(5+-5*3^(1/2))*(-4*a*g+7*b*d))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+-1//7*3^1//4*a^1//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-4*a*g+7*b*d)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+b*x^3)^-3//2*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(-2//3*e*a^-1*b^-1*(a+b*x^3)^(1/2)+-1//3*a^-1*b^-5//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(-8*a*g+2*b*d)+2//3*x*a^-1*b^-1*(a+b*x^3)^-1//2*(b*c+x*(b*d+-1*a*g)+-1*a*f+b*e*x^2)+1//3*3^1//4*a^-2//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(b*d+-4*a*g)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+2//9*3^3//4*a^-1*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(b^1//3*(b*c+2*a*f)+a^1//3*(1+-1*3^(1/2))*(b*d+-4*a*g))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+b*x^3)^-5//2*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(-1//27*a^-2*b^-1*(a+b*x^3)^-1//2*(-2*x*(x*(4*a*g+5*b*d)+2*a*f+7*b*c)+6*a*e)+-1//27*a^-2*b^-5//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(8*a*g+10*b*d)+2//9*x*a^-1*b^-1*(a+b*x^3)^-3//2*(b*c+x*(b*d+-1*a*g)+-1*a*f+b*e*x^2)+1//27*3^1//4*a^-5//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(4*a*g+5*b*d)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+2//81*3^3//4*a^-2*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(b^1//3*(2*a*f+7*b*c)+a^1//3*(1+-1*3^(1/2))*(4*a*g+5*b*d))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+b*x^3)^-7//2*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(-1//135*a^-2*b^-1*(a+b*x^3)^-3//2*(-2*x*(x*(4*a*g+11*b*d)+2*a*f+13*b*c)+18*a*e)+-1//81*a^-3*b^-5//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(8*a*g+22*b*d)+2//15*x*a^-1*b^-1*(a+b*x^3)^-5//2*(b*c+x*(b*d+-1*a*g)+-1*a*f+b*e*x^2)+2//405*x*a^-3*b^-1*(a+b*x^3)^-1//2*(x*(20*a*g+55*b*d)+14*a*f+91*b*c)+1//81*3^1//4*a^-8//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(4*a*g+11*b*d)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+2//1215*3^3//4*a^-3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(7*b^1//3*(2*a*f+13*b*c)+a^1//3*(5+-5*3^(1/2))*(4*a*g+11*b*d))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+b*x)^2*(c+d*x^3)^-1, x) == :(1//3*b^2*d^-1*log(c+d*x^3)+-1//3*a*c^-2//3*d^-2//3*(-1*a*d^1//3+2*b*c^1//3)*log(c^1//3+x*d^1//3)+1//6*a*c^-2//3*d^-2//3*(-1*a*d^1//3+2*b*c^1//3)*log(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3)+-1//3*a*3^(1/2)*c^-2//3*d^-2//3*(a*d^1//3+2*b*c^1//3)*arctan(1//3*3^(1/2)*c^-1//3*(c^1//3+-2*x*d^1//3)))
@test integrate((a+b*x)^3*(c+d*x^3)^-1, x) == :(x*b^3*d^-1+a*b^2*d^-1*log(c+d*x^3)+-1//3*c^-2//3*d^-4//3*(c*b^3+-1*d*a^3+3*b*a^2*c^1//3*d^2//3)*log(c^1//3+x*d^1//3)+1//6*c^-2//3*d^-4//3*(c*b^3+-1*d*a^3+3*b*a^2*c^1//3*d^2//3)*log(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3)+1//3*3^(1/2)*c^-2//3*d^-4//3*(c*b^3+-1*d*a^3+-3*b*a^2*c^1//3*d^2//3)*arctan(1//3*3^(1/2)*c^-1//3*(c^1//3+-2*x*d^1//3)))
@test integrate((a+b*x)^4*(c+d*x^3)^-1, x) == :((1/2)*b^4*d^-1*x^2+2*a^2*b^2*d^-1*log(c+d*x^3)+4*a*x*b^3*d^-1+-1//6*c^-2//3*d^-5//3*(-1*d^1//3*(-1*d*a^4+4*a*c*b^3)+b*c^1//3*(c*b^3+-4*d*a^3))*log(c^2//3+d^2//3*x^2+-1*x*c^1//3*d^1//3)+1//3*c^-2//3*d^-5//3*(-1*d^1//3*(-1*d*a^4+4*a*c*b^3)+b*c^1//3*(c*b^3+-4*d*a^3))*log(c^1//3+x*d^1//3)+1//3*3^(1/2)*c^-2//3*d^-5//3*(b^4*c^4//3+-1*a^4*d^4//3+-4*b*d*a^3*c^1//3+4*a*c*b^3*d^1//3)*arctan(1//3*3^(1/2)*c^-1//3*(c^1//3+-2*x*d^1//3)))
@test integrate((d+e*x^3)^-1*(a+b*x+c*x^2)^2, x) == :((1/2)*c^2*e^-1*x^2+1//3*e^-1*(b^2+2*a*c)*log(d+e*x^3)+2*b*c*x*e^-1+-1//3*d^-2//3*e^-5//3*(e^1//3*(-1*e*a^2+2*b*c*d)+-1*d^1//3*(d*c^2+-2*a*b*e))*log(d^1//3+x*e^1//3)+1//6*d^-2//3*e^-5//3*(e^1//3*(-1*e*a^2+2*b*c*d)+-1*d^1//3*(d*c^2+-2*a*b*e))*log(d^2//3+e^2//3*x^2+-1*x*d^1//3*e^1//3)+1//3*3^(1/2)*d^-2//3*e^-5//3*(c^2*d^4//3+-1*a*e*(a*e^1//3+2*b*d^1//3)+2*b*c*d*e^1//3)*arctan(1//3*3^(1/2)*d^-1//3*(d^1//3+-2*x*e^1//3)))
@test integrate((d+e*x^3)^-1*(a+b*x+c*x^2)^3, x) == :(-1*x*e^-2*(d*c^3+-1*e*b^3+-6*a*b*c*e)+-1*e^-2*(b*d*c^2+-1*a*e*b^2+-1*c*e*a^2)*log(d+e*x^3)+1//4*c^3*e^-1*x^4+b*c^2*e^-1*x^3+-1//6*d^-2//3*e^-7//3*(c^3*d^2+-1*e*(d*b^3+-1*e*a^3)+3*d^1//3*e^2//3*(a*d*c^2+c*d*b^2+-1*b*e*a^2)+-6*a*b*c*d*e)*log(d^2//3+e^2//3*x^2+-1*x*d^1//3*e^1//3)+1//3*d^-2//3*e^-7//3*(c^3*d^2+-1*e*(d*b^3+-1*e*a^3)+3*d^1//3*e^2//3*(a*d*c^2+c*d*b^2+-1*b*e*a^2)+-6*a*b*c*d*e)*log(d^1//3+x*e^1//3)+3//2*c*e^-1*x^2*(b^2+a*c)+-1//3*3^(1/2)*d^-2//3*e^-7//3*(a^3*e^2+c^3*d^2+-1*d*e*b^3+-3*a*c^2*d^4//3*e^2//3+-3*c*b^2*d^4//3*e^2//3+3*b*a^2*d^1//3*e^5//3+-6*a*b*c*d*e)*arctan(1//3*3^(1/2)*d^-1//3*(d^1//3+-2*x*e^1//3)))
@test integrate((d+e*x^3)^-1*(a+b*x+c*x^2)^4, x) == :(-1*x*e^-2*(-4*a*e*b^3+4*a*d*c^3+6*d*b^2*c^2+-12*b*c*e*a^2)+-1//2*e^-2*x^2*(-1*e*b^4+-6*e*a^2*c^2+4*b*d*c^3+-12*a*c*e*b^2)+1//3*e^-3*(c^4*d^2+-4*c*e*(d*b^3+-1*e*a^3)+6*a^2*b^2*e^2+-12*a*b*d*e*c^2)*log(d+e*x^3)+1//6*c^4*e^-1*x^6+(1/2)*c^2*e^-1*x^4*(3*b^2+2*a*c)+-1//3*c*e^-2*x^3*(d*c^3+-4*e*b^3+-12*a*b*c*e)+-1//6*d^-2//3*e^-8//3*(d^1//3*(-4*b*(a^3*e^2+c^3*d^2)+d*e*b^4+6*d*e*a^2*c^2+12*a*c*d*e*b^2)+e^1//3*(a^4*e^2+4*a*c^3*d^2+6*b^2*c^2*d^2+-4*a*d*e*b^3+-12*b*c*d*e*a^2))*log(d^2//3+e^2//3*x^2+-1*x*d^1//3*e^1//3)+1//3*d^-2//3*e^-8//3*(d^1//3*(-4*b*(a^3*e^2+c^3*d^2)+d*e*b^4+6*d*e*a^2*c^2+12*a*c*d*e*b^2)+e^1//3*(a^4*e^2+4*a*c^3*d^2+6*b^2*c^2*d^2+-4*a*d*e*b^3+-12*b*c*d*e*a^2))*log(d^1//3+x*e^1//3)+4//5*b*c^3*e^-1*x^5+-1//3*3^(1/2)*d^-2//3*e^-8//3*(a*e^1//3+b*d^1//3)*(-1*e*(d*b^3+-1*e*a^3+-3*b*a^2*d^1//3*e^2//3+3*a*b^2*d^2//3*e^1//3)+4*c^3*d^2+6*c^2*(b*d^5//3*e^1//3+-1*a*d^4//3*e^2//3)+-12*a*b*c*d*e)*arctan(1//3*3^(1/2)*d^-1//3*(d^1//3+-2*x*e^1//3)))
@test integrate((1+x^3)^-1*(x^4+2*x^2), x) == :((1/2)*x^2+(1/2)*log(1+x^2+-1x)+1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x))+log(1+x))
@test integrate((1+-1*x^3)^-1*(x^4+2*x^2), x) == :(-1*log(1+-1x)+-1//2*x^2+-1//2*log(1+x+x^2)+-1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+2x)))
@test integrate((1+x^3)^-1*(1+-1x+4*x^3), x) == :(4x+-2//3*log(1+x)+1//3*log(1+x^2+-1x)+4//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x)))
@test integrate((1+x^3)^-1//2*(1+x+3^(1/2)), x) == :(2*(1+x^3)^(1/2)*(1+x+3^(1/2))^-1+-1*3^1//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+x)*Elliptic.E(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2))+4*3^1//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((1+-1*x^3)^-1//2*(1+3^(1/2)+-1x), x) == :(-2*(1+-1*x^3)^(1/2)*(1+3^(1/2)+-1x)^-1+3^1//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+-1x)*Elliptic.E(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2))+-4*3^1//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+-1x)*Elliptic.F(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((-1+x^3)^-1//2*(1+3^(1/2)+-1x), x) == :(2*(-1+x^3)^(1/2)*(1+-1x+-1*3^(1/2))^-1+-1*3^1//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+-1x)*Elliptic.E(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2)))
@test integrate((-1+-1*x^3)^-1//2*(1+x+3^(1/2)), x) == :(-2*(-1+-1*x^3)^(1/2)*(1+x+-1*3^(1/2))^-1+3^1//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+x)*Elliptic.E(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2)))
@test integrate((a+b*x^3)^-1//2*(x*b^1//3+a^1//3*(1+3^(1/2))), x) == :(2*b^-1//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+-1*3^1//4*a^1//3*b^-1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+4*3^1//4*a^1//3*b^-1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+-1*b*x^3)^-1//2*(a^1//3*(1+3^(1/2))+-1*x*b^1//3), x) == :(-2*b^-1//3*(a+-1*b*x^3)^(1/2)*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-1+3^1//4*a^1//3*b^-1//3*((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+-1*b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)),-7+-4*3^(1/2))+-4*3^1//4*a^1//3*b^-1//3*((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+-1*b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)),-7+-4*3^(1/2)))
@test integrate((-1a+b*x^3)^-1//2*(a^1//3*(1+3^(1/2))+-1*x*b^1//3), x) == :(2*b^-1//3*(-1a+b*x^3)^(1/2)*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-1+-1*3^1//4*a^1//3*b^-1//3*((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(-1a+b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*Elliptic.E(arcsin((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)),-7+4*3^(1/2)))
@test integrate((-1a+-1*b*x^3)^-1//2*(x*b^1//3+a^1//3*(1+3^(1/2))), x) == :(-2*b^-1//3*(-1a+-1*b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-1+3^1//4*a^1//3*b^-1//3*((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(-1a+-1*b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+b*x^3)^-1//2*(1+3^(1/2)+x*(b*a^-1)^1//3), x) == :(2*b^-2//3*(b*a^-1)^1//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+2//3*3^3//4*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(b^1//3*(1+3^(1/2))+-1*a^1//3*(b*a^-1)^1//3*(1+-1*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+-1*3^1//4*a^1//3*b^-2//3*(b*a^-1)^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+-1*b*x^3)^-1//2*(1+3^(1/2)+-1*x*(b*a^-1)^1//3), x) == :(-2*b^-2//3*(b*a^-1)^1//3*(a+-1*b*x^3)^(1/2)*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-1+-2//3*3^3//4*b^-2//3*((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+-1*b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*(b^1//3*(1+3^(1/2))+-1*a^1//3*(b*a^-1)^1//3*(1+-1*3^(1/2)))*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)),-7+-4*3^(1/2))+3^1//4*a^1//3*b^-2//3*(b*a^-1)^1//3*((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+-1*b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)),-7+-4*3^(1/2)))
@test integrate((-1a+b*x^3)^-1//2*(1+3^(1/2)+-1*x*(b*a^-1)^1//3), x) == :(2*b^-1*(b*a^-1)^2//3*(-1a+b*x^3)^(1/2)*(1+-1*3^(1/2)+-1*x*(b*a^-1)^1//3)^-1+-1*3^1//4*(b*a^-1)^-1//3*((1+-1*3^(1/2)+-1*x*(b*a^-1)^1//3)^-2*(1+x*(b*a^-1)^1//3+x^2*(b*a^-1)^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*x*(b*a^-1)^1//3)^-2*(1+-1*x*(b*a^-1)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(-1a+b*x^3)^-1//2*(1+-1*x*(b*a^-1)^1//3)*Elliptic.E(arcsin((1+-1*3^(1/2)+-1*x*(b*a^-1)^1//3)^-1*(1+3^(1/2)+-1*x*(b*a^-1)^1//3)),-7+4*3^(1/2)))
@test integrate((-1a+-1*b*x^3)^-1//2*(1+3^(1/2)+x*(b*a^-1)^1//3), x) == :(-2*b^-1*(b*a^-1)^2//3*(-1a+-1*b*x^3)^(1/2)*(1+-1*3^(1/2)+x*(b*a^-1)^1//3)^-1+3^1//4*(b*a^-1)^-1//3*((1+-1*3^(1/2)+x*(b*a^-1)^1//3)^-2*(1+x^2*(b*a^-1)^2//3+-1*x*(b*a^-1)^1//3))^(1/2)*(-1*(1+-1*3^(1/2)+x*(b*a^-1)^1//3)^-2*(1+x*(b*a^-1)^1//3))^-1//2*(2+3^(1/2))^(1/2)*(-1a+-1*b*x^3)^-1//2*(1+x*(b*a^-1)^1//3)*Elliptic.E(arcsin((1+-1*3^(1/2)+x*(b*a^-1)^1//3)^-1*(1+3^(1/2)+x*(b*a^-1)^1//3)),-7+4*3^(1/2)))
@test integrate((1+x^3)^-1//2*(1+x+-1*3^(1/2)), x) == :(2*(1+x^3)^(1/2)*(1+x+3^(1/2))^-1+-1*3^1//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+x)*Elliptic.E(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((1+-1*x^3)^-1//2*(1+-1x+-1*3^(1/2)), x) == :(-2*(1+-1*x^3)^(1/2)*(1+3^(1/2)+-1x)^-1+3^1//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+-1x)*Elliptic.E(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((-1+x^3)^-1//2*(1+-1x+-1*3^(1/2)), x) == :(2*(-1+x^3)^(1/2)*(1+-1x+-1*3^(1/2))^-1+-1*3^1//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+-1x)*Elliptic.E(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2))+4*3^1//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+-1x)*Elliptic.F(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2)))
@test integrate((-1+-1*x^3)^-1//2*(1+x+-1*3^(1/2)), x) == :(-2*(-1+-1*x^3)^(1/2)*(1+x+-1*3^(1/2))^-1+3^1//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+x)*Elliptic.E(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2))+-4*3^1//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2)))
@test integrate((1+x^3)^-1//2*(-1+3^(1/2)+-1x), x) == :(-2*(1+x^3)^(1/2)*(1+x+3^(1/2))^-1+3^1//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+x)*Elliptic.E(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((1+-1*x^3)^-1//2*(-1+x+3^(1/2)), x) == :(2*(1+-1*x^3)^(1/2)*(1+3^(1/2)+-1x)^-1+-1*3^1//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+-1x)*Elliptic.E(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((-1+x^3)^-1//2*(-1+x+3^(1/2)), x) == :(-2*(-1+x^3)^(1/2)*(1+-1x+-1*3^(1/2))^-1+3^1//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+-1x)*Elliptic.E(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2))+-4*3^1//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+-1x)*Elliptic.F(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2)))
@test integrate((-1+-1*x^3)^-1//2*(-1+3^(1/2)+-1x), x) == :(2*(-1+-1*x^3)^(1/2)*(1+x+-1*3^(1/2))^-1+-1*3^1//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+x)*Elliptic.E(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2))+4*3^1//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2)))
@test integrate((a+b*x^3)^-1//2*(x*b^1//3+a^1//3*(1+-1*3^(1/2))), x) == :(2*b^-1//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+-1*3^1//4*a^1//3*b^-1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+-1*b*x^3)^-1//2*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3), x) == :(-2*b^-1//3*(a+-1*b*x^3)^(1/2)*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-1+3^1//4*a^1//3*b^-1//3*((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+-1*b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)),-7+-4*3^(1/2)))
@test integrate((-1a+b*x^3)^-1//2*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3), x) == :(2*b^-1//3*(-1a+b*x^3)^(1/2)*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-1+-1*3^1//4*a^1//3*b^-1//3*((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(-1a+b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*Elliptic.E(arcsin((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)),-7+4*3^(1/2))+4*3^1//4*a^1//3*b^-1//3*((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(-1a+b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*Elliptic.F(arcsin((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)),-7+4*3^(1/2)))
@test integrate((-1a+-1*b*x^3)^-1//2*(x*b^1//3+a^1//3*(1+-1*3^(1/2))), x) == :(-2*b^-1//3*(-1a+-1*b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-1+3^1//4*a^1//3*b^-1//3*((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(-1a+-1*b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+-4*3^1//4*a^1//3*b^-1//3*((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(-1a+-1*b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+b*x^3)^-1//2*(1+-1*3^(1/2)+x*(b*a^-1)^1//3), x) == :(2*b^-1*(b*a^-1)^2//3*(a+b*x^3)^(1/2)*(1+3^(1/2)+x*(b*a^-1)^1//3)^-1+-1*3^1//4*(b*a^-1)^-1//3*((1+3^(1/2)+x*(b*a^-1)^1//3)^-2*(1+x*(b*a^-1)^1//3))^-1//2*((1+3^(1/2)+x*(b*a^-1)^1//3)^-2*(1+x^2*(b*a^-1)^2//3+-1*x*(b*a^-1)^1//3))^(1/2)*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(1+x*(b*a^-1)^1//3)*Elliptic.E(arcsin((1+3^(1/2)+x*(b*a^-1)^1//3)^-1*(1+-1*3^(1/2)+x*(b*a^-1)^1//3)),-7+-4*3^(1/2)))
@test integrate((a+-1*b*x^3)^-1//2*(1+-1*3^(1/2)+-1*x*(b*a^-1)^1//3), x) == :(-2*b^-1*(b*a^-1)^2//3*(a+-1*b*x^3)^(1/2)*(1+3^(1/2)+-1*x*(b*a^-1)^1//3)^-1+3^1//4*(b*a^-1)^-1//3*((1+3^(1/2)+-1*x*(b*a^-1)^1//3)^-2*(1+-1*x*(b*a^-1)^1//3))^-1//2*((1+3^(1/2)+-1*x*(b*a^-1)^1//3)^-2*(1+x*(b*a^-1)^1//3+x^2*(b*a^-1)^2//3))^(1/2)*(2+-1*3^(1/2))^(1/2)*(a+-1*b*x^3)^-1//2*(1+-1*x*(b*a^-1)^1//3)*Elliptic.E(arcsin((1+3^(1/2)+-1*x*(b*a^-1)^1//3)^-1*(1+-1*3^(1/2)+-1*x*(b*a^-1)^1//3)),-7+-4*3^(1/2)))
@test integrate((-1a+b*x^3)^-1//2*(1+-1*3^(1/2)+-1*x*(b*a^-1)^1//3), x) == :(2*b^-2//3*(b*a^-1)^1//3*(-1a+b*x^3)^(1/2)*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-1+-2//3*3^3//4*b^-2//3*((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(-1a+b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*(b^1//3*(1+-1*3^(1/2))+-1*a^1//3*(b*a^-1)^1//3*(1+3^(1/2)))*Elliptic.F(arcsin((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)),-7+4*3^(1/2))+-1*3^1//4*a^1//3*b^-2//3*(b*a^-1)^1//3*((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(-1a+b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*Elliptic.E(arcsin((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)),-7+4*3^(1/2)))
@test integrate((-1a+-1*b*x^3)^-1//2*(1+-1*3^(1/2)+x*(b*a^-1)^1//3), x) == :(-2*b^-2//3*(b*a^-1)^1//3*(-1a+-1*b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-1+2//3*3^3//4*b^-2//3*((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(-1a+-1*b*x^3)^-1//2*(a^1//3+x*b^1//3)*(b^1//3*(1+-1*3^(1/2))+-1*a^1//3*(b*a^-1)^1//3*(1+3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+3^1//4*a^1//3*b^-2//3*(b*a^-1)^1//3*((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(-1a+-1*b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((a+b*x^3)^-1//2*(c+d*x), x) == :(2*d*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+2//3*3^3//4*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(c*b^1//3+-1*d*a^1//3*(1+-1*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+-1*d*3^1//4*a^1//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+-1*b*x^3)^-1//2*(c+d*x), x) == :(2*d*b^-2//3*(a+-1*b*x^3)^(1/2)*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-1+-2//3*3^3//4*b^-2//3*((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+-1*b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*(c*b^1//3+d*a^1//3*(1+-1*3^(1/2)))*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)),-7+-4*3^(1/2))+-1*d*3^1//4*a^1//3*b^-2//3*((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+-1*b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*Elliptic.E(arcsin((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)),-7+-4*3^(1/2)))
@test integrate((-1a+b*x^3)^-1//2*(c+d*x), x) == :(-2*d*b^-2//3*(-1a+b*x^3)^(1/2)*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-1+-2//3*3^3//4*b^-2//3*((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(-1a+b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*(c*b^1//3+d*a^1//3*(1+3^(1/2)))*Elliptic.F(arcsin((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)),-7+4*3^(1/2))+d*3^1//4*a^1//3*b^-2//3*((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(-1a+b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*Elliptic.E(arcsin((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)),-7+4*3^(1/2)))
@test integrate((-1a+-1*b*x^3)^-1//2*(c+d*x), x) == :(-2*d*b^-2//3*(-1a+-1*b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-1+2//3*3^3//4*b^-2//3*((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(-1a+-1*b*x^3)^-1//2*(a^1//3+x*b^1//3)*(c*b^1//3+-1*d*a^1//3*(1+3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2))+d*3^1//4*a^1//3*b^-2//3*((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(-1a+-1*b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((1+x^3)^-1//2*(c+d*x), x) == :(2*d*(1+x^3)^(1/2)*(1+x+3^(1/2))^-1+-1*d*3^1//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+x)*Elliptic.E(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2))+2//3*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+x)*(c+-1*d*(1+-1*3^(1/2)))*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((1+-1*x^3)^-1//2*(c+d*x), x) == :(2*d*(1+-1*x^3)^(1/2)*(1+3^(1/2)+-1x)^-1+-1*d*3^1//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+-1x)*Elliptic.E(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2))+-2//3*3^3//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+-1x)*(c+d+-1*d*3^(1/2))*Elliptic.F(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((-1+x^3)^-1//2*(c+d*x), x) == :(-2*d*(-1+x^3)^(1/2)*(1+-1x+-1*3^(1/2))^-1+d*3^1//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+-1x)*Elliptic.E(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2))+-2//3*3^3//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+-1x)*(c+d+d*3^(1/2))*Elliptic.F(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2)))
@test integrate((-1+-1*x^3)^-1//2*(c+d*x), x) == :(-2*d*(-1+-1*x^3)^(1/2)*(1+x+-1*3^(1/2))^-1+d*3^1//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+x)*Elliptic.E(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2))+2//3*3^3//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+x)*(c+-1*d*(1+3^(1/2)))*Elliptic.F(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2)))
@test integrate((a+-1*b*x^4)^-1*(c+d*x), x) == :((1/2)*c*a^-3//4*b^-1//4*arctan(x*a^-1//4*b^1//4)+(1/2)*c*a^-3//4*b^-1//4*arctanh(x*a^-1//4*b^1//4)+(1/2)*d*a^-1//2*b^-1//2*arctanh(a^-1//2*b^(1/2)*x^2))
@test integrate((a+b*x^4)^-1*(c+d*x), x) == :((1/2)*d*a^-1//2*b^-1//2*arctan(a^-1//2*b^(1/2)*x^2)+-1//4*c*2^(1/2)*a^-3//4*b^-1//4*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//8*c*2^(1/2)*a^-3//4*b^-1//4*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//4*c*2^(1/2)*a^-3//4*b^-1//4*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//8*c*2^(1/2)*a^-3//4*b^-1//4*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate((a+-1*b*x^4)^-2*(c+d*x), x) == :(1//4*d*a^-3//2*b^-1//2*arctanh(a^-1//2*b^(1/2)*x^2)+1//4*x*a^-1*(a+-1*b*x^4)^-1*(c+d*x)+3//8*c*a^-7//4*b^-1//4*arctan(x*a^-1//4*b^1//4)+3//8*c*a^-7//4*b^-1//4*arctanh(x*a^-1//4*b^1//4))
@test integrate((a+b*x^4)^-2*(c+d*x), x) == :(1//4*d*a^-3//2*b^-1//2*arctan(a^-1//2*b^(1/2)*x^2)+1//4*x*a^-1*(a+b*x^4)^-1*(c+d*x)+-3//16*c*2^(1/2)*a^-7//4*b^-1//4*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-3//32*c*2^(1/2)*a^-7//4*b^-1//4*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+3//16*c*2^(1/2)*a^-7//4*b^-1//4*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+3//32*c*2^(1/2)*a^-7//4*b^-1//4*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate((a+-1*b*x^4)^-3*(c+d*x), x) == :(1//8*x*a^-1*(a+-1*b*x^4)^-2*(c+d*x)+1//32*x*a^-2*(a+-1*b*x^4)^-1*(7c+6*d*x)+3//16*d*a^-5//2*b^-1//2*arctanh(a^-1//2*b^(1/2)*x^2)+21//64*c*a^-11//4*b^-1//4*arctan(x*a^-1//4*b^1//4)+21//64*c*a^-11//4*b^-1//4*arctanh(x*a^-1//4*b^1//4))
@test integrate((a+b*x^4)^-3*(c+d*x), x) == :(1//8*x*a^-1*(a+b*x^4)^-2*(c+d*x)+1//32*x*a^-2*(a+b*x^4)^-1*(7c+6*d*x)+3//16*d*a^-5//2*b^-1//2*arctan(a^-1//2*b^(1/2)*x^2)+-21//128*c*2^(1/2)*a^-11//4*b^-1//4*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-21//256*c*2^(1/2)*a^-11//4*b^-1//4*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+21//128*c*2^(1/2)*a^-11//4*b^-1//4*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+21//256*c*2^(1/2)*a^-11//4*b^-1//4*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate((a+-1*b*x^4)^-4*(c+d*x), x) == :(1//12*x*a^-1*(a+-1*b*x^4)^-3*(c+d*x)+1//96*x*a^-2*(a+-1*b*x^4)^-2*(11c+10*d*x)+1//384*x*a^-3*(a+-1*b*x^4)^-1*(77c+60*d*x)+5//32*d*a^-7//2*b^-1//2*arctanh(a^-1//2*b^(1/2)*x^2)+77//256*c*a^-15//4*b^-1//4*arctan(x*a^-1//4*b^1//4)+77//256*c*a^-15//4*b^-1//4*arctanh(x*a^-1//4*b^1//4))
@test integrate((a+b*x^4)^-4*(c+d*x), x) == :(1//12*x*a^-1*(a+b*x^4)^-3*(c+d*x)+1//96*x*a^-2*(a+b*x^4)^-2*(11c+10*d*x)+1//384*x*a^-3*(a+b*x^4)^-1*(77c+60*d*x)+5//32*d*a^-7//2*b^-1//2*arctan(a^-1//2*b^(1/2)*x^2)+-77//512*c*2^(1/2)*a^-15//4*b^-1//4*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-77//1024*c*2^(1/2)*a^-15//4*b^-1//4*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+77//512*c*2^(1/2)*a^-15//4*b^-1//4*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+77//1024*c*2^(1/2)*a^-15//4*b^-1//4*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate((1+-1*x^4)^-1*(c+d*x), x) == :((1/2)*c*arctan(x)+(1/2)*c*arctanh(x)+(1/2)*d*arctanh(x^2))
@test integrate((1+x^4)^-1*(c+d*x), x) == :((1/2)*d*arctan(x^2)+-1//4*c*2^(1/2)*arctan(1+-1*x*2^(1/2))+-1//8*c*2^(1/2)*log(1+x^2+-1*x*2^(1/2))+1//4*c*2^(1/2)*arctan(1+x*2^(1/2))+1//8*c*2^(1/2)*log(1+x^2+x*2^(1/2)))
@test integrate((a+-1*b*x^4)^-1*(c+d*x+e*x^2), x) == :((1/2)*d*a^-1//2*b^-1//2*arctanh(a^-1//2*b^(1/2)*x^2)+(1/2)*a^-3//4*b^-3//4*(c*b^(1/2)+e*a^(1/2))*arctanh(x*a^-1//4*b^1//4)+(1/2)*a^-3//4*b^-3//4*(c*b^(1/2)+-1*e*a^(1/2))*arctan(x*a^-1//4*b^1//4))
@test integrate((a+b*x^4)^-1*(c+d*x+e*x^2), x) == :((1/2)*d*a^-1//2*b^-1//2*arctan(a^-1//2*b^(1/2)*x^2)+-1//4*2^(1/2)*a^-3//4*b^-3//4*(c*b^(1/2)+e*a^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//8*2^(1/2)*a^-3//4*b^-3//4*(c*b^(1/2)+-1*e*a^(1/2))*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//4*2^(1/2)*a^-3//4*b^-3//4*(c*b^(1/2)+e*a^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//8*2^(1/2)*a^-3//4*b^-3//4*(c*b^(1/2)+-1*e*a^(1/2))*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate((a+-1*b*x^4)^-2*(c+d*x+e*x^2), x) == :(1//4*d*a^-3//2*b^-1//2*arctanh(a^-1//2*b^(1/2)*x^2)+1//4*x*a^-1*(a+-1*b*x^4)^-1*(c+d*x+e*x^2)+1//8*a^-7//4*b^-3//4*(e*a^(1/2)+3*c*b^(1/2))*arctanh(x*a^-1//4*b^1//4)+1//8*a^-7//4*b^-3//4*(-1*e*a^(1/2)+3*c*b^(1/2))*arctan(x*a^-1//4*b^1//4))
@test integrate((a+b*x^4)^-2*(c+d*x+e*x^2), x) == :(1//4*d*a^-3//2*b^-1//2*arctan(a^-1//2*b^(1/2)*x^2)+1//4*x*a^-1*(a+b*x^4)^-1*(c+d*x+e*x^2)+-1//16*2^(1/2)*a^-7//4*b^-3//4*(e*a^(1/2)+3*c*b^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//32*2^(1/2)*a^-7//4*b^-3//4*(-1*e*a^(1/2)+3*c*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//16*2^(1/2)*a^-7//4*b^-3//4*(e*a^(1/2)+3*c*b^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//32*2^(1/2)*a^-7//4*b^-3//4*(-1*e*a^(1/2)+3*c*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate((a+-1*b*x^4)^-3*(c+d*x+e*x^2), x) == :(1//8*x*a^-1*(a+-1*b*x^4)^-2*(c+d*x+e*x^2)+1//32*x*a^-2*(a+-1*b*x^4)^-1*(7c+5*e*x^2+6*d*x)+1//64*a^-11//4*b^-3//4*(-5*e*a^(1/2)+21*c*b^(1/2))*arctan(x*a^-1//4*b^1//4)+1//64*a^-11//4*b^-3//4*(5*e*a^(1/2)+21*c*b^(1/2))*arctanh(x*a^-1//4*b^1//4)+3//16*d*a^-5//2*b^-1//2*arctanh(a^-1//2*b^(1/2)*x^2))
@test integrate((a+b*x^4)^-3*(c+d*x+e*x^2), x) == :(1//8*x*a^-1*(a+b*x^4)^-2*(c+d*x+e*x^2)+1//32*x*a^-2*(a+b*x^4)^-1*(7c+5*e*x^2+6*d*x)+3//16*d*a^-5//2*b^-1//2*arctan(a^-1//2*b^(1/2)*x^2)+-1//128*2^(1/2)*a^-11//4*b^-3//4*(5*e*a^(1/2)+21*c*b^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//256*2^(1/2)*a^-11//4*b^-3//4*(-5*e*a^(1/2)+21*c*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//128*2^(1/2)*a^-11//4*b^-3//4*(5*e*a^(1/2)+21*c*b^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//256*2^(1/2)*a^-11//4*b^-3//4*(-5*e*a^(1/2)+21*c*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate((a+-1*b*x^4)^-4*(c+d*x+e*x^2), x) == :(1//12*x*a^-1*(a+-1*b*x^4)^-3*(c+d*x+e*x^2)+1//96*x*a^-2*(a+-1*b*x^4)^-2*(11c+9*e*x^2+10*d*x)+1//256*a^-15//4*b^-3//4*(-15*e*a^(1/2)+77*c*b^(1/2))*arctan(x*a^-1//4*b^1//4)+1//256*a^-15//4*b^-3//4*(15*e*a^(1/2)+77*c*b^(1/2))*arctanh(x*a^-1//4*b^1//4)+1//384*x*a^-3*(a+-1*b*x^4)^-1*(77c+45*e*x^2+60*d*x)+5//32*d*a^-7//2*b^-1//2*arctanh(a^-1//2*b^(1/2)*x^2))
@test integrate((a+b*x^4)^-4*(c+d*x+e*x^2), x) == :(1//12*x*a^-1*(a+b*x^4)^-3*(c+d*x+e*x^2)+1//96*x*a^-2*(a+b*x^4)^-2*(11c+9*e*x^2+10*d*x)+1//384*x*a^-3*(a+b*x^4)^-1*(77c+45*e*x^2+60*d*x)+5//32*d*a^-7//2*b^-1//2*arctan(a^-1//2*b^(1/2)*x^2)+-1//512*2^(1/2)*a^-15//4*b^-3//4*(15*e*a^(1/2)+77*c*b^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//1024*2^(1/2)*a^-15//4*b^-3//4*(-15*e*a^(1/2)+77*c*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//512*2^(1/2)*a^-15//4*b^-3//4*(15*e*a^(1/2)+77*c*b^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//1024*2^(1/2)*a^-15//4*b^-3//4*(-15*e*a^(1/2)+77*c*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate(a*(e+f*x^4)^2, x) == :(a*x*e^2+1//9*a*f^2*x^9+2//5*a*e*f*x^5)
@test integrate(b*x*(e+f*x^4)^2, x) == :((1/2)*b*e^2*x^2+1//10*b*f^2*x^10+1//3*b*e*f*x^6)
@test integrate((e+f*x^4)^2*(a+b*x), x) == :(a*x*e^2+(1/2)*b*e^2*x^2+1//9*a*f^2*x^9+1//10*b*f^2*x^10+1//3*b*e*f*x^6+2//5*a*e*f*x^5)
@test integrate(c*x^2*(e+f*x^4)^2, x) == :(1//3*c*e^2*x^3+1//11*c*f^2*x^11+2//7*c*e*f*x^7)
@test integrate((e+f*x^4)^2*(a+c*x^2), x) == :(a*x*e^2+1//3*c*e^2*x^3+1//9*a*f^2*x^9+1//11*c*f^2*x^11+2//5*a*e*f*x^5+2//7*c*e*f*x^7)
@test integrate((e+f*x^4)^2*(b*x+c*x^2), x) == :((1/2)*b*e^2*x^2+1//3*c*e^2*x^3+1//10*b*f^2*x^10+1//11*c*f^2*x^11+1//3*b*e*f*x^6+2//7*c*e*f*x^7)
@test integrate((e+f*x^4)^2*(a+b*x+c*x^2), x) == :(a*x*e^2+(1/2)*b*e^2*x^2+1//3*c*e^2*x^3+1//9*a*f^2*x^9+1//10*b*f^2*x^10+1//11*c*f^2*x^11+1//3*b*e*f*x^6+2//5*a*e*f*x^5+2//7*c*e*f*x^7)
@test integrate(d*x^3*(e+f*x^4)^2, x) == :(1//12*d*f^-1*(e+f*x^4)^3)
@test integrate((e+f*x^4)^2*(a+d*x^3), x) == :(a*x*e^2+1//9*a*f^2*x^9+1//12*d*f^-1*(e+f*x^4)^3+2//5*a*e*f*x^5)
@test integrate((e+f*x^4)^2*(b*x+d*x^3), x) == :((1/2)*b*e^2*x^2+1//10*b*f^2*x^10+1//12*d*f^-1*(e+f*x^4)^3+1//3*b*e*f*x^6)
@test integrate((e+f*x^4)^2*(a+b*x+d*x^3), x) == :(a*x*e^2+(1/2)*b*e^2*x^2+1//9*a*f^2*x^9+1//10*b*f^2*x^10+1//12*d*f^-1*(e+f*x^4)^3+1//3*b*e*f*x^6+2//5*a*e*f*x^5)
@test integrate((e+f*x^4)^2*(c*x^2+d*x^3), x) == :(1//3*c*e^2*x^3+1//11*c*f^2*x^11+1//12*d*f^-1*(e+f*x^4)^3+2//7*c*e*f*x^7)
@test integrate((e+f*x^4)^2*(a+c*x^2+d*x^3), x) == :(a*x*e^2+1//3*c*e^2*x^3+1//9*a*f^2*x^9+1//11*c*f^2*x^11+1//12*d*f^-1*(e+f*x^4)^3+2//5*a*e*f*x^5+2//7*c*e*f*x^7)
@test integrate((e+f*x^4)^2*(b*x+c*x^2+d*x^3), x) == :((1/2)*b*e^2*x^2+1//3*c*e^2*x^3+1//10*b*f^2*x^10+1//11*c*f^2*x^11+1//12*d*f^-1*(e+f*x^4)^3+1//3*b*e*f*x^6+2//7*c*e*f*x^7)
@test integrate((a+b*x^4)^2*(c+d*x+e*x^2+f*x^3), x) == :(c*x*a^2+(1/2)*d*a^2*x^2+1//3*e*a^2*x^3+1//9*c*b^2*x^9+1//10*d*b^2*x^10+1//11*e*b^2*x^11+1//12*f*b^-1*(a+b*x^4)^3+1//3*a*b*d*x^6+2//5*a*b*c*x^5+2//7*a*b*e*x^7)
@test integrate((a+b*x^4)^3*(c+d*x+e*x^2+f*x^3), x) == :(c*x*a^3+(1/2)*d*a^3*x^2+1//3*e*a^3*x^3+1//13*c*b^3*x^13+1//14*d*b^3*x^14+1//15*e*b^3*x^15+1//16*f*b^-1*(a+b*x^4)^4+(1/2)*b*d*a^2*x^6+1//3*a*c*b^2*x^9+3//5*b*c*a^2*x^5+3//7*b*e*a^2*x^7+3//10*a*d*b^2*x^10+3//11*a*e*b^2*x^11)
@test integrate((a+-1*b*x^4)^-2*(c+d*x+e*x^2+f*x^3), x) == :(1//4*d*a^-3//2*b^-1//2*arctanh(a^-1//2*b^(1/2)*x^2)+1//4*a^-1*b^-1*(a+-1*b*x^4)^-1*(a*f+b*x*(c+d*x+e*x^2))+1//8*a^-7//4*b^-3//4*(e*a^(1/2)+3*c*b^(1/2))*arctanh(x*a^-1//4*b^1//4)+1//8*a^-7//4*b^-3//4*(-1*e*a^(1/2)+3*c*b^(1/2))*arctan(x*a^-1//4*b^1//4))
@test integrate((a+-1*b*x^4)^-3*(c+d*x+e*x^2+f*x^3), x) == :(1//8*a^-1*b^-1*(a+-1*b*x^4)^-2*(a*f+b*x*(c+d*x+e*x^2))+1//32*x*a^-2*(a+-1*b*x^4)^-1*(7c+5*e*x^2+6*d*x)+1//64*a^-11//4*b^-3//4*(-5*e*a^(1/2)+21*c*b^(1/2))*arctan(x*a^-1//4*b^1//4)+1//64*a^-11//4*b^-3//4*(5*e*a^(1/2)+21*c*b^(1/2))*arctanh(x*a^-1//4*b^1//4)+3//16*d*a^-5//2*b^-1//2*arctanh(a^-1//2*b^(1/2)*x^2))
@test integrate((a+-1*b*x^4)^-4*(c+d*x+e*x^2+f*x^3), x) == :(1//12*a^-1*b^-1*(a+-1*b*x^4)^-3*(a*f+b*x*(c+d*x+e*x^2))+1//96*x*a^-2*(a+-1*b*x^4)^-2*(11c+9*e*x^2+10*d*x)+1//256*a^-15//4*b^-3//4*(-15*e*a^(1/2)+77*c*b^(1/2))*arctan(x*a^-1//4*b^1//4)+1//256*a^-15//4*b^-3//4*(15*e*a^(1/2)+77*c*b^(1/2))*arctanh(x*a^-1//4*b^1//4)+1//384*x*a^-3*(a+-1*b*x^4)^-1*(77c+45*e*x^2+60*d*x)+5//32*d*a^-7//2*b^-1//2*arctanh(a^-1//2*b^(1/2)*x^2))
@test integrate(a*(2+3*x^4)^-1, x) == :(-1//24*a*6^3//4*arctan(1+-1*x*6^1//4)+-1//48*a*6^3//4*log(6^(1/2)+3*x^2+-1*x*6^3//4)+1//24*a*6^3//4*arctan(1+x*6^1//4)+1//48*a*6^3//4*log(6^(1/2)+3*x^2+x*6^3//4))
@test integrate(b*x*(2+3*x^4)^-1, x) == :(1//12*b*6^(1/2)*arctan((1/2)*6^(1/2)*x^2))
@test integrate((2+3*x^4)^-1*(a+b*x), x) == :(-1//24*a*6^3//4*arctan(1+-1*x*6^1//4)+-1//48*a*6^3//4*log(6^(1/2)+3*x^2+-1*x*6^3//4)+1//12*b*6^(1/2)*arctan((1/2)*6^(1/2)*x^2)+1//24*a*6^3//4*arctan(1+x*6^1//4)+1//48*a*6^3//4*log(6^(1/2)+3*x^2+x*6^3//4))
@test integrate(c*x^2*(2+3*x^4)^-1, x) == :(-1//12*c*6^1//4*arctan(1+-1*x*6^1//4)+-1//24*c*6^1//4*log(6^(1/2)+3*x^2+x*6^3//4)+1//12*c*6^1//4*arctan(1+x*6^1//4)+1//24*c*6^1//4*log(6^(1/2)+3*x^2+-1*x*6^3//4))
@test integrate((2+3*x^4)^-1*(a+c*x^2), x) == :(-1//24*6^1//4*(2c+a*6^(1/2))*arctan(1+-1*x*6^1//4)+-1//48*6^1//4*(-2c+a*6^(1/2))*log(6^(1/2)+3*x^2+-1*x*6^3//4)+1//24*6^1//4*(2c+a*6^(1/2))*arctan(1+x*6^1//4)+1//48*6^1//4*(-2c+a*6^(1/2))*log(6^(1/2)+3*x^2+x*6^3//4))
@test integrate((2+3*x^4)^-1*(b*x+c*x^2), x) == :(-1//12*c*6^1//4*arctan(1+-1*x*6^1//4)+-1//24*c*6^1//4*log(6^(1/2)+3*x^2+x*6^3//4)+1//12*b*6^(1/2)*arctan((1/2)*6^(1/2)*x^2)+1//12*c*6^1//4*arctan(1+x*6^1//4)+1//24*c*6^1//4*log(6^(1/2)+3*x^2+-1*x*6^3//4))
@test integrate((2+3*x^4)^-1*(a+b*x+c*x^2), x) == :(-1//24*6^1//4*(2c+a*6^(1/2))*arctan(1+-1*x*6^1//4)+-1//48*6^1//4*(-2c+a*6^(1/2))*log(6^(1/2)+3*x^2+-1*x*6^3//4)+1//12*b*6^(1/2)*arctan((1/2)*6^(1/2)*x^2)+1//24*6^1//4*(2c+a*6^(1/2))*arctan(1+x*6^1//4)+1//48*6^1//4*(-2c+a*6^(1/2))*log(6^(1/2)+3*x^2+x*6^3//4))
@test integrate(d*x^3*(2+3*x^4)^-1, x) == :(1//12*d*log(2+3*x^4))
@test integrate((2+3*x^4)^-1*(a+d*x^3), x) == :(1//12*d*log(2+3*x^4)+-1//24*a*6^3//4*arctan(1+-1*x*6^1//4)+-1//48*a*6^3//4*log(6^(1/2)+3*x^2+-1*x*6^3//4)+1//24*a*6^3//4*arctan(1+x*6^1//4)+1//48*a*6^3//4*log(6^(1/2)+3*x^2+x*6^3//4))
@test integrate((2+3*x^4)^-1*(b*x+d*x^3), x) == :(1//12*d*log(2+3*x^4)+1//12*b*6^(1/2)*arctan((1/2)*6^(1/2)*x^2))
@test integrate((2+3*x^4)^-1*(a+b*x+d*x^3), x) == :(1//12*d*log(2+3*x^4)+-1//24*a*6^3//4*arctan(1+-1*x*6^1//4)+-1//48*a*6^3//4*log(6^(1/2)+3*x^2+-1*x*6^3//4)+1//12*b*6^(1/2)*arctan((1/2)*6^(1/2)*x^2)+1//24*a*6^3//4*arctan(1+x*6^1//4)+1//48*a*6^3//4*log(6^(1/2)+3*x^2+x*6^3//4))
@test integrate((2+3*x^4)^-1*(c*x^2+d*x^3), x) == :(1//12*d*log(2+3*x^4)+-1//12*c*6^1//4*arctan(1+-1*x*6^1//4)+-1//24*c*6^1//4*log(6^(1/2)+3*x^2+x*6^3//4)+1//12*c*6^1//4*arctan(1+x*6^1//4)+1//24*c*6^1//4*log(6^(1/2)+3*x^2+-1*x*6^3//4))
@test integrate((2+3*x^4)^-1*(a+c*x^2+d*x^3), x) == :(1//12*d*log(2+3*x^4)+-1//24*6^1//4*(2c+a*6^(1/2))*arctan(1+-1*x*6^1//4)+-1//48*6^1//4*(-2c+a*6^(1/2))*log(6^(1/2)+3*x^2+-1*x*6^3//4)+1//24*6^1//4*(2c+a*6^(1/2))*arctan(1+x*6^1//4)+1//48*6^1//4*(-2c+a*6^(1/2))*log(6^(1/2)+3*x^2+x*6^3//4))
@test integrate((2+3*x^4)^-1*(b*x+c*x^2+d*x^3), x) == :(1//12*d*log(2+3*x^4)+-1//12*c*6^1//4*arctan(1+-1*x*6^1//4)+-1//24*c*6^1//4*log(6^(1/2)+3*x^2+x*6^3//4)+1//12*b*6^(1/2)*arctan((1/2)*6^(1/2)*x^2)+1//12*c*6^1//4*arctan(1+x*6^1//4)+1//24*c*6^1//4*log(6^(1/2)+3*x^2+-1*x*6^3//4))
@test integrate((2+3*x^4)^-1*(a+b*x+c*x^2+d*x^3), x) == :(1//12*d*log(2+3*x^4)+-1//24*6^1//4*(2c+a*6^(1/2))*arctan(1+-1*x*6^1//4)+-1//48*6^1//4*(-2c+a*6^(1/2))*log(6^(1/2)+3*x^2+-1*x*6^3//4)+1//12*b*6^(1/2)*arctan((1/2)*6^(1/2)*x^2)+1//24*6^1//4*(2c+a*6^(1/2))*arctan(1+x*6^1//4)+1//48*6^1//4*(-2c+a*6^(1/2))*log(6^(1/2)+3*x^2+x*6^3//4))
@test integrate((1+-1*x^4)^-1*(1+x+x^2+x^3), x) == :(-1*log(1+-1x))
@test integrate((1+x^4)^-1*(1+x+x^2+x^3), x) == :((1/2)*arctan(x^2)+1//4*log(1+x^4)+(1/2)*2^(1/2)*arctan(1+x*2^(1/2))+-1//2*2^(1/2)*arctan(1+-1*x*2^(1/2)))
@test integrate((a+-1*b*x^4)^-1*(1+x+x^2+x^3), x) == :(-1//4*b^-1*log(a+-1*b*x^4)+(1/2)*a^-1//2*b^-1//2*arctanh(a^-1//2*b^(1/2)*x^2)+(1/2)*a^-3//4*b^-3//4*(a^(1/2)+b^(1/2))*arctanh(x*a^-1//4*b^1//4)+-1//2*a^-3//4*b^-3//4*(a^(1/2)+-1*b^(1/2))*arctan(x*a^-1//4*b^1//4))
@test integrate((a+b*x^4)^-1*(1+x+x^2+x^3), x) == :(1//4*b^-1*log(a+b*x^4)+(1/2)*a^-1//2*b^-1//2*arctan(a^-1//2*b^(1/2)*x^2)+-1//4*2^(1/2)*a^-3//4*b^-3//4*(a^(1/2)+b^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//8*2^(1/2)*a^-3//4*b^-3//4*(a^(1/2)+-1*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4)+1//4*2^(1/2)*a^-3//4*b^-3//4*(a^(1/2)+b^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//8*2^(1/2)*a^-3//4*b^-3//4*(a^(1/2)+-1*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4))
@test integrate((a+-1*b*x^4)^-1*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(-1*g*x*b^-1+-1//4*f*b^-1*log(a+-1*b*x^4)+(1/2)*d*a^-1//2*b^-1//2*arctanh(a^-1//2*b^(1/2)*x^2)+(1/2)*a^-3//4*b^-5//4*(a*g+b*c+e*a^(1/2)*b^(1/2))*arctanh(x*a^-1//4*b^1//4)+(1/2)*a^-3//4*b^-5//4*(a*g+b*c+-1*e*a^(1/2)*b^(1/2))*arctan(x*a^-1//4*b^1//4))
@test integrate((a+-1*b*x^4)^-2*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(1//4*d*a^-3//2*b^-1//2*arctanh(a^-1//2*b^(1/2)*x^2)+1//8*a^-7//4*b^-5//4*(-1*a*g+3*b*c+e*a^(1/2)*b^(1/2))*arctanh(x*a^-1//4*b^1//4)+1//8*a^-7//4*b^-5//4*(-1*a*g+3*b*c+-1*e*a^(1/2)*b^(1/2))*arctan(x*a^-1//4*b^1//4)+1//4*x*a^-1*b^-1*(a+-1*b*x^4)^-1*(a*g+b*c+b*d*x+b*e*x^2+b*f*x^3))
@test integrate((a+-1*b*x^4)^-3*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(1//32*a^-2*b^-1*(a+-1*b*x^4)^-1*(x*(-1*a*g+7*b*c+5*b*e*x^2+6*b*d*x)+4*a*f)+1//64*a^-11//4*b^-5//4*(-3*a*g+21*b*c+-5*e*a^(1/2)*b^(1/2))*arctan(x*a^-1//4*b^1//4)+1//64*a^-11//4*b^-5//4*(-3*a*g+21*b*c+5*e*a^(1/2)*b^(1/2))*arctanh(x*a^-1//4*b^1//4)+3//16*d*a^-5//2*b^-1//2*arctanh(a^-1//2*b^(1/2)*x^2)+1//8*x*a^-1*b^-1*(a+-1*b*x^4)^-2*(a*g+b*c+b*d*x+b*e*x^2+b*f*x^3))
@test integrate((a+-1*b*x^4)^-4*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(1//96*a^-2*b^-1*(a+-1*b*x^4)^-2*(x*(-1*a*g+11*b*c+9*b*e*x^2+10*b*d*x)+8*a*f)+1//256*a^-15//4*b^-5//4*(-7*a*g+77*b*c+-15*e*a^(1/2)*b^(1/2))*arctan(x*a^-1//4*b^1//4)+1//256*a^-15//4*b^-5//4*(-7*a*g+77*b*c+15*e*a^(1/2)*b^(1/2))*arctanh(x*a^-1//4*b^1//4)+5//32*d*a^-7//2*b^-1//2*arctanh(a^-1//2*b^(1/2)*x^2)+1//12*x*a^-1*b^-1*(a+-1*b*x^4)^-3*(a*g+b*c+b*d*x+b*e*x^2+b*f*x^3)+1//384*x*a^-3*b^-1*(a+-1*b*x^4)^-1*(-7*a*g+77*b*c+45*b*e*x^2+60*b*d*x))
@test integrate((a+b*x^4)^-1*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(g*x*b^-1+1//4*f*b^-1*log(a+b*x^4)+(1/2)*d*a^-1//2*b^-1//2*arctan(a^-1//2*b^(1/2)*x^2)+-1//4*2^(1/2)*a^-3//4*b^-5//4*(b*c+-1*a*g+e*a^(1/2)*b^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//8*2^(1/2)*a^-3//4*b^-5//4*(b*c+-1*a*g+-1*e*a^(1/2)*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//4*2^(1/2)*a^-3//4*b^-5//4*(b*c+-1*a*g+e*a^(1/2)*b^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//8*2^(1/2)*a^-3//4*b^-5//4*(b*c+-1*a*g+-1*e*a^(1/2)*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate((a+b*x^4)^-2*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(1//4*d*a^-3//2*b^-1//2*arctan(a^-1//2*b^(1/2)*x^2)+-1//16*2^(1/2)*a^-7//4*b^-5//4*(a*g+3*b*c+e*a^(1/2)*b^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//32*2^(1/2)*a^-7//4*b^-5//4*(a*g+3*b*c+-1*e*a^(1/2)*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//4*x*a^-1*b^-1*(a+b*x^4)^-1*(b*c+-1*a*g+b*d*x+b*e*x^2+b*f*x^3)+1//16*2^(1/2)*a^-7//4*b^-5//4*(a*g+3*b*c+e*a^(1/2)*b^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//32*2^(1/2)*a^-7//4*b^-5//4*(a*g+3*b*c+-1*e*a^(1/2)*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate((a+b*x^4)^-3*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(-1//32*a^-2*b^-1*(a+b*x^4)^-1*(-1*x*(a*g+7*b*c+5*b*e*x^2+6*b*d*x)+4*a*f)+3//16*d*a^-5//2*b^-1//2*arctan(a^-1//2*b^(1/2)*x^2)+-1//128*2^(1/2)*a^-11//4*b^-5//4*(3*a*g+21*b*c+5*e*a^(1/2)*b^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//256*2^(1/2)*a^-11//4*b^-5//4*(3*a*g+21*b*c+-5*e*a^(1/2)*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//8*x*a^-1*b^-1*(a+b*x^4)^-2*(b*c+-1*a*g+b*d*x+b*e*x^2+b*f*x^3)+1//128*2^(1/2)*a^-11//4*b^-5//4*(3*a*g+21*b*c+5*e*a^(1/2)*b^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//256*2^(1/2)*a^-11//4*b^-5//4*(3*a*g+21*b*c+-5*e*a^(1/2)*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate((a+b*x^4)^-4*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(-1//96*a^-2*b^-1*(a+b*x^4)^-2*(-1*x*(a*g+11*b*c+9*b*e*x^2+10*b*d*x)+8*a*f)+5//32*d*a^-7//2*b^-1//2*arctan(a^-1//2*b^(1/2)*x^2)+-1//512*2^(1/2)*a^-15//4*b^-5//4*(7*a*g+77*b*c+15*e*a^(1/2)*b^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//1024*2^(1/2)*a^-15//4*b^-5//4*(7*a*g+77*b*c+-15*e*a^(1/2)*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//12*x*a^-1*b^-1*(a+b*x^4)^-3*(b*c+-1*a*g+b*d*x+b*e*x^2+b*f*x^3)+1//384*x*a^-3*b^-1*(a+b*x^4)^-1*(7*a*g+77*b*c+45*b*e*x^2+60*b*d*x)+1//512*2^(1/2)*a^-15//4*b^-5//4*(7*a*g+77*b*c+15*e*a^(1/2)*b^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//1024*2^(1/2)*a^-15//4*b^-5//4*(7*a*g+77*b*c+-15*e*a^(1/2)*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate((1+-1*x^4)^3*(1+x+x^2+x^3)^-3, x) == :(-1//4*(1+-1x)^4)
@test integrate((1+-1*x^4)^2*(1+x+x^2+x^3)^-2, x) == :(-1//3*(1+-1x)^3)
@test integrate((1+x+x^2+x^3)^-1*(1+-1*x^4), x) == :(x+-1//2*x^2)
@test integrate((1+-1*x^4)^-1*(1+x+x^2+x^3), x) == :(-1*log(1+-1x))
@test integrate((1+-1*x^4)^-2*(1+x+x^2+x^3)^2, x) == :((1+-1x)^-1)
@test integrate((1+-1*x^4)^-3*(1+x+x^2+x^3)^3, x) == :((1/2)*(1+-1x)^-2)
@test integrate((1+-1*x^4)^-4*(1+x+x^2+x^3)^4, x) == :(1//3*(1+-1x)^-3)
@test integrate((a+-1*b*x^4)^-1*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(-1*g*x*b^-1+-1//2*h*b^-1*x^2+-1//4*f*b^-1*log(a+-1*b*x^4)+(1/2)*a^-3//4*b^-5//4*(a*g+b*c+e*a^(1/2)*b^(1/2))*arctanh(x*a^-1//4*b^1//4)+(1/2)*a^-3//4*b^-5//4*(a*g+b*c+-1*e*a^(1/2)*b^(1/2))*arctan(x*a^-1//4*b^1//4)+(1/2)*a^-1//2*b^-3//2*(a*h+b*d)*arctanh(a^-1//2*b^(1/2)*x^2))
@test integrate((a+-1*b*x^4)^-1*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5+i*x^6), x) == :(-1*g*x*b^-1+-1//2*h*b^-1*x^2+-1//3*i*b^-1*x^3+-1//4*f*b^-1*log(a+-1*b*x^4)+(1/2)*a^-1//2*b^-3//2*(a*h+b*d)*arctanh(a^-1//2*b^(1/2)*x^2)+(1/2)*a^-1//4*b^-7//4*(a*i+b*e+a^-1//2*b^(1/2)*(a*g+b*c))*arctanh(x*a^-1//4*b^1//4)+-1//2*a^-1//4*b^-7//4*(a*i+b*e+-1*a^-1//2*b^(1/2)*(a*g+b*c))*arctan(x*a^-1//4*b^1//4))
@test integrate((a+-1*b*x^4)^-1*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5+i*x^6+j*x^7), x) == :(-1*g*x*b^-1+-1//2*h*b^-1*x^2+-1//3*i*b^-1*x^3+-1//4*j*b^-1*x^4+-1//4*b^-2*(a*j+b*f)*log(a+-1*b*x^4)+(1/2)*a^-1//2*b^-3//2*(a*h+b*d)*arctanh(a^-1//2*b^(1/2)*x^2)+(1/2)*a^-1//4*b^-7//4*(a*i+b*e+a^-1//2*b^(1/2)*(a*g+b*c))*arctanh(x*a^-1//4*b^1//4)+-1//2*a^-1//4*b^-7//4*(a*i+b*e+-1*a^-1//2*b^(1/2)*(a*g+b*c))*arctan(x*a^-1//4*b^1//4))
@test integrate((a+b*x^4)^-1*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(g*x*b^-1+(1/2)*h*b^-1*x^2+1//4*f*b^-1*log(a+b*x^4)+(1/2)*a^-1//2*b^-3//2*(b*d+-1*a*h)*arctan(a^-1//2*b^(1/2)*x^2)+-1//4*2^(1/2)*a^-3//4*b^-5//4*(b*c+-1*a*g+e*a^(1/2)*b^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//8*2^(1/2)*a^-3//4*b^-5//4*(b*c+-1*a*g+-1*e*a^(1/2)*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//4*2^(1/2)*a^-3//4*b^-5//4*(b*c+-1*a*g+e*a^(1/2)*b^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//8*2^(1/2)*a^-3//4*b^-5//4*(b*c+-1*a*g+-1*e*a^(1/2)*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate((a+b*x^4)^-1*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5+i*x^6), x) == :(g*x*b^-1+(1/2)*h*b^-1*x^2+1//3*i*b^-1*x^3+1//4*f*b^-1*log(a+b*x^4)+(1/2)*a^-1//2*b^-3//2*(b*d+-1*a*h)*arctan(a^-1//2*b^(1/2)*x^2)+-1//4*2^(1/2)*a^-3//4*b^-7//4*(a^(1/2)*(b*e+-1*a*i)+b^(1/2)*(b*c+-1*a*g))*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//8*2^(1/2)*a^-3//4*b^-7//4*(b^(1/2)*(b*c+-1*a*g)+-1*a^(1/2)*(b*e+-1*a*i))*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//4*2^(1/2)*a^-3//4*b^-7//4*(a^(1/2)*(b*e+-1*a*i)+b^(1/2)*(b*c+-1*a*g))*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//8*2^(1/2)*a^-3//4*b^-7//4*(b^(1/2)*(b*c+-1*a*g)+-1*a^(1/2)*(b*e+-1*a*i))*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate((a+b*x^4)^-1*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5+i*x^6+j*x^7), x) == :(g*x*b^-1+(1/2)*h*b^-1*x^2+1//3*i*b^-1*x^3+1//4*j*b^-1*x^4+1//4*b^-2*(b*f+-1*a*j)*log(a+b*x^4)+(1/2)*a^-1//2*b^-3//2*(b*d+-1*a*h)*arctan(a^-1//2*b^(1/2)*x^2)+-1//4*2^(1/2)*a^-3//4*b^-7//4*(a^(1/2)*(b*e+-1*a*i)+b^(1/2)*(b*c+-1*a*g))*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//8*2^(1/2)*a^-3//4*b^-7//4*(b^(1/2)*(b*c+-1*a*g)+-1*a^(1/2)*(b*e+-1*a*i))*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//4*2^(1/2)*a^-3//4*b^-7//4*(a^(1/2)*(b*e+-1*a*i)+b^(1/2)*(b*c+-1*a*g))*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//8*2^(1/2)*a^-3//4*b^-7//4*(b^(1/2)*(b*c+-1*a*g)+-1*a^(1/2)*(b*e+-1*a*i))*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate((a+-1*b*x^4)^-2*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(1//4*a^-3//2*b^-3//2*(b*d+-1*a*h)*arctanh(a^-1//2*b^(1/2)*x^2)+1//8*a^-7//4*b^-5//4*(-1*a*g+3*b*c+e*a^(1/2)*b^(1/2))*arctanh(x*a^-1//4*b^1//4)+1//8*a^-7//4*b^-5//4*(-1*a*g+3*b*c+-1*e*a^(1/2)*b^(1/2))*arctan(x*a^-1//4*b^1//4)+1//4*x*a^-1*b^-1*(a+-1*b*x^4)^-1*(a*g+b*c+x*(a*h+b*d)+b*e*x^2+b*f*x^3))
@test integrate((a+-1*b*x^4)^-2*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5+i*x^6), x) == :(-1//8*a^-5//4*b^-7//4*(b*e+-3*a*i+-1*a^-1//2*b^(1/2)*(-1*a*g+3*b*c))*arctan(x*a^-1//4*b^1//4)+1//4*a^-3//2*b^-3//2*(b*d+-1*a*h)*arctanh(a^-1//2*b^(1/2)*x^2)+1//8*a^-5//4*b^-7//4*(b*e+-3*a*i+a^-1//2*b^(1/2)*(-1*a*g+3*b*c))*arctanh(x*a^-1//4*b^1//4)+1//4*x*a^-1*b^-1*(a+-1*b*x^4)^-1*(a*g+b*c+x*(a*h+b*d)+x^2*(a*i+b*e)+b*f*x^3))
@test integrate((a+-1*b*x^4)^-2*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5+i*x^6+j*x^7), x) == :(1//4*j*b^-2*log(a+-1*b*x^4)+-1//8*a^-5//4*b^-7//4*(b*e+-3*a*i+-1*a^-1//2*b^(1/2)*(-1*a*g+3*b*c))*arctan(x*a^-1//4*b^1//4)+1//4*a^-3//2*b^-3//2*(b*d+-1*a*h)*arctanh(a^-1//2*b^(1/2)*x^2)+1//8*a^-5//4*b^-7//4*(b*e+-3*a*i+a^-1//2*b^(1/2)*(-1*a*g+3*b*c))*arctanh(x*a^-1//4*b^1//4)+1//4*x*a^-1*b^-1*(a+-1*b*x^4)^-1*(a*g+b*c+x*(a*h+b*d)+x^2*(a*i+b*e)+x^3*(a*j+b*f)))
@test integrate((a+b*x^4)^-2*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(1//4*a^-3//2*b^-3//2*(a*h+b*d)*arctan(a^-1//2*b^(1/2)*x^2)+-1//16*2^(1/2)*a^-7//4*b^-5//4*(a*g+3*b*c+e*a^(1/2)*b^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//32*2^(1/2)*a^-7//4*b^-5//4*(a*g+3*b*c+-1*e*a^(1/2)*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//4*x*a^-1*b^-1*(a+b*x^4)^-1*(b*c+x*(b*d+-1*a*h)+-1*a*g+b*e*x^2+b*f*x^3)+1//16*2^(1/2)*a^-7//4*b^-5//4*(a*g+3*b*c+e*a^(1/2)*b^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//32*2^(1/2)*a^-7//4*b^-5//4*(a*g+3*b*c+-1*e*a^(1/2)*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate((a+b*x^4)^-2*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5+i*x^6), x) == :(1//4*a^-3//2*b^-3//2*(a*h+b*d)*arctan(a^-1//2*b^(1/2)*x^2)+-1//16*2^(1/2)*a^-7//4*b^-7//4*(a^(1/2)*(b*e+3*a*i)+b^(1/2)*(a*g+3*b*c))*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//32*2^(1/2)*a^-7//4*b^-7//4*(b^(1/2)*(a*g+3*b*c)+-1*a^(1/2)*(b*e+3*a*i))*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//4*x*a^-1*b^-1*(a+b*x^4)^-1*(b*c+x*(b*d+-1*a*h)+x^2*(b*e+-1*a*i)+-1*a*g+b*f*x^3)+1//16*2^(1/2)*a^-7//4*b^-7//4*(a^(1/2)*(b*e+3*a*i)+b^(1/2)*(a*g+3*b*c))*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//32*2^(1/2)*a^-7//4*b^-7//4*(b^(1/2)*(a*g+3*b*c)+-1*a^(1/2)*(b*e+3*a*i))*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate((a+b*x^4)^-2*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5+i*x^6+j*x^7), x) == :(1//4*j*b^-2*log(a+b*x^4)+1//4*a^-3//2*b^-3//2*(a*h+b*d)*arctan(a^-1//2*b^(1/2)*x^2)+-1//16*2^(1/2)*a^-7//4*b^-7//4*(a^(1/2)*(b*e+3*a*i)+b^(1/2)*(a*g+3*b*c))*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//32*2^(1/2)*a^-7//4*b^-7//4*(b^(1/2)*(a*g+3*b*c)+-1*a^(1/2)*(b*e+3*a*i))*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//4*x*a^-1*b^-1*(a+b*x^4)^-1*(b*c+x*(b*d+-1*a*h)+x^2*(b*e+-1*a*i)+x^3*(b*f+-1*a*j)+-1*a*g)+1//16*2^(1/2)*a^-7//4*b^-7//4*(a^(1/2)*(b*e+3*a*i)+b^(1/2)*(a*g+3*b*c))*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//32*2^(1/2)*a^-7//4*b^-7//4*(b^(1/2)*(a*g+3*b*c)+-1*a^(1/2)*(b*e+3*a*i))*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate((a+-1*b*x^4)^-3*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(1//16*a^-5//2*b^-3//2*(-1*a*h+3*b*d)*arctanh(a^-1//2*b^(1/2)*x^2)+1//32*a^-2*b^-1*(a+-1*b*x^4)^-1*(x*(x*(-2*a*h+6*b*d)+-1*a*g+7*b*c+5*b*e*x^2)+4*a*f)+1//64*a^-11//4*b^-5//4*(-3*a*g+21*b*c+-5*e*a^(1/2)*b^(1/2))*arctan(x*a^-1//4*b^1//4)+1//64*a^-11//4*b^-5//4*(-3*a*g+21*b*c+5*e*a^(1/2)*b^(1/2))*arctanh(x*a^-1//4*b^1//4)+1//8*x*a^-1*b^-1*(a+-1*b*x^4)^-2*(a*g+b*c+x*(a*h+b*d)+b*e*x^2+b*f*x^3))
@test integrate((a+-1*b*x^4)^-3*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5+i*x^6), x) == :(-1//64*a^-9//4*b^-7//4*(-3*a*i+5*b*e+-3*a^-1//2*b^(1/2)*(-1*a*g+7*b*c))*arctan(x*a^-1//4*b^1//4)+1//16*a^-5//2*b^-3//2*(-1*a*h+3*b*d)*arctanh(a^-1//2*b^(1/2)*x^2)+1//32*a^-2*b^-1*(a+-1*b*x^4)^-1*(x*(x*(-2*a*h+6*b*d)+x^2*(-3*a*i+5*b*e)+-1*a*g+7*b*c)+4*a*f)+1//64*a^-9//4*b^-7//4*(-3*a*i+5*b*e+3*a^-1//2*b^(1/2)*(-1*a*g+7*b*c))*arctanh(x*a^-1//4*b^1//4)+1//8*x*a^-1*b^-1*(a+-1*b*x^4)^-2*(a*g+b*c+x*(a*h+b*d)+x^2*(a*i+b*e)+b*f*x^3))
@test integrate((a+-1*b*x^4)^-3*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5+i*x^6+j*x^7), x) == :(-1//64*a^-9//4*b^-7//4*(-3*a*i+5*b*e+-3*a^-1//2*b^(1/2)*(-1*a*g+7*b*c))*arctan(x*a^-1//4*b^1//4)+1//16*a^-5//2*b^-3//2*(-1*a*h+3*b*d)*arctanh(a^-1//2*b^(1/2)*x^2)+1//32*a^-2*b^-2*(a+-1*b*x^4)^-1*(x*(b*(-1*a*g+7*b*c)+b*x^2*(-3*a*i+5*b*e)+2*b*x*(-1*a*h+3*b*d))+4*a*(b*f+-1*a*j))+1//64*a^-9//4*b^-7//4*(-3*a*i+5*b*e+3*a^-1//2*b^(1/2)*(-1*a*g+7*b*c))*arctanh(x*a^-1//4*b^1//4)+1//8*x*a^-1*b^-1*(a+-1*b*x^4)^-2*(a*g+b*c+x*(a*h+b*d)+x^2*(a*i+b*e)+x^3*(a*j+b*f)))
@test integrate((a+b*x^4)^-3*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(-1//32*a^-2*b^-1*(a+b*x^4)^-1*(-1*x*(a*g+x*(2*a*h+6*b*d)+7*b*c+5*b*e*x^2)+4*a*f)+1//16*a^-5//2*b^-3//2*(a*h+3*b*d)*arctan(a^-1//2*b^(1/2)*x^2)+-1//128*2^(1/2)*a^-11//4*b^-5//4*(3*a*g+21*b*c+5*e*a^(1/2)*b^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//256*2^(1/2)*a^-11//4*b^-5//4*(3*a*g+21*b*c+-5*e*a^(1/2)*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//8*x*a^-1*b^-1*(a+b*x^4)^-2*(b*c+x*(b*d+-1*a*h)+-1*a*g+b*e*x^2+b*f*x^3)+1//128*2^(1/2)*a^-11//4*b^-5//4*(3*a*g+21*b*c+5*e*a^(1/2)*b^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//256*2^(1/2)*a^-11//4*b^-5//4*(3*a*g+21*b*c+-5*e*a^(1/2)*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate((a+b*x^4)^-3*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5+i*x^6), x) == :(-1//32*a^-2*b^-1*(a+b*x^4)^-1*(-1*x*(a*g+x*(2*a*h+6*b*d)+x^2*(3*a*i+5*b*e)+7*b*c)+4*a*f)+1//16*a^-5//2*b^-3//2*(a*h+3*b*d)*arctan(a^-1//2*b^(1/2)*x^2)+-1//128*2^(1/2)*a^-11//4*b^-7//4*(a^(1/2)*(3*a*i+5*b*e)+3*b^(1/2)*(a*g+7*b*c))*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//256*2^(1/2)*a^-11//4*b^-7//4*(-1*a^(1/2)*(3*a*i+5*b*e)+3*b^(1/2)*(a*g+7*b*c))*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//8*x*a^-1*b^-1*(a+b*x^4)^-2*(b*c+x*(b*d+-1*a*h)+x^2*(b*e+-1*a*i)+-1*a*g+b*f*x^3)+1//128*2^(1/2)*a^-11//4*b^-7//4*(a^(1/2)*(3*a*i+5*b*e)+3*b^(1/2)*(a*g+7*b*c))*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//256*2^(1/2)*a^-11//4*b^-7//4*(-1*a^(1/2)*(3*a*i+5*b*e)+3*b^(1/2)*(a*g+7*b*c))*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate((a+b*x^4)^-3*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5+i*x^6+j*x^7), x) == :(-1//32*a^-2*b^-2*(a+b*x^4)^-1*(-1*x*(b*(a*g+7*b*c)+b*x^2*(3*a*i+5*b*e)+2*b*x*(a*h+3*b*d))+4*a*(a*j+b*f))+1//16*a^-5//2*b^-3//2*(a*h+3*b*d)*arctan(a^-1//2*b^(1/2)*x^2)+-1//128*2^(1/2)*a^-11//4*b^-7//4*(a^(1/2)*(3*a*i+5*b*e)+3*b^(1/2)*(a*g+7*b*c))*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//256*2^(1/2)*a^-11//4*b^-7//4*(-1*a^(1/2)*(3*a*i+5*b*e)+3*b^(1/2)*(a*g+7*b*c))*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//8*x*a^-1*b^-1*(a+b*x^4)^-2*(b*c+x*(b*d+-1*a*h)+x^2*(b*e+-1*a*i)+x^3*(b*f+-1*a*j)+-1*a*g)+1//128*2^(1/2)*a^-11//4*b^-7//4*(a^(1/2)*(3*a*i+5*b*e)+3*b^(1/2)*(a*g+7*b*c))*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//256*2^(1/2)*a^-11//4*b^-7//4*(-1*a^(1/2)*(3*a*i+5*b*e)+3*b^(1/2)*(a*g+7*b*c))*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate((a+-1*b*x^4)^-4*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(1//32*a^-7//2*b^-3//2*(-1*a*h+5*b*d)*arctanh(a^-1//2*b^(1/2)*x^2)+1//96*a^-2*b^-1*(a+-1*b*x^4)^-2*(x*(x*(-2*a*h+10*b*d)+-1*a*g+11*b*c+9*b*e*x^2)+8*a*f)+1//256*a^-15//4*b^-5//4*(-7*a*g+77*b*c+-15*e*a^(1/2)*b^(1/2))*arctan(x*a^-1//4*b^1//4)+1//256*a^-15//4*b^-5//4*(-7*a*g+77*b*c+15*e*a^(1/2)*b^(1/2))*arctanh(x*a^-1//4*b^1//4)+1//12*x*a^-1*b^-1*(a+-1*b*x^4)^-3*(a*g+b*c+x*(a*h+b*d)+b*e*x^2+b*f*x^3)+1//384*x*a^-3*b^-1*(a+-1*b*x^4)^-1*(x*(-12*a*h+60*b*d)+-7*a*g+77*b*c+45*b*e*x^2))
@test integrate((a+-1*b*x^4)^-4*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5+i*x^6), x) == :(1//32*a^-7//2*b^-3//2*(-1*a*h+5*b*d)*arctanh(a^-1//2*b^(1/2)*x^2)+1//96*a^-2*b^-1*(a+-1*b*x^4)^-2*(x*(x*(-2*a*h+10*b*d)+x^2*(-3*a*i+9*b*e)+-1*a*g+11*b*c)+8*a*f)+1//256*a^-13//4*b^-7//4*(-15*b*e+5*a*i+7*a^-1//2*b^(1/2)*(-1*a*g+11*b*c))*arctan(x*a^-1//4*b^1//4)+1//256*a^-13//4*b^-7//4*(-5*a*i+15*b*e+7*a^-1//2*b^(1/2)*(-1*a*g+11*b*c))*arctanh(x*a^-1//4*b^1//4)+1//12*x*a^-1*b^-1*(a+-1*b*x^4)^-3*(a*g+b*c+x*(a*h+b*d)+x^2*(a*i+b*e)+b*f*x^3)+1//384*x*a^-3*b^-1*(a+-1*b*x^4)^-1*(x*(-12*a*h+60*b*d)+x^2*(-15*a*i+45*b*e)+-7*a*g+77*b*c))
@test integrate((a+-1*b*x^4)^-4*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5+i*x^6+j*x^7), x) == :(1//32*a^-7//2*b^-3//2*(-1*a*h+5*b*d)*arctanh(a^-1//2*b^(1/2)*x^2)+1//96*a^-2*b^-2*(a+-1*b*x^4)^-2*(x*(b*(-1*a*g+11*b*c)+2*b*x*(-1*a*h+5*b*d)+3*b*x^2*(-1*a*i+3*b*e))+4*a*(-1*a*j+2*b*f))+1//256*a^-13//4*b^-7//4*(-15*b*e+5*a*i+7*a^-1//2*b^(1/2)*(-1*a*g+11*b*c))*arctan(x*a^-1//4*b^1//4)+1//256*a^-13//4*b^-7//4*(-5*a*i+15*b*e+7*a^-1//2*b^(1/2)*(-1*a*g+11*b*c))*arctanh(x*a^-1//4*b^1//4)+1//12*x*a^-1*b^-1*(a+-1*b*x^4)^-3*(a*g+b*c+x*(a*h+b*d)+x^2*(a*i+b*e)+x^3*(a*j+b*f))+1//384*x*a^-3*b^-1*(a+-1*b*x^4)^-1*(x*(-12*a*h+60*b*d)+x^2*(-15*a*i+45*b*e)+-7*a*g+77*b*c))
@test integrate((a+b*x^4)^-4*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(-1//96*a^-2*b^-1*(a+b*x^4)^-2*(-1*x*(a*g+x*(2*a*h+10*b*d)+11*b*c+9*b*e*x^2)+8*a*f)+1//32*a^-7//2*b^-3//2*(a*h+5*b*d)*arctan(a^-1//2*b^(1/2)*x^2)+-1//512*2^(1/2)*a^-15//4*b^-5//4*(7*a*g+77*b*c+15*e*a^(1/2)*b^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//1024*2^(1/2)*a^-15//4*b^-5//4*(7*a*g+77*b*c+-15*e*a^(1/2)*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//12*x*a^-1*b^-1*(a+b*x^4)^-3*(b*c+x*(b*d+-1*a*h)+-1*a*g+b*e*x^2+b*f*x^3)+1//384*x*a^-3*b^-1*(a+b*x^4)^-1*(x*(12*a*h+60*b*d)+7*a*g+77*b*c+45*b*e*x^2)+1//512*2^(1/2)*a^-15//4*b^-5//4*(7*a*g+77*b*c+15*e*a^(1/2)*b^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//1024*2^(1/2)*a^-15//4*b^-5//4*(7*a*g+77*b*c+-15*e*a^(1/2)*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate((a+b*x^4)^-4*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5+i*x^6), x) == :(-1//96*a^-2*b^-1*(a+b*x^4)^-2*(-1*x*(a*g+x*(2*a*h+10*b*d)+x^2*(3*a*i+9*b*e)+11*b*c)+8*a*f)+1//32*a^-7//2*b^-3//2*(a*h+5*b*d)*arctan(a^-1//2*b^(1/2)*x^2)+-1//512*2^(1/2)*a^-15//4*b^-7//4*(5*a^(1/2)*(a*i+3*b*e)+7*b^(1/2)*(a*g+11*b*c))*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//1024*2^(1/2)*a^-15//4*b^-7//4*(-5*a^(1/2)*(a*i+3*b*e)+7*b^(1/2)*(a*g+11*b*c))*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//12*x*a^-1*b^-1*(a+b*x^4)^-3*(b*c+x*(b*d+-1*a*h)+x^2*(b*e+-1*a*i)+-1*a*g+b*f*x^3)+1//384*x*a^-3*b^-1*(a+b*x^4)^-1*(x*(12*a*h+60*b*d)+x^2*(15*a*i+45*b*e)+7*a*g+77*b*c)+1//512*2^(1/2)*a^-15//4*b^-7//4*(5*a^(1/2)*(a*i+3*b*e)+7*b^(1/2)*(a*g+11*b*c))*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//1024*2^(1/2)*a^-15//4*b^-7//4*(-5*a^(1/2)*(a*i+3*b*e)+7*b^(1/2)*(a*g+11*b*c))*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate((a+b*x^4)^-4*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5+i*x^6+j*x^7), x) == :(-1//96*a^-2*b^-2*(a+b*x^4)^-2*(-1*x*(b*(a*g+11*b*c)+2*b*x*(a*h+5*b*d)+3*b*x^2*(a*i+3*b*e))+4*a*(a*j+2*b*f))+1//32*a^-7//2*b^-3//2*(a*h+5*b*d)*arctan(a^-1//2*b^(1/2)*x^2)+-1//512*2^(1/2)*a^-15//4*b^-7//4*(5*a^(1/2)*(a*i+3*b*e)+7*b^(1/2)*(a*g+11*b*c))*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//1024*2^(1/2)*a^-15//4*b^-7//4*(-5*a^(1/2)*(a*i+3*b*e)+7*b^(1/2)*(a*g+11*b*c))*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//12*x*a^-1*b^-1*(a+b*x^4)^-3*(b*c+x*(b*d+-1*a*h)+x^2*(b*e+-1*a*i)+x^3*(b*f+-1*a*j)+-1*a*g)+1//384*x*a^-3*b^-1*(a+b*x^4)^-1*(x*(12*a*h+60*b*d)+x^2*(15*a*i+45*b*e)+7*a*g+77*b*c)+1//512*2^(1/2)*a^-15//4*b^-7//4*(5*a^(1/2)*(a*i+3*b*e)+7*b^(1/2)*(a*g+11*b*c))*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//1024*2^(1/2)*a^-15//4*b^-7//4*(-5*a^(1/2)*(a*i+3*b*e)+7*b^(1/2)*(a*g+11*b*c))*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate((a+b*x^4)^-1//2*(c+d*x), x) == :((1/2)*d*b^-1//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+(1/2)*c*a^-1//4*b^-1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate((a+-1*b*x^4)^-1//2*(c+d*x), x) == :((1/2)*d*b^-1//2*arctan(b^(1/2)*x^2*(a+-1*b*x^4)^-1//2)+c*a^1//4*b^-1//4*(1+-1*b*a^-1*x^4)^(1/2)*(a+-1*b*x^4)^-1//2*Elliptic.F(arcsin(x*a^-1//4*b^1//4),-1))
@test integrate((-1a+b*x^4)^-1//2*(c+d*x), x) == :((1/2)*d*b^-1//2*arctanh(b^(1/2)*x^2*(-1a+b*x^4)^-1//2)+c*a^1//4*b^-1//4*(1+-1*b*a^-1*x^4)^(1/2)*(-1a+b*x^4)^-1//2*Elliptic.F(arcsin(x*a^-1//4*b^1//4),-1))
@test integrate((-1a+-1*b*x^4)^-1//2*(c+d*x), x) == :((1/2)*d*b^-1//2*arctan(b^(1/2)*x^2*(-1a+-1*b*x^4)^-1//2)+(1/2)*c*a^-1//4*b^-1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(-1a+-1*b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate((a+b*x^4)^-1//2*(c+d*x+e*x^2), x) == :((1/2)*d*b^-1//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+e*x*b^-1//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+(1/2)*a^1//4*b^-3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(e+c*a^-1//2*b^(1/2))*(a^(1/2)+b^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2)+-1*e*a^1//4*b^-3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate((a+b*x^4)^-3//2*(a*g+-1*b*g*x^4), x) == :(g*x*(a+b*x^4)^-1//2)
@test integrate((a+b*x^4)^-3//2*(a*g+e*x+-1*b*g*x^4), x) == :((1/2)*a^-1*(a+b*x^4)^-1//2*(e*x^2+2*a*g*x))
@test integrate((a+b*x^4)^-3//2*(a*g+f*x^3+-1*b*g*x^4), x) == :(-1//2*b^-1*(a+b*x^4)^-1//2*(f+-2*b*g*x))
@test integrate((a+b*x^4)^-3//2*(a*g+e*x+f*x^3+-1*b*g*x^4), x) == :(-1//2*a^-1*b^-1*(a+b*x^4)^-1//2*(a*f+-1*b*e*x^2+-2*a*b*g*x))
@test integrate((1+x^4)^-3//2*(-1+x^4), x) == :(-1*x*(1+x^4)^-1//2)
@test integrate((a+b*x^4)^-1//2*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5+i*x^6), x) == :((1/2)*f*b^-1*(a+b*x^4)^(1/2)+1//4*b^-3//2*(-1*a*h+2*b*d)*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+1//3*g*x*b^-1*(a+b*x^4)^(1/2)+1//4*h*b^-1*x^2*(a+b*x^4)^(1/2)+1//5*i*b^-1*x^3*(a+b*x^4)^(1/2)+1//5*x*b^-3//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1*(-3*a*i+5*b*e)+-1//5*a^1//4*b^-7//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(-3*a*i+5*b*e)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+1//30*a^1//4*b^-7//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(-9*a*i+15*b*e+5*a^-1//2*b^(1/2)*(-1*a*g+3*b*c))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate((1+x^5)^-1*(1+x), x) == :(-1//5*(-1)^1//5*(1+(-1)^1//5)*log((-1)^1//5+-1x)+-1//5*(-1)^3//5*(1+(-1)^3//5)*log(x+-1*(-1)^3//5)+1//5*(-1)^2//5*(1+-1*(-1)^2//5)*log(x+(-1)^2//5)+1//5*(-1)^4//5*(1+-1*(-1)^4//5)*log(-1x+-1*(-1)^4//5))
@test integrate((1+-1*x^5)^-1*(1+-1x), x) == :(-1//5*(-1)^2//5*(1+-1*(-1)^2//5)*log((-1)^2//5+-1x)+-1//5*(-1)^4//5*(1+-1*(-1)^4//5)*log(x+-1*(-1)^4//5)+1//5*(-1)^1//5*(1+(-1)^1//5)*log(x+(-1)^1//5)+1//5*(-1)^3//5*(1+(-1)^3//5)*log(-1x+-1*(-1)^3//5))
@test integrate(x^11*(a+b*x^3)^-1*(c+d*x^3+e*x^6+f*x^9), x) == :(1//9*b^-4*x^9*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//12*b^-3*x^12*(d*b^2+f*a^2+-1*a*b*e)+1//15*b^-2*x^15*(b*e+-1*a*f)+1//18*f*b^-1*x^18+-1//3*a^3*b^-7*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a+b*x^3)+-1//6*a*b^-5*x^6*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//3*a^2*b^-6*x^3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2))
@test integrate(x^8*(a+b*x^3)^-1*(c+d*x^3+e*x^6+f*x^9), x) == :(1//6*b^-4*x^6*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//9*b^-3*x^9*(d*b^2+f*a^2+-1*a*b*e)+1//12*b^-2*x^12*(b*e+-1*a*f)+1//15*f*b^-1*x^15+-1//3*a*b^-5*x^3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//3*a^2*b^-6*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a+b*x^3))
@test integrate(x^5*(a+b*x^3)^-1*(c+d*x^3+e*x^6+f*x^9), x) == :(1//3*b^-4*x^3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//6*b^-3*x^6*(d*b^2+f*a^2+-1*a*b*e)+1//9*b^-2*x^9*(b*e+-1*a*f)+1//12*f*b^-1*x^12+-1//3*a*b^-5*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a+b*x^3))
@test integrate(x^2*(a+b*x^3)^-1*(c+d*x^3+e*x^6+f*x^9), x) == :(1//3*b^-4*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a+b*x^3)+1//3*b^-3*x^3*(d*b^2+f*a^2+-1*a*b*e)+1//6*b^-2*x^6*(b*e+-1*a*f)+1//9*f*b^-1*x^9)
@test integrate(x^-1*(a+b*x^3)^-1*(c+d*x^3+e*x^6+f*x^9), x) == :(c*a^-1*log(x)+1//3*b^-2*x^3*(b*e+-1*a*f)+1//6*f*b^-1*x^6+-1//3*a^-1*b^-3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a+b*x^3))
@test integrate(x^-4*(a+b*x^3)^-1*(c+d*x^3+e*x^6+f*x^9), x) == :(-1*a^-2*(b*c+-1*a*d)*log(x)+-1//3*c*a^-1*x^-3+1//3*f*b^-1*x^3+1//3*a^-2*b^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a+b*x^3))
@test integrate(x^-7*(a+b*x^3)^-1*(c+d*x^3+e*x^6+f*x^9), x) == :(a^-3*(c*b^2+e*a^2+-1*a*b*d)*log(x)+-1//6*c*a^-1*x^-6+1//3*a^-2*x^-3*(b*c+-1*a*d)+-1//3*a^-3*b^-1*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a+b*x^3))
@test integrate(x^-10*(a+b*x^3)^-1*(c+d*x^3+e*x^6+f*x^9), x) == :(-1*a^-4*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(x)+-1//3*a^-3*x^-3*(c*b^2+e*a^2+-1*a*b*d)+-1//9*c*a^-1*x^-9+1//3*a^-4*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a+b*x^3)+1//6*a^-2*x^-6*(b*c+-1*a*d))
@test integrate(x^-13*(a+b*x^3)^-1*(c+d*x^3+e*x^6+f*x^9), x) == :(-1//6*a^-3*x^-6*(c*b^2+e*a^2+-1*a*b*d)+-1//12*c*a^-1*x^-12+1//3*a^-4*x^-3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//9*a^-2*x^-9*(b*c+-1*a*d)+b*a^-5*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(x)+-1//3*b*a^-5*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a+b*x^3))
@test integrate(x^-16*(a+b*x^3)^-1*(c+d*x^3+e*x^6+f*x^9), x) == :(-1//9*a^-3*x^-9*(c*b^2+e*a^2+-1*a*b*d)+-1//15*c*a^-1*x^-15+1//6*a^-4*x^-6*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//12*a^-2*x^-12*(b*c+-1*a*d)+-1*a^-6*b^2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(x)+-1//3*b*a^-5*x^-3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//3*a^-6*b^2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a+b*x^3))
@test integrate(x^9*(a+b*x^3)^-1*(c+d*x^3+e*x^6+f*x^9), x) == :(1//7*b^-4*x^7*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//10*b^-3*x^10*(d*b^2+f*a^2+-1*a*b*e)+1//13*b^-2*x^13*(b*e+-1*a*f)+1//16*f*b^-1*x^16+x*a^2*b^-6*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+-1//3*a^7//3*b^-19//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^1//3+x*b^1//3)+-1//4*a*b^-5*x^4*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//6*a^7//3*b^-19//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*3^(1/2)*a^7//3*b^-19//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^7*(a+b*x^3)^-1*(c+d*x^3+e*x^6+f*x^9), x) == :(1//5*b^-4*x^5*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//8*b^-3*x^8*(d*b^2+f*a^2+-1*a*b*e)+1//11*b^-2*x^11*(b*e+-1*a*f)+1//14*f*b^-1*x^14+-1//2*a*b^-5*x^2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+-1//3*a^5//3*b^-17//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^1//3+x*b^1//3)+1//6*a^5//3*b^-17//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*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^-17//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^6*(a+b*x^3)^-1*(c+d*x^3+e*x^6+f*x^9), x) == :(1//4*b^-4*x^4*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//7*b^-3*x^7*(d*b^2+f*a^2+-1*a*b*e)+1//10*b^-2*x^10*(b*e+-1*a*f)+1//13*f*b^-1*x^13+-1*a*x*b^-5*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+-1//6*a^4//3*b^-16//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^4//3*b^-16//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^1//3+x*b^1//3)+-1//3*3^(1/2)*a^4//3*b^-16//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^4*(a+b*x^3)^-1*(c+d*x^3+e*x^6+f*x^9), x) == :((1/2)*b^-4*x^2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//5*b^-3*x^5*(d*b^2+f*a^2+-1*a*b*e)+1//8*b^-2*x^8*(b*e+-1*a*f)+1//11*f*b^-1*x^11+-1//6*a^2//3*b^-14//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^2//3*b^-14//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^1//3+x*b^1//3)+1//3*3^(1/2)*a^2//3*b^-14//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^3*(a+b*x^3)^-1*(c+d*x^3+e*x^6+f*x^9), x) == :(x*b^-4*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//4*b^-3*x^4*(d*b^2+f*a^2+-1*a*b*e)+1//7*b^-2*x^7*(b*e+-1*a*f)+1//10*f*b^-1*x^10+-1//3*a^1//3*b^-13//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^1//3+x*b^1//3)+1//6*a^1//3*b^-13//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*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^-13//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x*(a+b*x^3)^-1*(c+d*x^3+e*x^6+f*x^9), x) == :((1/2)*b^-3*x^2*(d*b^2+f*a^2+-1*a*b*e)+1//5*b^-2*x^5*(b*e+-1*a*f)+1//8*f*b^-1*x^8+-1//3*a^-1//3*b^-11//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^1//3+x*b^1//3)+1//6*a^-1//3*b^-11//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*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^-11//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate((a+b*x^3)^-1*(c+d*x^3+e*x^6+f*x^9), x) == :(x*b^-3*(d*b^2+f*a^2+-1*a*b*e)+1//4*b^-2*x^4*(b*e+-1*a*f)+1//7*f*b^-1*x^7+-1//6*a^-2//3*b^-10//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-2//3*b^-10//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^1//3+x*b^1//3)+-1//3*3^(1/2)*a^-2//3*b^-10//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-2*(a+b*x^3)^-1*(c+d*x^3+e*x^6+f*x^9), x) == :((1/2)*b^-2*x^2*(b*e+-1*a*f)+-1*c*a^-1*x^-1+1//5*f*b^-1*x^5+-1//6*a^-4//3*b^-8//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-4//3*b^-8//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^1//3+x*b^1//3)+1//3*3^(1/2)*a^-4//3*b^-8//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-3*(a+b*x^3)^-1*(c+d*x^3+e*x^6+f*x^9), x) == :(x*b^-2*(b*e+-1*a*f)+-1//2*c*a^-1*x^-2+1//4*f*b^-1*x^4+-1//3*a^-5//3*b^-7//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^1//3+x*b^1//3)+1//6*a^-5//3*b^-7//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*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^-7//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-5*(a+b*x^3)^-1*(c+d*x^3+e*x^6+f*x^9), x) == :(a^-2*x^-1*(b*c+-1*a*d)+(1/2)*f*b^-1*x^2+-1//4*c*a^-1*x^-4+-1//3*a^-7//3*b^-5//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^1//3+x*b^1//3)+1//6*a^-7//3*b^-5//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//3*3^(1/2)*a^-7//3*b^-5//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-6*(a+b*x^3)^-1*(c+d*x^3+e*x^6+f*x^9), x) == :(f*x*b^-1+(1/2)*a^-2*x^-2*(b*c+-1*a*d)+-1//5*c*a^-1*x^-5+-1//6*a^-8//3*b^-4//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-8//3*b^-4//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^1//3+x*b^1//3)+-1//3*3^(1/2)*a^-8//3*b^-4//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-8*(a+b*x^3)^-1*(c+d*x^3+e*x^6+f*x^9), x) == :(-1*a^-3*x^-1*(c*b^2+e*a^2+-1*a*b*d)+-1//7*c*a^-1*x^-7+1//4*a^-2*x^-4*(b*c+-1*a*d)+-1//6*a^-10//3*b^-2//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-10//3*b^-2//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^1//3+x*b^1//3)+1//3*3^(1/2)*a^-10//3*b^-2//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-9*(a+b*x^3)^-1*(c+d*x^3+e*x^6+f*x^9), x) == :(-1//2*a^-3*x^-2*(c*b^2+e*a^2+-1*a*b*d)+-1//8*c*a^-1*x^-8+1//5*a^-2*x^-5*(b*c+-1*a*d)+-1//3*a^-11//3*b^-1//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^1//3+x*b^1//3)+1//6*a^-11//3*b^-1//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*3^(1/2)*a^-11//3*b^-1//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-11*(a+b*x^3)^-1*(c+d*x^3+e*x^6+f*x^9), x) == :(a^-4*x^-1*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+-1//4*a^-3*x^-4*(c*b^2+e*a^2+-1*a*b*d)+-1//10*c*a^-1*x^-10+1//7*a^-2*x^-7*(b*c+-1*a*d)+-1//3*a^-13//3*b^1//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^1//3+x*b^1//3)+1//6*a^-13//3*b^1//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//3*3^(1/2)*a^-13//3*b^1//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-12*(a+b*x^3)^-1*(c+d*x^3+e*x^6+f*x^9), x) == :((1/2)*a^-4*x^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+-1//5*a^-3*x^-5*(c*b^2+e*a^2+-1*a*b*d)+-1//11*c*a^-1*x^-11+1//8*a^-2*x^-8*(b*c+-1*a*d)+-1//6*a^-14//3*b^2//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-14//3*b^2//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^1//3+x*b^1//3)+-1//3*3^(1/2)*a^-14//3*b^2//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-14*(a+b*x^3)^-1*(c+d*x^3+e*x^6+f*x^9), x) == :(-1//7*a^-3*x^-7*(c*b^2+e*a^2+-1*a*b*d)+-1//13*c*a^-1*x^-13+1//4*a^-4*x^-4*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//10*a^-2*x^-10*(b*c+-1*a*d)+-1*b*a^-5*x^-1*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+-1//6*a^-16//3*b^4//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-16//3*b^4//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^1//3+x*b^1//3)+1//3*3^(1/2)*a^-16//3*b^4//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-15*(a+b*x^3)^-1*(c+d*x^3+e*x^6+f*x^9), x) == :(-1//8*a^-3*x^-8*(c*b^2+e*a^2+-1*a*b*d)+-1//14*c*a^-1*x^-14+1//5*a^-4*x^-5*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//11*a^-2*x^-11*(b*c+-1*a*d)+-1//2*b*a^-5*x^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+-1//3*a^-17//3*b^5//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^1//3+x*b^1//3)+1//6*a^-17//3*b^5//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*3^(1/2)*a^-17//3*b^5//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-17*(a+b*x^3)^-1*(c+d*x^3+e*x^6+f*x^9), x) == :(-1//10*a^-3*x^-10*(c*b^2+e*a^2+-1*a*b*d)+-1//16*c*a^-1*x^-16+1//7*a^-4*x^-7*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//13*a^-2*x^-13*(b*c+-1*a*d)+a^-6*b^2*x^-1*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+-1//3*a^-19//3*b^7//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^1//3+x*b^1//3)+-1//4*b*a^-5*x^-4*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//6*a^-19//3*b^7//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//3*3^(1/2)*a^-19//3*b^7//3*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^11*(a+b*x^3)^-2*(c+d*x^3+e*x^6+f*x^9), x) == :(1//6*b^-5*x^6*(c*b^3+-4*f*a^3+-2*a*d*b^2+3*b*e*a^2)+1//9*b^-4*x^9*(d*b^2+3*f*a^2+-2*a*b*e)+1//12*b^-3*x^12*(b*e+-2*a*f)+1//15*f*b^-2*x^15+-1//3*a*b^-6*x^3*(-5*f*a^3+2*c*b^3+-3*a*d*b^2+4*b*e*a^2)+1//3*a^2*b^-7*(-6*f*a^3+3*c*b^3+-4*a*d*b^2+5*b*e*a^2)*log(a+b*x^3)+1//3*a^3*b^-7*(a+b*x^3)^-1*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2))
@test integrate(x^8*(a+b*x^3)^-2*(c+d*x^3+e*x^6+f*x^9), x) == :(1//3*b^-5*x^3*(c*b^3+-4*f*a^3+-2*a*d*b^2+3*b*e*a^2)+1//6*b^-4*x^6*(d*b^2+3*f*a^2+-2*a*b*e)+1//9*b^-3*x^9*(b*e+-2*a*f)+1//12*f*b^-2*x^12+-1//3*a*b^-6*(-5*f*a^3+2*c*b^3+-3*a*d*b^2+4*b*e*a^2)*log(a+b*x^3)+-1//3*a^2*b^-6*(a+b*x^3)^-1*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2))
@test integrate(x^5*(a+b*x^3)^-2*(c+d*x^3+e*x^6+f*x^9), x) == :(1//3*b^-5*(c*b^3+-4*f*a^3+-2*a*d*b^2+3*b*e*a^2)*log(a+b*x^3)+1//3*b^-4*x^3*(d*b^2+3*f*a^2+-2*a*b*e)+1//6*b^-3*x^6*(b*e+-2*a*f)+1//9*f*b^-2*x^9+1//3*a*b^-5*(a+b*x^3)^-1*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2))
@test integrate(x^2*(a+b*x^3)^-2*(c+d*x^3+e*x^6+f*x^9), x) == :(-1//3*b^-4*(a+b*x^3)^-1*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//3*b^-4*(d*b^2+3*f*a^2+-2*a*b*e)*log(a+b*x^3)+1//3*b^-3*x^3*(b*e+-2*a*f)+1//6*f*b^-2*x^6)
@test integrate(x^-1*(a+b*x^3)^-2*(c+d*x^3+e*x^6+f*x^9), x) == :(c*a^-2*log(x)+1//3*f*b^-2*x^3+-1//3*a^-2*b^-3*(c*b^3+2*f*a^3+-1*b*e*a^2)*log(a+b*x^3)+1//3*a^-1*b^-3*(a+b*x^3)^-1*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2))
@test integrate(x^-4*(a+b*x^3)^-2*(c+d*x^3+e*x^6+f*x^9), x) == :(-1*a^-3*(-1*a*d+2*b*c)*log(x)+-1//3*c*a^-2*x^-3+-1//3*a^-2*b^-2*(a+b*x^3)^-1*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//3*a^-3*b^-2*(f*a^3+2*c*b^3+-1*a*d*b^2)*log(a+b*x^3))
@test integrate(x^-7*(a+b*x^3)^-2*(c+d*x^3+e*x^6+f*x^9), x) == :(a^-4*(e*a^2+3*c*b^2+-2*a*b*d)*log(x)+-1//3*a^-4*(e*a^2+3*c*b^2+-2*a*b*d)*log(a+b*x^3)+-1//6*c*a^-2*x^-6+1//3*a^-3*x^-3*(-1*a*d+2*b*c)+1//3*a^-3*b^-1*(a+b*x^3)^-1*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2))
@test integrate(x^-10*(a+b*x^3)^-2*(c+d*x^3+e*x^6+f*x^9), x) == :(-1*a^-5*(-1*f*a^3+4*c*b^3+-3*a*d*b^2+2*b*e*a^2)*log(x)+-1//3*a^-4*x^-3*(e*a^2+3*c*b^2+-2*a*b*d)+-1//3*a^-4*(a+b*x^3)^-1*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+-1//9*c*a^-2*x^-9+1//3*a^-5*(-1*f*a^3+4*c*b^3+-3*a*d*b^2+2*b*e*a^2)*log(a+b*x^3)+1//6*a^-3*x^-6*(-1*a*d+2*b*c))
@test integrate(x^-13*(a+b*x^3)^-2*(c+d*x^3+e*x^6+f*x^9), x) == :(-1//6*a^-4*x^-6*(e*a^2+3*c*b^2+-2*a*b*d)+-1//12*c*a^-2*x^-12+1//3*a^-5*x^-3*(-1*f*a^3+4*c*b^3+-3*a*d*b^2+2*b*e*a^2)+1//9*a^-3*x^-9*(-1*a*d+2*b*c)+b*a^-6*(-2*f*a^3+5*c*b^3+-4*a*d*b^2+3*b*e*a^2)*log(x)+-1//3*b*a^-6*(-2*f*a^3+5*c*b^3+-4*a*d*b^2+3*b*e*a^2)*log(a+b*x^3)+1//3*b*a^-5*(a+b*x^3)^-1*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2))
@test integrate(x^9*(a+b*x^3)^-2*(c+d*x^3+e*x^6+f*x^9), x) == :(1//4*b^-5*x^4*(c*b^3+-4*f*a^3+-2*a*d*b^2+3*b*e*a^2)+1//7*b^-4*x^7*(d*b^2+3*f*a^2+-2*a*b*e)+1//10*b^-3*x^10*(b*e+-2*a*f)+1//13*f*b^-2*x^13+-1*a*x*b^-6*(-5*f*a^3+2*c*b^3+-3*a*d*b^2+4*b*e*a^2)+-1//18*a^4//3*b^-19//3*(-16*f*a^3+7*c*b^3+-10*a*d*b^2+13*b*e*a^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*a^4//3*b^-19//3*(-16*f*a^3+7*c*b^3+-10*a*d*b^2+13*b*e*a^2)*log(a^1//3+x*b^1//3)+-1//3*x*a^2*b^-6*(a+b*x^3)^-1*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+-1//9*3^(1/2)*a^4//3*b^-19//3*(-16*f*a^3+7*c*b^3+-10*a*d*b^2+13*b*e*a^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^7*(a+b*x^3)^-2*(c+d*x^3+e*x^6+f*x^9), x) == :((1/2)*b^-5*x^2*(c*b^3+-4*f*a^3+-2*a*d*b^2+3*b*e*a^2)+1//5*b^-4*x^5*(d*b^2+3*f*a^2+-2*a*b*e)+1//8*b^-3*x^8*(b*e+-2*a*f)+1//11*f*b^-2*x^11+-1//18*a^2//3*b^-17//3*(-14*f*a^3+5*c*b^3+-8*a*d*b^2+11*b*e*a^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*a^2//3*b^-17//3*(-14*f*a^3+5*c*b^3+-8*a*d*b^2+11*b*e*a^2)*log(a^1//3+x*b^1//3)+1//3*a*b^-5*x^2*(a+b*x^3)^-1*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//9*3^(1/2)*a^2//3*b^-17//3*(-14*f*a^3+5*c*b^3+-8*a*d*b^2+11*b*e*a^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^6*(a+b*x^3)^-2*(c+d*x^3+e*x^6+f*x^9), x) == :(x*b^-5*(c*b^3+-4*f*a^3+-2*a*d*b^2+3*b*e*a^2)+1//4*b^-4*x^4*(d*b^2+3*f*a^2+-2*a*b*e)+1//7*b^-3*x^7*(b*e+-2*a*f)+1//10*f*b^-2*x^10+-1//9*a^1//3*b^-16//3*(-13*f*a^3+4*c*b^3+-7*a*d*b^2+10*b*e*a^2)*log(a^1//3+x*b^1//3)+1//18*a^1//3*b^-16//3*(-13*f*a^3+4*c*b^3+-7*a*d*b^2+10*b*e*a^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a*x*b^-5*(a+b*x^3)^-1*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//9*3^(1/2)*a^1//3*b^-16//3*(-13*f*a^3+4*c*b^3+-7*a*d*b^2+10*b*e*a^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^4*(a+b*x^3)^-2*(c+d*x^3+e*x^6+f*x^9), x) == :((1/2)*b^-4*x^2*(d*b^2+3*f*a^2+-2*a*b*e)+1//5*b^-3*x^5*(b*e+-2*a*f)+1//8*f*b^-2*x^8+-1//3*b^-4*x^2*(a+b*x^3)^-1*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+-1//9*a^-1//3*b^-14//3*(-11*f*a^3+2*c*b^3+-5*a*d*b^2+8*b*e*a^2)*log(a^1//3+x*b^1//3)+1//18*a^-1//3*b^-14//3*(-11*f*a^3+2*c*b^3+-5*a*d*b^2+8*b*e*a^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//9*3^(1/2)*a^-1//3*b^-14//3*(-11*f*a^3+2*c*b^3+-5*a*d*b^2+8*b*e*a^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^3*(a+b*x^3)^-2*(c+d*x^3+e*x^6+f*x^9), x) == :(x*b^-4*(d*b^2+3*f*a^2+-2*a*b*e)+1//4*b^-3*x^4*(b*e+-2*a*f)+1//7*f*b^-2*x^7+-1//3*x*b^-4*(a+b*x^3)^-1*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+-1//18*a^-2//3*b^-13//3*(c*b^3+-10*f*a^3+-4*a*d*b^2+7*b*e*a^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*a^-2//3*b^-13//3*(c*b^3+-10*f*a^3+-4*a*d*b^2+7*b*e*a^2)*log(a^1//3+x*b^1//3)+-1//9*3^(1/2)*a^-2//3*b^-13//3*(c*b^3+-10*f*a^3+-4*a*d*b^2+7*b*e*a^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x*(a+b*x^3)^-2*(c+d*x^3+e*x^6+f*x^9), x) == :((1/2)*b^-3*x^2*(b*e+-2*a*f)+1//5*f*b^-2*x^5+-1//9*a^-4//3*b^-11//3*(c*b^3+8*f*a^3+-5*b*e*a^2+2*a*d*b^2)*log(a^1//3+x*b^1//3)+1//18*a^-4//3*b^-11//3*(c*b^3+8*f*a^3+-5*b*e*a^2+2*a*d*b^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//9*3^(1/2)*a^-4//3*b^-11//3*(c*b^3+8*f*a^3+-5*b*e*a^2+2*a*d*b^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//3*a^-1*b^-3*x^2*(a+b*x^3)^-1*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2))
@test integrate((a+b*x^3)^-2*(c+d*x^3+e*x^6+f*x^9), x) == :(x*b^-3*(b*e+-2*a*f)+1//4*f*b^-2*x^4+-1//18*a^-5//3*b^-10//3*(2*c*b^3+7*f*a^3+a*d*b^2+-4*b*e*a^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*a^-5//3*b^-10//3*(2*c*b^3+7*f*a^3+a*d*b^2+-4*b*e*a^2)*log(a^1//3+x*b^1//3)+-1//9*3^(1/2)*a^-5//3*b^-10//3*(2*c*b^3+7*f*a^3+a*d*b^2+-4*b*e*a^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//3*x*a^-1*b^-3*(a+b*x^3)^-1*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2))
@test integrate(x^-2*(a+b*x^3)^-2*(c+d*x^3+e*x^6+f*x^9), x) == :((1/2)*f*b^-2*x^2+-1*c*a^-2*x^-1+-1//18*a^-7//3*b^-8//3*(4*c*b^3+5*f*a^3+-1*a*d*b^2+-2*b*e*a^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*a^-7//3*b^-8//3*(4*c*b^3+5*f*a^3+-1*a*d*b^2+-2*b*e*a^2)*log(a^1//3+x*b^1//3)+-1//3*a^-2*b^-2*x^2*(a+b*x^3)^-1*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//9*3^(1/2)*a^-7//3*b^-8//3*(4*c*b^3+5*f*a^3+-1*a*d*b^2+-2*b*e*a^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-3*(a+b*x^3)^-2*(c+d*x^3+e*x^6+f*x^9), x) == :(f*x*b^-2+-1//2*c*a^-2*x^-2+-1//9*a^-8//3*b^-7//3*(4*f*a^3+5*c*b^3+-1*b*e*a^2+-2*a*d*b^2)*log(a^1//3+x*b^1//3)+1//18*a^-8//3*b^-7//3*(4*f*a^3+5*c*b^3+-1*b*e*a^2+-2*a*d*b^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//3*x*a^-2*b^-2*(a+b*x^3)^-1*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//9*3^(1/2)*a^-8//3*b^-7//3*(4*f*a^3+5*c*b^3+-1*b*e*a^2+-2*a*d*b^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-5*(a+b*x^3)^-2*(c+d*x^3+e*x^6+f*x^9), x) == :(a^-3*x^-1*(-1*a*d+2*b*c)+-1//4*c*a^-2*x^-4+-1//9*a^-10//3*b^-5//3*(2*f*a^3+7*c*b^3+b*e*a^2+-4*a*d*b^2)*log(a^1//3+x*b^1//3)+1//18*a^-10//3*b^-5//3*(2*f*a^3+7*c*b^3+b*e*a^2+-4*a*d*b^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//9*3^(1/2)*a^-10//3*b^-5//3*(2*f*a^3+7*c*b^3+b*e*a^2+-4*a*d*b^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//3*a^-3*b^-1*x^2*(a+b*x^3)^-1*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2))
@test integrate(x^-6*(a+b*x^3)^-2*(c+d*x^3+e*x^6+f*x^9), x) == :((1/2)*a^-3*x^-2*(-1*a*d+2*b*c)+-1//5*c*a^-2*x^-5+-1//18*a^-11//3*b^-4//3*(f*a^3+8*c*b^3+-5*a*d*b^2+2*b*e*a^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*a^-11//3*b^-4//3*(f*a^3+8*c*b^3+-5*a*d*b^2+2*b*e*a^2)*log(a^1//3+x*b^1//3)+-1//9*3^(1/2)*a^-11//3*b^-4//3*(f*a^3+8*c*b^3+-5*a*d*b^2+2*b*e*a^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//3*x*a^-3*b^-1*(a+b*x^3)^-1*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2))
@test integrate(x^-8*(a+b*x^3)^-2*(c+d*x^3+e*x^6+f*x^9), x) == :(-1*a^-4*x^-1*(e*a^2+3*c*b^2+-2*a*b*d)+-1//7*c*a^-2*x^-7+1//4*a^-3*x^-4*(-1*a*d+2*b*c)+-1//3*a^-4*x^2*(a+b*x^3)^-1*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+-1//18*a^-13//3*b^-2//3*(-1*f*a^3+10*c*b^3+-7*a*d*b^2+4*b*e*a^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*a^-13//3*b^-2//3*(-1*f*a^3+10*c*b^3+-7*a*d*b^2+4*b*e*a^2)*log(a^1//3+x*b^1//3)+1//9*3^(1/2)*a^-13//3*b^-2//3*(-1*f*a^3+10*c*b^3+-7*a*d*b^2+4*b*e*a^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-9*(a+b*x^3)^-2*(c+d*x^3+e*x^6+f*x^9), x) == :(-1//2*a^-4*x^-2*(e*a^2+3*c*b^2+-2*a*b*d)+-1//8*c*a^-2*x^-8+1//5*a^-3*x^-5*(-1*a*d+2*b*c)+-1//3*x*a^-4*(a+b*x^3)^-1*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+-1//9*a^-14//3*b^-1//3*(-2*f*a^3+11*c*b^3+-8*a*d*b^2+5*b*e*a^2)*log(a^1//3+x*b^1//3)+1//18*a^-14//3*b^-1//3*(-2*f*a^3+11*c*b^3+-8*a*d*b^2+5*b*e*a^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*3^(1/2)*a^-14//3*b^-1//3*(-2*f*a^3+11*c*b^3+-8*a*d*b^2+5*b*e*a^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-11*(a+b*x^3)^-2*(c+d*x^3+e*x^6+f*x^9), x) == :(a^-5*x^-1*(-1*f*a^3+4*c*b^3+-3*a*d*b^2+2*b*e*a^2)+-1//4*a^-4*x^-4*(e*a^2+3*c*b^2+-2*a*b*d)+-1//10*c*a^-2*x^-10+1//7*a^-3*x^-7*(-1*a*d+2*b*c)+-1//9*a^-16//3*b^1//3*(-4*f*a^3+13*c*b^3+-10*a*d*b^2+7*b*e*a^2)*log(a^1//3+x*b^1//3)+1//18*a^-16//3*b^1//3*(-4*f*a^3+13*c*b^3+-10*a*d*b^2+7*b*e*a^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//9*3^(1/2)*a^-16//3*b^1//3*(-4*f*a^3+13*c*b^3+-10*a*d*b^2+7*b*e*a^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//3*b*a^-5*x^2*(a+b*x^3)^-1*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2))
@test integrate(x^-12*(a+b*x^3)^-2*(c+d*x^3+e*x^6+f*x^9), x) == :((1/2)*a^-5*x^-2*(-1*f*a^3+4*c*b^3+-3*a*d*b^2+2*b*e*a^2)+-1//5*a^-4*x^-5*(e*a^2+3*c*b^2+-2*a*b*d)+-1//11*c*a^-2*x^-11+1//8*a^-3*x^-8*(-1*a*d+2*b*c)+-1//18*a^-17//3*b^2//3*(-5*f*a^3+14*c*b^3+-11*a*d*b^2+8*b*e*a^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*a^-17//3*b^2//3*(-5*f*a^3+14*c*b^3+-11*a*d*b^2+8*b*e*a^2)*log(a^1//3+x*b^1//3)+-1//9*3^(1/2)*a^-17//3*b^2//3*(-5*f*a^3+14*c*b^3+-11*a*d*b^2+8*b*e*a^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//3*b*x*a^-5*(a+b*x^3)^-1*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2))
@test integrate(x^-14*(a+b*x^3)^-2*(c+d*x^3+e*x^6+f*x^9), x) == :(-1//7*a^-4*x^-7*(e*a^2+3*c*b^2+-2*a*b*d)+-1//13*c*a^-2*x^-13+1//4*a^-5*x^-4*(-1*f*a^3+4*c*b^3+-3*a*d*b^2+2*b*e*a^2)+1//10*a^-3*x^-10*(-1*a*d+2*b*c)+-1*b*a^-6*x^-1*(-2*f*a^3+5*c*b^3+-4*a*d*b^2+3*b*e*a^2)+-1//18*a^-19//3*b^4//3*(-7*f*a^3+16*c*b^3+-13*a*d*b^2+10*b*e*a^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*a^-19//3*b^4//3*(-7*f*a^3+16*c*b^3+-13*a*d*b^2+10*b*e*a^2)*log(a^1//3+x*b^1//3)+-1//3*a^-6*b^2*x^2*(a+b*x^3)^-1*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//9*3^(1/2)*a^-19//3*b^4//3*(-7*f*a^3+16*c*b^3+-13*a*d*b^2+10*b*e*a^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^14*(a+b*x^3)^-3*(c+d*x^3+e*x^6+f*x^9), x) == :(1//6*b^-6*x^6*(c*b^3+-10*f*a^3+-3*a*d*b^2+6*b*e*a^2)+1//9*b^-5*x^9*(d*b^2+6*f*a^2+-3*a*b*e)+1//12*b^-4*x^12*(b*e+-3*a*f)+1//15*f*b^-3*x^15+-1//3*a*b^-7*x^3*(-15*f*a^3+3*c*b^3+-6*a*d*b^2+10*b*e*a^2)+-1//6*a^4*b^-8*(a+b*x^3)^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//3*a^2*b^-8*(-21*f*a^3+6*c*b^3+-10*a*d*b^2+15*b*e*a^2)*log(a+b*x^3)+1//3*a^3*b^-8*(a+b*x^3)^-1*(-7*f*a^3+4*c*b^3+-5*a*d*b^2+6*b*e*a^2))
@test integrate(x^11*(a+b*x^3)^-3*(c+d*x^3+e*x^6+f*x^9), x) == :(1//3*b^-6*x^3*(c*b^3+-10*f*a^3+-3*a*d*b^2+6*b*e*a^2)+1//6*b^-5*x^6*(d*b^2+6*f*a^2+-3*a*b*e)+1//9*b^-4*x^9*(b*e+-3*a*f)+1//12*f*b^-3*x^12+-1//3*a*b^-7*(-15*f*a^3+3*c*b^3+-6*a*d*b^2+10*b*e*a^2)*log(a+b*x^3)+-1//3*a^2*b^-7*(a+b*x^3)^-1*(-6*f*a^3+3*c*b^3+-4*a*d*b^2+5*b*e*a^2)+1//6*a^3*b^-7*(a+b*x^3)^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2))
@test integrate(x^8*(a+b*x^3)^-3*(c+d*x^3+e*x^6+f*x^9), x) == :(1//3*b^-6*(c*b^3+-10*f*a^3+-3*a*d*b^2+6*b*e*a^2)*log(a+b*x^3)+1//3*b^-5*x^3*(d*b^2+6*f*a^2+-3*a*b*e)+1//6*b^-4*x^6*(b*e+-3*a*f)+1//9*f*b^-3*x^9+-1//6*a^2*b^-6*(a+b*x^3)^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//3*a*b^-6*(a+b*x^3)^-1*(-5*f*a^3+2*c*b^3+-3*a*d*b^2+4*b*e*a^2))
@test integrate(x^5*(a+b*x^3)^-3*(c+d*x^3+e*x^6+f*x^9), x) == :(-1//3*b^-5*(a+b*x^3)^-1*(c*b^3+-4*f*a^3+-2*a*d*b^2+3*b*e*a^2)+1//3*b^-5*(d*b^2+6*f*a^2+-3*a*b*e)*log(a+b*x^3)+1//3*b^-4*x^3*(b*e+-3*a*f)+1//6*f*b^-3*x^6+1//6*a*b^-5*(a+b*x^3)^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2))
@test integrate(x^2*(a+b*x^3)^-3*(c+d*x^3+e*x^6+f*x^9), x) == :(-1//3*b^-4*(a+b*x^3)^-1*(d*b^2+3*f*a^2+-2*a*b*e)+-1//6*b^-4*(a+b*x^3)^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//3*f*b^-3*x^3+1//3*b^-4*(b*e+-3*a*f)*log(a+b*x^3))
@test integrate(x^-1*(a+b*x^3)^-3*(c+d*x^3+e*x^6+f*x^9), x) == :(-1*(-1//3*f*b^-3+1//3*c*a^-3)*log(a+b*x^3)+c*a^-3*log(x)+1//3*a^-2*b^-3*(a+b*x^3)^-1*(c*b^3+2*f*a^3+-1*b*e*a^2)+1//6*a^-1*b^-3*(a+b*x^3)^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2))
@test integrate(x^-4*(a+b*x^3)^-3*(c+d*x^3+e*x^6+f*x^9), x) == :(-1*a^-4*(-1*a*d+3*b*c)*log(x)+-1//3*c*a^-3*x^-3+1//3*a^-4*(-1*a*d+3*b*c)*log(a+b*x^3)+-1//3*a^-3*b^-2*(a+b*x^3)^-1*(f*a^3+2*c*b^3+-1*a*d*b^2)+-1//6*a^-2*b^-2*(a+b*x^3)^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2))
@test integrate(x^-7*(a+b*x^3)^-3*(c+d*x^3+e*x^6+f*x^9), x) == :(a^-5*(e*a^2+6*c*b^2+-3*a*b*d)*log(x)+-1//3*a^-5*(e*a^2+6*c*b^2+-3*a*b*d)*log(a+b*x^3)+-1//6*c*a^-3*x^-6+1//3*a^-4*x^-3*(-1*a*d+3*b*c)+1//3*a^-4*(a+b*x^3)^-1*(e*a^2+3*c*b^2+-2*a*b*d)+1//6*a^-3*b^-1*(a+b*x^3)^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2))
@test integrate(x^-10*(a+b*x^3)^-3*(c+d*x^3+e*x^6+f*x^9), x) == :(-1*a^-6*(-1*f*a^3+10*c*b^3+-6*a*d*b^2+3*b*e*a^2)*log(x)+-1//3*a^-5*x^-3*(e*a^2+6*c*b^2+-3*a*b*d)+-1//3*a^-5*(a+b*x^3)^-1*(-1*f*a^3+4*c*b^3+-3*a*d*b^2+2*b*e*a^2)+-1//6*a^-4*(a+b*x^3)^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+-1//9*c*a^-3*x^-9+1//3*a^-6*(-1*f*a^3+10*c*b^3+-6*a*d*b^2+3*b*e*a^2)*log(a+b*x^3)+1//6*a^-4*x^-6*(-1*a*d+3*b*c))
@test integrate(x^-13*(a+b*x^3)^-3*(c+d*x^3+e*x^6+f*x^9), x) == :(-1//6*a^-5*x^-6*(e*a^2+6*c*b^2+-3*a*b*d)+-1//12*c*a^-3*x^-12+1//3*a^-6*x^-3*(-1*f*a^3+10*c*b^3+-6*a*d*b^2+3*b*e*a^2)+1//9*a^-4*x^-9*(-1*a*d+3*b*c)+b*a^-7*(-3*f*a^3+15*c*b^3+-10*a*d*b^2+6*b*e*a^2)*log(x)+-1//3*b*a^-7*(-3*f*a^3+15*c*b^3+-10*a*d*b^2+6*b*e*a^2)*log(a+b*x^3)+1//3*b*a^-6*(a+b*x^3)^-1*(-2*f*a^3+5*c*b^3+-4*a*d*b^2+3*b*e*a^2)+1//6*b*a^-5*(a+b*x^3)^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2))
@test integrate(x^12*(a+b*x^3)^-3*(c+d*x^3+e*x^6+f*x^9), x) == :(1//4*b^-6*x^4*(c*b^3+-10*f*a^3+-3*a*d*b^2+6*b*e*a^2)+1//7*b^-5*x^7*(d*b^2+6*f*a^2+-3*a*b*e)+1//10*b^-4*x^10*(b*e+-3*a*f)+1//13*f*b^-3*x^13+-1*a*x*b^-7*(-15*f*a^3+3*c*b^3+-6*a*d*b^2+10*b*e*a^2)+-1//54*a^4//3*b^-22//3*(-152*f*a^3+35*c*b^3+-65*a*d*b^2+104*b*e*a^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//27*a^4//3*b^-22//3*(-152*f*a^3+35*c*b^3+-65*a*d*b^2+104*b*e*a^2)*log(a^1//3+x*b^1//3)+-1//18*x*a^2*b^-7*(a+b*x^3)^-1*(-37*f*a^3+19*c*b^3+-25*a*d*b^2+31*b*e*a^2)+-1//27*3^(1/2)*a^4//3*b^-22//3*(-152*f*a^3+35*c*b^3+-65*a*d*b^2+104*b*e*a^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//6*x*a^3*b^-7*(a+b*x^3)^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2))
@test integrate(x^10*(a+b*x^3)^-3*(c+d*x^3+e*x^6+f*x^9), x) == :((1/2)*b^-6*x^2*(c*b^3+-10*f*a^3+-3*a*d*b^2+6*b*e*a^2)+1//5*b^-5*x^5*(d*b^2+6*f*a^2+-3*a*b*e)+1//8*b^-4*x^8*(b*e+-3*a*f)+1//11*f*b^-3*x^11+-1//54*a^2//3*b^-20//3*(-119*f*a^3+20*c*b^3+-44*a*d*b^2+77*b*e*a^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//27*a^2//3*b^-20//3*(-119*f*a^3+20*c*b^3+-44*a*d*b^2+77*b*e*a^2)*log(a^1//3+x*b^1//3)+-1//6*a^2*b^-6*x^2*(a+b*x^3)^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//9*a*b^-6*x^2*(a+b*x^3)^-1*(-16*f*a^3+7*c*b^3+-10*a*d*b^2+13*b*e*a^2)+1//27*3^(1/2)*a^2//3*b^-20//3*(-119*f*a^3+20*c*b^3+-44*a*d*b^2+77*b*e*a^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^9*(a+b*x^3)^-3*(c+d*x^3+e*x^6+f*x^9), x) == :(x*b^-6*(c*b^3+-10*f*a^3+-3*a*d*b^2+6*b*e*a^2)+1//4*b^-5*x^4*(d*b^2+6*f*a^2+-3*a*b*e)+1//7*b^-4*x^7*(b*e+-3*a*f)+1//10*f*b^-3*x^10+-1//27*a^1//3*b^-19//3*(-104*f*a^3+14*c*b^3+-35*a*d*b^2+65*b*e*a^2)*log(a^1//3+x*b^1//3)+1//54*a^1//3*b^-19//3*(-104*f*a^3+14*c*b^3+-35*a*d*b^2+65*b*e*a^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//6*x*a^2*b^-6*(a+b*x^3)^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//18*a*x*b^-6*(a+b*x^3)^-1*(-31*f*a^3+13*c*b^3+-19*a*d*b^2+25*b*e*a^2)+1//27*3^(1/2)*a^1//3*b^-19//3*(-104*f*a^3+14*c*b^3+-35*a*d*b^2+65*b*e*a^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^7*(a+b*x^3)^-3*(c+d*x^3+e*x^6+f*x^9), x) == :((1/2)*b^-5*x^2*(d*b^2+6*f*a^2+-3*a*b*e)+1//5*b^-4*x^5*(b*e+-3*a*f)+1//8*f*b^-3*x^8+-1//9*b^-5*x^2*(a+b*x^3)^-1*(-13*f*a^3+4*c*b^3+-7*a*d*b^2+10*b*e*a^2)+-1//27*a^-1//3*b^-17//3*(-77*f*a^3+5*c*b^3+-20*a*d*b^2+44*b*e*a^2)*log(a^1//3+x*b^1//3)+1//54*a^-1//3*b^-17//3*(-77*f*a^3+5*c*b^3+-20*a*d*b^2+44*b*e*a^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//27*3^(1/2)*a^-1//3*b^-17//3*(-77*f*a^3+5*c*b^3+-20*a*d*b^2+44*b*e*a^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//6*a*b^-5*x^2*(a+b*x^3)^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2))
@test integrate(x^6*(a+b*x^3)^-3*(c+d*x^3+e*x^6+f*x^9), x) == :(x*b^-5*(d*b^2+6*f*a^2+-3*a*b*e)+1//4*b^-4*x^4*(b*e+-3*a*f)+1//7*f*b^-3*x^7+-1//18*x*b^-5*(a+b*x^3)^-1*(-25*f*a^3+7*c*b^3+-13*a*d*b^2+19*b*e*a^2)+-1//54*a^-2//3*b^-16//3*(-65*f*a^3+2*c*b^3+-14*a*d*b^2+35*b*e*a^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//27*a^-2//3*b^-16//3*(-65*f*a^3+2*c*b^3+-14*a*d*b^2+35*b*e*a^2)*log(a^1//3+x*b^1//3)+-1//27*3^(1/2)*a^-2//3*b^-16//3*(-65*f*a^3+2*c*b^3+-14*a*d*b^2+35*b*e*a^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//6*a*x*b^-5*(a+b*x^3)^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2))
@test integrate(x^4*(a+b*x^3)^-3*(c+d*x^3+e*x^6+f*x^9), x) == :((1/2)*b^-4*x^2*(b*e+-3*a*f)+1//5*f*b^-3*x^5+-1//6*b^-4*x^2*(a+b*x^3)^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+-1//27*a^-4//3*b^-14//3*(c*b^3+44*f*a^3+-20*b*e*a^2+5*a*d*b^2)*log(a^1//3+x*b^1//3)+1//54*a^-4//3*b^-14//3*(c*b^3+44*f*a^3+-20*b*e*a^2+5*a*d*b^2)*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^-14//3*(c*b^3+44*f*a^3+-20*b*e*a^2+5*a*d*b^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//9*a^-1*b^-4*x^2*(a+b*x^3)^-1*(c*b^3+-10*f*a^3+-4*a*d*b^2+7*b*e*a^2))
@test integrate(x^3*(a+b*x^3)^-3*(c+d*x^3+e*x^6+f*x^9), x) == :(x*b^-4*(b*e+-3*a*f)+1//4*f*b^-3*x^4+-1//6*x*b^-4*(a+b*x^3)^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+-1//54*a^-5//3*b^-13//3*(c*b^3+35*f*a^3+-14*b*e*a^2+2*a*d*b^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//27*a^-5//3*b^-13//3*(c*b^3+35*f*a^3+-14*b*e*a^2+2*a*d*b^2)*log(a^1//3+x*b^1//3)+-1//27*3^(1/2)*a^-5//3*b^-13//3*(c*b^3+35*f*a^3+-14*b*e*a^2+2*a*d*b^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//18*x*a^-1*b^-4*(a+b*x^3)^-1*(c*b^3+-19*f*a^3+-7*a*d*b^2+13*b*e*a^2))
@test integrate(x*(a+b*x^3)^-3*(c+d*x^3+e*x^6+f*x^9), x) == :((1/2)*f*b^-3*x^2+-1//27*a^-7//3*b^-11//3*(-20*f*a^3+2*c*b^3+a*d*b^2+5*b*e*a^2)*log(a^1//3+x*b^1//3)+1//54*a^-7//3*b^-11//3*(-20*f*a^3+2*c*b^3+a*d*b^2+5*b*e*a^2)*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^-11//3*(-20*f*a^3+2*c*b^3+a*d*b^2+5*b*e*a^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//6*a^-1*b^-3*x^2*(a+b*x^3)^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//9*a^-2*b^-3*x^2*(a+b*x^3)^-1*(2*c*b^3+7*f*a^3+a*d*b^2+-4*b*e*a^2))
@test integrate((a+b*x^3)^-3*(c+d*x^3+e*x^6+f*x^9), x) == :(f*x*b^-3+-1//54*a^-8//3*b^-10//3*(-14*f*a^3+5*c*b^3+a*d*b^2+2*b*e*a^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//27*a^-8//3*b^-10//3*(-14*f*a^3+5*c*b^3+a*d*b^2+2*b*e*a^2)*log(a^1//3+x*b^1//3)+-1//27*3^(1/2)*a^-8//3*b^-10//3*(-14*f*a^3+5*c*b^3+a*d*b^2+2*b*e*a^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//6*x*a^-1*b^-3*(a+b*x^3)^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//18*x*a^-2*b^-3*(a+b*x^3)^-1*(5*c*b^3+13*f*a^3+a*d*b^2+-7*b*e*a^2))
@test integrate(x^-2*(a+b*x^3)^-3*(c+d*x^3+e*x^6+f*x^9), x) == :(-1*c*a^-3*x^-1+-1//54*a^-10//3*b^-8//3*(-5*f*a^3+14*c*b^3+-1*b*e*a^2+-2*a*d*b^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//27*a^-10//3*b^-8//3*(-5*f*a^3+14*c*b^3+-1*b*e*a^2+-2*a*d*b^2)*log(a^1//3+x*b^1//3)+-1//6*a^-2*b^-2*x^2*(a+b*x^3)^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+-1//9*a^-3*b^-2*x^2*(a+b*x^3)^-1*(4*f*a^3+5*c*b^3+-1*b*e*a^2+-2*a*d*b^2)+1//27*3^(1/2)*a^-10//3*b^-8//3*(-5*f*a^3+14*c*b^3+-1*b*e*a^2+-2*a*d*b^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-3*(a+b*x^3)^-3*(c+d*x^3+e*x^6+f*x^9), x) == :(-1//2*c*a^-3*x^-2+-1//27*a^-11//3*b^-7//3*(-2*f*a^3+20*c*b^3+-1*b*e*a^2+-5*a*d*b^2)*log(a^1//3+x*b^1//3)+1//54*a^-11//3*b^-7//3*(-2*f*a^3+20*c*b^3+-1*b*e*a^2+-5*a*d*b^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//6*x*a^-2*b^-2*(a+b*x^3)^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+-1//18*x*a^-3*b^-2*(a+b*x^3)^-1*(7*f*a^3+11*c*b^3+-1*b*e*a^2+-5*a*d*b^2)+1//27*3^(1/2)*a^-11//3*b^-7//3*(-2*f*a^3+20*c*b^3+-1*b*e*a^2+-5*a*d*b^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-5*(a+b*x^3)^-3*(c+d*x^3+e*x^6+f*x^9), x) == :(a^-4*x^-1*(-1*a*d+3*b*c)+-1//4*c*a^-3*x^-4+-1//27*a^-13//3*b^-5//3*(f*a^3+35*c*b^3+-14*a*d*b^2+2*b*e*a^2)*log(a^1//3+x*b^1//3)+1//54*a^-13//3*b^-5//3*(f*a^3+35*c*b^3+-14*a*d*b^2+2*b*e*a^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//27*3^(1/2)*a^-13//3*b^-5//3*(f*a^3+35*c*b^3+-14*a*d*b^2+2*b*e*a^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//6*a^-3*b^-1*x^2*(a+b*x^3)^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//9*a^-4*b^-1*x^2*(a+b*x^3)^-1*(f*a^3+8*c*b^3+-5*a*d*b^2+2*b*e*a^2))
@test integrate(x^-6*(a+b*x^3)^-3*(c+d*x^3+e*x^6+f*x^9), x) == :((1/2)*a^-4*x^-2*(-1*a*d+3*b*c)+-1//5*c*a^-3*x^-5+-1//54*a^-14//3*b^-4//3*(f*a^3+44*c*b^3+-20*a*d*b^2+5*b*e*a^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//27*a^-14//3*b^-4//3*(f*a^3+44*c*b^3+-20*a*d*b^2+5*b*e*a^2)*log(a^1//3+x*b^1//3)+-1//27*3^(1/2)*a^-14//3*b^-4//3*(f*a^3+44*c*b^3+-20*a*d*b^2+5*b*e*a^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//6*x*a^-3*b^-1*(a+b*x^3)^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//18*x*a^-4*b^-1*(a+b*x^3)^-1*(f*a^3+17*c*b^3+-11*a*d*b^2+5*b*e*a^2))
@test integrate(x^-8*(a+b*x^3)^-3*(c+d*x^3+e*x^6+f*x^9), x) == :(-1*a^-5*x^-1*(e*a^2+6*c*b^2+-3*a*b*d)+-1//7*c*a^-3*x^-7+1//4*a^-4*x^-4*(-1*a*d+3*b*c)+-1//6*a^-4*x^2*(a+b*x^3)^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+-1//9*a^-5*x^2*(a+b*x^3)^-1*(-2*f*a^3+11*c*b^3+-8*a*d*b^2+5*b*e*a^2)+-1//54*a^-16//3*b^-2//3*(-2*f*a^3+65*c*b^3+-35*a*d*b^2+14*b*e*a^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//27*a^-16//3*b^-2//3*(-2*f*a^3+65*c*b^3+-35*a*d*b^2+14*b*e*a^2)*log(a^1//3+x*b^1//3)+1//27*3^(1/2)*a^-16//3*b^-2//3*(-2*f*a^3+65*c*b^3+-35*a*d*b^2+14*b*e*a^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-9*(a+b*x^3)^-3*(c+d*x^3+e*x^6+f*x^9), x) == :(-1//2*a^-5*x^-2*(e*a^2+6*c*b^2+-3*a*b*d)+-1//8*c*a^-3*x^-8+1//5*a^-4*x^-5*(-1*a*d+3*b*c)+-1//6*x*a^-4*(a+b*x^3)^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+-1//18*x*a^-5*(a+b*x^3)^-1*(-5*f*a^3+23*c*b^3+-17*a*d*b^2+11*b*e*a^2)+-1//27*a^-17//3*b^-1//3*(-5*f*a^3+77*c*b^3+-44*a*d*b^2+20*b*e*a^2)*log(a^1//3+x*b^1//3)+1//54*a^-17//3*b^-1//3*(-5*f*a^3+77*c*b^3+-44*a*d*b^2+20*b*e*a^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//27*3^(1/2)*a^-17//3*b^-1//3*(-5*f*a^3+77*c*b^3+-44*a*d*b^2+20*b*e*a^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-11*(a+b*x^3)^-3*(c+d*x^3+e*x^6+f*x^9), x) == :(a^-6*x^-1*(-1*f*a^3+10*c*b^3+-6*a*d*b^2+3*b*e*a^2)+-1//4*a^-5*x^-4*(e*a^2+6*c*b^2+-3*a*b*d)+-1//10*c*a^-3*x^-10+1//7*a^-4*x^-7*(-1*a*d+3*b*c)+-1//27*a^-19//3*b^1//3*(-14*f*a^3+104*c*b^3+-65*a*d*b^2+35*b*e*a^2)*log(a^1//3+x*b^1//3)+1//54*a^-19//3*b^1//3*(-14*f*a^3+104*c*b^3+-65*a*d*b^2+35*b*e*a^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//27*3^(1/2)*a^-19//3*b^1//3*(-14*f*a^3+104*c*b^3+-65*a*d*b^2+35*b*e*a^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//6*b*a^-5*x^2*(a+b*x^3)^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//9*b*a^-6*x^2*(a+b*x^3)^-1*(-5*f*a^3+14*c*b^3+-11*a*d*b^2+8*b*e*a^2))
@test integrate(x^-12*(a+b*x^3)^-3*(c+d*x^3+e*x^6+f*x^9), x) == :((1/2)*a^-6*x^-2*(-1*f*a^3+10*c*b^3+-6*a*d*b^2+3*b*e*a^2)+-1//5*a^-5*x^-5*(e*a^2+6*c*b^2+-3*a*b*d)+-1//11*c*a^-3*x^-11+1//8*a^-4*x^-8*(-1*a*d+3*b*c)+-1//54*a^-20//3*b^2//3*(-20*f*a^3+119*c*b^3+-77*a*d*b^2+44*b*e*a^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//27*a^-20//3*b^2//3*(-20*f*a^3+119*c*b^3+-77*a*d*b^2+44*b*e*a^2)*log(a^1//3+x*b^1//3)+-1//27*3^(1/2)*a^-20//3*b^2//3*(-20*f*a^3+119*c*b^3+-77*a*d*b^2+44*b*e*a^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//6*b*x*a^-5*(a+b*x^3)^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+1//18*b*x*a^-6*(a+b*x^3)^-1*(-11*f*a^3+29*c*b^3+-23*a*d*b^2+17*b*e*a^2))
@test integrate(x^-14*(a+b*x^3)^-3*(c+d*x^3+e*x^6+f*x^9), x) == :(-1//7*a^-5*x^-7*(e*a^2+6*c*b^2+-3*a*b*d)+-1//13*c*a^-3*x^-13+1//4*a^-6*x^-4*(-1*f*a^3+10*c*b^3+-6*a*d*b^2+3*b*e*a^2)+1//10*a^-4*x^-10*(-1*a*d+3*b*c)+-1*b*a^-7*x^-1*(-3*f*a^3+15*c*b^3+-10*a*d*b^2+6*b*e*a^2)+-1//54*a^-22//3*b^4//3*(-35*f*a^3+152*c*b^3+-104*a*d*b^2+65*b*e*a^2)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//27*a^-22//3*b^4//3*(-35*f*a^3+152*c*b^3+-104*a*d*b^2+65*b*e*a^2)*log(a^1//3+x*b^1//3)+-1//6*a^-6*b^2*x^2*(a+b*x^3)^-2*(c*b^3+-1*f*a^3+b*e*a^2+-1*a*d*b^2)+-1//9*a^-7*b^2*x^2*(a+b*x^3)^-1*(-8*f*a^3+17*c*b^3+-14*a*d*b^2+11*b*e*a^2)+1//27*3^(1/2)*a^-22//3*b^4//3*(-35*f*a^3+152*c*b^3+-104*a*d*b^2+65*b*e*a^2)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^4*(1+x^3)^-1*(1+-1x), x) == :((1/2)*x^2+-1//3*x^3+1//6*log(1+x^2+-1x)+2//3*log(1+x)+1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x)))
@test integrate(x^3*(1+x^3)^-1*(1+-1x), x) == :(x+-2//3*log(1+x)+-1//2*x^2+1//3*log(1+x^2+-1x))
@test integrate(x^2*(1+x^3)^-1*(1+-1x), x) == :(-1x+1//6*log(1+x^2+-1x)+2//3*log(1+x)+-1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x)))
@test integrate(x*(1+x^3)^-1*(1+-1x), x) == :(-2//3*log(1+x)+-1//6*log(1+x^2+-1x)+-1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x)))
@test integrate(x^-1*(1+x^3)^-1*(1+-1x), x) == :(-2//3*log(1+x)+-1//6*log(1+x^2+-1x)+1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x))+log(x))
@test integrate(x^-2*(1+x^3)^-1*(1+-1x), x) == :(-1*x^-1+-1*log(x)+1//6*log(1+x^2+-1x)+2//3*log(1+x)+1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x)))
@test integrate(x^-3*(1+x^3)^-1*(1+-1x), x) == :(x^-1+-2//3*log(1+x)+-1//2*x^-2+1//3*log(1+x^2+-1x))
@test integrate(x*(1+x^3)^-1*(1+2x), x) == :(1//3*log(1+x)+5//6*log(1+x^2+-1x)+-1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2x)))
@test integrate(x*(1+-1*x^3)^-1*(1+2x), x) == :(-1*log(1+-1x)+-1//2*log(1+x+x^2)+-1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+2x)))
@test integrate(x^2*(a+b*x^3)*(c+d*x+e*x^2), x) == :(1//3*a*c*x^3+1//4*a*d*x^4+1//5*a*e*x^5+1//6*b*c*x^6+1//7*b*d*x^7+1//8*b*e*x^8)
@test integrate(x*(a+b*x^3)*(c+d*x+e*x^2), x) == :((1/2)*a*c*x^2+1//3*a*d*x^3+1//4*a*e*x^4+1//5*b*c*x^5+1//6*b*d*x^6+1//7*b*e*x^7)
@test integrate((a+b*x^3)*(c+d*x+e*x^2), x) == :(a*c*x+(1/2)*a*d*x^2+1//3*a*e*x^3+1//4*b*c*x^4+1//5*b*d*x^5+1//6*b*e*x^6)
@test integrate(x^-1*(a+b*x^3)*(c+d*x+e*x^2), x) == :(a*c*log(x)+a*d*x+(1/2)*a*e*x^2+1//3*b*c*x^3+1//4*b*d*x^4+1//5*b*e*x^5)
@test integrate(x^-2*(a+b*x^3)*(c+d*x+e*x^2), x) == :(a*d*log(x)+a*e*x+(1/2)*b*c*x^2+-1*a*c*x^-1+1//3*b*d*x^3+1//4*b*e*x^4)
@test integrate(x^-3*(a+b*x^3)*(c+d*x+e*x^2), x) == :(a*e*log(x)+b*c*x+(1/2)*b*d*x^2+-1*a*d*x^-1+-1//2*a*c*x^-2+1//3*b*e*x^3)
@test integrate(x^2*(a+b*x^3)^2*(c+d*x+e*x^2), x) == :(1//4*d*a^2*x^4+1//5*e*a^2*x^5+1//9*c*b^-1*(a+b*x^3)^3+1//10*d*b^2*x^10+1//11*e*b^2*x^11+1//4*a*b*e*x^8+2//7*a*b*d*x^7)
@test integrate(x*(a+b*x^3)^2*(c+d*x+e*x^2), x) == :((1/2)*c*a^2*x^2+1//4*e*a^2*x^4+1//8*c*b^2*x^8+1//9*d*b^-1*(a+b*x^3)^3+1//10*e*b^2*x^10+2//5*a*b*c*x^5+2//7*a*b*e*x^7)
@test integrate((a+b*x^3)^2*(c+d*x+e*x^2), x) == :(c*x*a^2+(1/2)*d*a^2*x^2+1//7*c*b^2*x^7+1//8*d*b^2*x^8+1//9*e*b^-1*(a+b*x^3)^3+(1/2)*a*b*c*x^4+2//5*a*b*d*x^5)
@test integrate(x^-1*(a+b*x^3)^2*(c+d*x+e*x^2), x) == :(c*a^2*log(x)+d*x*a^2+(1/2)*e*a^2*x^2+1//6*c*b^2*x^6+1//7*d*b^2*x^7+1//8*e*b^2*x^8+(1/2)*a*b*d*x^4+2//3*a*b*c*x^3+2//5*a*b*e*x^5)
@test integrate(x^-2*(a+b*x^3)^2*(c+d*x+e*x^2), x) == :(d*a^2*log(x)+e*x*a^2+-1*c*a^2*x^-1+1//5*c*b^2*x^5+1//6*d*b^2*x^6+1//7*e*b^2*x^7+a*b*c*x^2+(1/2)*a*b*e*x^4+2//3*a*b*d*x^3)
@test integrate(x^-3*(a+b*x^3)^2*(c+d*x+e*x^2), x) == :(e*a^2*log(x)+-1*d*a^2*x^-1+-1//2*c*a^2*x^-2+1//4*c*b^2*x^4+1//5*d*b^2*x^5+1//6*e*b^2*x^6+a*b*d*x^2+2*a*b*c*x+2//3*a*b*e*x^3)
@test integrate(x^2*(a+b*x^3)^3*(c+d*x+e*x^2), x) == :(1//4*d*a^3*x^4+1//5*e*a^3*x^5+1//12*c*b^-1*(a+b*x^3)^4+1//13*d*b^3*x^13+1//14*e*b^3*x^14+3//7*b*d*a^2*x^7+3//8*b*e*a^2*x^8+3//10*a*d*b^2*x^10+3//11*a*e*b^2*x^11)
@test integrate(x*(a+b*x^3)^3*(c+d*x+e*x^2), x) == :((1/2)*c*a^3*x^2+1//4*e*a^3*x^4+1//11*c*b^3*x^11+1//12*d*b^-1*(a+b*x^3)^4+1//13*e*b^3*x^13+3//5*b*c*a^2*x^5+3//7*b*e*a^2*x^7+3//8*a*c*b^2*x^8+3//10*a*e*b^2*x^10)
@test integrate((a+b*x^3)^3*(c+d*x+e*x^2), x) == :(c*x*a^3+(1/2)*d*a^3*x^2+1//10*c*b^3*x^10+1//11*d*b^3*x^11+1//12*e*b^-1*(a+b*x^3)^4+3//4*b*c*a^2*x^4+3//5*b*d*a^2*x^5+3//7*a*c*b^2*x^7+3//8*a*d*b^2*x^8)
@test integrate(x^-1*(a+b*x^3)^3*(c+d*x+e*x^2), x) == :(c*a^3*log(x)+d*x*a^3+(1/2)*e*a^3*x^2+1//9*c*b^3*x^9+1//10*d*b^3*x^10+1//11*e*b^3*x^11+b*c*a^2*x^3+(1/2)*a*c*b^2*x^6+3//4*b*d*a^2*x^4+3//5*b*e*a^2*x^5+3//7*a*d*b^2*x^7+3//8*a*e*b^2*x^8)
@test integrate(x^-2*(a+b*x^3)^3*(c+d*x+e*x^2), x) == :(d*a^3*log(x)+e*x*a^3+-1*c*a^3*x^-1+1//8*c*b^3*x^8+1//9*d*b^3*x^9+1//10*e*b^3*x^10+b*d*a^2*x^3+(1/2)*a*d*b^2*x^6+3//2*b*c*a^2*x^2+3//4*b*e*a^2*x^4+3//5*a*c*b^2*x^5+3//7*a*e*b^2*x^7)
@test integrate(x^-3*(a+b*x^3)^3*(c+d*x+e*x^2), x) == :(e*a^3*log(x)+-1*d*a^3*x^-1+-1//2*c*a^3*x^-2+1//7*c*b^3*x^7+1//8*d*b^3*x^8+1//9*e*b^3*x^9+b*e*a^2*x^3+(1/2)*a*e*b^2*x^6+3*b*c*x*a^2+3//2*b*d*a^2*x^2+3//4*a*c*b^2*x^4+3//5*a*d*b^2*x^5)
@test integrate(x^2*(a+b*x^3)^4*(c+d*x+e*x^2), x) == :(1//4*d*a^4*x^4+1//5*e*a^4*x^5+1//15*c*b^-1*(a+b*x^3)^5+1//16*d*b^4*x^16+1//17*e*b^4*x^17+(1/2)*b*e*a^3*x^8+2//7*a*e*b^3*x^14+3//5*d*a^2*b^2*x^10+4//7*b*d*a^3*x^7+4//13*a*d*b^3*x^13+6//11*e*a^2*b^2*x^11)
@test integrate(x*(a+b*x^3)^4*(c+d*x+e*x^2), x) == :((1/2)*c*a^4*x^2+1//4*e*a^4*x^4+1//14*c*b^4*x^14+1//15*d*b^-1*(a+b*x^3)^5+1//16*e*b^4*x^16+3//4*c*a^2*b^2*x^8+3//5*e*a^2*b^2*x^10+4//5*b*c*a^3*x^5+4//7*b*e*a^3*x^7+4//11*a*c*b^3*x^11+4//13*a*e*b^3*x^13)
@test integrate((a+b*x^3)^4*(c+d*x+e*x^2), x) == :(c*x*a^4+(1/2)*d*a^4*x^2+1//13*c*b^4*x^13+1//14*d*b^4*x^14+1//15*e*b^-1*(a+b*x^3)^5+b*c*a^3*x^4+2//5*a*c*b^3*x^10+3//4*d*a^2*b^2*x^8+4//5*b*d*a^3*x^5+4//11*a*d*b^3*x^11+6//7*c*a^2*b^2*x^7)
@test integrate(x^-1*(a+b*x^3)^4*(c+d*x+e*x^2), x) == :(c*a^4*log(x)+d*x*a^4+(1/2)*e*a^4*x^2+1//12*c*b^4*x^12+1//13*d*b^4*x^13+1//14*e*b^4*x^14+b*d*a^3*x^4+c*a^2*b^2*x^6+2//5*a*d*b^3*x^10+3//4*e*a^2*b^2*x^8+4//3*b*c*a^3*x^3+4//5*b*e*a^3*x^5+4//9*a*c*b^3*x^9+4//11*a*e*b^3*x^11+6//7*d*a^2*b^2*x^7)
@test integrate(x^-2*(a+b*x^3)^4*(c+d*x+e*x^2), x) == :(d*a^4*log(x)+e*x*a^4+-1*c*a^4*x^-1+1//11*c*b^4*x^11+1//12*d*b^4*x^12+1//13*e*b^4*x^13+b*e*a^3*x^4+d*a^2*b^2*x^6+(1/2)*a*c*b^3*x^8+2*b*c*a^3*x^2+2//5*a*e*b^3*x^10+4//3*b*d*a^3*x^3+4//9*a*d*b^3*x^9+6//5*c*a^2*b^2*x^5+6//7*e*a^2*b^2*x^7)
@test integrate(x^-3*(a+b*x^3)^4*(c+d*x+e*x^2), x) == :(e*a^4*log(x)+-1*d*a^4*x^-1+-1//2*c*a^4*x^-2+1//10*c*b^4*x^10+1//11*d*b^4*x^11+1//12*e*b^4*x^12+e*a^2*b^2*x^6+(1/2)*a*d*b^3*x^8+2*b*d*a^3*x^2+4*b*c*x*a^3+3//2*c*a^2*b^2*x^4+4//3*b*e*a^3*x^3+4//7*a*c*b^3*x^7+4//9*a*e*b^3*x^9+6//5*d*a^2*b^2*x^5)
@test integrate(x^3*(a+b*x^3)^-1*(c+d*x+e*x^2), x) == :(c*x*b^-1+(1/2)*d*b^-1*x^2+1//3*e*b^-1*x^3+-1//3*a*e*b^-2*log(a+b*x^3)+-1//3*a^1//3*b^-5//3*(c*b^1//3+-1*d*a^1//3)*log(a^1//3+x*b^1//3)+1//6*a^1//3*b^-4//3*(c+-1*d*a^1//3*b^-1//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^-5//3*(c*b^1//3+d*a^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^2*(a+b*x^3)^-1*(c+d*x+e*x^2), x) == :(d*x*b^-1+(1/2)*e*b^-1*x^2+1//3*c*b^-1*log(a+b*x^3)+-1//3*a^1//3*b^-5//3*(d*b^1//3+-1*e*a^1//3)*log(a^1//3+x*b^1//3)+1//6*a^1//3*b^-4//3*(d+-1*e*a^1//3*b^-1//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^-5//3*(d*b^1//3+e*a^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x*(a+b*x^3)^-1*(c+d*x+e*x^2), x) == :(e*x*b^-1+1//3*d*b^-1*log(a+b*x^3)+-1//3*a^-1//3*b^-4//3*(c*b^2//3+e*a^2//3)*log(a^1//3+x*b^1//3)+1//6*a^-1//3*b^-4//3*(c*b^2//3+e*a^2//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*(c*b^2//3+-1*e*a^2//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate((a+b*x^3)^-1*(c+d*x+e*x^2), x) == :(1//3*e*b^-1*log(a+b*x^3)+-1//6*a^-2//3*b^-1//3*(c+-1*d*a^1//3*b^-1//3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-2//3*b^-2//3*(c*b^1//3+-1*d*a^1//3)*log(a^1//3+x*b^1//3)+-1//3*3^(1/2)*a^-2//3*b^-2//3*(c*b^1//3+d*a^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-1*(a+b*x^3)^-1*(c+d*x+e*x^2), x) == :(c*a^-1*log(x)+-1//3*c*a^-1*log(a+b*x^3)+-1//6*a^-2//3*b^-1//3*(d+-1*e*a^1//3*b^-1//3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-2//3*b^-2//3*(d*b^1//3+-1*e*a^1//3)*log(a^1//3+x*b^1//3)+-1//3*3^(1/2)*a^-2//3*b^-2//3*(d*b^1//3+e*a^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-2*(a+b*x^3)^-1*(c+d*x+e*x^2), x) == :(d*a^-1*log(x)+-1*c*a^-1*x^-1+-1//3*d*a^-1*log(a+b*x^3)+-1//6*a^-4//3*b^-1//3*(c*b^2//3+e*a^2//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*(c*b^2//3+e*a^2//3)*log(a^1//3+x*b^1//3)+1//3*3^(1/2)*a^-4//3*b^-1//3*(c*b^2//3+-1*e*a^2//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-3*(a+b*x^3)^-1*(c+d*x+e*x^2), x) == :(e*a^-1*log(x)+-1*d*a^-1*x^-1+-1//2*c*a^-1*x^-2+-1//3*e*a^-1*log(a+b*x^3)+-1//3*a^-5//3*b^1//3*(c*b^1//3+-1*d*a^1//3)*log(a^1//3+x*b^1//3)+1//6*a^-5//3*b^2//3*(c+-1*d*a^1//3*b^-1//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^1//3*(c*b^1//3+d*a^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^2*(a+b*x^3)^-2*(c+d*x+e*x^2), x) == :(-1//3*b^-1*(a+b*x^3)^-1*(c+d*x+e*x^2)+-1//18*a^-2//3*b^-4//3*(d+-2*e*a^1//3*b^-1//3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*a^-2//3*b^-5//3*(d*b^1//3+-2*e*a^1//3)*log(a^1//3+x*b^1//3)+-1//9*3^(1/2)*a^-2//3*b^-5//3*(d*b^1//3+2*e*a^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x*(a+b*x^3)^-2*(c+d*x+e*x^2), x) == :(-1//9*a^-4//3*b^-4//3*(c*b^2//3+-1*e*a^2//3)*log(a^1//3+x*b^1//3)+1//18*a^-4//3*b^-4//3*(c*b^2//3+-1*e*a^2//3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//3*x*a^-1*b^-1*(a+b*x^3)^-1*(a*e+-1*b*c*x+-1*b*d*x^2)+-1//9*3^(1/2)*a^-4//3*b^-4//3*(c*b^2//3+e*a^2//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate((a+b*x^3)^-2*(c+d*x+e*x^2), x) == :(-1//3*a^-1*b^-1*(a+b*x^3)^-1*(a*e+-1*b*x*(c+d*x))+-1//18*a^-5//3*b^-2//3*(-1*d*a^1//3+2*c*b^1//3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*a^-5//3*b^-2//3*(-1*d*a^1//3+2*c*b^1//3)*log(a^1//3+x*b^1//3)+-1//9*3^(1/2)*a^-5//3*b^-2//3*(d*a^1//3+2*c*b^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-1*(a+b*x^3)^-2*(c+d*x+e*x^2), x) == :(c*a^-2*log(x)+-1//3*c*a^-2*log(a+b*x^3)+-1//18*a^-5//3*b^-2//3*(-1*e*a^1//3+2*d*b^1//3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*x*a^-2*(a+b*x^3)^-1*(a*d+a*e*x+-1*b*c*x^2)+1//9*a^-5//3*b^-2//3*(-1*e*a^1//3+2*d*b^1//3)*log(a^1//3+x*b^1//3)+-1//9*3^(1/2)*a^-5//3*b^-2//3*(e*a^1//3+2*d*b^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-2*(a+b*x^3)^-2*(c+d*x+e*x^2), x) == :(d*a^-2*log(x)+-1*c*a^-2*x^-1+-1//3*d*a^-2*log(a+b*x^3)+-1//9*a^-7//3*b^-1//3*(e*a^2//3+2*c*b^2//3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*x*a^-2*(a+b*x^3)^-1*(a*e+-1*b*c*x+-1*b*d*x^2)+1//9*a^-7//3*b^-1//3*(2*e*a^2//3+4*c*b^2//3)*log(a^1//3+x*b^1//3)+1//9*3^(1/2)*a^-7//3*b^-1//3*(-2*e*a^2//3+4*c*b^2//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-3*(a+b*x^3)^-2*(c+d*x+e*x^2), x) == :(e*a^-2*log(x)+-1*d*a^-2*x^-1+-1//2*c*a^-2*x^-2+-1//3*e*a^-2*log(a+b*x^3)+-1//3*x*a^-2*(a+b*x^3)^-1*(b*c+b*d*x+b*e*x^2)+-1//9*a^-8//3*b^1//3*(-4*d*a^1//3+5*c*b^1//3)*log(a^1//3+x*b^1//3)+1//18*a^-8//3*b^1//3*(-4*d*a^1//3+5*c*b^1//3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*3^(1/2)*a^-8//3*b^1//3*(4*d*a^1//3+5*c*b^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-4*(a+b*x^3)^-2*(c+d*x+e*x^2), x) == :(-1*e*a^-2*x^-1+-1//2*d*a^-2*x^-2+-1//3*c*a^-2*x^-3+-2*b*c*a^-3*log(x)+-1//3*x*a^-2*(a+b*x^3)^-1*(b*d+b*e*x+-1*c*a^-1*b^2*x^2)+-1//9*a^-8//3*b^1//3*(-4*e*a^1//3+5*d*b^1//3)*log(a^1//3+x*b^1//3)+1//18*a^-8//3*b^1//3*(-4*e*a^1//3+5*d*b^1//3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+2//3*b*c*a^-3*log(a+b*x^3)+1//9*3^(1/2)*a^-8//3*b^1//3*(4*e*a^1//3+5*d*b^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^2*(a+b*x^3)^-3*(c+d*x+e*x^2), x) == :(-1//6*b^-1*(a+b*x^3)^-2*(c+d*x+e*x^2)+-1//54*a^-5//3*b^-4//3*(d+-1*e*a^1//3*b^-1//3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//27*a^-5//3*b^-5//3*(d*b^1//3+-1*e*a^1//3)*log(a^1//3+x*b^1//3)+-1//27*3^(1/2)*a^-5//3*b^-5//3*(d*b^1//3+e*a^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//18*x*a^-1*b^-1*(a+b*x^3)^-1*(d+2*e*x))
@test integrate(x*(a+b*x^3)^-3*(c+d*x+e*x^2), x) == :(-1//18*a^-2*b^-1*(a+b*x^3)^-1*(-1*x*(a*e+4*b*c*x)+3*a*d)+-1//27*a^-7//3*b^-4//3*(-1*e*a^2//3+2*c*b^2//3)*log(a^1//3+x*b^1//3)+1//54*a^-7//3*b^-4//3*(-1*e*a^2//3+2*c*b^2//3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//6*x*a^-1*b^-1*(a+b*x^3)^-2*(a*e+-1*b*c*x+-1*b*d*x^2)+-1//27*3^(1/2)*a^-7//3*b^-4//3*(e*a^2//3+2*c*b^2//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate((a+b*x^3)^-3*(c+d*x+e*x^2), x) == :(-1//6*a^-1*b^-1*(a+b*x^3)^-2*(a*e+-1*b*x*(c+d*x))+-1//54*a^-8//3*b^-2//3*(-2*d*a^1//3+5*c*b^1//3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//18*x*a^-2*(a+b*x^3)^-1*(5c+4*d*x)+1//27*a^-8//3*b^-2//3*(-2*d*a^1//3+5*c*b^1//3)*log(a^1//3+x*b^1//3)+-1//27*3^(1/2)*a^-8//3*b^-2//3*(2*d*a^1//3+5*c*b^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-1*(a+b*x^3)^-3*(c+d*x+e*x^2), x) == :(c*a^-3*log(x)+-1//3*c*a^-3*log(a+b*x^3)+-1//54*a^-8//3*b^-2//3*(-2*e*a^1//3+5*d*b^1//3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//6*x*a^-2*(a+b*x^3)^-2*(a*d+a*e*x+-1*b*c*x^2)+1//18*x*a^-3*(a+b*x^3)^-1*(5*a*d+-9*b*c*x^2+4*a*e*x)+1//27*a^-8//3*b^-2//3*(-2*e*a^1//3+5*d*b^1//3)*log(a^1//3+x*b^1//3)+-1//27*3^(1/2)*a^-8//3*b^-2//3*(2*e*a^1//3+5*d*b^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-2*(a+b*x^3)^-3*(c+d*x+e*x^2), x) == :(d*a^-3*log(x)+-1*c*a^-3*x^-1+-1//3*d*a^-3*log(a+b*x^3)+-1//54*a^-10//3*b^-1//3*(5*e*a^2//3+14*c*b^2//3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//6*x*a^-2*(a+b*x^3)^-2*(a*e+-1*b*c*x+-1*b*d*x^2)+1//18*x*a^-3*(a+b*x^3)^-1*(5*a*e+-10*b*c*x+-9*b*d*x^2)+1//27*a^-10//3*b^-1//3*(5*e*a^2//3+14*c*b^2//3)*log(a^1//3+x*b^1//3)+1//27*3^(1/2)*a^-10//3*b^-1//3*(-5*e*a^2//3+14*c*b^2//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-3*(a+b*x^3)^-3*(c+d*x+e*x^2), x) == :(e*a^-3*log(x)+-1*d*a^-3*x^-1+-1//2*c*a^-3*x^-2+-1//3*e*a^-3*log(a+b*x^3)+-2//27*a^-11//3*b^1//3*(-7*d*a^1//3+10*c*b^1//3)*log(a^1//3+x*b^1//3)+-1//6*x*a^-2*(a+b*x^3)^-2*(b*c+b*d*x+b*e*x^2)+-1//18*x*a^-3*(a+b*x^3)^-1*(11*b*c+9*b*e*x^2+10*b*d*x)+1//27*a^-11//3*b^1//3*(-7*d*a^1//3+10*c*b^1//3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+2//27*3^(1/2)*a^-11//3*b^1//3*(7*d*a^1//3+10*c*b^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-4*(a+b*x^3)^-3*(c+d*x+e*x^2), x) == :(-1*e*a^-3*x^-1+-1//2*d*a^-3*x^-2+-1//3*c*a^-3*x^-3+b*c*a^-4*log(a+b*x^3)+-3*b*c*a^-4*log(x)+-2//27*a^-11//3*b^1//3*(-7*e*a^1//3+10*d*b^1//3)*log(a^1//3+x*b^1//3)+-1//6*x*a^-2*(a+b*x^3)^-2*(b*d+b*e*x+-1*c*a^-1*b^2*x^2)+-1//18*x*a^-3*(a+b*x^3)^-1*(11*b*d+10*b*e*x+-15*c*a^-1*b^2*x^2)+1//27*a^-11//3*b^1//3*(-7*e*a^1//3+10*d*b^1//3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+2//27*3^(1/2)*a^-11//3*b^1//3*(7*e*a^1//3+10*d*b^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^2*(a+b*x^3)^-4*(c+d*x+e*x^2), x) == :(-1//9*b^-1*(a+b*x^3)^-3*(c+d*x+e*x^2)+-1//486*a^-8//3*b^-5//3*(-4*e*a^1//3+5*d*b^1//3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//243*a^-8//3*b^-5//3*(-4*e*a^1//3+5*d*b^1//3)*log(a^1//3+x*b^1//3)+-1//243*3^(1/2)*a^-8//3*b^-5//3*(4*e*a^1//3+5*d*b^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//54*x*a^-1*b^-1*(a+b*x^3)^-2*(d+2*e*x)+1//162*x*a^-2*b^-1*(a+b*x^3)^-1*(5d+8*e*x))
@test integrate(x*(a+b*x^3)^-4*(c+d*x+e*x^2), x) == :(-1//54*a^-2*b^-1*(a+b*x^3)^-2*(-1*x*(a*e+7*b*c*x)+6*a*d)+-1//243*a^-10//3*b^-4//3*(-5*e*a^2//3+14*c*b^2//3)*log(a^1//3+x*b^1//3)+1//486*a^-10//3*b^-4//3*(-5*e*a^2//3+14*c*b^2//3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//9*x*a^-1*b^-1*(a+b*x^3)^-3*(a*e+-1*b*c*x+-1*b*d*x^2)+-1//243*3^(1/2)*a^-10//3*b^-4//3*(5*e*a^2//3+14*c*b^2//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//162*x*a^-3*b^-1*(a+b*x^3)^-1*(5*a*e+28*b*c*x))
@test integrate((a+b*x^3)^-4*(c+d*x+e*x^2), x) == :(-1//9*a^-1*b^-1*(a+b*x^3)^-3*(a*e+-1*b*x*(c+d*x))+-1//243*a^-11//3*b^-2//3*(-7*d*a^1//3+20*c*b^1//3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//54*x*a^-2*(a+b*x^3)^-2*(8c+7*d*x)+1//243*a^-11//3*b^-2//3*(-14*d*a^1//3+40*c*b^1//3)*log(a^1//3+x*b^1//3)+2//81*x*a^-3*(a+b*x^3)^-1*(10c+7*d*x)+-1//243*3^(1/2)*a^-11//3*b^-2//3*(14*d*a^1//3+40*c*b^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-1*(a+b*x^3)^-4*(c+d*x+e*x^2), x) == :(c*a^-4*log(x)+-1//3*c*a^-4*log(a+b*x^3)+-1//243*a^-11//3*b^-2//3*(-7*e*a^1//3+20*d*b^1//3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*x*a^-2*(a+b*x^3)^-3*(a*d+a*e*x+-1*b*c*x^2)+1//54*x*a^-3*(a+b*x^3)^-2*(8*a*d+-15*b*c*x^2+7*a*e*x)+1//162*x*a^-4*(a+b*x^3)^-1*(40*a*d+-99*b*c*x^2+28*a*e*x)+1//243*a^-11//3*b^-2//3*(-14*e*a^1//3+40*d*b^1//3)*log(a^1//3+x*b^1//3)+-1//243*3^(1/2)*a^-11//3*b^-2//3*(14*e*a^1//3+40*d*b^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-2*(a+b*x^3)^-4*(c+d*x+e*x^2), x) == :(d*a^-4*log(x)+-1*c*a^-4*x^-1+-1//3*d*a^-4*log(a+b*x^3)+-1//243*a^-13//3*b^-1//3*(20*e*a^2//3+70*c*b^2//3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*x*a^-2*(a+b*x^3)^-3*(a*e+-1*b*c*x+-1*b*d*x^2)+1//54*x*a^-3*(a+b*x^3)^-2*(8*a*e+-16*b*c*x+-15*b*d*x^2)+1//162*x*a^-4*(a+b*x^3)^-1*(40*a*e+-118*b*c*x+-99*b*d*x^2)+1//243*a^-13//3*b^-1//3*(40*e*a^2//3+140*c*b^2//3)*log(a^1//3+x*b^1//3)+1//243*3^(1/2)*a^-13//3*b^-1//3*(-40*e*a^2//3+140*c*b^2//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-3*(a+b*x^3)^-4*(c+d*x+e*x^2), x) == :(e*a^-4*log(x)+-1*d*a^-4*x^-1+-1//2*c*a^-4*x^-2+-1//3*e*a^-4*log(a+b*x^3)+-20//243*a^-14//3*b^1//3*(-7*d*a^1//3+11*c*b^1//3)*log(a^1//3+x*b^1//3)+-1//9*x*a^-2*(a+b*x^3)^-3*(b*c+b*d*x+b*e*x^2)+-1//54*x*a^-3*(a+b*x^3)^-2*(17*b*c+15*b*e*x^2+16*b*d*x)+-1//162*x*a^-4*(a+b*x^3)^-1*(139*b*c+99*b*e*x^2+118*b*d*x)+10//243*a^-14//3*b^1//3*(-7*d*a^1//3+11*c*b^1//3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+20//243*3^(1/2)*a^-14//3*b^1//3*(7*d*a^1//3+11*c*b^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-4*(a+b*x^3)^-4*(c+d*x+e*x^2), x) == :(-1*e*a^-4*x^-1+-1//2*d*a^-4*x^-2+-1//3*c*a^-4*x^-3+-4*b*c*a^-5*log(x)+-20//243*a^-14//3*b^1//3*(-7*e*a^1//3+11*d*b^1//3)*log(a^1//3+x*b^1//3)+-1//9*x*a^-2*(a+b*x^3)^-3*(b*d+b*e*x+-1*c*a^-1*b^2*x^2)+-1//54*x*a^-3*(a+b*x^3)^-2*(17*b*d+16*b*e*x+-24*c*a^-1*b^2*x^2)+-1//162*x*a^-4*(a+b*x^3)^-1*(139*b*d+118*b*e*x+-234*c*a^-1*b^2*x^2)+4//3*b*c*a^-5*log(a+b*x^3)+10//243*a^-14//3*b^1//3*(-7*e*a^1//3+11*d*b^1//3)*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+20//243*3^(1/2)*a^-14//3*b^1//3*(7*e*a^1//3+11*d*b^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate((a^3+x^3)^-1*(-1*x^2+2*a*x), x) == :(-1*log(a+x)+-2//3*3^(1/2)*arctan(1//3*3^(1/2)*a^-1*(a+-2x)))
@test integrate(x*(a^3+x^3)^-1*(-1x+2a), x) == :(-1*log(a+x)+-2//3*3^(1/2)*arctan(1//3*3^(1/2)*a^-1*(a+-2x)))
@test integrate((a^3+-1*x^3)^-1*(x^2+2*a*x), x) == :(-1*log(a+-1x)+-2//3*3^(1/2)*arctan(1//3*3^(1/2)*a^-1*(a+2x)))
@test integrate(x*(a^3+-1*x^3)^-1*(x+2a), x) == :(-1*log(a+-1x)+-2//3*3^(1/2)*arctan(1//3*3^(1/2)*a^-1*(a+2x)))
@test integrate(x*(a+b*x^3)^-1*(C*x+-2*C*(a*b^-1)^1//3), x) == :(C*b^-1*log(x+(a*b^-1)^1//3)+2//3*C*3^(1/2)*b^-1*arctan(1//3*3^(1/2)*(1+-2*x*(a*b^-1)^-1//3)))
@test integrate(x*(a+-1*b*x^3)^-1*(C*x+-2*C*(-1*a*b^-1)^1//3), x) == :(-1*C*b^-1*log(x+(-1*a*b^-1)^1//3)+-2//3*C*3^(1/2)*b^-1*arctan(1//3*3^(1/2)*(1+-2*x*(-1*a*b^-1)^-1//3)))
@test integrate(x*(a+b*x^3)^-1*(C*x+2*C*(-1*a*b^-1)^1//3), x) == :(C*b^-1*log((-1*a*b^-1)^1//3+-1x)+2//3*C*3^(1/2)*b^-1*arctan(1//3*3^(1/2)*(1+2*x*(-1*a*b^-1)^-1//3)))
@test integrate(x*(a+-1*b*x^3)^-1*(C*x+2*C*(a*b^-1)^1//3), x) == :(-1*C*b^-1*log((a*b^-1)^1//3+-1x)+-2//3*C*3^(1/2)*b^-1*arctan(1//3*3^(1/2)*(1+2*x*(a*b^-1)^-1//3)))
@test integrate(x^4*(a+b*x^3)*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(1//8*x^8*(a*f+b*c)+1//9*x^9*(a*g+b*d)+1//10*x^10*(a*h+b*e)+1//5*a*c*x^5+1//6*a*d*x^6+1//7*a*e*x^7+1//11*b*f*x^11+1//12*b*g*x^12+1//13*b*h*x^13)
@test integrate(x^3*(a+b*x^3)*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(1//7*x^7*(a*f+b*c)+1//8*x^8*(a*g+b*d)+1//9*x^9*(a*h+b*e)+1//4*a*c*x^4+1//5*a*d*x^5+1//6*a*e*x^6+1//10*b*f*x^10+1//11*b*g*x^11+1//12*b*h*x^12)
@test integrate(x^2*(a+b*x^3)*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(1//6*x^6*(a*f+b*c)+1//7*x^7*(a*g+b*d)+1//8*x^8*(a*h+b*e)+1//3*a*c*x^3+1//4*a*d*x^4+1//5*a*e*x^5+1//9*b*f*x^9+1//10*b*g*x^10+1//11*b*h*x^11)
@test integrate(x*(a+b*x^3)*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(1//5*x^5*(a*f+b*c)+1//6*x^6*(a*g+b*d)+1//7*x^7*(a*h+b*e)+(1/2)*a*c*x^2+1//3*a*d*x^3+1//4*a*e*x^4+1//8*b*f*x^8+1//9*b*g*x^9+1//10*b*h*x^10)
@test integrate((a+b*x^3)*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(1//4*x^4*(a*f+b*c)+1//5*x^5*(a*g+b*d)+1//6*x^6*(a*h+b*e)+a*c*x+(1/2)*a*d*x^2+1//3*a*e*x^3+1//7*b*f*x^7+1//8*b*g*x^8+1//9*b*h*x^9)
@test integrate(x^-1*(a+b*x^3)*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(1//3*x^3*(a*f+b*c)+1//4*x^4*(a*g+b*d)+1//5*x^5*(a*h+b*e)+a*c*log(x)+a*d*x+(1/2)*a*e*x^2+1//6*b*f*x^6+1//7*b*g*x^7+1//8*b*h*x^8)
@test integrate(x^-2*(a+b*x^3)*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :((1/2)*x^2*(a*f+b*c)+1//3*x^3*(a*g+b*d)+1//4*x^4*(a*h+b*e)+a*d*log(x)+a*e*x+-1*a*c*x^-1+1//5*b*f*x^5+1//6*b*g*x^6+1//7*b*h*x^7)
@test integrate(x^-3*(a+b*x^3)*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(x*(a*f+b*c)+(1/2)*x^2*(a*g+b*d)+1//3*x^3*(a*h+b*e)+a*e*log(x)+-1*a*d*x^-1+-1//2*a*c*x^-2+1//4*b*f*x^4+1//5*b*g*x^5+1//6*b*h*x^6)
@test integrate(x^-4*(a+b*x^3)*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(x*(a*g+b*d)+(a*f+b*c)*log(x)+(1/2)*x^2*(a*h+b*e)+-1*a*e*x^-1+-1//2*a*d*x^-2+-1//3*a*c*x^-3+1//3*b*f*x^3+1//4*b*g*x^4+1//5*b*h*x^5)
@test integrate(x^-5*(a+b*x^3)*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(x*(a*h+b*e)+(a*g+b*d)*log(x)+-1*x^-1*(a*f+b*c)+(1/2)*b*f*x^2+-1//2*a*e*x^-2+-1//3*a*d*x^-3+-1//4*a*c*x^-4+1//3*b*g*x^3+1//4*b*h*x^4)
@test integrate(x^4*(a+b*x^3)^2*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(1//5*c*a^2*x^5+1//6*d*a^2*x^6+1//7*e*a^2*x^7+1//8*a*x^8*(a*f+2*b*c)+1//9*a*x^9*(a*g+2*b*d)+1//10*a*x^10*(a*h+2*b*e)+1//11*b*x^11*(b*c+2*a*f)+1//12*b*x^12*(b*d+2*a*g)+1//13*b*x^13*(b*e+2*a*h)+1//14*f*b^2*x^14+1//15*g*b^2*x^15+1//16*h*b^2*x^16)
@test integrate(x^3*(a+b*x^3)^2*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(1//4*c*a^2*x^4+1//5*d*a^2*x^5+1//6*e*a^2*x^6+1//7*a*x^7*(a*f+2*b*c)+1//8*a*x^8*(a*g+2*b*d)+1//9*a*x^9*(a*h+2*b*e)+1//10*b*x^10*(b*c+2*a*f)+1//11*b*x^11*(b*d+2*a*g)+1//12*b*x^12*(b*e+2*a*h)+1//13*f*b^2*x^13+1//14*g*b^2*x^14+1//15*h*b^2*x^15)
@test integrate(x^2*(a+b*x^3)^2*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(1//4*d*a^2*x^4+1//5*e*a^2*x^5+1//6*f*a^2*x^6+1//7*a*x^7*(a*g+2*b*d)+1//8*a*x^8*(a*h+2*b*e)+1//9*c*b^-1*(a+b*x^3)^3+1//10*b*x^10*(b*d+2*a*g)+1//11*b*x^11*(b*e+2*a*h)+1//12*f*b^2*x^12+1//13*g*b^2*x^13+1//14*h*b^2*x^14+2//9*a*b*f*x^9)
@test integrate(x*(a+b*x^3)^2*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :((1/2)*c*a^2*x^2+1//4*e*a^2*x^4+1//5*a*x^5*(a*f+2*b*c)+1//6*g*a^2*x^6+1//7*a*x^7*(a*h+2*b*e)+1//8*b*x^8*(b*c+2*a*f)+1//9*d*b^-1*(a+b*x^3)^3+1//10*b*x^10*(b*e+2*a*h)+1//11*f*b^2*x^11+1//12*g*b^2*x^12+1//13*h*b^2*x^13+2//9*a*b*g*x^9)
@test integrate((a+b*x^3)^2*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(c*x*a^2+(1/2)*d*a^2*x^2+1//4*a*x^4*(a*f+2*b*c)+1//5*a*x^5*(a*g+2*b*d)+1//6*h*a^2*x^6+1//7*b*x^7*(b*c+2*a*f)+1//8*b*x^8*(b*d+2*a*g)+1//9*e*b^-1*(a+b*x^3)^3+1//10*f*b^2*x^10+1//11*g*b^2*x^11+1//12*h*b^2*x^12+2//9*a*b*h*x^9)
@test integrate(x^-1*(a+b*x^3)^2*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(c*a^2*log(x)+d*x*a^2+(1/2)*e*a^2*x^2+1//4*a*x^4*(a*g+2*b*d)+1//5*a*x^5*(a*h+2*b*e)+1//6*c*b^2*x^6+1//7*b*x^7*(b*d+2*a*g)+1//8*b*x^8*(b*e+2*a*h)+1//9*f*b^-1*(a+b*x^3)^3+1//10*g*b^2*x^10+1//11*h*b^2*x^11+2//3*a*b*c*x^3)
@test integrate(x^-2*(a+b*x^3)^2*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(d*a^2*log(x)+e*x*a^2+(1/2)*a*x^2*(a*f+2*b*c)+-1*c*a^2*x^-1+1//4*a*x^4*(a*h+2*b*e)+1//5*b*x^5*(b*c+2*a*f)+1//6*d*b^2*x^6+1//7*b*x^7*(b*e+2*a*h)+1//8*f*b^2*x^8+1//9*g*b^-1*(a+b*x^3)^3+1//10*h*b^2*x^10+2//3*a*b*d*x^3)
@test integrate(x^-3*(a+b*x^3)^2*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(a*x*(a*f+2*b*c)+e*a^2*log(x)+(1/2)*a*x^2*(a*g+2*b*d)+-1*d*a^2*x^-1+-1//2*c*a^2*x^-2+1//4*b*x^4*(b*c+2*a*f)+1//5*b*x^5*(b*d+2*a*g)+1//6*e*b^2*x^6+1//7*f*b^2*x^7+1//8*g*b^2*x^8+1//9*h*b^-1*(a+b*x^3)^3+2//3*a*b*e*x^3)
@test integrate(x^-4*(a+b*x^3)^2*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(a*x*(a*g+2*b*d)+a*(a*f+2*b*c)*log(x)+(1/2)*a*x^2*(a*h+2*b*e)+-1*e*a^2*x^-1+-1//2*d*a^2*x^-2+-1//3*c*a^2*x^-3+1//3*b*x^3*(b*c+2*a*f)+1//4*b*x^4*(b*d+2*a*g)+1//5*b*x^5*(b*e+2*a*h)+1//6*f*b^2*x^6+1//7*g*b^2*x^7+1//8*h*b^2*x^8)
@test integrate(x^-5*(a+b*x^3)^2*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(a*x*(a*h+2*b*e)+a*(a*g+2*b*d)*log(x)+(1/2)*b*x^2*(b*c+2*a*f)+-1*a*x^-1*(a*f+2*b*c)+-1//2*e*a^2*x^-2+-1//3*d*a^2*x^-3+-1//4*c*a^2*x^-4+1//3*b*x^3*(b*d+2*a*g)+1//4*b*x^4*(b*e+2*a*h)+1//5*f*b^2*x^5+1//6*g*b^2*x^6+1//7*h*b^2*x^7)
@test integrate(x^4*(a+b*x^3)^3*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(1//5*c*a^3*x^5+1//6*d*a^3*x^6+1//7*e*a^3*x^7+1//8*a^2*x^8*(a*f+3*b*c)+1//9*a^2*x^9*(a*g+3*b*d)+1//10*a^2*x^10*(a*h+3*b*e)+1//14*b^2*x^14*(b*c+3*a*f)+1//15*b^2*x^15*(b*d+3*a*g)+1//16*b^2*x^16*(b*e+3*a*h)+1//17*f*b^3*x^17+1//18*g*b^3*x^18+1//19*h*b^3*x^19+1//4*a*b*x^12*(a*g+b*d)+3//11*a*b*x^11*(a*f+b*c)+3//13*a*b*x^13*(a*h+b*e))
@test integrate(x^3*(a+b*x^3)^3*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(1//4*c*a^3*x^4+1//5*d*a^3*x^5+1//6*e*a^3*x^6+1//7*a^2*x^7*(a*f+3*b*c)+1//8*a^2*x^8*(a*g+3*b*d)+1//9*a^2*x^9*(a*h+3*b*e)+1//13*b^2*x^13*(b*c+3*a*f)+1//14*b^2*x^14*(b*d+3*a*g)+1//15*b^2*x^15*(b*e+3*a*h)+1//16*f*b^3*x^16+1//17*g*b^3*x^17+1//18*h*b^3*x^18+1//4*a*b*x^12*(a*h+b*e)+3//10*a*b*x^10*(a*f+b*c)+3//11*a*b*x^11*(a*g+b*d))
@test integrate(x^2*(a+b*x^3)^3*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(1//4*d*a^3*x^4+1//5*e*a^3*x^5+1//6*f*a^3*x^6+1//7*a^2*x^7*(a*g+3*b*d)+1//8*a^2*x^8*(a*h+3*b*e)+1//12*c*b^-1*(a+b*x^3)^4+1//13*b^2*x^13*(b*d+3*a*g)+1//14*b^2*x^14*(b*e+3*a*h)+1//15*f*b^3*x^15+1//16*g*b^3*x^16+1//17*h*b^3*x^17+1//3*b*f*a^2*x^9+1//4*a*f*b^2*x^12+3//10*a*b*x^10*(a*g+b*d)+3//11*a*b*x^11*(a*h+b*e))
@test integrate(x*(a+b*x^3)^3*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :((1/2)*c*a^3*x^2+1//4*e*a^3*x^4+1//5*a^2*x^5*(a*f+3*b*c)+1//6*g*a^3*x^6+1//7*a^2*x^7*(a*h+3*b*e)+1//11*b^2*x^11*(b*c+3*a*f)+1//12*d*b^-1*(a+b*x^3)^4+1//13*b^2*x^13*(b*e+3*a*h)+1//14*f*b^3*x^14+1//15*g*b^3*x^15+1//16*h*b^3*x^16+1//3*b*g*a^2*x^9+1//4*a*g*b^2*x^12+3//8*a*b*x^8*(a*f+b*c)+3//10*a*b*x^10*(a*h+b*e))
@test integrate((a+b*x^3)^3*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(c*x*a^3+(1/2)*d*a^3*x^2+1//4*a^2*x^4*(a*f+3*b*c)+1//5*a^2*x^5*(a*g+3*b*d)+1//6*h*a^3*x^6+1//10*b^2*x^10*(b*c+3*a*f)+1//11*b^2*x^11*(b*d+3*a*g)+1//12*e*b^-1*(a+b*x^3)^4+1//13*f*b^3*x^13+1//14*g*b^3*x^14+1//15*h*b^3*x^15+1//3*b*h*a^2*x^9+1//4*a*h*b^2*x^12+3//7*a*b*x^7*(a*f+b*c)+3//8*a*b*x^8*(a*g+b*d))
@test integrate(x^-1*(a+b*x^3)^3*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(c*a^3*log(x)+d*x*a^3+(1/2)*e*a^3*x^2+1//4*a^2*x^4*(a*g+3*b*d)+1//5*a^2*x^5*(a*h+3*b*e)+1//9*c*b^3*x^9+1//10*b^2*x^10*(b*d+3*a*g)+1//11*b^2*x^11*(b*e+3*a*h)+1//12*f*b^-1*(a+b*x^3)^4+1//13*g*b^3*x^13+1//14*h*b^3*x^14+b*c*a^2*x^3+(1/2)*a*c*b^2*x^6+3//7*a*b*x^7*(a*g+b*d)+3//8*a*b*x^8*(a*h+b*e))
@test integrate(x^-2*(a+b*x^3)^3*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(d*a^3*log(x)+e*x*a^3+(1/2)*a^2*x^2*(a*f+3*b*c)+-1*c*a^3*x^-1+1//4*a^2*x^4*(a*h+3*b*e)+1//8*b^2*x^8*(b*c+3*a*f)+1//9*d*b^3*x^9+1//10*b^2*x^10*(b*e+3*a*h)+1//11*f*b^3*x^11+1//12*g*b^-1*(a+b*x^3)^4+1//13*h*b^3*x^13+b*d*a^2*x^3+(1/2)*a*d*b^2*x^6+3//5*a*b*x^5*(a*f+b*c)+3//7*a*b*x^7*(a*h+b*e))
@test integrate(x^-3*(a+b*x^3)^3*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(e*a^3*log(x)+x*a^2*(a*f+3*b*c)+(1/2)*a^2*x^2*(a*g+3*b*d)+-1*d*a^3*x^-1+-1//2*c*a^3*x^-2+1//7*b^2*x^7*(b*c+3*a*f)+1//8*b^2*x^8*(b*d+3*a*g)+1//9*e*b^3*x^9+1//10*f*b^3*x^10+1//11*g*b^3*x^11+1//12*h*b^-1*(a+b*x^3)^4+b*e*a^2*x^3+(1/2)*a*e*b^2*x^6+3//4*a*b*x^4*(a*f+b*c)+3//5*a*b*x^5*(a*g+b*d))
@test integrate(x^-4*(a+b*x^3)^3*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(x*a^2*(a*g+3*b*d)+a^2*(a*f+3*b*c)*log(x)+(1/2)*a^2*x^2*(a*h+3*b*e)+-1*e*a^3*x^-1+-1//2*d*a^3*x^-2+-1//3*c*a^3*x^-3+1//6*b^2*x^6*(b*c+3*a*f)+1//7*b^2*x^7*(b*d+3*a*g)+1//8*b^2*x^8*(b*e+3*a*h)+1//9*f*b^3*x^9+1//10*g*b^3*x^10+1//11*h*b^3*x^11+a*b*x^3*(a*f+b*c)+3//4*a*b*x^4*(a*g+b*d)+3//5*a*b*x^5*(a*h+b*e))
@test integrate(x^-5*(a+b*x^3)^3*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(x*a^2*(a*h+3*b*e)+a^2*(a*g+3*b*d)*log(x)+-1*a^2*x^-1*(a*f+3*b*c)+-1//2*e*a^3*x^-2+-1//3*d*a^3*x^-3+-1//4*c*a^3*x^-4+1//5*b^2*x^5*(b*c+3*a*f)+1//6*b^2*x^6*(b*d+3*a*g)+1//7*b^2*x^7*(b*e+3*a*h)+1//8*f*b^3*x^8+1//9*g*b^3*x^9+1//10*h*b^3*x^10+a*b*x^3*(a*g+b*d)+3//2*a*b*x^2*(a*f+b*c)+3//4*a*b*x^4*(a*h+b*e))
@test integrate(x^4*(a+b*x^3)^-1*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :((1/2)*b^-2*x^2*(b*c+-1*a*f)+1//3*b^-2*x^3*(b*d+-1*a*g)+1//4*b^-2*x^4*(b*e+-1*a*h)+1//5*f*b^-1*x^5+1//6*g*b^-1*x^6+1//7*h*b^-1*x^7+-1*a*x*b^-3*(b*e+-1*a*h)+-1//3*a*b^-3*(b*d+-1*a*g)*log(a+b*x^3)+-1//6*a^2//3*b^-10//3*(a^2//3*(b*e+-1*a*h)+b^2//3*(b*c+-1*a*f))*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^2//3*b^-10//3*(a^2//3*(b*e+-1*a*h)+b^2//3*(b*c+-1*a*f))*log(a^1//3+x*b^1//3)+1//3*3^(1/2)*a^2//3*b^-10//3*(c*b^5//3+h*a^5//3+-1*a*f*b^2//3+-1*b*e*a^2//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^3*(a+b*x^3)^-1*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(x*b^-2*(b*c+-1*a*f)+(1/2)*b^-2*x^2*(b*d+-1*a*g)+1//3*b^-2*x^3*(b*e+-1*a*h)+1//4*f*b^-1*x^4+1//5*g*b^-1*x^5+1//6*h*b^-1*x^6+-1//3*a*b^-3*(b*e+-1*a*h)*log(a+b*x^3)+-1//3*a^1//3*b^-8//3*(b^1//3*(b*c+-1*a*f)+-1*a^1//3*(b*d+-1*a*g))*log(a^1//3+x*b^1//3)+1//6*a^1//3*b^-8//3*(b^1//3*(b*c+-1*a*f)+-1*a^1//3*(b*d+-1*a*g))*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^-8//3*(c*b^4//3+-1*g*a^4//3+b*d*a^1//3+-1*a*f*b^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^2*(a+b*x^3)^-1*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(x*b^-2*(b*d+-1*a*g)+(1/2)*b^-2*x^2*(b*e+-1*a*h)+1//3*f*b^-1*x^3+1//3*b^-2*(b*c+-1*a*f)*log(a+b*x^3)+1//4*g*b^-1*x^4+1//5*h*b^-1*x^5+-1//3*a^1//3*b^-8//3*(b^1//3*(b*d+-1*a*g)+-1*a^1//3*(b*e+-1*a*h))*log(a^1//3+x*b^1//3)+1//6*a^1//3*b^-8//3*(b^1//3*(b*d+-1*a*g)+-1*a^1//3*(b*e+-1*a*h))*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^-8//3*(d*b^4//3+-1*h*a^4//3+b*e*a^1//3+-1*a*g*b^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x*(a+b*x^3)^-1*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(x*b^-2*(b*e+-1*a*h)+(1/2)*f*b^-1*x^2+1//3*g*b^-1*x^3+1//3*b^-2*(b*d+-1*a*g)*log(a+b*x^3)+1//4*h*b^-1*x^4+-1//3*a^-1//3*b^-7//3*(a^2//3*(b*e+-1*a*h)+b^2//3*(b*c+-1*a*f))*log(a^1//3+x*b^1//3)+1//6*a^-1//3*b^-7//3*(a^2//3*(b*e+-1*a*h)+b^2//3*(b*c+-1*a*f))*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//3*3^(1/2)*a^-1//3*b^-7//3*(c*b^5//3+h*a^5//3+-1*a*f*b^2//3+-1*b*e*a^2//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate((a+b*x^3)^-1*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(f*x*b^-1+(1/2)*g*b^-1*x^2+1//3*h*b^-1*x^3+1//3*b^-2*(b*e+-1*a*h)*log(a+b*x^3)+-1//6*a^-2//3*b^-5//3*(b^1//3*(b*c+-1*a*f)+-1*a^1//3*(b*d+-1*a*g))*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*(b^1//3*(b*c+-1*a*f)+-1*a^1//3*(b*d+-1*a*g))*log(a^1//3+x*b^1//3)+-1//3*3^(1/2)*a^-2//3*b^-5//3*(c*b^4//3+-1*g*a^4//3+b*d*a^1//3+-1*a*f*b^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-1*(a+b*x^3)^-1*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(c*a^-1*log(x)+g*x*b^-1+(1/2)*h*b^-1*x^2+-1//3*a^-1*b^-1*(b*c+-1*a*f)*log(a+b*x^3)+-1//6*a^-2//3*b^-5//3*(b^1//3*(b*d+-1*a*g)+-1*a^1//3*(b*e+-1*a*h))*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*(b^1//3*(b*d+-1*a*g)+-1*a^1//3*(b*e+-1*a*h))*log(a^1//3+x*b^1//3)+-1//3*3^(1/2)*a^-2//3*b^-5//3*(d*b^4//3+-1*h*a^4//3+b*e*a^1//3+-1*a*g*b^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-2*(a+b*x^3)^-1*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(d*a^-1*log(x)+h*x*b^-1+-1*c*a^-1*x^-1+-1//3*a^-1*b^-1*(b*d+-1*a*g)*log(a+b*x^3)+-1//6*a^-4//3*b^-4//3*(a^2//3*(b*e+-1*a*h)+b^2//3*(b*c+-1*a*f))*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//3*a^-4//3*b^-4//3*(a^2//3*(b*e+-1*a*h)+b^2//3*(b*c+-1*a*f))*log(a^1//3+x*b^1//3)+1//3*3^(1/2)*a^-4//3*b^-4//3*(c*b^5//3+h*a^5//3+-1*a*f*b^2//3+-1*b*e*a^2//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-3*(a+b*x^3)^-1*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(e*a^-1*log(x)+-1*d*a^-1*x^-1+-1//2*c*a^-1*x^-2+-1//3*a^-1*b^-1*(b*e+-1*a*h)*log(a+b*x^3)+-1//3*a^-5//3*b^-2//3*(b^1//3*(b*c+-1*a*f)+-1*a^1//3*(b*d+-1*a*g))*log(a^1//3+x*b^1//3)+1//6*a^-5//3*b^-2//3*(b^1//3*(b*c+-1*a*f)+-1*a^1//3*(b*d+-1*a*g))*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*(c*b^4//3+-1*g*a^4//3+b*d*a^1//3+-1*a*f*b^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-4*(a+b*x^3)^-1*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(-1*e*a^-1*x^-1+-1*a^-2*(b*c+-1*a*f)*log(x)+-1//2*d*a^-1*x^-2+-1//3*c*a^-1*x^-3+1//3*a^-2*(b*c+-1*a*f)*log(a+b*x^3)+-1//3*a^-5//3*b^-2//3*(b^1//3*(b*d+-1*a*g)+-1*a^1//3*(b*e+-1*a*h))*log(a^1//3+x*b^1//3)+1//6*a^-5//3*b^-2//3*(b^1//3*(b*d+-1*a*g)+-1*a^1//3*(b*e+-1*a*h))*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*(d*b^4//3+-1*h*a^4//3+b*e*a^1//3+-1*a*g*b^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^4*(a+b*x^3)^-2*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(x*b^-3*(b*e+-2*a*h)+(1/2)*f*b^-2*x^2+1//3*g*b^-2*x^3+1//3*b^-3*(b*d+-2*a*g)*log(a+b*x^3)+1//4*h*b^-2*x^4+-1//9*a^-1//3*b^-10//3*(a^2//3*(-7*a*h+4*b*e)+b^2//3*(-5*a*f+2*b*c))*log(a^1//3+x*b^1//3)+1//3*x*b^-3*(a+b*x^3)^-1*(a*(b*e+-1*a*h)+-1*b*x*(b*c+-1*a*f)+-1*b*x^2*(b*d+-1*a*g))+1//18*a^-1//3*b^-10//3*(a^2//3*(-7*a*h+4*b*e)+b^2//3*(-5*a*f+2*b*c))*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//9*3^(1/2)*a^-1//3*b^-10//3*(2*c*b^5//3+7*h*a^5//3+-5*a*f*b^2//3+-4*b*e*a^2//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^3*(a+b*x^3)^-2*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(f*x*b^-2+(1/2)*g*b^-2*x^2+1//3*h*b^-2*x^3+1//3*b^-3*(b*e+-2*a*h)*log(a+b*x^3)+-1//3*x*b^-2*(a+b*x^3)^-1*(b*c+x*(b*d+-1*a*g)+x^2*(b*e+-1*a*h)+-1*a*f)+-1//18*a^-2//3*b^-8//3*(b^1//3*(b*c+-4*a*f)+-1*a^1//3*(-5*a*g+2*b*d))*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*a^-2//3*b^-8//3*(b^1//3*(b*c+-4*a*f)+-1*a^1//3*(-5*a*g+2*b*d))*log(a^1//3+x*b^1//3)+-1//9*3^(1/2)*a^-2//3*b^-8//3*(c*b^4//3+-5*g*a^4//3+-4*a*f*b^1//3+2*b*d*a^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^2*(a+b*x^3)^-2*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(-1//3*b^-1*(a+b*x^3)^-1*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5)+1//3*f*b^-2*log(a+b*x^3)+4//3*g*x*b^-2+5//6*h*b^-2*x^2+-1//18*a^-2//3*b^-8//3*(b^1//3*(b*d+-4*a*g)+-1*a^1//3*(-5*a*h+2*b*e))*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*a^-2//3*b^-8//3*(b^1//3*(b*d+-4*a*g)+-1*a^1//3*(-5*a*h+2*b*e))*log(a^1//3+x*b^1//3)+-1//9*3^(1/2)*a^-2//3*b^-8//3*(d*b^4//3+-5*h*a^4//3+-4*a*g*b^1//3+2*b*e*a^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x*(a+b*x^3)^-2*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(h*x*b^-2+1//3*g*b^-2*log(a+b*x^3)+-1//9*a^-4//3*b^-7//3*(b^2//3*(b*c+2*a*f)+-1*a^2//3*(b*e+-4*a*h))*log(a^1//3+x*b^1//3)+1//18*a^-4//3*b^-7//3*(b^2//3*(b*c+2*a*f)+-1*a^2//3*(b*e+-4*a*h))*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//3*x*a^-1*b^-2*(a+b*x^3)^-1*(a*(b*e+-1*a*h)+-1*b*x*(b*c+-1*a*f)+-1*b*x^2*(b*d+-1*a*g))+-1//9*3^(1/2)*a^-4//3*b^-7//3*(c*b^5//3+-4*h*a^5//3+b*e*a^2//3+2*a*f*b^2//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate((a+b*x^3)^-2*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(1//3*h*b^-2*log(a+b*x^3)+-1//18*a^-5//3*b^-5//3*(b^1//3*(a*f+2*b*c)+-1*a^1//3*(b*d+2*a*g))*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*a^-5//3*b^-5//3*(b^1//3*(a*f+2*b*c)+-1*a^1//3*(b*d+2*a*g))*log(a^1//3+x*b^1//3)+-1//9*3^(1/2)*a^-5//3*b^-5//3*(2*c*b^4//3+2*g*a^4//3+a*f*b^1//3+b*d*a^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//3*x*a^-1*b^-1*(a+b*x^3)^-1*(b*c+x*(b*d+-1*a*g)+x^2*(b*e+-1*a*h)+-1*a*f))
@test integrate(x^-1*(a+b*x^3)^-2*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(c*a^-2*log(x)+-1//3*c*a^-2*log(a+b*x^3)+-1//18*a^-5//3*b^-5//3*(b^1//3*(a*g+2*b*d)+-1*a^1//3*(b*e+2*a*h))*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*a^-5//3*b^-5//3*(b^1//3*(a*g+2*b*d)+-1*a^1//3*(b*e+2*a*h))*log(a^1//3+x*b^1//3)+-1//9*3^(1/2)*a^-5//3*b^-5//3*(2*d*b^4//3+2*h*a^4//3+a*g*b^1//3+b*e*a^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//3*x*a^-2*b^-1*(a+b*x^3)^-1*(a*(b*d+-1*a*g)+a*x*(b*e+-1*a*h)+-1*b*x^2*(b*c+-1*a*f)))
@test integrate(x^-2*(a+b*x^3)^-2*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(d*a^-2*log(x)+-1*c*a^-2*x^-1+-1//3*d*a^-2*log(a+b*x^3)+-1//18*a^-7//3*b^-4//3*(a^2//3*(a*h+2*b*e)+b^2//3*(-1*a*f+4*b*c))*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*a^-7//3*b^-4//3*(a^2//3*(a*h+2*b*e)+b^2//3*(-1*a*f+4*b*c))*log(a^1//3+x*b^1//3)+1//3*x*a^-2*b^-1*(a+b*x^3)^-1*(a*(b*e+-1*a*h)+-1*b*x*(b*c+-1*a*f)+-1*b*x^2*(b*d+-1*a*g))+1//9*3^(1/2)*a^-7//3*b^-4//3*(-1*h*a^5//3+4*c*b^5//3+-1*a*f*b^2//3+-2*b*e*a^2//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-3*(a+b*x^3)^-2*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(e*a^-2*log(x)+-1*d*a^-2*x^-1+-1//2*c*a^-2*x^-2+-1//3*e*a^-2*log(a+b*x^3)+-1//3*x*a^-2*(a+b*x^3)^-1*(b*c+x*(b*d+-1*a*g)+x^2*(b*e+-1*a*h)+-1*a*f)+-1//9*a^-8//3*b^-2//3*(b^1//3*(-2*a*f+5*b*c)+-1*a^1//3*(-1*a*g+4*b*d))*log(a^1//3+x*b^1//3)+1//18*a^-8//3*b^-2//3*(b^1//3*(-2*a*f+5*b*c)+-1*a^1//3*(-1*a*g+4*b*d))*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*3^(1/2)*a^-8//3*b^-2//3*(-1*g*a^4//3+5*c*b^4//3+-2*a*f*b^1//3+4*b*d*a^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-4*(a+b*x^3)^-2*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(-1*e*a^-2*x^-1+-1*a^-3*(-1*a*f+2*b*c)*log(x)+-1//2*d*a^-2*x^-2+-1//3*c*a^-2*x^-3+1//3*a^-3*(-1*a*f+2*b*c)*log(a+b*x^3)+-1//3*x*a^-2*(a+b*x^3)^-1*(b*d+x*(b*e+-1*a*h)+-1*a*g+-1*b*x^2*(-1*f+b*c*a^-1))+-1//9*a^-8//3*b^-2//3*(b^1//3*(-2*a*g+5*b*d)+-1*a^1//3*(-1*a*h+4*b*e))*log(a^1//3+x*b^1//3)+1//18*a^-8//3*b^-2//3*(b^1//3*(-2*a*g+5*b*d)+-1*a^1//3*(-1*a*h+4*b*e))*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//9*3^(1/2)*a^-8//3*b^-2//3*(-1*h*a^4//3+5*d*b^4//3+-2*a*g*b^1//3+4*b*e*a^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^4*(a+b*x^3)^-3*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(h*x*b^-3+1//3*g*b^-3*log(a+b*x^3)+-1//27*a^-4//3*b^-10//3*(b^2//3*(b*c+5*a*f)+-2*a^2//3*(b*e+-7*a*h))*log(a^1//3+x*b^1//3)+1//6*x*b^-3*(a+b*x^3)^-2*(a*(b*e+-1*a*h)+-1*b*x*(b*c+-1*a*f)+-1*b*x^2*(b*d+-1*a*g))+1//54*a^-4//3*b^-10//3*(b^2//3*(b*c+5*a*f)+-2*a^2//3*(b*e+-7*a*h))*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//18*x*a^-1*b^-3*(a+b*x^3)^-1*(a*(-13*a*h+7*b*e)+-3*b*x^2*(b*d+-3*a*g)+-2*b*x*(b*c+-4*a*f))+-1//27*3^(1/2)*a^-4//3*b^-10//3*(c*b^5//3+-14*h*a^5//3+2*b*e*a^2//3+5*a*f*b^2//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^3*(a+b*x^3)^-3*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(1//3*h*b^-3*log(a+b*x^3)+-1//6*x*b^-2*(a+b*x^3)^-2*(b*c+x*(b*d+-1*a*g)+x^2*(b*e+-1*a*h)+-1*a*f)+-1//54*a^-5//3*b^-8//3*(b^1//3*(b*c+2*a*f)+-1*a^1//3*(b*d+5*a*g))*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//27*a^-5//3*b^-8//3*(b^1//3*(b*c+2*a*f)+-1*a^1//3*(b*d+5*a*g))*log(a^1//3+x*b^1//3)+-1//27*3^(1/2)*a^-5//3*b^-8//3*(c*b^4//3+5*g*a^4//3+b*d*a^1//3+2*a*f*b^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//18*x*a^-1*b^-2*(a+b*x^3)^-1*(b*c+x*(-8*a*g+2*b*d)+x^2*(-9*a*h+3*b*e)+-7*a*f))
@test integrate(x^2*(a+b*x^3)^-3*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(-1//6*b^-1*(a+b*x^3)^-2*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5)+-1//54*a^-5//3*b^-8//3*(b^1//3*(b*d+2*a*g)+-1*a^1//3*(b*e+5*a*h))*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//27*a^-5//3*b^-8//3*(b^1//3*(b*d+2*a*g)+-1*a^1//3*(b*e+5*a*h))*log(a^1//3+x*b^1//3)+-1//27*3^(1/2)*a^-5//3*b^-8//3*(d*b^4//3+5*h*a^4//3+b*e*a^1//3+2*a*g*b^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//18*x*a^-1*b^-2*(a+b*x^3)^-1*(b*d+x*(-5*a*h+2*b*e)+-4*a*g+3*b*f*x^2))
@test integrate(x*(a+b*x^3)^-3*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(-1//27*a^-7//3*b^-7//3*(b^2//3*(a*f+2*b*c)+-1*a^2//3*(b*e+2*a*h))*log(a^1//3+x*b^1//3)+1//54*a^-7//3*b^-7//3*(b^2//3*(a*f+2*b*c)+-1*a^2//3*(b*e+2*a*h))*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+-1//6*x*a^-1*b^-2*(a+b*x^3)^-2*(a*(b*e+-1*a*h)+-1*b*x*(b*c+-1*a*f)+-1*b*x^2*(b*d+-1*a*g))+-1//27*3^(1/2)*a^-7//3*b^-7//3*(2*c*b^5//3+2*h*a^5//3+a*f*b^2//3+b*e*a^2//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//18*x*a^-2*b^-2*(a+b*x^3)^-1*(a*(b*e+-7*a*h)+2*b*x*(a*f+2*b*c)+3*b*x^2*(a*g+b*d)))
@test integrate((a+b*x^3)^-3*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(-1//18*a^-2*b^-2*(a+b*x^3)^-1*(3*a*(a*h+b*e)+-1*b*x*(a*f+x*(2*a*g+4*b*d)+5*b*c))+-1//54*a^-8//3*b^-5//3*(b^1//3*(a*f+5*b*c)+-1*a^1//3*(a*g+2*b*d))*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//27*a^-8//3*b^-5//3*(b^1//3*(a*f+5*b*c)+-1*a^1//3*(a*g+2*b*d))*log(a^1//3+x*b^1//3)+-1//27*3^(1/2)*a^-8//3*b^-5//3*(g*a^4//3+5*c*b^4//3+a*f*b^1//3+2*b*d*a^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//6*x*a^-1*b^-1*(a+b*x^3)^-2*(b*c+x*(b*d+-1*a*g)+x^2*(b*e+-1*a*h)+-1*a*f))
@test integrate(x^-1*(a+b*x^3)^-3*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(c*a^-3*log(x)+-1//3*c*a^-3*log(a+b*x^3)+-1//54*a^-8//3*b^-5//3*(b^1//3*(a*g+5*b*d)+-1*a^1//3*(a*h+2*b*e))*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//27*a^-8//3*b^-5//3*(b^1//3*(a*g+5*b*d)+-1*a^1//3*(a*h+2*b*e))*log(a^1//3+x*b^1//3)+-1//27*3^(1/2)*a^-8//3*b^-5//3*(h*a^4//3+5*d*b^4//3+a*g*b^1//3+2*b*e*a^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3))+1//6*x*a^-2*b^-1*(a+b*x^3)^-2*(a*(b*d+-1*a*g)+a*x*(b*e+-1*a*h)+-1*b*x^2*(b*c+-1*a*f))+1//18*x*a^-3*b^-1*(a+b*x^3)^-1*(a*(a*g+5*b*d)+-3*b*x^2*(-1*a*f+3*b*c)+2*a*x*(a*h+2*b*e)))
@test integrate(x^-2*(a+b*x^3)^-3*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(d*a^-3*log(x)+-1*c*a^-3*x^-1+-1//3*d*a^-3*log(a+b*x^3)+-1//54*a^-10//3*b^-4//3*(a^2//3*(a*h+5*b*e)+2*b^2//3*(-1*a*f+7*b*c))*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//27*a^-10//3*b^-4//3*(a^2//3*(a*h+5*b*e)+2*b^2//3*(-1*a*f+7*b*c))*log(a^1//3+x*b^1//3)+1//6*x*a^-2*b^-1*(a+b*x^3)^-2*(a*(b*e+-1*a*h)+-1*b*x*(b*c+-1*a*f)+-1*b*x^2*(b*d+-1*a*g))+1//18*x*a^-3*b^-1*(a+b*x^3)^-1*(a*(a*h+5*b*e)+-3*b*x^2*(-1*a*g+3*b*d)+-2*b*x*(-2*a*f+5*b*c))+1//27*3^(1/2)*a^-10//3*b^-4//3*(-1*h*a^5//3+14*c*b^5//3+-5*b*e*a^2//3+-2*a*f*b^2//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-3*(a+b*x^3)^-3*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(e*a^-3*log(x)+-1*d*a^-3*x^-1+-1//2*c*a^-3*x^-2+-1//3*e*a^-3*log(a+b*x^3)+-1//6*x*a^-2*(a+b*x^3)^-2*(b*c+x*(b*d+-1*a*g)+x^2*(b*e+-1*a*h)+-1*a*f)+-1//18*x*a^-3*(a+b*x^3)^-1*(x*(-4*a*g+10*b*d)+x^2*(-3*a*h+9*b*e)+-5*a*f+11*b*c)+-1//27*a^-11//3*b^-2//3*(-2*a^1//3*(-1*a*g+7*b*d)+5*b^1//3*(-1*a*f+4*b*c))*log(a^1//3+x*b^1//3)+1//54*a^-11//3*b^-2//3*(-2*a^1//3*(-1*a*g+7*b*d)+5*b^1//3*(-1*a*f+4*b*c))*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//27*3^(1/2)*a^-11//3*b^-2//3*(-2*g*a^4//3+20*c*b^4//3+-5*a*f*b^1//3+14*b*d*a^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^-4*(a+b*x^3)^-3*(c+d*x+e*x^2+f*x^3+g*x^4+h*x^5), x) == :(-1*e*a^-3*x^-1+-1*a^-4*(-1*a*f+3*b*c)*log(x)+-1//2*d*a^-3*x^-2+-1//3*c*a^-3*x^-3+1//3*a^-4*(-1*a*f+3*b*c)*log(a+b*x^3)+-1//6*x*a^-2*(a+b*x^3)^-2*(b*d+x*(b*e+-1*a*h)+-1*a*g+-1*b*x^2*(-1*f+b*c*a^-1))+-1//18*x*a^-3*(a+b*x^3)^-1*(x*(-4*a*h+10*b*e)+-5*a*g+11*b*d+-3*b*x^2*(-3*f+5*b*c*a^-1))+-1//27*a^-11//3*b^-2//3*(-2*a^1//3*(-1*a*h+7*b*e)+5*b^1//3*(-1*a*g+4*b*d))*log(a^1//3+x*b^1//3)+1//54*a^-11//3*b^-2//3*(-2*a^1//3*(-1*a*h+7*b*e)+5*b^1//3*(-1*a*g+4*b*d))*log(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3)+1//27*3^(1/2)*a^-11//3*b^-2//3*(-2*h*a^4//3+20*d*b^4//3+-5*a*g*b^1//3+14*b*e*a^1//3)*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*x*b^1//3)))
@test integrate(x^3*(a+b*x^3)^-1//2*(c+d*x+e*x^2), x) == :(-4//9*a*e*b^-2*(a+b*x^3)^(1/2)+2//5*c*x*b^-1*(a+b*x^3)^(1/2)+2//7*d*b^-1*x^2*(a+b*x^3)^(1/2)+2//9*e*b^-1*x^3*(a+b*x^3)^(1/2)+-8//7*a*d*b^-5//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+-4//105*a*3^3//4*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(7*c*b^1//3+-1*d*a^1//3*(10+-10*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+4//7*d*3^1//4*a^4//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^2*(a+b*x^3)^-1//2*(c+d*x+e*x^2), x) == :(2//3*c*b^-1*(a+b*x^3)^(1/2)+2//5*d*x*b^-1*(a+b*x^3)^(1/2)+2//7*e*b^-1*x^2*(a+b*x^3)^(1/2)+-8//7*a*e*b^-5//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+-4//105*a*3^3//4*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(7*d*b^1//3+-1*e*a^1//3*(10+-10*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+4//7*e*3^1//4*a^4//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(a+b*x^3)^-1//2*(c+d*x+e*x^2), x) == :(2//3*d*b^-1*(a+b*x^3)^(1/2)+2*c*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+2//5*e*x*b^-1*(a+b*x^3)^(1/2)+-1*c*3^1//4*a^1//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+-2//15*3^3//4*a^1//3*b^-4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(2*e*a^2//3+c*b^2//3*(5+-5*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+b*x^3)^-1//2*(c+d*x+e*x^2), x) == :(2//3*e*b^-1*(a+b*x^3)^(1/2)+2*d*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+2//3*3^3//4*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(c*b^1//3+-1*d*a^1//3*(1+-1*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+-1*d*3^1//4*a^1//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-1*(a+b*x^3)^-1//2*(c+d*x+e*x^2), x) == :(-2//3*c*a^-1//2*arctanh(a^-1//2*(a+b*x^3)^(1/2))+2*e*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+2//3*3^3//4*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(d*b^1//3+-1*e*a^1//3*(1+-1*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+-1*e*3^1//4*a^1//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-2*(a+b*x^3)^-1//2*(c+d*x+e*x^2), x) == :(-2//3*d*a^-1//2*arctanh(a^-1//2*(a+b*x^3)^(1/2))+-1*c*a^-1*x^-1*(a+b*x^3)^(1/2)+c*a^-1*b^1//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+-1//2*c*3^1//4*a^-2//3*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+-1//3*3^3//4*a^-2//3*b^-1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-2*e*a^2//3+c*b^2//3*(1+-1*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-3*(a+b*x^3)^-1//2*(c+d*x+e*x^2), x) == :(-2//3*e*a^-1//2*arctanh(a^-1//2*(a+b*x^3)^(1/2))+-1*d*a^-1*x^-1*(a+b*x^3)^(1/2)+-1//2*c*a^-1*x^-2*(a+b*x^3)^(1/2)+d*a^-1*b^1//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+-1//2*d*3^1//4*a^-2//3*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+-1//6*3^3//4*a^-1*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(c*b^1//3+d*a^1//3*(2+-2*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^5*(a+b*x^3)^-3//2*(c+d*x+e*x^2), x) == :(4//3*c*b^-2*(a+b*x^3)^(1/2)+2//3*x*b^-2*(a+b*x^3)^-1//2*(a*d+a*e*x+-1*b*c*x^2)+2//5*d*x*b^-2*(a+b*x^3)^(1/2)+2//7*e*b^-2*x^2*(a+b*x^3)^(1/2)+-80//21*a*e*b^-8//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+-16//315*a*3^3//4*b^-8//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(14*d*b^1//3+-1*e*a^1//3*(25+-25*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+40//21*e*3^1//4*a^4//3*b^-8//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^4*(a+b*x^3)^-3//2*(c+d*x+e*x^2), x) == :(4//3*d*b^-2*(a+b*x^3)^(1/2)+2//3*x*b^-2*(a+b*x^3)^-1//2*(a*e+-1*b*c*x+-1*b*d*x^2)+2//5*e*x*b^-2*(a+b*x^3)^(1/2)+8//3*c*b^-5//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+-8//45*3^3//4*a^1//3*b^-7//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(4*e*a^2//3+c*b^2//3*(5+-5*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+-4//3*c*3^1//4*a^1//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^3*(a+b*x^3)^-3//2*(c+d*x+e*x^2), x) == :(4//3*e*b^-2*(a+b*x^3)^(1/2)+-2//3*x*b^-1*(a+b*x^3)^-1//2*(c+d*x+e*x^2)+8//3*d*b^-5//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+4//9*3^3//4*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(c*b^1//3+-1*d*a^1//3*(2+-2*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+-4//3*d*3^1//4*a^1//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^2*(a+b*x^3)^-3//2*(c+d*x+e*x^2), x) == :(-1//3*b^-1*(a+b*x^3)^-1//2*(2c+2*d*x+2*e*x^2)+8//3*e*b^-5//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+4//9*3^3//4*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(d*b^1//3+-1*e*a^1//3*(2+-2*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+-4//3*e*3^1//4*a^1//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(a+b*x^3)^-3//2*(c+d*x+e*x^2), x) == :(-2//3*d*a^-1*b^-1*(a+b*x^3)^(1/2)+-2//3*c*a^-1*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+-2//3*x*a^-1*b^-1*(a+b*x^3)^-1//2*(a*e+-1*b*c*x+-1*b*d*x^2)+1//3*c*3^1//4*a^-2//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+2//9*3^3//4*a^-2//3*b^-4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(b^2//3*(c+-1*c*3^(1/2))+2*e*a^2//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+b*x^3)^-3//2*(c+d*x+e*x^2), x) == :(-1//3*a^-1*b^-1*(a+b*x^3)^-1//2*(2*a*e+-2*b*x*(c+d*x))+-2//3*d*a^-1*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+1//3*d*3^1//4*a^-2//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+2//9*3^3//4*a^-1*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(c*b^1//3+d*a^1//3*(1+-1*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-1*(a+b*x^3)^-3//2*(c+d*x+e*x^2), x) == :(-2//3*c*a^-3//2*arctanh(a^-1//2*(a+b*x^3)^(1/2))+2//3*c*a^-2*(a+b*x^3)^(1/2)+2//3*x*a^-2*(a+b*x^3)^-1//2*(a*d+a*e*x+-1*b*c*x^2)+-2//3*e*a^-1*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+1//3*e*3^1//4*a^-2//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+2//9*3^3//4*a^-1*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(d*b^1//3+e*a^1//3*(1+-1*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-2*(a+b*x^3)^-3//2*(c+d*x+e*x^2), x) == :(-2//3*d*a^-3//2*arctanh(a^-1//2*(a+b*x^3)^(1/2))+2//3*d*a^-2*(a+b*x^3)^(1/2)+-1*c*a^-2*x^-1*(a+b*x^3)^(1/2)+2//3*x*a^-2*(a+b*x^3)^-1//2*(a*e+-1*b*c*x+-1*b*d*x^2)+5//3*c*a^-2*b^1//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+-5//6*c*3^1//4*a^-5//3*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+-1//9*3^3//4*a^-5//3*b^-1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-2*e*a^2//3+c*b^2//3*(5+-5*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^3*(a+b*x^3)^(1/2)*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(2//692835*x^3*(a+b*x^3)^(1/2)*(36465*g*x^5+40755*f*x^4+46189*e*x^3+53295*d*x^2+62985*c*x)+-4//45*e*a^2*b^-2*(a+b*x^3)^(1/2)+-24//1729*a^2*b^-8//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(-10*a*g+19*b*d)+2//45*a*e*b^-1*x^3*(a+b*x^3)^(1/2)+6//187*a*f*b^-1*x^4*(a+b*x^3)^(1/2)+6//247*a*g*b^-1*x^5*(a+b*x^3)^(1/2)+6//935*a*x*b^-2*(a+b*x^3)^(1/2)*(-8*a*f+17*b*c)+6//1729*a*b^-2*x^2*(a+b*x^3)^(1/2)*(-10*a*g+19*b*d)+-4//1616615*3^3//4*a^2*b^-8//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(1729*b^1//3*(-8*a*f+17*b*c)+-1*a^1//3*(1870+-1870*3^(1/2))*(-10*a*g+19*b*d))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+12//1729*3^1//4*a^7//3*b^-8//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-10*a*g+19*b*d)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^2*(a+b*x^3)^(1/2)*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(2//109395*x^2*(a+b*x^3)^(1/2)*(6435*g*x^5+7293*f*x^4+8415*e*x^3+9945*d*x^2+12155*c*x)+2//45*a*b^-2*(a+b*x^3)^(1/2)*(-2*a*f+5*b*c)+-24//91*e*a^2*b^-5//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+2//45*a*f*b^-1*x^3*(a+b*x^3)^(1/2)+6//91*a*e*b^-1*x^2*(a+b*x^3)^(1/2)+6//187*a*g*b^-1*x^4*(a+b*x^3)^(1/2)+6//935*a*x*b^-2*(a+b*x^3)^(1/2)*(-8*a*g+17*b*d)+-4//85085*3^3//4*a^2*b^-7//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-728*a*g+1547*b*d+-1*e*a^1//3*b^2//3*(1870+-1870*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+12//91*e*3^1//4*a^7//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(a+b*x^3)^(1/2)*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(2//45045*x*(a+b*x^3)^(1/2)*(3003*g*x^5+3465*f*x^4+4095*e*x^3+5005*d*x^2+6435*c*x)+2//45*a*b^-2*(a+b*x^3)^(1/2)*(-2*a*g+5*b*d)+2//45*a*g*b^-1*x^3*(a+b*x^3)^(1/2)+6//55*a*e*x*b^-1*(a+b*x^3)^(1/2)+6//91*a*f*b^-1*x^2*(a+b*x^3)^(1/2)+6//91*a*b^-5//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(-4*a*f+13*b*c)+-3//91*3^1//4*a^4//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-4*a*f+13*b*c)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+-2//5005*3^3//4*a^4//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*((55+-55*3^(1/2))*(-4*a*f+13*b*c)+182*e*a^2//3*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+b*x^3)^(1/2)*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(2//45045*(a+b*x^3)^(1/2)*(3465*g*x^5+4095*f*x^4+5005*e*x^3+6435*d*x^2+9009*c*x)+2//9*a*e*b^-1*(a+b*x^3)^(1/2)+6//55*a*f*x*b^-1*(a+b*x^3)^(1/2)+6//91*a*g*b^-1*x^2*(a+b*x^3)^(1/2)+6//91*a*b^-5//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(-4*a*g+13*b*d)+-3//91*3^1//4*a^4//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-4*a*g+13*b*d)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+2//5005*a*3^3//4*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(91*b^1//3*(-2*a*f+11*b*c)+-1*a^1//3*(55+-55*3^(1/2))*(-4*a*g+13*b*d))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-1*(a+b*x^3)^(1/2)*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(-2//3*c*a^(1/2)*arctanh(a^-1//2*(a+b*x^3)^(1/2))+2//3465*x^-1*(a+b*x^3)^(1/2)*(315*g*x^5+385*f*x^4+495*e*x^3+693*d*x^2+1155*c*x)+2//9*a*f*b^-1*(a+b*x^3)^(1/2)+6//7*a*e*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+6//55*a*g*x*b^-1*(a+b*x^3)^(1/2)+-3//7*e*3^1//4*a^4//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+2//385*a*3^3//4*b^-4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-14*a*g+77*b*d+-1*e*a^1//3*b^2//3*(55+-55*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-2*(a+b*x^3)^(1/2)*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(-3*c*x^-1*(a+b*x^3)^(1/2)+-2//3*d*a^(1/2)*arctanh(a^-1//2*(a+b*x^3)^(1/2))+2//315*x^-2*(a+b*x^3)^(1/2)*(35*g*x^5+45*f*x^4+63*e*x^3+105*d*x^2+315*c*x)+1//7*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(6*a*f+21*b*c)+2//9*a*g*b^-1*(a+b*x^3)^(1/2)+-3//14*3^1//4*a^1//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(2*a*f+7*b*c)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//35*3^3//4*a^1//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-1*(5+-5*3^(1/2))*(2*a*f+7*b*c)+14*e*a^2//3*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-3*(a+b*x^3)^(1/2)*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(-3*d*x^-1*(a+b*x^3)^(1/2)+-2//3*e*a^(1/2)*arctanh(a^-1//2*(a+b*x^3)^(1/2))+-2//105*x^-3*(a+b*x^3)^(1/2)*(-105*d*x^2+-35*e*x^3+-21*f*x^4+-15*g*x^5+105*c*x)+3//2*c*x^-2*(a+b*x^3)^(1/2)+1//7*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(6*a*g+21*b*d)+1//70*3^3//4*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(7*b^1//3*(4*a*f+5*b*c)+-1*a^1//3*(10+-10*3^(1/2))*(2*a*g+7*b*d))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+-3//14*3^1//4*a^1//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(2*a*g+7*b*d)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-4*(a+b*x^3)^(1/2)*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(-3*e*x^-1*(a+b*x^3)^(1/2)+-2//15*x^-4*(a+b*x^3)^(1/2)*(-15*e*x^3+-5*f*x^4+-3*g*x^5+5*c*x+15*d*x^2)+-1//3*a^-1//2*(b*c+2*a*f)*arctanh(a^-1//2*(a+b*x^3)^(1/2))+1//3*c*x^-3*(a+b*x^3)^(1/2)+3//2*d*x^-2*(a+b*x^3)^(1/2)+3*e*b^1//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+1//10*3^3//4*b^-1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(4*a*g+5*b*d+-1*e*a^1//3*b^2//3*(10+-10*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+-3//2*e*3^1//4*a^1//3*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-5*(a+b*x^3)^(1/2)*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(-2//15*x^-5*(a+b*x^3)^(1/2)*(-15*f*x^4+-5*g*x^5+3*c*x+5*d*x^2+15*e*x^3)+-1//3*a^-1//2*(b*d+2*a*g)*arctanh(a^-1//2*(a+b*x^3)^(1/2))+1//3*d*x^-3*(a+b*x^3)^(1/2)+3//2*e*x^-2*(a+b*x^3)^(1/2)+3//20*c*x^-4*(a+b*x^3)^(1/2)+-1//8*a^-1*x^-1*(a+b*x^3)^(1/2)*(3*b*c+24*a*f)+3//8*a^-1*b^1//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(b*c+8*a*f)+-3//16*3^1//4*a^-2//3*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(b*c+8*a*f)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+1//8*3^3//4*a^-2//3*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-1*(1+-1*3^(1/2))*(b*c+8*a*f)+4*e*a^2//3*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-6*(a+b*x^3)^(1/2)*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :((a+b*x^3)^(1/2)*(-1*g*x^-1+-1//2*f*x^-2+-1//3*e*x^-3+-1//4*d*x^-4+-1//5*c*x^-5)+-1//3*b*e*a^-1//2*arctanh(a^-1//2*(a+b*x^3)^(1/2))+-3//8*b*d*a^-1*x^-1*(a+b*x^3)^(1/2)+-3//20*b*c*a^-1*x^-2*(a+b*x^3)^(1/2)+3//8*a^-1*b^1//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(b*d+8*a*g)+-3//16*3^1//4*a^-2//3*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(b*d+8*a*g)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+-1//40*3^3//4*a^-1*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(2*b^1//3*(b*c+-10*a*f)+a^1//3*(5+-5*3^(1/2))*(b*d+8*a*g))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-7*(a+b*x^3)^(1/2)*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :((a+b*x^3)^(1/2)*(-1//2*g*x^-2+-1//3*f*x^-3+-1//4*e*x^-4+-1//5*d*x^-5+-1//6*c*x^-6)+1//12*b*a^-3//2*(b*c+-4*a*f)*arctanh(a^-1//2*(a+b*x^3)^(1/2))+-3//8*b*e*a^-1*x^-1*(a+b*x^3)^(1/2)+-3//20*b*d*a^-1*x^-2*(a+b*x^3)^(1/2)+-1//12*b*c*a^-1*x^-3*(a+b*x^3)^(1/2)+3//8*e*a^-1*b^4//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+-3//16*e*3^1//4*a^-2//3*b^4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+-1//40*3^3//4*a^-1*b^2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-20*a*g+2*b*d+e*a^1//3*b^2//3*(5+-5*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-8*(a+b*x^3)^(1/2)*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :((a+b*x^3)^(1/2)*(-1//3*g*x^-3+-1//4*f*x^-4+-1//5*e*x^-5+-1//6*d*x^-6+-1//7*c*x^-7)+1//12*b*a^-3//2*(b*d+-4*a*g)*arctanh(a^-1//2*(a+b*x^3)^(1/2))+-3//20*b*e*a^-1*x^-2*(a+b*x^3)^(1/2)+-3//56*b*c*a^-1*x^-4*(a+b*x^3)^(1/2)+-3//112*a^-2*b^4//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(-14*a*f+5*b*c)+-1//12*b*d*a^-1*x^-3*(a+b*x^3)^(1/2)+3//112*b*a^-2*x^-1*(a+b*x^3)^(1/2)*(-14*a*f+5*b*c)+-1//560*3^3//4*a^-5//3*b^4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-1*(5+-5*3^(1/2))*(-14*a*f+5*b*c)+28*e*a^2//3*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+3//224*3^1//4*a^-5//3*b^4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-14*a*f+5*b*c)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-9*(a+b*x^3)^(1/2)*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :((a+b*x^3)^(1/2)*(-1//4*g*x^-4+-1//5*f*x^-5+-1//6*e*x^-6+-1//7*d*x^-7+-1//8*c*x^-8)+1//12*e*a^-3//2*b^2*arctanh(a^-1//2*(a+b*x^3)^(1/2))+-3//56*b*d*a^-1*x^-4*(a+b*x^3)^(1/2)+-3//80*b*c*a^-1*x^-5*(a+b*x^3)^(1/2)+-3//112*a^-2*b^4//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(-14*a*g+5*b*d)+-1//12*b*e*a^-1*x^-3*(a+b*x^3)^(1/2)+3//112*b*a^-2*x^-1*(a+b*x^3)^(1/2)*(-14*a*g+5*b*d)+3//320*b*a^-2*x^-2*(a+b*x^3)^(1/2)*(-16*a*f+7*b*c)+1//2240*3^3//4*a^-2*b^4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(7*b^1//3*(-16*a*f+7*b*c)+a^1//3*(20+-20*3^(1/2))*(-14*a*g+5*b*d))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+3//224*3^1//4*a^-5//3*b^4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-14*a*g+5*b*d)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^3*(a+b*x^3)^3//2*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(2//3900225*x^3*(a+b*x^3)^3//2*(156009*g*x^5+169575*f*x^4+185725*e*x^3+205275*d*x^2+229425*c*x)+-4//105*e*a^3*b^-2*(a+b*x^3)^(1/2)+2//185910725*a*x^3*(a+b*x^3)^(1/2)*(3522519*g*x^5+4279275*f*x^4+5311735*e*x^3+6774075*d*x^2+8947575*c*x)+-216//8645*a^3*b^-8//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(-2*a*g+5*b*d)+2//105*e*a^2*b^-1*x^3*(a+b*x^3)^(1/2)+54//4301*f*a^2*b^-1*x^4*(a+b*x^3)^(1/2)+54//6175*g*a^2*b^-1*x^5*(a+b*x^3)^(1/2)+54//8645*a^2*b^-2*x^2*(a+b*x^3)^(1/2)*(-2*a*g+5*b*d)+54//21505*x*a^2*b^-2*(a+b*x^3)^(1/2)*(-8*a*f+23*b*c)+-36//37182145*3^3//4*a^3*b^-8//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(1729*b^1//3*(-8*a*f+23*b*c)+-1*a^1//3*(8602+-8602*3^(1/2))*(-2*a*g+5*b*d))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+108//8645*3^1//4*a^10//3*b^-8//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-2*a*g+5*b*d)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^2*(a+b*x^3)^3//2*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(2//780045*x^2*(a+b*x^3)^3//2*(33915*g*x^5+37145*f*x^4+41055*e*x^3+45885*d*x^2+52003*c*x)+2//105*a^2*b^-2*(a+b*x^3)^(1/2)*(-2*a*f+7*b*c)+2//111546435*a*x^2*(a+b*x^3)^(1/2)*(2567565*g*x^5+3187041*f*x^4+4064445*e*x^3+5368545*d*x^2+7436429*c*x)+-216//1729*e*a^3*b^-5//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+2//105*f*a^2*b^-1*x^3*(a+b*x^3)^(1/2)+54//1729*e*a^2*b^-1*x^2*(a+b*x^3)^(1/2)+54//4301*g*a^2*b^-1*x^4*(a+b*x^3)^(1/2)+54//21505*x*a^2*b^-2*(a+b*x^3)^(1/2)*(-8*a*g+23*b*d)+36//37182145*3^3//4*a^3*b^-7//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-39767*b*d+13832*a*g+e*a^1//3*b^2//3*(43010+-43010*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+108//1729*e*3^1//4*a^10//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(a+b*x^3)^3//2*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(2//440895*x*(a+b*x^3)^3//2*(20995*g*x^5+23205*f*x^4+25935*e*x^3+29393*d*x^2+33915*c*x)+2//105*a^2*b^-2*(a+b*x^3)^(1/2)*(-2*a*g+7*b*d)+2//4849845*a*x*(a+b*x^3)^(1/2)*(138567*g*x^5+176715*f*x^4+233415*e*x^3+323323*d*x^2+479655*c*x)+2//105*g*a^2*b^-1*x^3*(a+b*x^3)^(1/2)+54//935*e*x*a^2*b^-1*(a+b*x^3)^(1/2)+54//1729*f*a^2*b^-1*x^2*(a+b*x^3)^(1/2)+54//1729*a^2*b^-5//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(-4*a*f+19*b*c)+-27//1729*3^1//4*a^7//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-4*a*f+19*b*c)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+-18//1616615*3^3//4*a^7//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*((935+-935*3^(1/2))*(-4*a*f+19*b*c)+3458*e*a^2//3*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+b*x^3)^3//2*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(2//692835*(a+b*x^3)^3//2*(36465*g*x^5+40755*f*x^4+46189*e*x^3+53295*d*x^2+62985*c*x)+2//4849845*a*(a+b*x^3)^(1/2)*(176715*g*x^5+233415*f*x^4+323323*e*x^3+479655*d*x^2+793611*c*x)+2//15*e*a^2*b^-1*(a+b*x^3)^(1/2)+54//935*f*x*a^2*b^-1*(a+b*x^3)^(1/2)+54//1729*g*a^2*b^-1*x^2*(a+b*x^3)^(1/2)+54//1729*a^2*b^-5//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(-4*a*g+19*b*d)+-27//1729*3^1//4*a^7//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-4*a*g+19*b*d)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+18//1616615*3^3//4*a^2*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(1729*b^1//3*(-2*a*f+17*b*c)+-1*a^1//3*(935+-935*3^(1/2))*(-4*a*g+19*b*d))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-1*(a+b*x^3)^3//2*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(-2//3*c*a^3//2*arctanh(a^-1//2*(a+b*x^3)^(1/2))+2//109395*x^-1*(a+b*x^3)^3//2*(6435*g*x^5+7293*f*x^4+8415*e*x^3+9945*d*x^2+12155*c*x)+2//15*f*a^2*b^-1*(a+b*x^3)^(1/2)+2//255255*a*x^-1*(a+b*x^3)^(1/2)*(12285*g*x^5+17017*f*x^4+25245*e*x^3+41769*d*x^2+85085*c*x)+54//91*e*a^2*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+54//935*g*x*a^2*b^-1*(a+b*x^3)^(1/2)+-27//91*e*3^1//4*a^7//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+18//85085*3^3//4*a^2*b^-4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-182*a*g+1547*b*d+-1*e*a^1//3*b^2//3*(935+-935*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-2*(a+b*x^3)^3//2*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(-2//3*d*a^3//2*arctanh(a^-1//2*(a+b*x^3)^(1/2))+2//45045*x^-2*(a+b*x^3)^3//2*(3003*g*x^5+3465*f*x^4+4095*e*x^3+5005*d*x^2+6435*c*x)+-27//7*a*c*x^-1*(a+b*x^3)^(1/2)+2//15*g*a^2*b^-1*(a+b*x^3)^(1/2)+2//15015*a*x^-2*(a+b*x^3)^(1/2)*(1001*g*x^5+1485*f*x^4+2457*e*x^3+5005*d*x^2+19305*c*x)+27//91*a*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(2*a*f+13*b*c)+-27//182*3^1//4*a^4//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(2*a*f+13*b*c)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+9//5005*3^3//4*a^4//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-1*(55+-55*3^(1/2))*(2*a*f+13*b*c)+182*e*a^2//3*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-3*(a+b*x^3)^3//2*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(-2//3*e*a^3//2*arctanh(a^-1//2*(a+b*x^3)^(1/2))+2//45045*x^-3*(a+b*x^3)^3//2*(3465*g*x^5+4095*f*x^4+5005*e*x^3+6435*d*x^2+9009*c*x)+-27//7*a*d*x^-1*(a+b*x^3)^(1/2)+-2//15015*a*x^-3*(a+b*x^3)^(1/2)*(-19305*d*x^2+-5005*e*x^3+-2457*f*x^4+-1485*g*x^5+27027*c*x)+27//10*a*c*x^-2*(a+b*x^3)^(1/2)+27//91*a*b^-2//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(2*a*g+13*b*d)+-27//182*3^1//4*a^4//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(2*a*g+13*b*d)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+9//10010*a*3^3//4*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(91*b^1//3*(4*a*f+11*b*c)+-1*a^1//3*(110+-110*3^(1/2))*(2*a*g+13*b*d))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-4*(a+b*x^3)^3//2*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(-1//3*a^(1/2)*(2*a*f+3*b*c)*arctanh(a^-1//2*(a+b*x^3)^(1/2))+2//3465*x^-4*(a+b*x^3)^3//2*(315*g*x^5+385*f*x^4+495*e*x^3+693*d*x^2+1155*c*x)+a*c*x^-3*(a+b*x^3)^(1/2)+-27//7*a*e*x^-1*(a+b*x^3)^(1/2)+-2//1155*a*x^-4*(a+b*x^3)^(1/2)*(-1485*e*x^3+-385*f*x^4+-189*g*x^5+1155*c*x+2079*d*x^2)+27//10*a*d*x^-2*(a+b*x^3)^(1/2)+27*a*e*b^1//3*(a+b*x^3)^(1/2)*(7*x*b^1//3+7*a^1//3*(1+3^(1/2)))^-1+-27//14*e*3^1//4*a^4//3*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+9//770*a*3^3//4*b^-1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(28*a*g+77*b*d+-1*e*a^1//3*b^2//3*(110+-110*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-5*(a+b*x^3)^3//2*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(-1//3*a^(1/2)*(2*a*g+3*b*d)*arctanh(a^-1//2*(a+b*x^3)^(1/2))+-1//56*x^-1*(a+b*x^3)^(1/2)*(189*b*c+216*a*f)+2//315*x^-5*(a+b*x^3)^3//2*(35*g*x^5+45*f*x^4+63*e*x^3+105*d*x^2+315*c*x)+a*d*x^-3*(a+b*x^3)^(1/2)+27*b^1//3*(a+b*x^3)^(1/2)*(56*x*b^1//3+56*a^1//3*(1+3^(1/2)))^-1*(7*b*c+8*a*f)+-2//105*a*x^-5*(a+b*x^3)^(1/2)*(-135*f*x^4+-35*g*x^5+105*d*x^2+189*c*x+189*e*x^3)+27//10*a*e*x^-2*(a+b*x^3)^(1/2)+27//20*a*c*x^-4*(a+b*x^3)^(1/2)+-27//112*3^1//4*a^1//3*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(7*b*c+8*a*f)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+9//280*3^3//4*a^1//3*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-1*(5+-5*3^(1/2))*(7*b*c+8*a*f)+28*e*a^2//3*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-6*(a+b*x^3)^3//2*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(-1*(a+b*x^3)^3//2*(g*x^-1+(1/2)*f*x^-2+1//3*e*x^-3+1//4*d*x^-4+1//5*c*x^-5)+-1*b*e*a^(1/2)*arctanh(a^-1//2*(a+b*x^3)^(1/2))+27*b^1//3*(a+b*x^3)^(1/2)*(56*x*b^1//3+56*a^1//3*(1+3^(1/2)))^-1*(7*b*d+8*a*g)+-27//8*b*d*x^-1*(a+b*x^3)^(1/2)+-1//140*b*x^-3*(a+b*x^3)^(1/2)*(-315*d*x^2+-180*g*x^5+-140*e*x^3+-126*f*x^4+252*c*x)+27//20*b*c*x^-2*(a+b*x^3)^(1/2)+9//280*3^3//4*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(14*b^1//3*(b*c+2*a*f)+-1*a^1//3*(5+-5*3^(1/2))*(7*b*d+8*a*g))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+-27//112*3^1//4*a^1//3*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(7*b*d+8*a*g)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-7*(a+b*x^3)^3//2*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(-1*(a+b*x^3)^3//2*((1/2)*g*x^-2+1//3*f*x^-3+1//4*e*x^-4+1//5*d*x^-5+1//6*c*x^-6)+27*e*b^4//3*(a+b*x^3)^(1/2)*(8*x*b^1//3+8*a^1//3*(1+3^(1/2)))^-1+-27//8*b*e*x^-1*(a+b*x^3)^(1/2)+-1//4*b*a^-1//2*(b*c+4*a*f)*arctanh(a^-1//2*(a+b*x^3)^(1/2))+-1//20*b*x^-4*(a+b*x^3)^(1/2)*(-45*e*x^3+-20*f*x^4+-18*g*x^5+10*c*x+36*d*x^2)+1//4*b*c*x^-3*(a+b*x^3)^(1/2)+27//20*b*d*x^-2*(a+b*x^3)^(1/2)+9//40*3^3//4*b^2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(2*b*d+4*a*g+-1*e*a^1//3*b^2//3*(5+-5*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+-27//16*e*3^1//4*a^1//3*b^4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-8*(a+b*x^3)^3//2*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(-1*(a+b*x^3)^3//2*(1//3*g*x^-3+1//4*f*x^-4+1//5*e*x^-5+1//6*d*x^-6+1//7*c*x^-7)+-1//4*b*a^-1//2*(b*d+4*a*g)*arctanh(a^-1//2*(a+b*x^3)^(1/2))+-1//140*b*x^-5*(a+b*x^3)^(1/2)*(-315*f*x^4+-140*g*x^5+36*c*x+70*d*x^2+252*e*x^3)+1//4*b*d*x^-3*(a+b*x^3)^(1/2)+27//20*b*e*x^-2*(a+b*x^3)^(1/2)+27//280*b*c*x^-4*(a+b*x^3)^(1/2)+-27//112*b*a^-1*x^-1*(a+b*x^3)^(1/2)*(b*c+14*a*f)+27//112*a^-1*b^4//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(b*c+14*a*f)+-27//224*3^1//4*a^-2//3*b^4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(b*c+14*a*f)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+9//560*3^3//4*a^-2//3*b^4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-1*(5+-5*3^(1/2))*(b*c+14*a*f)+28*e*a^2//3*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-9*(a+b*x^3)^3//2*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(-1*(a+b*x^3)^3//2*(1//4*g*x^-4+1//5*f*x^-5+1//6*e*x^-6+1//7*d*x^-7+1//8*c*x^-8)+-1//560*b*(a+b*x^3)^(1/2)*(63*c*x^-5+90*d*x^-4+140*e*x^-3+252*f*x^-2+630*g*x^-1)+-1//4*e*a^-1//2*b^2*arctanh(a^-1//2*(a+b*x^3)^(1/2))+-27//112*d*a^-1*b^2*x^-1*(a+b*x^3)^(1/2)+-27//320*c*a^-1*b^2*x^-2*(a+b*x^3)^(1/2)+27//112*a^-1*b^4//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(b*d+14*a*g)+-27//224*3^1//4*a^-2//3*b^4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(b*d+14*a*g)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+-9//2240*3^3//4*a^-1*b^4//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(7*b^1//3*(b*c+-16*a*f)+a^1//3*(20+-20*3^(1/2))*(b*d+14*a*g))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-10*(a+b*x^3)^3//2*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(-1//2520*(a+b*x^3)^3//2*(280*c*x^-9+315*d*x^-8+360*e*x^-7+420*f*x^-6+504*g*x^-5)+-1//1680*b*(a+b*x^3)^(1/2)*(140*c*x^-6+189*d*x^-5+270*e*x^-4+420*f*x^-3+756*g*x^-2)+1//24*a^-3//2*b^2*(b*c+-6*a*f)*arctanh(a^-1//2*(a+b*x^3)^(1/2))+-27//112*e*a^-1*b^2*x^-1*(a+b*x^3)^(1/2)+-27//320*d*a^-1*b^2*x^-2*(a+b*x^3)^(1/2)+-1//24*c*a^-1*b^2*x^-3*(a+b*x^3)^(1/2)+27//112*e*a^-1*b^7//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1+-27//224*e*3^1//4*a^-2//3*b^7//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+-9//2240*3^3//4*a^-1*b^5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-112*a*g+7*b*d+e*a^1//3*b^2//3*(20+-20*3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-11*(a+b*x^3)^3//2*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(-1//2520*(a+b*x^3)^3//2*(252*c*x^-10+280*d*x^-9+315*e*x^-8+360*f*x^-7+420*g*x^-6)+-1//1680*b*(a+b*x^3)^(1/2)*(108*c*x^-7+140*d*x^-6+189*e*x^-5+270*f*x^-4+420*g*x^-3)+1//24*a^-3//2*b^2*(b*d+-6*a*g)*arctanh(a^-1//2*(a+b*x^3)^(1/2))+-27//320*e*a^-1*b^2*x^-2*(a+b*x^3)^(1/2)+-27//448*a^-2*b^7//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(b*c+-4*a*f)+-27//1120*c*a^-1*b^2*x^-4*(a+b*x^3)^(1/2)+-1//24*d*a^-1*b^2*x^-3*(a+b*x^3)^(1/2)+27//448*a^-2*b^2*x^-1*(a+b*x^3)^(1/2)*(b*c+-4*a*f)+-9//2240*3^3//4*a^-5//3*b^7//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(-1*(5+-5*3^(1/2))*(b*c+-4*a*f)+7*e*a^2//3*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+27//896*3^1//4*a^-5//3*b^7//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(b*c+-4*a*f)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-12*(a+b*x^3)^3//2*(c+d*x+e*x^2+f*x^3+g*x^4), x) == :(-1//27720*(a+b*x^3)^3//2*(2520*c*x^-11+2772*d*x^-10+3080*e*x^-9+3465*f*x^-8+3960*g*x^-7)+-1//18480*b*(a+b*x^3)^(1/2)*(945*c*x^-8+1188*d*x^-7+1540*e*x^-6+2079*f*x^-5+2970*g*x^-4)+1//24*e*a^-3//2*b^3*arctanh(a^-1//2*(a+b*x^3)^(1/2))+-27//448*a^-2*b^7//3*(a+b*x^3)^(1/2)*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(b*d+-4*a*g)+-27//1120*d*a^-1*b^2*x^-4*(a+b*x^3)^(1/2)+-27//1760*c*a^-1*b^2*x^-5*(a+b*x^3)^(1/2)+-1//24*e*a^-1*b^2*x^-3*(a+b*x^3)^(1/2)+27//448*a^-2*b^2*x^-1*(a+b*x^3)^(1/2)*(b*d+-4*a*g)+27//7040*a^-2*b^2*x^-2*(a+b*x^3)^(1/2)*(-22*a*f+7*b*c)+9//49280*3^3//4*a^-2*b^7//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(7*b^1//3*(-22*a*f+7*b*c)+a^1//3*(110+-110*3^(1/2))*(b*d+-4*a*g))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+27//896*3^1//4*a^-5//3*b^7//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(b*d+-4*a*g)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+b*x^4)*(c+d*x+e*x^2+f*x^3), x) == :(a*c*x+(1/2)*a*d*x^2+1//3*a*e*x^3+1//4*a*f*x^4+1//5*b*c*x^5+1//6*b*d*x^6+1//7*b*e*x^7+1//8*b*f*x^8)
@test integrate(x^3*(a+b*x^4)*(c+d*x+e*x^2+f*x^3), x) == :(1//4*a*c*x^4+1//5*a*d*x^5+1//6*a*e*x^6+1//7*a*f*x^7+1//8*b*c*x^8+1//9*b*d*x^9+1//10*b*e*x^10+1//11*b*f*x^11)
@test integrate((a+b*x^4)^2*(c+d*x+e*x^2+f*x^3), x) == :(c*x*a^2+(1/2)*d*a^2*x^2+1//3*e*a^2*x^3+1//9*c*b^2*x^9+1//10*d*b^2*x^10+1//11*e*b^2*x^11+1//12*f*b^-1*(a+b*x^4)^3+1//3*a*b*d*x^6+2//5*a*b*c*x^5+2//7*a*b*e*x^7)
@test integrate(x^3*(a+b*x^4)^2*(c+d*x+e*x^2+f*x^3), x) == :(1//5*d*a^2*x^5+1//6*e*a^2*x^6+1//7*f*a^2*x^7+1//12*c*b^-1*(a+b*x^4)^3+1//13*d*b^2*x^13+1//14*e*b^2*x^14+1//15*f*b^2*x^15+1//5*a*b*e*x^10+2//9*a*b*d*x^9+2//11*a*b*f*x^11)
@test integrate((a+b*x^4)^3*(c+d*x+e*x^2+f*x^3), x) == :(c*x*a^3+(1/2)*d*a^3*x^2+1//3*e*a^3*x^3+1//13*c*b^3*x^13+1//14*d*b^3*x^14+1//15*e*b^3*x^15+1//16*f*b^-1*(a+b*x^4)^4+(1/2)*b*d*a^2*x^6+1//3*a*c*b^2*x^9+3//5*b*c*a^2*x^5+3//7*b*e*a^2*x^7+3//10*a*d*b^2*x^10+3//11*a*e*b^2*x^11)
@test integrate(x^3*(a+b*x^4)^3*(c+d*x+e*x^2+f*x^3), x) == :(1//5*d*a^3*x^5+1//6*e*a^3*x^6+1//7*f*a^3*x^7+1//16*c*b^-1*(a+b*x^4)^4+1//17*d*b^3*x^17+1//18*e*b^3*x^18+1//19*f*b^3*x^19+1//3*b*d*a^2*x^9+1//5*a*f*b^2*x^15+3//10*b*e*a^2*x^10+3//11*b*f*a^2*x^11+3//13*a*d*b^2*x^13+3//14*a*e*b^2*x^14)
@test integrate((a+b*x^4)^4*(c+d*x+e*x^2+f*x^3), x) == :(c*x*a^4+(1/2)*d*a^4*x^2+1//3*e*a^4*x^3+1//17*c*b^4*x^17+1//18*d*b^4*x^18+1//19*e*b^4*x^19+1//20*f*b^-1*(a+b*x^4)^5+2//3*b*d*a^3*x^6+2//3*c*a^2*b^2*x^9+2//7*a*d*b^3*x^14+3//5*d*a^2*b^2*x^10+4//5*b*c*a^3*x^5+4//7*b*e*a^3*x^7+4//13*a*c*b^3*x^13+4//15*a*e*b^3*x^15+6//11*e*a^2*b^2*x^11)
@test integrate(x^3*(a+b*x^4)^4*(c+d*x+e*x^2+f*x^3), x) == :(1//5*d*a^4*x^5+1//6*e*a^4*x^6+1//7*f*a^4*x^7+1//20*c*b^-1*(a+b*x^4)^5+1//21*d*b^4*x^21+1//22*e*b^4*x^22+1//23*f*b^4*x^23+2//5*b*e*a^3*x^10+2//5*f*a^2*b^2*x^15+2//9*a*e*b^3*x^18+3//7*e*a^2*b^2*x^14+4//9*b*d*a^3*x^9+4//11*b*f*a^3*x^11+4//17*a*d*b^3*x^17+4//19*a*f*b^3*x^19+6//13*d*a^2*b^2*x^13)
@test integrate((a+-1*b*x^4)^-1*(c+d*x+e*x^2+f*x^3), x) == :(-1//4*f*b^-1*log(a+-1*b*x^4)+(1/2)*d*a^-1//2*b^-1//2*arctanh(a^-1//2*b^(1/2)*x^2)+(1/2)*a^-3//4*b^-3//4*(c*b^(1/2)+e*a^(1/2))*arctanh(x*a^-1//4*b^1//4)+(1/2)*a^-3//4*b^-3//4*(c*b^(1/2)+-1*e*a^(1/2))*arctan(x*a^-1//4*b^1//4))
@test integrate(x^3*(a+-1*b*x^4)^-1*(c+d*x+e*x^2+f*x^3), x) == :(-1*d*x*b^-1+-1//2*e*b^-1*x^2+-1//3*f*b^-1*x^3+-1//4*c*b^-1*log(a+-1*b*x^4)+(1/2)*e*a^(1/2)*b^-3//2*arctanh(a^-1//2*b^(1/2)*x^2)+(1/2)*a^1//4*b^-7//4*(d*b^(1/2)+f*a^(1/2))*arctanh(x*a^-1//4*b^1//4)+(1/2)*a^1//4*b^-7//4*(d*b^(1/2)+-1*f*a^(1/2))*arctan(x*a^-1//4*b^1//4))
@test integrate((a+b*x^4)^-1*(c+d*x+e*x^2+f*x^3), x) == :(1//4*f*b^-1*log(a+b*x^4)+(1/2)*d*a^-1//2*b^-1//2*arctan(a^-1//2*b^(1/2)*x^2)+-1//4*2^(1/2)*a^-3//4*b^-3//4*(c*b^(1/2)+e*a^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//8*2^(1/2)*a^-3//4*b^-3//4*(c*b^(1/2)+-1*e*a^(1/2))*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//4*2^(1/2)*a^-3//4*b^-3//4*(c*b^(1/2)+e*a^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//8*2^(1/2)*a^-3//4*b^-3//4*(c*b^(1/2)+-1*e*a^(1/2))*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate(x^3*(a+b*x^4)^-1*(c+d*x+e*x^2+f*x^3), x) == :(d*x*b^-1+(1/2)*e*b^-1*x^2+1//3*f*b^-1*x^3+1//4*c*b^-1*log(a+b*x^4)+-1//2*e*a^(1/2)*b^-3//2*arctan(a^-1//2*b^(1/2)*x^2)+-1//4*2^(1/2)*a^1//4*b^-7//4*(d*b^(1/2)+f*a^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+-1//8*2^(1/2)*a^1//4*b^-7//4*(d*b^(1/2)+-1*f*a^(1/2))*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4)+1//4*2^(1/2)*a^1//4*b^-7//4*(d*b^(1/2)+f*a^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+1//8*2^(1/2)*a^1//4*b^-7//4*(d*b^(1/2)+-1*f*a^(1/2))*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4))
@test integrate((a+b*x^4)^-2*(c+d*x+e*x^2+f*x^3), x) == :(-1//4*a^-1*b^-1*(a+b*x^4)^-1*(a*f+-1*b*x*(c+d*x+e*x^2))+1//4*d*a^-3//2*b^-1//2*arctan(a^-1//2*b^(1/2)*x^2)+-1//16*2^(1/2)*a^-7//4*b^-3//4*(e*a^(1/2)+3*c*b^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//32*2^(1/2)*a^-7//4*b^-3//4*(-1*e*a^(1/2)+3*c*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//16*2^(1/2)*a^-7//4*b^-3//4*(e*a^(1/2)+3*c*b^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//32*2^(1/2)*a^-7//4*b^-3//4*(-1*e*a^(1/2)+3*c*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate(x^3*(a+b*x^4)^-2*(c+d*x+e*x^2+f*x^3), x) == :(-1//4*b^-1*(a+b*x^4)^-1*(c+d*x+e*x^2+f*x^3)+1//4*e*a^-1//2*b^-3//2*arctan(a^-1//2*b^(1/2)*x^2)+-1//16*2^(1/2)*a^-3//4*b^-7//4*(d*b^(1/2)+3*f*a^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//32*2^(1/2)*a^-3//4*b^-7//4*(d*b^(1/2)+-3*f*a^(1/2))*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//16*2^(1/2)*a^-3//4*b^-7//4*(d*b^(1/2)+3*f*a^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//32*2^(1/2)*a^-3//4*b^-7//4*(d*b^(1/2)+-3*f*a^(1/2))*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate((a+b*x^4)^-3*(c+d*x+e*x^2+f*x^3), x) == :(-1//8*a^-1*b^-1*(a+b*x^4)^-2*(a*f+-1*b*x*(c+d*x+e*x^2))+1//32*x*a^-2*(a+b*x^4)^-1*(7c+5*e*x^2+6*d*x)+3//16*d*a^-5//2*b^-1//2*arctan(a^-1//2*b^(1/2)*x^2)+-1//128*2^(1/2)*a^-11//4*b^-3//4*(5*e*a^(1/2)+21*c*b^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//256*2^(1/2)*a^-11//4*b^-3//4*(-5*e*a^(1/2)+21*c*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//128*2^(1/2)*a^-11//4*b^-3//4*(5*e*a^(1/2)+21*c*b^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//256*2^(1/2)*a^-11//4*b^-3//4*(-5*e*a^(1/2)+21*c*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate(x^3*(a+b*x^4)^-3*(c+d*x+e*x^2+f*x^3), x) == :(-1//8*b^-1*(a+b*x^4)^-2*(c+d*x+e*x^2+f*x^3)+1//16*e*a^-3//2*b^-3//2*arctan(a^-1//2*b^(1/2)*x^2)+-1//128*2^(1/2)*a^-7//4*b^-7//4*(3*d*b^(1/2)+3*f*a^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//256*2^(1/2)*a^-7//4*b^-7//4*(-3*f*a^(1/2)+3*d*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//32*x*a^-1*b^-1*(a+b*x^4)^-1*(d+2*e*x+3*f*x^2)+1//128*2^(1/2)*a^-7//4*b^-7//4*(3*d*b^(1/2)+3*f*a^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//256*2^(1/2)*a^-7//4*b^-7//4*(-3*f*a^(1/2)+3*d*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate((a+b*x^4)^-4*(c+d*x+e*x^2+f*x^3), x) == :(-1//12*a^-1*b^-1*(a+b*x^4)^-3*(a*f+-1*b*x*(c+d*x+e*x^2))+1//96*x*a^-2*(a+b*x^4)^-2*(11c+9*e*x^2+10*d*x)+1//384*x*a^-3*(a+b*x^4)^-1*(77c+45*e*x^2+60*d*x)+5//32*d*a^-7//2*b^-1//2*arctan(a^-1//2*b^(1/2)*x^2)+-1//512*2^(1/2)*a^-15//4*b^-3//4*(15*e*a^(1/2)+77*c*b^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//1024*2^(1/2)*a^-15//4*b^-3//4*(-15*e*a^(1/2)+77*c*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//512*2^(1/2)*a^-15//4*b^-3//4*(15*e*a^(1/2)+77*c*b^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//1024*2^(1/2)*a^-15//4*b^-3//4*(-15*e*a^(1/2)+77*c*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate(x^3*(a+b*x^4)^-4*(c+d*x+e*x^2+f*x^3), x) == :(-1//12*b^-1*(a+b*x^4)^-3*(c+d*x+e*x^2+f*x^3)+1//32*e*a^-5//2*b^-3//2*arctan(a^-1//2*b^(1/2)*x^2)+-1//512*2^(1/2)*a^-11//4*b^-7//4*(5*f*a^(1/2)+7*d*b^(1/2))*arctan(1+-1*x*2^(1/2)*a^-1//4*b^1//4)+-1//1024*2^(1/2)*a^-11//4*b^-7//4*(-5*f*a^(1/2)+7*d*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*b^1//4)+1//96*x*a^-1*b^-1*(a+b*x^4)^-2*(d+2*e*x+3*f*x^2)+1//384*x*a^-2*b^-1*(a+b*x^4)^-1*(7d+12*e*x+15*f*x^2)+1//512*2^(1/2)*a^-11//4*b^-7//4*(5*f*a^(1/2)+7*d*b^(1/2))*arctan(1+x*2^(1/2)*a^-1//4*b^1//4)+1//1024*2^(1/2)*a^-11//4*b^-7//4*(-5*f*a^(1/2)+7*d*b^(1/2))*log(a^(1/2)+b^(1/2)*x^2+x*2^(1/2)*a^1//4*b^1//4))
@test integrate(x^4*(a+b*x^4)^(1/2)*(c+d*x+e*x^2+f*x^3), x) == :(-1//120*b^-2*(a+b*x^4)^3//2*(8*a*f+-15*b*d*x^2)+1//63*x^5*(a+b*x^4)^(1/2)*(9c+7*e*x^2)+-1//16*d*a^2*b^-3//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+1//10*f*b^-1*x^4*(a+b*x^4)^3//2+-1//16*a*d*b^-1*x^2*(a+b*x^4)^(1/2)+2//21*a*c*x*b^-1*(a+b*x^4)^(1/2)+2//45*a*e*b^-1*x^3*(a+b*x^4)^(1/2)+-2//15*e*x*a^2*b^-3//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-1//105*a^7//4*b^-7//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(5*c*b^(1/2)+7*e*a^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2)+2//15*e*a^9//4*b^-7//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^3*(a+b*x^4)^(1/2)*(c+d*x+e*x^2+f*x^3), x) == :(1//24*b^-1*(a+b*x^4)^3//2*(4c+3*e*x^2)+1//63*x^5*(a+b*x^4)^(1/2)*(9d+7*f*x^2)+-1//16*e*a^2*b^-3//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+-1//16*a*e*b^-1*x^2*(a+b*x^4)^(1/2)+2//21*a*d*x*b^-1*(a+b*x^4)^(1/2)+2//45*a*f*b^-1*x^3*(a+b*x^4)^(1/2)+-2//15*f*x*a^2*b^-3//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-1//105*a^7//4*b^-7//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(5*d*b^(1/2)+7*f*a^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2)+2//15*f*a^9//4*b^-7//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^2*(a+b*x^4)^(1/2)*(c+d*x+e*x^2+f*x^3), x) == :(1//24*b^-1*(a+b*x^4)^3//2*(4d+3*f*x^2)+1//35*x^3*(a+b*x^4)^(1/2)*(7c+5*e*x^2)+-1//16*f*a^2*b^-3//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+-1//16*a*f*b^-1*x^2*(a+b*x^4)^(1/2)+2//21*a*e*x*b^-1*(a+b*x^4)^(1/2)+2//5*a*c*x*b^-1//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-2//5*c*a^5//4*b^-3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+1//105*a^5//4*b^-5//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(-5*e*a^(1/2)+21*c*b^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x*(a+b*x^4)^(1/2)*(c+d*x+e*x^2+f*x^3), x) == :(1//4*c*x^2*(a+b*x^4)^(1/2)+1//6*e*b^-1*(a+b*x^4)^3//2+1//35*x^3*(a+b*x^4)^(1/2)*(7d+5*f*x^2)+1//4*a*c*b^-1//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+2//21*a*f*x*b^-1*(a+b*x^4)^(1/2)+2//5*a*d*x*b^-1//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-2//5*d*a^5//4*b^-3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+1//105*a^5//4*b^-5//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(-5*f*a^(1/2)+21*d*b^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate((a+b*x^4)^(1/2)*(c+d*x+e*x^2+f*x^3), x) == :(1//4*d*x^2*(a+b*x^4)^(1/2)+1//6*f*b^-1*(a+b*x^4)^3//2+1//15*x*(a+b*x^4)^(1/2)*(5c+3*e*x^2)+1//4*a*d*b^-1//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+2//5*a*e*x*b^-1//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-2//5*e*a^5//4*b^-3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+1//15*a^3//4*b^-3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(3*e*a^(1/2)+5*c*b^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-1*(a+b*x^4)^(1/2)*(c+d*x+e*x^2+f*x^3), x) == :(1//4*(a+b*x^4)^(1/2)*(2c+e*x^2)+-1//2*c*a^(1/2)*arctanh(a^-1//2*(a+b*x^4)^(1/2))+1//15*x*(a+b*x^4)^(1/2)*(5d+3*f*x^2)+1//4*a*e*b^-1//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+2//5*a*f*x*b^-1//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-2//5*f*a^5//4*b^-3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+1//15*a^3//4*b^-3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(3*f*a^(1/2)+5*d*b^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-2*(a+b*x^4)^(1/2)*(c+d*x+e*x^2+f*x^3), x) == :(1//4*(a+b*x^4)^(1/2)*(2d+f*x^2)+-1//2*d*a^(1/2)*arctanh(a^-1//2*(a+b*x^4)^(1/2))+-1//3*x^-1*(a+b*x^4)^(1/2)*(3c+-1*e*x^2)+1//4*a*f*b^-1//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+2*c*x*b^(1/2)*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-2*c*a^1//4*b^1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+1//3*a^1//4*b^-1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(e*a^(1/2)+3*c*b^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-3*(a+b*x^4)^(1/2)*(c+d*x+e*x^2+f*x^3), x) == :((1/2)*c*b^(1/2)*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+-1//2*e*a^(1/2)*arctanh(a^-1//2*(a+b*x^4)^(1/2))+-1//2*x^-2*(a+b*x^4)^(1/2)*(c+-1*e*x^2)+-1//3*x^-1*(a+b*x^4)^(1/2)*(3d+-1*f*x^2)+2*d*x*b^(1/2)*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-2*d*a^1//4*b^1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+1//3*a^1//4*b^-1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(f*a^(1/2)+3*d*b^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-4*(a+b*x^4)^(1/2)*(c+d*x+e*x^2+f*x^3), x) == :((1/2)*d*b^(1/2)*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+-2*e*x^-1*(a+b*x^4)^(1/2)+-1//2*f*a^(1/2)*arctanh(a^-1//2*(a+b*x^4)^(1/2))+-1//2*x^-2*(a+b*x^4)^(1/2)*(d+-1*f*x^2)+-1//3*x^-3*(a+b*x^4)^(1/2)*(c+-3*e*x^2)+2*e*x*b^(1/2)*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-2*e*a^1//4*b^1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+1//3*a^-1//4*b^1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(c*b^(1/2)+3*e*a^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-5*(a+b*x^4)^(1/2)*(c+d*x+e*x^2+f*x^3), x) == :(-1//12*(a+b*x^4)^(1/2)*(3*c*x^-4+4*d*x^-3+6*e*x^-2+12*f*x^-1)+(1/2)*e*b^(1/2)*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+-1//4*b*c*a^-1//2*arctanh(a^-1//2*(a+b*x^4)^(1/2))+2*f*x*b^(1/2)*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-2*f*a^1//4*b^1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+1//3*a^-1//4*b^1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(d*b^(1/2)+3*f*a^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-6*(a+b*x^4)^(1/2)*(c+d*x+e*x^2+f*x^3), x) == :(-1//60*(a+b*x^4)^(1/2)*(12*c*x^-5+15*d*x^-4+20*e*x^-3+30*f*x^-2)+(1/2)*f*b^(1/2)*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+-1//4*b*d*a^-1//2*arctanh(a^-1//2*(a+b*x^4)^(1/2))+-2//5*b*c*a^-1*x^-1*(a+b*x^4)^(1/2)+2//5*c*x*a^-1*b^3//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-2//5*c*a^-3//4*b^5//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+1//15*a^-3//4*b^3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(3*c*b^(1/2)+5*e*a^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-7*(a+b*x^4)^(1/2)*(c+d*x+e*x^2+f*x^3), x) == :(-1//60*(a+b*x^4)^(1/2)*(10*c*x^-6+12*d*x^-5+15*e*x^-4+20*f*x^-3)+-1//4*b*e*a^-1//2*arctanh(a^-1//2*(a+b*x^4)^(1/2))+-2//5*b*d*a^-1*x^-1*(a+b*x^4)^(1/2)+-1//6*b*c*a^-1*x^-2*(a+b*x^4)^(1/2)+2//5*d*x*a^-1*b^3//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-2//5*d*a^-3//4*b^5//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+1//15*a^-3//4*b^3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(3*d*b^(1/2)+5*f*a^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-8*(a+b*x^4)^(1/2)*(c+d*x+e*x^2+f*x^3), x) == :(-1//420*(a+b*x^4)^(1/2)*(60*c*x^-7+70*d*x^-6+84*e*x^-5+105*f*x^-4)+-1//4*b*f*a^-1//2*arctanh(a^-1//2*(a+b*x^4)^(1/2))+-2//5*b*e*a^-1*x^-1*(a+b*x^4)^(1/2)+-2//21*b*c*a^-1*x^-3*(a+b*x^4)^(1/2)+-1//6*b*d*a^-1*x^-2*(a+b*x^4)^(1/2)+2//5*e*x*a^-1*b^3//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-2//5*e*a^-3//4*b^5//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+-1//105*a^-5//4*b^5//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(-21*e*a^(1/2)+5*c*b^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-9*(a+b*x^4)^(1/2)*(c+d*x+e*x^2+f*x^3), x) == :(-1//840*(a+b*x^4)^(1/2)*(105*c*x^-8+120*d*x^-7+140*e*x^-6+168*f*x^-5)+1//16*c*a^-3//2*b^2*arctanh(a^-1//2*(a+b*x^4)^(1/2))+-2//5*b*f*a^-1*x^-1*(a+b*x^4)^(1/2)+-2//21*b*d*a^-1*x^-3*(a+b*x^4)^(1/2)+-1//6*b*e*a^-1*x^-2*(a+b*x^4)^(1/2)+-1//16*b*c*a^-1*x^-4*(a+b*x^4)^(1/2)+2//5*f*x*a^-1*b^3//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-2//5*f*a^-3//4*b^5//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+-1//105*a^-5//4*b^5//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(-21*f*a^(1/2)+5*d*b^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-10*(a+b*x^4)^(1/2)*(c+d*x+e*x^2+f*x^3), x) == :(-1//504*(a+b*x^4)^(1/2)*(56*c*x^-9+63*d*x^-8+72*e*x^-7+84*f*x^-6)+1//16*d*a^-3//2*b^2*arctanh(a^-1//2*(a+b*x^4)^(1/2))+-2//21*b*e*a^-1*x^-3*(a+b*x^4)^(1/2)+-2//45*b*c*a^-1*x^-5*(a+b*x^4)^(1/2)+-1//6*b*f*a^-1*x^-2*(a+b*x^4)^(1/2)+-1//16*b*d*a^-1*x^-4*(a+b*x^4)^(1/2)+2//15*c*a^-2*b^2*x^-1*(a+b*x^4)^(1/2)+-2//15*c*x*a^-2*b^5//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-1//105*a^-7//4*b^7//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(5*e*a^(1/2)+7*c*b^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2)+2//15*c*a^-7//4*b^9//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^4*(a+b*x^4)^3//2*(c+d*x+e*x^2+f*x^3), x) == :(-1//420*b^-2*(a+b*x^4)^5//2*(12*a*f+-35*b*d*x^2)+1//143*x^5*(a+b*x^4)^3//2*(13c+11*e*x^2)+-1//32*d*a^3*b^-3//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+1//14*f*b^-1*x^4*(a+b*x^4)^5//2+2//3003*a*x^5*(a+b*x^4)^(1/2)*(117c+77*e*x^2)+-1//32*d*a^2*b^-1*x^2*(a+b*x^4)^(1/2)+-1//48*a*d*b^-1*x^2*(a+b*x^4)^3//2+4//77*c*x*a^2*b^-1*(a+b*x^4)^(1/2)+4//195*e*a^2*b^-1*x^3*(a+b*x^4)^(1/2)+-4//65*e*x*a^3*b^-3//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-2//5005*a^11//4*b^-7//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(65*c*b^(1/2)+77*e*a^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2)+4//65*e*a^13//4*b^-7//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^3*(a+b*x^4)^3//2*(c+d*x+e*x^2+f*x^3), x) == :(1//60*b^-1*(a+b*x^4)^5//2*(6c+5*e*x^2)+1//143*x^5*(a+b*x^4)^3//2*(13d+11*f*x^2)+-1//32*e*a^3*b^-3//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+2//3003*a*x^5*(a+b*x^4)^(1/2)*(117d+77*f*x^2)+-1//32*e*a^2*b^-1*x^2*(a+b*x^4)^(1/2)+-1//48*a*e*b^-1*x^2*(a+b*x^4)^3//2+4//77*d*x*a^2*b^-1*(a+b*x^4)^(1/2)+4//195*f*a^2*b^-1*x^3*(a+b*x^4)^(1/2)+-4//65*f*x*a^3*b^-3//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-2//5005*a^11//4*b^-7//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(65*d*b^(1/2)+77*f*a^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2)+4//65*f*a^13//4*b^-7//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^2*(a+b*x^4)^3//2*(c+d*x+e*x^2+f*x^3), x) == :(1//60*b^-1*(a+b*x^4)^5//2*(6d+5*f*x^2)+1//99*x^3*(a+b*x^4)^3//2*(11c+9*e*x^2)+-1//32*f*a^3*b^-3//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+2//1155*a*x^3*(a+b*x^4)^(1/2)*(77c+45*e*x^2)+-1//32*f*a^2*b^-1*x^2*(a+b*x^4)^(1/2)+-1//48*a*f*b^-1*x^2*(a+b*x^4)^3//2+4//77*e*x*a^2*b^-1*(a+b*x^4)^(1/2)+4//15*c*x*a^2*b^-1//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-4//15*c*a^9//4*b^-3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+2//1155*a^9//4*b^-5//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(-15*e*a^(1/2)+77*c*b^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x*(a+b*x^4)^3//2*(c+d*x+e*x^2+f*x^3), x) == :(1//8*c*x^2*(a+b*x^4)^3//2+1//10*e*b^-1*(a+b*x^4)^5//2+1//99*x^3*(a+b*x^4)^3//2*(11d+9*f*x^2)+2//1155*a*x^3*(a+b*x^4)^(1/2)*(77d+45*f*x^2)+3//16*a*c*x^2*(a+b*x^4)^(1/2)+3//16*c*a^2*b^-1//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+4//77*f*x*a^2*b^-1*(a+b*x^4)^(1/2)+4//15*d*x*a^2*b^-1//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-4//15*d*a^9//4*b^-3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+2//1155*a^9//4*b^-5//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(-15*f*a^(1/2)+77*d*b^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate((a+b*x^4)^3//2*(c+d*x+e*x^2+f*x^3), x) == :(1//8*d*x^2*(a+b*x^4)^3//2+1//10*f*b^-1*(a+b*x^4)^5//2+1//63*x*(a+b*x^4)^3//2*(9c+7*e*x^2)+2//105*a*x*(a+b*x^4)^(1/2)*(15c+7*e*x^2)+3//16*a*d*x^2*(a+b*x^4)^(1/2)+3//16*d*a^2*b^-1//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+4//15*e*x*a^2*b^-1//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-4//15*e*a^9//4*b^-3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+2//105*a^7//4*b^-3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(7*e*a^(1/2)+15*c*b^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-1*(a+b*x^4)^3//2*(c+d*x+e*x^2+f*x^3), x) == :(1//24*(a+b*x^4)^3//2*(4c+3*e*x^2)+-1//2*c*a^3//2*arctanh(a^-1//2*(a+b*x^4)^(1/2))+1//16*a*(a+b*x^4)^(1/2)*(8c+3*e*x^2)+1//63*x*(a+b*x^4)^3//2*(9d+7*f*x^2)+2//105*a*x*(a+b*x^4)^(1/2)*(15d+7*f*x^2)+3//16*e*a^2*b^-1//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+4//15*f*x*a^2*b^-1//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-4//15*f*a^9//4*b^-3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+2//105*a^7//4*b^-3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(7*f*a^(1/2)+15*d*b^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-2*(a+b*x^4)^3//2*(c+d*x+e*x^2+f*x^3), x) == :(1//24*(a+b*x^4)^3//2*(4d+3*f*x^2)+-1//2*d*a^3//2*arctanh(a^-1//2*(a+b*x^4)^(1/2))+-1//7*x^-1*(a+b*x^4)^3//2*(7c+-1*e*x^2)+1//16*a*(a+b*x^4)^(1/2)*(8d+3*f*x^2)+2//35*x*(a+b*x^4)^(1/2)*(5*a*e+21*b*c*x^2)+3//16*f*a^2*b^-1//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+12*a*c*x*b^(1/2)*(a+b*x^4)^(1/2)*(5*a^(1/2)+5*b^(1/2)*x^2)^-1+-12//5*c*a^5//4*b^1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+2//35*a^5//4*b^-1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(5*e*a^(1/2)+21*c*b^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-3*(a+b*x^4)^3//2*(c+d*x+e*x^2+f*x^3), x) == :(1//4*(a+b*x^4)^(1/2)*(2*a*e+3*b*c*x^2)+-1//2*e*a^3//2*arctanh(a^-1//2*(a+b*x^4)^(1/2))+-1//6*x^-2*(a+b*x^4)^3//2*(3c+-1*e*x^2)+-1//7*x^-1*(a+b*x^4)^3//2*(7d+-1*f*x^2)+2//35*x*(a+b*x^4)^(1/2)*(5*a*f+21*b*d*x^2)+3//4*a*c*b^(1/2)*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+12*a*d*x*b^(1/2)*(a+b*x^4)^(1/2)*(5*a^(1/2)+5*b^(1/2)*x^2)^-1+-12//5*d*a^5//4*b^1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+2//35*a^5//4*b^-1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(5*f*a^(1/2)+21*d*b^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-4*(a+b*x^4)^3//2*(c+d*x+e*x^2+f*x^3), x) == :(1//4*(a+b*x^4)^(1/2)*(2*a*f+3*b*d*x^2)+-1//2*f*a^3//2*arctanh(a^-1//2*(a+b*x^4)^(1/2))+-1//6*x^-2*(a+b*x^4)^3//2*(3d+-1*f*x^2)+-1//15*x^-1*(a+b*x^4)^(1/2)*(18*a*e+-10*b*c*x^2)+-1//15*x^-3*(a+b*x^4)^3//2*(5c+-3*e*x^2)+3//4*a*d*b^(1/2)*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+12*a*e*x*b^(1/2)*(a+b*x^4)^(1/2)*(5*a^(1/2)+5*b^(1/2)*x^2)^-1+-12//5*e*a^5//4*b^1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+2//15*a^3//4*b^1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(5*c*b^(1/2)+9*e*a^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-5*(a+b*x^4)^3//2*(c+d*x+e*x^2+f*x^3), x) == :(-1//12*(a+b*x^4)^3//2*(3*c*x^-4+4*d*x^-3+6*e*x^-2+12*f*x^-1)+3//4*b*(a+b*x^4)^(1/2)*(c+e*x^2)+-3//4*b*c*a^(1/2)*arctanh(a^-1//2*(a+b*x^4)^(1/2))+2//15*b*x*(a+b*x^4)^(1/2)*(5d+9*f*x^2)+3//4*a*e*b^(1/2)*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+12*a*f*x*b^(1/2)*(a+b*x^4)^(1/2)*(5*a^(1/2)+5*b^(1/2)*x^2)^-1+-12//5*f*a^5//4*b^1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+2//15*a^3//4*b^1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(5*d*b^(1/2)+9*f*a^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-6*(a+b*x^4)^3//2*(c+d*x+e*x^2+f*x^3), x) == :(-1//60*(a+b*x^4)^3//2*(12*c*x^-5+15*d*x^-4+20*e*x^-3+30*f*x^-2)+3//4*b*(a+b*x^4)^(1/2)*(d+f*x^2)+-3//4*b*d*a^(1/2)*arctanh(a^-1//2*(a+b*x^4)^(1/2))+-2//15*b*x^-1*(a+b*x^4)^(1/2)*(9c+-5*e*x^2)+3//4*a*f*b^(1/2)*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+12*c*x*b^3//2*(a+b*x^4)^(1/2)*(5*a^(1/2)+5*b^(1/2)*x^2)^-1+-12//5*c*a^1//4*b^5//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+2//15*a^1//4*b^3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(5*e*a^(1/2)+9*c*b^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-7*(a+b*x^4)^3//2*(c+d*x+e*x^2+f*x^3), x) == :(-1//60*(a+b*x^4)^3//2*(10*c*x^-6+12*d*x^-5+15*e*x^-4+20*f*x^-3)+(1/2)*c*b^3//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+-3//4*b*e*a^(1/2)*arctanh(a^-1//2*(a+b*x^4)^(1/2))+-2//15*b*x^-1*(a+b*x^4)^(1/2)*(9d+-5*f*x^2)+-1//4*b*x^-2*(a+b*x^4)^(1/2)*(2c+-3*e*x^2)+12*d*x*b^3//2*(a+b*x^4)^(1/2)*(5*a^(1/2)+5*b^(1/2)*x^2)^-1+-12//5*d*a^1//4*b^5//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+2//15*a^1//4*b^3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(5*f*a^(1/2)+9*d*b^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-8*(a+b*x^4)^3//2*(c+d*x+e*x^2+f*x^3), x) == :(-1//420*(a+b*x^4)^3//2*(60*c*x^-7+70*d*x^-6+84*e*x^-5+105*f*x^-4)+(1/2)*d*b^3//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+-12//5*b*e*x^-1*(a+b*x^4)^(1/2)+-3//4*b*f*a^(1/2)*arctanh(a^-1//2*(a+b*x^4)^(1/2))+-2//35*b*x^-3*(a+b*x^4)^(1/2)*(5c+-21*e*x^2)+-1//4*b*x^-2*(a+b*x^4)^(1/2)*(2d+-3*f*x^2)+12*e*x*b^3//2*(a+b*x^4)^(1/2)*(5*a^(1/2)+5*b^(1/2)*x^2)^-1+-12//5*e*a^1//4*b^5//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+2//35*a^-1//4*b^5//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(5*c*b^(1/2)+21*e*a^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-9*(a+b*x^4)^3//2*(c+d*x+e*x^2+f*x^3), x) == :(-1//840*(a+b*x^4)^3//2*(105*c*x^-8+120*d*x^-7+140*e*x^-6+168*f*x^-5)+(1/2)*e*b^3//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+-1//560*b*(a+b*x^4)^(1/2)*(105*c*x^-4+160*d*x^-3+280*e*x^-2+672*f*x^-1)+-3//16*c*a^-1//2*b^2*arctanh(a^-1//2*(a+b*x^4)^(1/2))+12*f*x*b^3//2*(a+b*x^4)^(1/2)*(5*a^(1/2)+5*b^(1/2)*x^2)^-1+-12//5*f*a^1//4*b^5//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+2//35*a^-1//4*b^5//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(5*d*b^(1/2)+21*f*a^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-10*(a+b*x^4)^3//2*(c+d*x+e*x^2+f*x^3), x) == :(-1//504*(a+b*x^4)^3//2*(56*c*x^-9+63*d*x^-8+72*e*x^-7+84*f*x^-6)+(1/2)*f*b^3//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+-1//1680*b*(a+b*x^4)^(1/2)*(224*c*x^-5+315*d*x^-4+480*e*x^-3+840*f*x^-2)+-3//16*d*a^-1//2*b^2*arctanh(a^-1//2*(a+b*x^4)^(1/2))+-4//15*c*a^-1*b^2*x^-1*(a+b*x^4)^(1/2)+4//15*c*x*a^-1*b^5//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-4//15*c*a^-3//4*b^9//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+2//105*a^-3//4*b^7//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(7*c*b^(1/2)+15*e*a^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-11*(a+b*x^4)^3//2*(c+d*x+e*x^2+f*x^3), x) == :(-1//2520*(a+b*x^4)^3//2*(252*c*x^-10+280*d*x^-9+315*e*x^-8+360*f*x^-7)+-1//1680*b*(a+b*x^4)^(1/2)*(168*c*x^-6+224*d*x^-5+315*e*x^-4+480*f*x^-3)+-3//16*e*a^-1//2*b^2*arctanh(a^-1//2*(a+b*x^4)^(1/2))+-4//15*d*a^-1*b^2*x^-1*(a+b*x^4)^(1/2)+-1//10*c*a^-1*b^2*x^-2*(a+b*x^4)^(1/2)+4//15*d*x*a^-1*b^5//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-4//15*d*a^-3//4*b^9//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+2//105*a^-3//4*b^7//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(7*d*b^(1/2)+15*f*a^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-12*(a+b*x^4)^3//2*(c+d*x+e*x^2+f*x^3), x) == :(-1//3960*(a+b*x^4)^3//2*(360*c*x^-11+396*d*x^-10+440*e*x^-9+495*f*x^-8)+-1//18480*b*(a+b*x^4)^(1/2)*(1440*c*x^-7+1848*d*x^-6+2464*e*x^-5+3465*f*x^-4)+-3//16*f*a^-1//2*b^2*arctanh(a^-1//2*(a+b*x^4)^(1/2))+-4//15*e*a^-1*b^2*x^-1*(a+b*x^4)^(1/2)+-4//77*c*a^-1*b^2*x^-3*(a+b*x^4)^(1/2)+-1//10*d*a^-1*b^2*x^-2*(a+b*x^4)^(1/2)+4//15*e*x*a^-1*b^5//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-4//15*e*a^-3//4*b^9//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+-2//1155*a^-5//4*b^9//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(-77*e*a^(1/2)+15*c*b^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-13*(a+b*x^4)^3//2*(c+d*x+e*x^2+f*x^3), x) == :(-1//1980*(a+b*x^4)^3//2*(165*c*x^-12+180*d*x^-11+198*e*x^-10+220*f*x^-9)+-1//18480*b*(a+b*x^4)^(1/2)*(1155*c*x^-8+1440*d*x^-7+1848*e*x^-6+2464*f*x^-5)+1//32*c*a^-3//2*b^3*arctanh(a^-1//2*(a+b*x^4)^(1/2))+-4//15*f*a^-1*b^2*x^-1*(a+b*x^4)^(1/2)+-4//77*d*a^-1*b^2*x^-3*(a+b*x^4)^(1/2)+-1//10*e*a^-1*b^2*x^-2*(a+b*x^4)^(1/2)+-1//32*c*a^-1*b^2*x^-4*(a+b*x^4)^(1/2)+4//15*f*x*a^-1*b^5//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-4//15*f*a^-3//4*b^9//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+-2//1155*a^-5//4*b^9//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(-77*f*a^(1/2)+15*d*b^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-14*(a+b*x^4)^3//2*(c+d*x+e*x^2+f*x^3), x) == :(-1//8580*(a+b*x^4)^3//2*(660*c*x^-13+715*d*x^-12+780*e*x^-11+858*f*x^-10)+-1//240240*b*(a+b*x^4)^(1/2)*(12320*c*x^-9+15015*d*x^-8+18720*e*x^-7+24024*f*x^-6)+1//32*d*a^-3//2*b^3*arctanh(a^-1//2*(a+b*x^4)^(1/2))+-4//77*e*a^-1*b^2*x^-3*(a+b*x^4)^(1/2)+-4//195*c*a^-1*b^2*x^-5*(a+b*x^4)^(1/2)+-1//10*f*a^-1*b^2*x^-2*(a+b*x^4)^(1/2)+-1//32*d*a^-1*b^2*x^-4*(a+b*x^4)^(1/2)+4//65*c*a^-2*b^3*x^-1*(a+b*x^4)^(1/2)+-4//65*c*x*a^-2*b^7//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-2//5005*a^-7//4*b^11//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(65*e*a^(1/2)+77*c*b^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2)+4//65*c*a^-7//4*b^13//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^4*(a+b*x^4)^-1//2*(c+d*x+e*x^2+f*x^3), x) == :(-1//12*b^-2*(a+b*x^4)^(1/2)*(4*a*f+-3*b*d*x^2)+-1//4*a*d*b^-3//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+1//3*c*x*b^-1*(a+b*x^4)^(1/2)+1//5*e*b^-1*x^3*(a+b*x^4)^(1/2)+1//6*f*b^-1*x^4*(a+b*x^4)^(1/2)+-3//5*a*e*x*b^-3//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-1//30*a^3//4*b^-7//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(5*c*b^(1/2)+9*e*a^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2)+3//5*e*a^5//4*b^-7//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^3*(a+b*x^4)^-1//2*(c+d*x+e*x^2+f*x^3), x) == :(1//4*b^-1*(a+b*x^4)^(1/2)*(2c+e*x^2)+-1//4*a*e*b^-3//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+1//3*d*x*b^-1*(a+b*x^4)^(1/2)+1//5*f*b^-1*x^3*(a+b*x^4)^(1/2)+-3//5*a*f*x*b^-3//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-1//30*a^3//4*b^-7//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(5*d*b^(1/2)+9*f*a^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2)+3//5*f*a^5//4*b^-7//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^2*(a+b*x^4)^-1//2*(c+d*x+e*x^2+f*x^3), x) == :(1//4*b^-1*(a+b*x^4)^(1/2)*(2d+f*x^2)+-1//4*a*f*b^-3//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+1//3*e*x*b^-1*(a+b*x^4)^(1/2)+c*x*b^-1//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-1*c*a^1//4*b^-3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+1//6*a^1//4*b^-5//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(-1*e*a^(1/2)+3*c*b^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x*(a+b*x^4)^-1//2*(c+d*x+e*x^2+f*x^3), x) == :((1/2)*c*b^-1//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+(1/2)*e*b^-1*(a+b*x^4)^(1/2)+1//3*f*x*b^-1*(a+b*x^4)^(1/2)+d*x*b^-1//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-1*d*a^1//4*b^-3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+1//6*a^1//4*b^-5//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(-1*f*a^(1/2)+3*d*b^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate((a+b*x^4)^-1//2*(c+d*x+e*x^2+f*x^3), x) == :((1/2)*d*b^-1//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+(1/2)*f*b^-1*(a+b*x^4)^(1/2)+e*x*b^-1//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+(1/2)*a^1//4*b^-3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(e+c*a^-1//2*b^(1/2))*(a^(1/2)+b^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2)+-1*e*a^1//4*b^-3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-1*(a+b*x^4)^-1//2*(c+d*x+e*x^2+f*x^3), x) == :((1/2)*e*b^-1//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+-1//2*c*a^-1//2*arctanh(a^-1//2*(a+b*x^4)^(1/2))+f*x*b^-1//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+(1/2)*a^1//4*b^-3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(f+d*a^-1//2*b^(1/2))*(a^(1/2)+b^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2)+-1*f*a^1//4*b^-3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-2*(a+b*x^4)^-1//2*(c+d*x+e*x^2+f*x^3), x) == :((1/2)*f*b^-1//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+-1//2*d*a^-1//2*arctanh(a^-1//2*(a+b*x^4)^(1/2))+-1*c*a^-1*x^-1*(a+b*x^4)^(1/2)+c*x*a^-1*b^(1/2)*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+(1/2)*a^-3//4*b^-1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(c*b^(1/2)+e*a^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2)+-1*c*a^-3//4*b^1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-3*(a+b*x^4)^-1//2*(c+d*x+e*x^2+f*x^3), x) == :(-1//2*e*a^-1//2*arctanh(a^-1//2*(a+b*x^4)^(1/2))+-1*d*a^-1*x^-1*(a+b*x^4)^(1/2)+-1//2*c*a^-1*x^-2*(a+b*x^4)^(1/2)+d*x*a^-1*b^(1/2)*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+(1/2)*a^-3//4*b^-1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(d*b^(1/2)+f*a^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2)+-1*d*a^-3//4*b^1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-4*(a+b*x^4)^-1//2*(c+d*x+e*x^2+f*x^3), x) == :(-1//2*f*a^-1//2*arctanh(a^-1//2*(a+b*x^4)^(1/2))+-1*e*a^-1*x^-1*(a+b*x^4)^(1/2)+-1//2*d*a^-1*x^-2*(a+b*x^4)^(1/2)+-1//3*c*a^-1*x^-3*(a+b*x^4)^(1/2)+e*x*a^-1*b^(1/2)*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-1*e*a^-3//4*b^1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+-1//6*a^-5//4*b^1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(c*b^(1/2)+-3*e*a^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-5*(a+b*x^4)^-1//2*(c+d*x+e*x^2+f*x^3), x) == :(-1*f*a^-1*x^-1*(a+b*x^4)^(1/2)+-1//2*e*a^-1*x^-2*(a+b*x^4)^(1/2)+-1//3*d*a^-1*x^-3*(a+b*x^4)^(1/2)+-1//4*c*a^-1*x^-4*(a+b*x^4)^(1/2)+1//4*b*c*a^-3//2*arctanh(a^-1//2*(a+b*x^4)^(1/2))+f*x*a^-1*b^(1/2)*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-1*f*a^-3//4*b^1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+-1//6*a^-5//4*b^1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(d*b^(1/2)+-3*f*a^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-6*(a+b*x^4)^-1//2*(c+d*x+e*x^2+f*x^3), x) == :(-1//2*f*a^-1*x^-2*(a+b*x^4)^(1/2)+-1//3*e*a^-1*x^-3*(a+b*x^4)^(1/2)+-1//4*d*a^-1*x^-4*(a+b*x^4)^(1/2)+-1//5*c*a^-1*x^-5*(a+b*x^4)^(1/2)+1//4*b*d*a^-3//2*arctanh(a^-1//2*(a+b*x^4)^(1/2))+3//5*b*c*a^-2*x^-1*(a+b*x^4)^(1/2)+-3//5*c*x*a^-2*b^3//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-1//30*a^-7//4*b^3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(5*e*a^(1/2)+9*c*b^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2)+3//5*c*a^-7//4*b^5//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^6*(a+b*x^4)^-3//2*(c+d*x+e*x^2+f*x^3), x) == :(d*b^-2*(a+b*x^4)^(1/2)+(1/2)*x*b^-2*(a+b*x^4)^-1//2*(a*e+a*f*x+-1*b*c*x^2+-1*b*d*x^3)+-3//4*a*f*b^-5//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+1//3*e*x*b^-2*(a+b*x^4)^(1/2)+1//4*f*b^-2*x^2*(a+b*x^4)^(1/2)+3//2*c*x*b^-3//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-3//2*c*a^1//4*b^-7//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+1//12*a^1//4*b^-9//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(-5*e*a^(1/2)+9*c*b^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^5*(a+b*x^4)^-3//2*(c+d*x+e*x^2+f*x^3), x) == :(e*b^-2*(a+b*x^4)^(1/2)+(1/2)*c*b^-3//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+(1/2)*x*b^-2*(a+b*x^4)^-1//2*(a*f+-1*b*c*x+-1*b*d*x^2+-1*b*e*x^3)+1//3*f*x*b^-2*(a+b*x^4)^(1/2)+3//2*d*x*b^-3//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-3//2*d*a^1//4*b^-7//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+1//12*a^1//4*b^-9//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(-5*f*a^(1/2)+9*d*b^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^4*(a+b*x^4)^-3//2*(c+d*x+e*x^2+f*x^3), x) == :(f*b^-2*(a+b*x^4)^(1/2)+(1/2)*d*b^-3//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+-1//2*x*b^-1*(a+b*x^4)^-1//2*(c+d*x+e*x^2+f*x^3)+3//2*e*x*b^-3//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-3//2*e*a^1//4*b^-7//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+1//4*a^-1//4*b^-7//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(c*b^(1/2)+3*e*a^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^3*(a+b*x^4)^-3//2*(c+d*x+e*x^2+f*x^3), x) == :((1/2)*e*b^-3//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+(1/2)*b^-1*(a+b*x^4)^-1//2*(-1c+-1*d*x+-1*e*x^2+-1*f*x^3)+3//2*f*x*b^-3//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-3//2*f*a^1//4*b^-7//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+1//4*a^-1//4*b^-7//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(d*b^(1/2)+3*f*a^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^2*(a+b*x^4)^-3//2*(c+d*x+e*x^2+f*x^3), x) == :((1/2)*f*b^-3//2*arctanh(b^(1/2)*x^2*(a+b*x^4)^-1//2)+-1//2*d*a^-1*b^-1*(a+b*x^4)^(1/2)+-1//2*x*a^-1*b^-1*(a+b*x^4)^-1//2*(a*e+a*f*x+-1*b*c*x^2+-1*b*d*x^3)+-1//2*c*x*a^-1*b^-1//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+(1/2)*c*a^-3//4*b^-3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+-1//4*a^-3//4*b^-5//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(c*b^(1/2)+-1*e*a^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x*(a+b*x^4)^-3//2*(c+d*x+e*x^2+f*x^3), x) == :(-1//2*e*a^-1*b^-1*(a+b*x^4)^(1/2)+-1//2*x*a^-1*b^-1*(a+b*x^4)^-1//2*(a*f+-1*b*c*x+-1*b*d*x^2+-1*b*e*x^3)+-1//2*d*x*a^-1*b^-1//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+(1/2)*d*a^-3//4*b^-3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+-1//4*a^-3//4*b^-5//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(d*b^(1/2)+-1*f*a^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate((a+b*x^4)^-3//2*(c+d*x+e*x^2+f*x^3), x) == :(-1//2*a^-1*b^-1*(a+b*x^4)^-1//2*(a*f+-1*b*x*(c+d*x+e*x^2))+-1//2*e*x*a^-1*b^-1//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+(1/2)*e*a^-3//4*b^-3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+1//4*a^-5//4*b^-3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(c*b^(1/2)+-1*e*a^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-1*(a+b*x^4)^-3//2*(c+d*x+e*x^2+f*x^3), x) == :((1/2)*c*a^-2*(a+b*x^4)^(1/2)+-1//2*c*a^-3//2*arctanh(a^-1//2*(a+b*x^4)^(1/2))+(1/2)*x*a^-2*(a+b*x^4)^-1//2*(a*d+a*e*x+a*f*x^2+-1*b*c*x^3)+-1//2*f*x*a^-1*b^-1//2*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+(1/2)*f*a^-3//4*b^-3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+1//4*a^-5//4*b^-3//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(d*b^(1/2)+-1*f*a^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-2*(a+b*x^4)^-3//2*(c+d*x+e*x^2+f*x^3), x) == :((1/2)*d*a^-2*(a+b*x^4)^(1/2)+-1//2*d*a^-3//2*arctanh(a^-1//2*(a+b*x^4)^(1/2))+(1/2)*x*a^-2*(a+b*x^4)^-1//2*(a*e+a*f*x+-1*b*c*x^2+-1*b*d*x^3)+-1*c*a^-2*x^-1*(a+b*x^4)^(1/2)+3//2*c*x*a^-2*b^(1/2)*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-3//2*c*a^-7//4*b^1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+1//4*a^-7//4*b^-1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(e*a^(1/2)+3*c*b^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-3*(a+b*x^4)^-3//2*(c+d*x+e*x^2+f*x^3), x) == :((1/2)*e*a^-2*(a+b*x^4)^(1/2)+-1//2*e*a^-3//2*arctanh(a^-1//2*(a+b*x^4)^(1/2))+(1/2)*x*a^-2*(a+b*x^4)^-1//2*(a*f+-1*b*c*x+-1*b*d*x^2+-1*b*e*x^3)+-1*d*a^-2*x^-1*(a+b*x^4)^(1/2)+-1//2*c*a^-2*x^-2*(a+b*x^4)^(1/2)+3//2*d*x*a^-2*b^(1/2)*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-3//2*d*a^-7//4*b^1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+1//4*a^-7//4*b^-1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(f*a^(1/2)+3*d*b^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate(x^-4*(a+b*x^4)^-3//2*(c+d*x+e*x^2+f*x^3), x) == :((1/2)*f*a^-2*(a+b*x^4)^(1/2)+-1//2*f*a^-3//2*arctanh(a^-1//2*(a+b*x^4)^(1/2))+-1*e*a^-2*x^-1*(a+b*x^4)^(1/2)+-1//2*d*a^-2*x^-2*(a+b*x^4)^(1/2)+-1//2*x*a^-2*(a+b*x^4)^-1//2*(b*c+b*d*x+b*e*x^2+b*f*x^3)+-1//3*c*a^-2*x^-3*(a+b*x^4)^(1/2)+3//2*e*x*a^-2*b^(1/2)*(a+b*x^4)^(1/2)*(a^(1/2)+b^(1/2)*x^2)^-1+-3//2*e*a^-7//4*b^1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*b^1//4),1/2)+-1//12*a^-9//4*b^1//4*((a^(1/2)+b^(1/2)*x^2)^-2*(a+b*x^4))^(1/2)*(a+b*x^4)^-1//2*(a^(1/2)+b^(1/2)*x^2)*(-9*e*a^(1/2)+5*c*b^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*b^1//4),1/2))
@test integrate((1+-1*x^5)^-1*(1+x+x^2+x^3+x^4), x) == :(-1*log(1+-1x))
@test integrate((729+-64*x^6)^-1*(243+-162x+-72*x^3+-32*x^5+48*x^4+108*x^2), x) == :((1/2)*log(3+2x))
@test integrate((729+-64*x^6)^-1*(243+32*x^5+48*x^4+72*x^3+108*x^2+162x), x) == :(-1//2*log(3+-2x))
@test integrate((729+-64*x^6)^-1*(81+16*x^4+36*x^2), x) == :(1//6*arctanh(2//3*x))
@test integrate((729+-64*x^6)^-1*(81+-24*x^3+-16*x^4+54x), x) == :(-1//9*3^(1/2)*arctan(1//9*3^(1/2)*(3+-4x)))
@test integrate((729+-64*x^6)^-1*(3+-2x), x) == :(-1//972*log(9+-6x+4*x^2)+1//486*log(3+2x)+1//486*3^(1/2)*arctan(1//9*3^(1/2)*(3+4x)))
@test integrate((729+-64*x^6)^-1*(3+2x), x) == :(-1//486*log(3+-2x)+1//972*log(9+4*x^2+6x)+-1//486*3^(1/2)*arctan(1//9*3^(1/2)*(3+-4x)))
@test integrate((729+-64*x^6)^-1*(9+-6x+4*x^2), x) == :(-1//324*log(3+-2x)+-1//324*log(9+4*x^2+6x)+1//108*log(3+2x)+1//162*3^(1/2)*arctan(1//9*3^(1/2)*(3+4x)))
@test integrate((729+-64*x^6)^-1*(9+4*x^2+6x), x) == :(-1//108*log(3+-2x)+1//324*log(3+2x)+1//324*log(9+-6x+4*x^2)+-1//162*3^(1/2)*arctan(1//9*3^(1/2)*(3+-4x)))
@test integrate((729+-64*x^6)^-1*(27+-8*x^3), x) == :(-1//108*log(9+-6x+4*x^2)+1//54*log(3+2x)+-1//54*3^(1/2)*arctan(1//9*3^(1/2)*(3+-4x)))
@test integrate((729+-64*x^6)^-1*(27+8*x^3+24*x^2+36x), x) == :(-1//18*log(3+-2x)+1//36*log(9+-6x+4*x^2)+-1//54*3^(1/2)*arctan(1//9*3^(1/2)*(3+-4x)))
@test integrate((729+-64*x^6)^-2*(243+-162x+-72*x^3+-32*x^5+48*x^4+108*x^2), x) == :(-1*(8748+5832x)^-1+-1//17496*log(3+-2x)+-1//17496*log(9+-6x+4*x^2)+-1//17496*log(9+4*x^2+6x)+5//17496*log(3+2x)+-1//26244*3^(1/2)*arctan(1//9*3^(1/2)*(3+-4x))+1//8748*3^(1/2)*arctan(1//9*3^(1/2)*(3+4x)))
@test integrate((729+-64*x^6)^-2*(243+32*x^5+48*x^4+72*x^3+108*x^2+162x), x) == :((8748+-5832x)^-1+-5//17496*log(3+-2x)+1//17496*log(3+2x)+1//17496*log(9+-6x+4*x^2)+1//17496*log(9+4*x^2+6x)+-1//8748*3^(1/2)*arctan(1//9*3^(1/2)*(3+-4x))+1//26244*3^(1/2)*arctan(1//9*3^(1/2)*(3+4x)))
@test integrate((729+-64*x^6)^-2*(81+16*x^4+36*x^2), x) == :((52488+-34992x)^-1+-1*(52488+34992x)^-1+1//8748*arctanh(2//3*x)+-1//39366*3^(1/2)*arctan(1//9*3^(1/2)*(3+-4x))+1//39366*3^(1/2)*arctan(1//9*3^(1/2)*(3+4x)))
@test integrate((729+-64*x^6)^-2*(81+-24*x^3+-16*x^4+54x), x) == :(-1//26244*log(3+-2x)+-1//157464*log(9+-6x+4*x^2)+1//52488*log(9+4*x^2+6x)+1//78732*log(3+2x)+x*(39366+-26244x+17496*x^2)^-1+-1//13122*3^(1/2)*arctan(1//9*3^(1/2)*(3+-4x)))
@test integrate((729+-64*x^6)^-2*(3+-2x), x) == :(-1*(2125764+1417176x)^-1+-1//944784*log(9+-6x+4*x^2)+-1//4251528*log(3+-2x)+1//472392*log(3+2x)+1//8503056*log(9+4*x^2+6x)+x*(2125764+944784*x^2+1417176x)^-1+(6377292+-4251528x+2834352*x^2)^-1*(3+-1x)+-1//4251528*3^(1/2)*arctan(1//9*3^(1/2)*(3+-4x))+1//472392*3^(1/2)*arctan(1//9*3^(1/2)*(3+4x)))
@test integrate((729+-64*x^6)^-2*(3+2x), x) == :((2125764+-1417176x)^-1+-1//472392*log(3+-2x)+-1//8503056*log(9+-6x+4*x^2)+1//944784*log(9+4*x^2+6x)+1//4251528*log(3+2x)+x*(2125764+-1417176x+944784*x^2)^-1+-1*(6377292+2834352*x^2+4251528x)^-1*(3+x)+-1//472392*3^(1/2)*arctan(1//9*3^(1/2)*(3+-4x))+1//4251528*3^(1/2)*arctan(1//9*3^(1/2)*(3+4x)))
@test integrate((729+-64*x^6)^-2*(9+-6x+4*x^2), x) == :((1417176+-944784x)^-1+-1*(472392+314928x)^-1+-5//2834352*log(9+4*x^2+6x)+-1//354294*log(3+-2x)+-1//944784*log(9+-6x+4*x^2)+1//118098*log(3+2x)+(2125764+944784*x^2+1417176x)^-1*(3+4x)+-1//1417176*3^(1/2)*arctan(1//9*3^(1/2)*(3+-4x))+1//157464*3^(1/2)*arctan(1//9*3^(1/2)*(3+4x)))
@test integrate((729+-64*x^6)^-2*(9+4*x^2+6x), x) == :((472392+-314928x)^-1+-1*(1417176+944784x)^-1+-1//118098*log(3+-2x)+1//354294*log(3+2x)+1//944784*log(9+4*x^2+6x)+5//2834352*log(9+-6x+4*x^2)+-1*(2125764+-1417176x+944784*x^2)^-1*(3+-4x)+-1//157464*3^(1/2)*arctan(1//9*3^(1/2)*(3+-4x))+1//1417176*3^(1/2)*arctan(1//9*3^(1/2)*(3+4x)))
@test integrate((729+-64*x^6)^-2*(27+-8*x^3), x) == :(-7//944784*log(9+-6x+4*x^2)+-1//157464*log(3+-2x)+1//314928*log(9+4*x^2+6x)+7//472392*log(3+2x)+x*(118098+34992*x^3)^-1+-7//472392*3^(1/2)*arctan(1//9*3^(1/2)*(3+-4x))+1//157464*3^(1/2)*arctan(1//9*3^(1/2)*(3+4x)))
@test integrate((729+-64*x^6)^-2*(27+8*x^3+24*x^2+36x), x) == :((78732+-52488x)^-1+-7//157464*log(3+-2x)+1//314928*log(9+4*x^2+6x)+1//472392*log(3+2x)+17//944784*log(9+-6x+4*x^2)+-1*(236196+-157464x+104976*x^2)^-1*(3+-2x)+-11//472392*3^(1/2)*arctan(1//9*3^(1/2)*(3+-4x))+-1//472392*3^(1/2)*arctan(1//9*3^(1/2)*(3+4x)))
@test integrate(x*(729+-64*x^6)^-1*(27+-2*x^3), x) == :(-5//288*log(3+2x)+-1//96*log(3+-2x)+1//192*log(9+4*x^2+6x)+5//576*log(9+-6x+4*x^2)+-5//288*3^(1/2)*arctan(1//9*3^(1/2)*(3+-4x))+-1//96*3^(1/2)*arctan(1//9*3^(1/2)*(3+4x)))
@test integrate((a+b*x^n)^3*(c+d*x^(-1+n)), x) == :(c*x*a^3+c*b^3*x^(1+3n)*(1+3n)^-1+1//4*d*b^-1*n^-1*(a+b*x^n)^4+3*a*c*b^2*x^(1+2n)*(1+2n)^-1+3*b*c*a^2*x^(1+n)*(1+n)^-1)
@test integrate((a+b*x^n)^2*(c+d*x^(-1+n)), x) == :(c*x*a^2+c*b^2*x^(1+2n)*(1+2n)^-1+1//3*d*b^-1*n^-1*(a+b*x^n)^3+2*a*b*c*x^(1+n)*(1+n)^-1)
@test integrate((a+b*x^n)*(c+d*x^(-1+n)), x) == :(a*c*x+a*d*n^-1*x^n+b*c*x^(1+n)*(1+n)^-1+(1/2)*b*d*n^-1*x^(2n))
@test integrate(c+d*x^(-1+n), x) == :(c*x+d*n^-1*x^n)
@test integrate((a+b*x^n)^-3//2*(b*f*x^(-1+(1/2)*n)+b*g*x^(-1+n)+b*h*x^(-1+5//4*n)+-1*a*h*x^(-1+1//4*n)), x) == :(-1*a^-1*n^-1*(a+b*x^n)^-1//2*(2*a*g+-2*b*f*x^((1/2)*n)+4*a*h*x^(1//4*n)))
@test integrate((a+b*x^2)^-1//2*(c+d*x^2)^-1//2*(a*c+x^2*(2*a*d+2*b*c)+3*b*d*x^4), x) == :(x*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2))
@test integrate((1+x^4)^-1//4*(1+-1*x^4)^-1*(1+x^3), x) == :(-1//4*2^3//4*arctan((1/2)*2^3//4*(1+x^4)^1//4)+1//4*2^3//4*arctan(x*2^1//4*(1+x^4)^-1//4)+1//4*2^3//4*arctanh((1/2)*2^3//4*(1+x^4)^1//4)+1//4*2^3//4*arctanh(x*2^1//4*(1+x^4)^-1//4))
@test integrate((a+b*x^n)^(n^-1*(-1+-1n))*(c+d*x^n)^(n^-1*(-1+-1n))*(a*c+-1*b*d*x^(2n)), x) == :(x*(a+b*x^n)^(-1*n^-1)*(c+d*x^n)^(-1*n^-1))
@test integrate((h*x)^(-1+-1n+-1*n*p)*(a+b*x^n)^p*(c+d*x^n)^p*(a*c+-1*b*d*x^(2n)), x) == :(-1*h^-1*n^-1*(h*x)^(-1*n*(1+p))*(1+p)^-1*(a+b*x^n)^(1+p)*(c+d*x^n)^(1+p))
@test integrate((a+b*x^n)^p*(c+d*x^n)^p*(e+e*a^-1*c^-1*x^n*(a*d+b*c)*(1+n+n*p)+b*d*e*a^-1*c^-1*x^(2n)*(1+2n+2*n*p)), x) == :(e*x*a^-1*c^-1*(a+b*x^n)^(1+p)*(c+d*x^n)^(1+p))
@test integrate((h*x)^m*(a+b*x^n)^p*(c+d*x^n)^p*(e+e*a^-1*c^-1*x^n*(1+m)^-1*(a*d+b*c)*(1+m+n+n*p)+b*d*e*a^-1*c^-1*x^(2n)*(1+m)^-1*(1+m+2n+2*n*p)), x) == :(e*a^-1*c^-1*h^-1*(h*x)^(1+m)*(1+m)^-1*(a+b*x^n)^(1+p)*(c+d*x^n)^(1+p))

max_stars_repo_path: test/1 Algebraic functions/1.1 Binomial products/1.1.3 General/1.1.3.8 P(x) (c x)^m (a+b x^n)^p.jl