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

@test integrate(x^2*(a*x+b*x^3), x) == :(1//4*a*x^4+1//6*b*x^6)
@test integrate(x*(a*x+b*x^3), x) == :(1//3*a*x^3+1//5*b*x^5)
@test integrate(a*x+b*x^3, x) == :((1/2)*a*x^2+1//4*b*x^4)
@test integrate(x^-1*(a*x+b*x^3), x) == :(a*x+1//3*b*x^3)
@test integrate(x^-2*(a*x+b*x^3), x) == :(a*log(x)+(1/2)*b*x^2)
@test integrate(x^2*(a*x+b*x^3)^2, x) == :(1//5*a^2*x^5+1//9*b^2*x^9+2//7*a*b*x^7)
@test integrate(x*(a*x+b*x^3)^2, x) == :(1//4*a^2*x^4+1//8*b^2*x^8+1//3*a*b*x^6)
@test integrate((a*x+b*x^3)^2, x) == :(1//3*a^2*x^3+1//7*b^2*x^7+2//5*a*b*x^5)
@test integrate(x^-1*(a*x+b*x^3)^2, x) == :(1//6*b^-1*(a+b*x^2)^3)
@test integrate(x^-2*(a*x+b*x^3)^2, x) == :(x*a^2+1//5*b^2*x^5+2//3*a*b*x^3)
@test integrate((-4x+3*x^3)^6, x) == :(-2048*x^9+1296*x^15+-34560//13*x^13+-5832//17*x^17+729//19*x^19+4096//7*x^7+34560//11*x^11)
@test integrate(x^4*(a*x+b*x^3)^-1, x) == :((1/2)*b^-1*x^2+-1//2*a*b^-2*log(a+b*x^2))
@test integrate(x^3*(a*x+b*x^3)^-1, x) == :(x*b^-1+-1*a^(1/2)*b^-3//2*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^2*(a*x+b*x^3)^-1, x) == :((1/2)*b^-1*log(a+b*x^2))
@test integrate(x*(a*x+b*x^3)^-1, x) == :(a^-1//2*b^-1//2*arctan(x*a^-1//2*b^(1/2)))
@test integrate((a*x+b*x^3)^-1, x) == :(a^-1*log(x)+-1//2*a^-1*log(a+b*x^2))
@test integrate(x^-1*(a*x+b*x^3)^-1, x) == :(-1*a^-1*x^-1+-1*a^-3//2*b^(1/2)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-2*(a*x+b*x^3)^-1, x) == :(-1//2*a^-1*x^-2+(1/2)*b*a^-2*log(a+b*x^2)+-1*b*a^-2*log(x))
@test integrate(x^-3*(a*x+b*x^3)^-1, x) == :(-1//3*a^-1*x^-3+b*a^-2*x^-1+a^-5//2*b^3//2*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-4*(a*x+b*x^3)^-1, x) == :(-1//4*a^-1*x^-4+a^-3*b^2*log(x)+(1/2)*b*a^-2*x^-2+-1//2*a^-3*b^2*log(a+b*x^2))
@test integrate(x^2*(a*x+b*x^3)^-2, x) == :((1/2)*x*a^-1*(a+b*x^2)^-1+(1/2)*a^-3//2*b^-1//2*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x*(a*x+b*x^3)^-2, x) == :(a^-2*log(x)+(1/2)*a^-1*(a+b*x^2)^-1+-1//2*a^-2*log(a+b*x^2))
@test integrate((a*x+b*x^3)^-2, x) == :(-3//2*a^-2*x^-1+(1/2)*a^-1*x^-1*(a+b*x^2)^-1+-3//2*a^-5//2*b^(1/2)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-1*(a*x+b*x^3)^-2, x) == :(-1//2*a^-2*x^-2+b*a^-3*log(a+b*x^2)+-2*b*a^-3*log(x)+-1//2*b*a^-2*(a+b*x^2)^-1)
@test integrate(x^-2*(a*x+b*x^3)^-2, x) == :(-5//6*a^-2*x^-3+(1/2)*a^-1*x^-3*(a+b*x^2)^-1+5//2*b*a^-3*x^-1+5//2*a^-7//2*b^3//2*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^5*(x+-1*x^3)^-1, x) == :(-1x+-1//3*x^3+arctanh(x))
@test integrate(x^4*(x+-1*x^3)^-1, x) == :(-1//2*x^2+-1//2*log(1+-1*x^2))
@test integrate(x^3*(x+-1*x^3)^-1, x) == :(-1x+arctanh(x))
@test integrate(x^2*(x+-1*x^3)^-1, x) == :(-1//2*log(1+-1*x^2))
@test integrate(x*(x+-1*x^3)^-1, x) == :(arctanh(x))
@test integrate((x+-1*x^3)^-1, x) == :(-1//2*log(1+-1*x^2)+log(x))
@test integrate(x^-1*(x+-1*x^3)^-1, x) == :(-1*x^-1+arctanh(x))
@test integrate(x^-2*(x+-1*x^3)^-1, x) == :(-1//2*x^-2+-1//2*log(1+-1*x^2)+log(x))
@test integrate(x^-3*(x+-1*x^3)^-1, x) == :(-1*x^-1+-1//3*x^-3+arctanh(x))
@test integrate(x^-4*(x+-1*x^3)^-1, x) == :(-1//2*x^-2+-1//2*log(1+-1*x^2)+-1//4*x^-4+log(x))
@test integrate((x+b*x^3)^-1, x) == :(-1//2*log(1+b*x^2)+log(x))
@test integrate((-1x+b*x^3)^-1, x) == :((1/2)*log(1+-1*b*x^2)+-1*log(x))
@test integrate(x^3*(a*x+b*x^3)^(1/2), x) == :(2//11*x^4*(a*x+b*x^3)^(1/2)+-20//231*a^2*b^-2*(a*x+b*x^3)^(1/2)+4//77*a*b^-1*x^2*(a*x+b*x^3)^(1/2)+10//231*a^11//4*b^-9//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^2*(a*x+b*x^3)^(1/2), x) == :(2//9*x^3*(a*x+b*x^3)^(1/2)+4//45*a*x*b^-1*(a*x+b*x^3)^(1/2)+-4//15*x*a^2*b^-3//2*(a^(1/2)+x*b^(1/2))^-1*(a*x+b*x^3)^-1//2*(a+b*x^2)+-2//15*a^9//4*b^-7//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2)+4//15*a^9//4*b^-7//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.E(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x*(a*x+b*x^3)^(1/2), x) == :(2//7*x^2*(a*x+b*x^3)^(1/2)+4//21*a*b^-1*(a*x+b*x^3)^(1/2)+-2//21*a^7//4*b^-5//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate((a*x+b*x^3)^(1/2), x) == :(2//5*x*(a*x+b*x^3)^(1/2)+4//5*a*x*b^-1//2*(a^(1/2)+x*b^(1/2))^-1*(a*x+b*x^3)^-1//2*(a+b*x^2)+-4//5*a^5//4*b^-3//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.E(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2)+2//5*a^5//4*b^-3//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^-1*(a*x+b*x^3)^(1/2), x) == :(2//3*(a*x+b*x^3)^(1/2)+2//3*a^3//4*b^-1//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^-2*(a*x+b*x^3)^(1/2), x) == :(-2*x^-1*(a*x+b*x^3)^(1/2)+4*x*b^(1/2)*(a^(1/2)+x*b^(1/2))^-1*(a*x+b*x^3)^-1//2*(a+b*x^2)+-4*a^1//4*b^1//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.E(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2)+2*a^1//4*b^1//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^-3*(a*x+b*x^3)^(1/2), x) == :(-2//3*x^-2*(a*x+b*x^3)^(1/2)+2//3*a^-1//4*b^3//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^-4*(a*x+b*x^3)^(1/2), x) == :(-2//5*x^-3*(a*x+b*x^3)^(1/2)+-4//5*b*a^-1*x^-1*(a*x+b*x^3)^(1/2)+4//5*x*a^-1*b^3//2*(a^(1/2)+x*b^(1/2))^-1*(a*x+b*x^3)^-1//2*(a+b*x^2)+-4//5*a^-3//4*b^5//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.E(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2)+2//5*a^-3//4*b^5//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^2*(a*x+b*x^3)^3//2, x) == :(2//15*x^3*(a*x+b*x^3)^3//2+-8//231*a^3*b^-2*(a*x+b*x^3)^(1/2)+4//55*a*x^4*(a*x+b*x^3)^(1/2)+8//385*a^2*b^-1*x^2*(a*x+b*x^3)^(1/2)+4//231*a^15//4*b^-9//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x*(a*x+b*x^3)^3//2, x) == :(2//13*x^2*(a*x+b*x^3)^3//2+4//39*a*x^3*(a*x+b*x^3)^(1/2)+8//195*x*a^2*b^-1*(a*x+b*x^3)^(1/2)+-8//65*x*a^3*b^-3//2*(a^(1/2)+x*b^(1/2))^-1*(a*x+b*x^3)^-1//2*(a+b*x^2)+-4//65*a^13//4*b^-7//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2)+8//65*a^13//4*b^-7//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.E(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate((a*x+b*x^3)^3//2, x) == :(2//11*x*(a*x+b*x^3)^3//2+8//77*a^2*b^-1*(a*x+b*x^3)^(1/2)+12//77*a*x^2*(a*x+b*x^3)^(1/2)+-4//77*a^11//4*b^-5//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^-1*(a*x+b*x^3)^3//2, x) == :(2//9*(a*x+b*x^3)^3//2+4//15*a*x*(a*x+b*x^3)^(1/2)+8//15*x*a^2*b^-1//2*(a^(1/2)+x*b^(1/2))^-1*(a*x+b*x^3)^-1//2*(a+b*x^2)+-8//15*a^9//4*b^-3//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.E(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2)+4//15*a^9//4*b^-3//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^-2*(a*x+b*x^3)^3//2, x) == :(2//7*x^-1*(a*x+b*x^3)^3//2+4//7*a*(a*x+b*x^3)^(1/2)+4//7*a^7//4*b^-1//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^-3*(a*x+b*x^3)^3//2, x) == :(-2*x^-2*(a*x+b*x^3)^3//2+12//5*b*x*(a*x+b*x^3)^(1/2)+24*a*x*b^(1/2)*(5*a^(1/2)+5*x*b^(1/2))^-1*(a*x+b*x^3)^-1//2*(a+b*x^2)+-24//5*a^5//4*b^1//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.E(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2)+12//5*a^5//4*b^1//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^-4*(a*x+b*x^3)^3//2, x) == :(-2//3*x^-3*(a*x+b*x^3)^3//2+4//3*b*(a*x+b*x^3)^(1/2)+4//3*a^3//4*b^3//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^-5*(a*x+b*x^3)^3//2, x) == :(-2//5*x^-4*(a*x+b*x^3)^3//2+-12//5*b*x^-1*(a*x+b*x^3)^(1/2)+24*x*b^3//2*(5*a^(1/2)+5*x*b^(1/2))^-1*(a*x+b*x^3)^-1//2*(a+b*x^2)+-24//5*a^1//4*b^5//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.E(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2)+12//5*a^1//4*b^5//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^-6*(a*x+b*x^3)^3//2, x) == :(-2//7*x^-5*(a*x+b*x^3)^3//2+-4//7*b*x^-2*(a*x+b*x^3)^(1/2)+4//7*a^-1//4*b^7//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^-7*(a*x+b*x^3)^3//2, x) == :(-2//9*x^-6*(a*x+b*x^3)^3//2+-4//15*b*x^-3*(a*x+b*x^3)^(1/2)+-8//15*a^-1*b^2*x^-1*(a*x+b*x^3)^(1/2)+8//15*x*a^-1*b^5//2*(a^(1/2)+x*b^(1/2))^-1*(a*x+b*x^3)^-1//2*(a+b*x^2)+-8//15*a^-3//4*b^9//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.E(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2)+4//15*a^-3//4*b^9//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^-8*(a*x+b*x^3)^3//2, x) == :(-2//11*x^-7*(a*x+b*x^3)^3//2+-12//77*b*x^-4*(a*x+b*x^3)^(1/2)+-8//77*a^-1*b^2*x^-2*(a*x+b*x^3)^(1/2)+-4//77*a^-5//4*b^11//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^4*(a*x+b*x^3)^-1//2, x) == :(-10//21*a*b^-2*(a*x+b*x^3)^(1/2)+2//7*b^-1*x^2*(a*x+b*x^3)^(1/2)+5//21*a^7//4*b^-9//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^3*(a*x+b*x^3)^-1//2, x) == :(2//5*x*b^-1*(a*x+b*x^3)^(1/2)+-6//5*a*x*b^-3//2*(a^(1/2)+x*b^(1/2))^-1*(a*x+b*x^3)^-1//2*(a+b*x^2)+-3//5*a^5//4*b^-7//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2)+6//5*a^5//4*b^-7//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.E(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^2*(a*x+b*x^3)^-1//2, x) == :(2//3*b^-1*(a*x+b*x^3)^(1/2)+-1//3*a^3//4*b^-5//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x*(a*x+b*x^3)^-1//2, x) == :(2*x*b^-1//2*(a^(1/2)+x*b^(1/2))^-1*(a*x+b*x^3)^-1//2*(a+b*x^2)+a^1//4*b^-3//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2)+-2*a^1//4*b^-3//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.E(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate((a*x+b*x^3)^-1//2, x) == :(a^-1//4*b^-1//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^-1*(a*x+b*x^3)^-1//2, x) == :(-2*a^-1*x^-1*(a*x+b*x^3)^(1/2)+2*x*a^-1*b^(1/2)*(a^(1/2)+x*b^(1/2))^-1*(a*x+b*x^3)^-1//2*(a+b*x^2)+a^-3//4*b^1//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2)+-2*a^-3//4*b^1//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.E(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^-2*(a*x+b*x^3)^-1//2, x) == :(-2//3*a^-1*x^-2*(a*x+b*x^3)^(1/2)+-1//3*a^-5//4*b^3//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^-3*(a*x+b*x^3)^-1//2, x) == :(-2//5*a^-1*x^-3*(a*x+b*x^3)^(1/2)+6//5*b*a^-2*x^-1*(a*x+b*x^3)^(1/2)+-6//5*x*a^-2*b^3//2*(a^(1/2)+x*b^(1/2))^-1*(a*x+b*x^3)^-1//2*(a+b*x^2)+-3//5*a^-7//4*b^5//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2)+6//5*a^-7//4*b^5//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.E(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^7*(a*x+b*x^3)^-3//2, x) == :(-1*b^-1*x^5*(a*x+b*x^3)^-1//2+-15//7*a*b^-3*(a*x+b*x^3)^(1/2)+9//7*b^-2*x^2*(a*x+b*x^3)^(1/2)+15//14*a^7//4*b^-13//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^6*(a*x+b*x^3)^-3//2, x) == :(-1*b^-1*x^4*(a*x+b*x^3)^-1//2+7//5*x*b^-2*(a*x+b*x^3)^(1/2)+-21//5*a*x*b^-5//2*(a^(1/2)+x*b^(1/2))^-1*(a*x+b*x^3)^-1//2*(a+b*x^2)+-21//10*a^5//4*b^-11//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2)+21//5*a^5//4*b^-11//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.E(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^5*(a*x+b*x^3)^-3//2, x) == :(5//3*b^-2*(a*x+b*x^3)^(1/2)+-1*b^-1*x^3*(a*x+b*x^3)^-1//2+-5//6*a^3//4*b^-9//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^4*(a*x+b*x^3)^-3//2, x) == :(-1*b^-1*x^2*(a*x+b*x^3)^-1//2+3*x*b^-3//2*(a^(1/2)+x*b^(1/2))^-1*(a*x+b*x^3)^-1//2*(a+b*x^2)+-3*a^1//4*b^-7//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.E(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2)+3//2*a^1//4*b^-7//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^3*(a*x+b*x^3)^-3//2, x) == :(-1*x*b^-1*(a*x+b*x^3)^-1//2+(1/2)*a^-1//4*b^-5//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^2*(a*x+b*x^3)^-3//2, x) == :(a^-1*x^2*(a*x+b*x^3)^-1//2+-1*x*a^-1*b^-1//2*(a^(1/2)+x*b^(1/2))^-1*(a*x+b*x^3)^-1//2*(a+b*x^2)+a^-3//4*b^-3//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.E(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2)+-1//2*a^-3//4*b^-3//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x*(a*x+b*x^3)^-3//2, x) == :(x*a^-1*(a*x+b*x^3)^-1//2+(1/2)*a^-5//4*b^-1//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate((a*x+b*x^3)^-3//2, x) == :(a^-1*(a*x+b*x^3)^-1//2+-3*a^-2*x^-1*(a*x+b*x^3)^(1/2)+3*x*a^-2*b^(1/2)*(a^(1/2)+x*b^(1/2))^-1*(a*x+b*x^3)^-1//2*(a+b*x^2)+-3*a^-7//4*b^1//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.E(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2)+3//2*a^-7//4*b^1//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^-1*(a*x+b*x^3)^-3//2, x) == :(a^-1*x^-1*(a*x+b*x^3)^-1//2+-5//3*a^-2*x^-2*(a*x+b*x^3)^(1/2)+-5//6*a^-9//4*b^3//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^-2*(a*x+b*x^3)^-3//2, x) == :(a^-1*x^-2*(a*x+b*x^3)^-1//2+-7//5*a^-2*x^-3*(a*x+b*x^3)^(1/2)+21//5*b*a^-3*x^-1*(a*x+b*x^3)^(1/2)+-21//5*x*a^-3*b^3//2*(a^(1/2)+x*b^(1/2))^-1*(a*x+b*x^3)^-1//2*(a+b*x^2)+-21//10*a^-11//4*b^5//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.F(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2)+21//5*a^-11//4*b^5//4*x^(1/2)*((a^(1/2)+x*b^(1/2))^-2*(a+b*x^2))^(1/2)*(a*x+b*x^3)^-1//2*(a^(1/2)+x*b^(1/2))*Elliptic.E(2*arctan(a^-1//4*b^1//4*x^(1/2)),1/2))
@test integrate(x^29//2*(a*x+b*x^3)^-9//2, x) == :(-3*b^-4*x^7//2*(a*x+b*x^3)^-1//2+-9//2*a*b^-11//2*arctanh(b^(1/2)*x^3//2*(a*x+b*x^3)^-1//2)+-9//35*b^-2*x^19//2*(a*x+b*x^3)^-5//2+-3//5*b^-3*x^13//2*(a*x+b*x^3)^-3//2+-1//7*b^-1*x^25//2*(a*x+b*x^3)^-7//2+9//2*b^-5*x^(1/2)*(a*x+b*x^3)^(1/2))
@test integrate(x^27//2*(a*x+b*x^3)^-9//2, x) == :(-64//35*b^-4*x^5//2*(a*x+b*x^3)^-1//2+-16//35*b^-3*x^11//2*(a*x+b*x^3)^-3//2+-8//35*b^-2*x^17//2*(a*x+b*x^3)^-5//2+-1//7*b^-1*x^23//2*(a*x+b*x^3)^-7//2+128//35*b^-5*x^-1//2*(a*x+b*x^3)^(1/2))
@test integrate(x^25//2*(a*x+b*x^3)^-9//2, x) == :(b^-9//2*arctanh(b^(1/2)*x^3//2*(a*x+b*x^3)^-1//2)+-1*b^-4*x^3//2*(a*x+b*x^3)^-1//2+-1//3*b^-3*x^9//2*(a*x+b*x^3)^-3//2+-1//5*b^-2*x^15//2*(a*x+b*x^3)^-5//2+-1//7*b^-1*x^21//2*(a*x+b*x^3)^-7//2)
@test integrate(x^23//2*(a*x+b*x^3)^-9//2, x) == :(-16//35*b^-4*x^(1/2)*(a*x+b*x^3)^-1//2+-8//35*b^-3*x^7//2*(a*x+b*x^3)^-3//2+-6//35*b^-2*x^13//2*(a*x+b*x^3)^-5//2+-1//7*b^-1*x^19//2*(a*x+b*x^3)^-7//2)
@test integrate(x^21//2*(a*x+b*x^3)^-9//2, x) == :(1//7*a^-1*x^21//2*(a*x+b*x^3)^-7//2)
@test integrate(x^19//2*(a*x+b*x^3)^-9//2, x) == :(-8//105*b^-3*x^3//2*(a*x+b*x^3)^-3//2+-4//35*b^-2*x^9//2*(a*x+b*x^3)^-5//2+-1//7*b^-1*x^15//2*(a*x+b*x^3)^-7//2)
@test integrate(x^17//2*(a*x+b*x^3)^-9//2, x) == :(1//7*a^-1*x^17//2*(a*x+b*x^3)^-7//2+2//35*a^-2*x^15//2*(a*x+b*x^3)^-5//2)
@test integrate(x^15//2*(a*x+b*x^3)^-9//2, x) == :(-2//35*b^-2*x^5//2*(a*x+b*x^3)^-5//2+-1//7*b^-1*x^11//2*(a*x+b*x^3)^-7//2)
@test integrate(x^13//2*(a*x+b*x^3)^-9//2, x) == :(1//7*a^-1*x^13//2*(a*x+b*x^3)^-7//2+4//35*a^-2*x^11//2*(a*x+b*x^3)^-5//2+8//105*a^-3*x^9//2*(a*x+b*x^3)^-3//2)
@test integrate(x^11//2*(a*x+b*x^3)^-9//2, x) == :(-1//7*b^-1*x^7//2*(a*x+b*x^3)^-7//2)
@test integrate(x^9//2*(a*x+b*x^3)^-9//2, x) == :(1//7*a^-1*x^9//2*(a*x+b*x^3)^-7//2+6//35*a^-2*x^7//2*(a*x+b*x^3)^-5//2+8//35*a^-3*x^5//2*(a*x+b*x^3)^-3//2+16//35*a^-4*x^3//2*(a*x+b*x^3)^-1//2)
@test integrate(x^7//2*(a*x+b*x^3)^-9//2, x) == :(-1*a^-9//2*arctanh(a^(1/2)*x^(1/2)*(a*x+b*x^3)^-1//2)+a^-4*x^(1/2)*(a*x+b*x^3)^-1//2+1//3*a^-3*x^3//2*(a*x+b*x^3)^-3//2+1//5*a^-2*x^5//2*(a*x+b*x^3)^-5//2+1//7*a^-1*x^7//2*(a*x+b*x^3)^-7//2)
@test integrate(x^5//2*(a*x+b*x^3)^-9//2, x) == :(-128//35*a^-5*x^-3//2*(a*x+b*x^3)^(1/2)+1//7*a^-1*x^5//2*(a*x+b*x^3)^-7//2+8//35*a^-2*x^3//2*(a*x+b*x^3)^-5//2+16//35*a^-3*x^(1/2)*(a*x+b*x^3)^-3//2+64//35*a^-4*x^-1//2*(a*x+b*x^3)^-1//2)
@test integrate(x^3//2*(a*x+b*x^3)^-9//2, x) == :(3*a^-4*x^-3//2*(a*x+b*x^3)^-1//2+-9//2*a^-5*x^-5//2*(a*x+b*x^3)^(1/2)+1//7*a^-1*x^3//2*(a*x+b*x^3)^-7//2+3//5*a^-3*x^-1//2*(a*x+b*x^3)^-3//2+9//2*b*a^-11//2*arctanh(a^(1/2)*x^(1/2)*(a*x+b*x^3)^-1//2)+9//35*a^-2*x^(1/2)*(a*x+b*x^3)^-5//2)
@test integrate(x^(1/2)*(a*x+b*x^3)^-9//2, x) == :(-128//21*a^-5*x^-7//2*(a*x+b*x^3)^(1/2)+1//7*a^-1*x^(1/2)*(a*x+b*x^3)^-7//2+2//7*a^-2*x^-1//2*(a*x+b*x^3)^-5//2+16//21*a^-3*x^-3//2*(a*x+b*x^3)^-3//2+32//7*a^-4*x^-5//2*(a*x+b*x^3)^-1//2+256//21*b*a^-6*x^-3//2*(a*x+b*x^3)^(1/2))
@test integrate(x^-1//2*(a*x+b*x^3)^-9//2, x) == :(-99//8*a^-13//2*b^2*arctanh(a^(1/2)*x^(1/2)*(a*x+b*x^3)^-1//2)+-33//4*a^-5*x^-9//2*(a*x+b*x^3)^(1/2)+1//7*a^-1*x^-1//2*(a*x+b*x^3)^-7//2+11//35*a^-2*x^-3//2*(a*x+b*x^3)^-5//2+33//5*a^-4*x^-7//2*(a*x+b*x^3)^-1//2+33//35*a^-3*x^-5//2*(a*x+b*x^3)^-3//2+99//8*b*a^-6*x^-5//2*(a*x+b*x^3)^(1/2))
@test integrate(x^-3//2*(a*x+b*x^3)^-9//2, x) == :(-384//35*a^-5*x^-11//2*(a*x+b*x^3)^(1/2)+1//7*a^-1*x^-3//2*(a*x+b*x^3)^-7//2+8//7*a^-3*x^-7//2*(a*x+b*x^3)^-3//2+12//35*a^-2*x^-5//2*(a*x+b*x^3)^-5//2+64//7*a^-4*x^-9//2*(a*x+b*x^3)^-1//2+-1024//35*a^-7*b^2*x^-3//2*(a*x+b*x^3)^(1/2)+512//35*b*a^-6*x^-7//2*(a*x+b*x^3)^(1/2))
@test integrate(x^4*(a*x+b*x^4)^-1//2, x) == :(-1//3*a*b^-3//2*arctanh(b^(1/2)*x^2*(a*x+b*x^4)^-1//2)+1//3*x*b^-1*(a*x+b*x^4)^(1/2))
@test integrate(x*(a*x+b*x^4)^-1//2, x) == :(2//3*b^-1//2*arctanh(b^(1/2)*x^2*(a*x+b*x^4)^-1//2))
@test integrate(x^-2*(a*x+b*x^4)^-1//2, x) == :(-2//3*a^-1*x^-2*(a*x+b*x^4)^(1/2))
@test integrate(x^-5*(a*x+b*x^4)^-1//2, x) == :(-2//9*a^-1*x^-5*(a*x+b*x^4)^(1/2)+4//9*b*a^-2*x^-2*(a*x+b*x^4)^(1/2))
@test integrate(x^-8*(a*x+b*x^4)^-1//2, x) == :(-2//15*a^-1*x^-8*(a*x+b*x^4)^(1/2)+-16//45*a^-3*b^2*x^-2*(a*x+b*x^4)^(1/2)+8//45*b*a^-2*x^-5*(a*x+b*x^4)^(1/2))
@test integrate(x^3*(a*x+b*x^4)^-1//2, x) == :((1/2)*b^-1*(a*x+b*x^4)^(1/2)+-1//12*x*3^3//4*a^2//3*b^-1*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a*x+b*x^4)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a*x+b*x^4)^-1//2, x) == :(1//3*x*3^3//4*a^-1//3*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a*x+b*x^4)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate(x^-3*(a*x+b*x^4)^-1//2, x) == :(-2//5*a^-1*x^-3*(a*x+b*x^4)^(1/2)+-2//15*b*x*3^3//4*a^-4//3*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a*x+b*x^4)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate(x^5*(a*x+b*x^4)^-1//2, x) == :(1//4*b^-1*x^2*(a*x+b*x^4)^(1/2)+-1//8*a*x*b^-5//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a*x+b*x^4)^-1//2*(5+5*3^(1/2))*(a+b*x^3)+5//8*x*3^1//4*a^4//3*b^-5//3*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a*x+b*x^4)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+1//48*x*3^3//4*a^4//3*b^-5//3*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a*x+b*x^4)^-1//2*(5+-5*3^(1/2))*(a^1//3+x*b^1//3)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate(x^2*(a*x+b*x^4)^-1//2, x) == :(x*b^-2//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a*x+b*x^4)^-1//2*(1+3^(1/2))*(a+b*x^3)+-1*x*3^1//4*a^1//3*b^-2//3*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a*x+b*x^4)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-1//6*x*3^3//4*a^1//3*b^-2//3*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a*x+b*x^4)^-1//2*(1+-1*3^(1/2))*(a^1//3+x*b^1//3)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate(x^-1*(a*x+b*x^4)^-1//2, x) == :(-2*a^-1*x^-1*(a*x+b*x^4)^(1/2)+x*a^-1*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a*x+b*x^4)^-1//2*(2+2*3^(1/2))*(a+b*x^3)+-2*x*3^1//4*a^-2//3*b^1//3*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a*x+b*x^4)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-1//3*x*3^3//4*a^-2//3*b^1//3*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a*x+b*x^4)^-1//2*(1+-1*3^(1/2))*(a^1//3+x*b^1//3)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate(x^2*(a*x+b*x^(1/2))^-1//2, x) == :(-63//64*a^-11//2*b^5*arctanh(a^(1/2)*x^(1/2)*(a*x+b*x^(1/2))^-1//2)+2//5*a^-1*x^2*(a*x+b*x^(1/2))^(1/2)+63//64*a^-5*b^4*(a*x+b*x^(1/2))^(1/2)+-21//32*a^-4*b^3*x^(1/2)*(a*x+b*x^(1/2))^(1/2)+-9//20*b*a^-2*x^3//2*(a*x+b*x^(1/2))^(1/2)+21//40*x*a^-3*b^2*(a*x+b*x^(1/2))^(1/2))
@test integrate(x*(a*x+b*x^(1/2))^-1//2, x) == :(-5//4*a^-7//2*b^3*arctanh(a^(1/2)*x^(1/2)*(a*x+b*x^(1/2))^-1//2)+2//3*x*a^-1*(a*x+b*x^(1/2))^(1/2)+5//4*a^-3*b^2*(a*x+b*x^(1/2))^(1/2)+-5//6*b*a^-2*x^(1/2)*(a*x+b*x^(1/2))^(1/2))
@test integrate((a*x+b*x^(1/2))^-1//2, x) == :(2*a^-1*(a*x+b*x^(1/2))^(1/2)+-2*b*a^-3//2*arctanh(a^(1/2)*x^(1/2)*(a*x+b*x^(1/2))^-1//2))
@test integrate(x^-1*(a*x+b*x^(1/2))^-1//2, x) == :(-4*b^-1*x^-1//2*(a*x+b*x^(1/2))^(1/2))
@test integrate(x^-2*(a*x+b*x^(1/2))^-1//2, x) == :(-4//5*b^-1*x^-3//2*(a*x+b*x^(1/2))^(1/2)+-32//15*a^2*b^-3*x^-1//2*(a*x+b*x^(1/2))^(1/2)+16//15*a*b^-2*x^-1*(a*x+b*x^(1/2))^(1/2))
@test integrate(x^-3*(a*x+b*x^(1/2))^-1//2, x) == :(-4//9*b^-1*x^-5//2*(a*x+b*x^(1/2))^(1/2)+-512//315*a^4*b^-5*x^-1//2*(a*x+b*x^(1/2))^(1/2)+-64//105*a^2*b^-3*x^-3//2*(a*x+b*x^(1/2))^(1/2)+32//63*a*b^-2*x^-2*(a*x+b*x^(1/2))^(1/2)+256//315*a^3*b^-4*x^-1*(a*x+b*x^(1/2))^(1/2))
@test integrate(x^-4*(a*x+b*x^(1/2))^-1//2, x) == :(-4//13*b^-1*x^-7//2*(a*x+b*x^(1/2))^(1/2)+-4096//3003*a^6*b^-7*x^-1//2*(a*x+b*x^(1/2))^(1/2)+-512//1001*a^4*b^-5*x^-3//2*(a*x+b*x^(1/2))^(1/2)+-160//429*a^2*b^-3*x^-5//2*(a*x+b*x^(1/2))^(1/2)+48//143*a*b^-2*x^-3*(a*x+b*x^(1/2))^(1/2)+1280//3003*a^3*b^-4*x^-2*(a*x+b*x^(1/2))^(1/2)+2048//3003*a^5*b^-6*x^-1*(a*x+b*x^(1/2))^(1/2))
@test integrate(x^3*(a*x+b*x^(1/2))^-3//2, x) == :(-4*a^-1*x^3*(a*x+b*x^(1/2))^-1//2+-693//64*a^-13//2*b^5*arctanh(a^(1/2)*x^(1/2)*(a*x+b*x^(1/2))^-1//2)+22//5*a^-2*x^2*(a*x+b*x^(1/2))^(1/2)+693//64*a^-6*b^4*(a*x+b*x^(1/2))^(1/2)+-231//32*a^-5*b^3*x^(1/2)*(a*x+b*x^(1/2))^(1/2)+-99//20*b*a^-3*x^3//2*(a*x+b*x^(1/2))^(1/2)+231//40*x*a^-4*b^2*(a*x+b*x^(1/2))^(1/2))
@test integrate(x^2*(a*x+b*x^(1/2))^-3//2, x) == :(-4*a^-1*x^2*(a*x+b*x^(1/2))^-1//2+-35//4*a^-9//2*b^3*arctanh(a^(1/2)*x^(1/2)*(a*x+b*x^(1/2))^-1//2)+14//3*x*a^-2*(a*x+b*x^(1/2))^(1/2)+35//4*a^-4*b^2*(a*x+b*x^(1/2))^(1/2)+-35//6*b*a^-3*x^(1/2)*(a*x+b*x^(1/2))^(1/2))
@test integrate(x*(a*x+b*x^(1/2))^-3//2, x) == :(6*a^-2*(a*x+b*x^(1/2))^(1/2)+-6*b*a^-5//2*arctanh(a^(1/2)*x^(1/2)*(a*x+b*x^(1/2))^-1//2)+-4*x*a^-1*(a*x+b*x^(1/2))^-1//2)
@test integrate((a*x+b*x^(1/2))^-3//2, x) == :(4*b^-1*x^(1/2)*(a*x+b*x^(1/2))^-1//2)
@test integrate(x^-1*(a*x+b*x^(1/2))^-3//2, x) == :(4*b^-1*x^-1//2*(a*x+b*x^(1/2))^-1//2+-16//3*b^-2*x^-1*(a*x+b*x^(1/2))^(1/2)+32//3*a*b^-3*x^-1//2*(a*x+b*x^(1/2))^(1/2))
@test integrate(x^-2*(a*x+b*x^(1/2))^-3//2, x) == :(4*b^-1*x^-3//2*(a*x+b*x^(1/2))^-1//2+-32//7*b^-2*x^-2*(a*x+b*x^(1/2))^(1/2)+-256//35*a^2*b^-4*x^-1*(a*x+b*x^(1/2))^(1/2)+192//35*a*b^-3*x^-3//2*(a*x+b*x^(1/2))^(1/2)+512//35*a^3*b^-5*x^-1//2*(a*x+b*x^(1/2))^(1/2))
@test integrate(x^-3*(a*x+b*x^(1/2))^-3//2, x) == :(4*b^-1*x^-5//2*(a*x+b*x^(1/2))^-1//2+-48//11*b^-2*x^-3*(a*x+b*x^(1/2))^(1/2)+-2048//231*a^4*b^-6*x^-1*(a*x+b*x^(1/2))^(1/2)+-1280//231*a^2*b^-4*x^-2*(a*x+b*x^(1/2))^(1/2)+160//33*a*b^-3*x^-5//2*(a*x+b*x^(1/2))^(1/2)+512//77*a^3*b^-5*x^-3//2*(a*x+b*x^(1/2))^(1/2)+4096//231*a^5*b^-7*x^-1//2*(a*x+b*x^(1/2))^(1/2))
@test integrate(x^5//2*(a*x+b*x^(1/2))^-1//2, x) == :(-231//256*a^-6*b^5*(a*x+b*x^(1/2))^(1/2)+1//3*a^-1*x^5//2*(a*x+b*x^(1/2))^(1/2)+231//256*a^-13//2*b^6*arctanh(a^(1/2)*x^(1/2)*(a*x+b*x^(1/2))^-1//2)+-77//160*x*a^-4*b^3*(a*x+b*x^(1/2))^(1/2)+-11//30*b*a^-2*x^2*(a*x+b*x^(1/2))^(1/2)+33//80*a^-3*b^2*x^3//2*(a*x+b*x^(1/2))^(1/2)+77//128*a^-5*b^4*x^(1/2)*(a*x+b*x^(1/2))^(1/2))
@test integrate(x^3//2*(a*x+b*x^(1/2))^-1//2, x) == :((1/2)*a^-1*x^3//2*(a*x+b*x^(1/2))^(1/2)+-35//32*a^-4*b^3*(a*x+b*x^(1/2))^(1/2)+35//32*a^-9//2*b^4*arctanh(a^(1/2)*x^(1/2)*(a*x+b*x^(1/2))^-1//2)+-7//12*b*x*a^-2*(a*x+b*x^(1/2))^(1/2)+35//48*a^-3*b^2*x^(1/2)*(a*x+b*x^(1/2))^(1/2))
@test integrate(x^(1/2)*(a*x+b*x^(1/2))^-1//2, x) == :(a^-1*x^(1/2)*(a*x+b*x^(1/2))^(1/2)+-3//2*b*a^-2*(a*x+b*x^(1/2))^(1/2)+3//2*a^-5//2*b^2*arctanh(a^(1/2)*x^(1/2)*(a*x+b*x^(1/2))^-1//2))
@test integrate(x^-1//2*(a*x+b*x^(1/2))^-1//2, x) == :(4*a^-1//2*arctanh(a^(1/2)*x^(1/2)*(a*x+b*x^(1/2))^-1//2))
@test integrate(x^-3//2*(a*x+b*x^(1/2))^-1//2, x) == :(-4//3*b^-1*x^-1*(a*x+b*x^(1/2))^(1/2)+8//3*a*b^-2*x^-1//2*(a*x+b*x^(1/2))^(1/2))
@test integrate(x^-5//2*(a*x+b*x^(1/2))^-1//2, x) == :(-4//7*b^-1*x^-2*(a*x+b*x^(1/2))^(1/2)+-32//35*a^2*b^-3*x^-1*(a*x+b*x^(1/2))^(1/2)+24//35*a*b^-2*x^-3//2*(a*x+b*x^(1/2))^(1/2)+64//35*a^3*b^-4*x^-1//2*(a*x+b*x^(1/2))^(1/2))
@test integrate(x^-7//2*(a*x+b*x^(1/2))^-1//2, x) == :(-4//11*b^-1*x^-3*(a*x+b*x^(1/2))^(1/2)+-512//693*a^4*b^-5*x^-1*(a*x+b*x^(1/2))^(1/2)+-320//693*a^2*b^-3*x^-2*(a*x+b*x^(1/2))^(1/2)+40//99*a*b^-2*x^-5//2*(a*x+b*x^(1/2))^(1/2)+128//231*a^3*b^-4*x^-3//2*(a*x+b*x^(1/2))^(1/2)+1024//693*a^5*b^-6*x^-1//2*(a*x+b*x^(1/2))^(1/2))
@test integrate(x^5//2*(a*x+b*x^(1/2))^-3//2, x) == :(-4*a^-1*x^5//2*(a*x+b*x^(1/2))^-1//2+-315//32*a^-5*b^3*(a*x+b*x^(1/2))^(1/2)+9//2*a^-2*x^3//2*(a*x+b*x^(1/2))^(1/2)+315//32*a^-11//2*b^4*arctanh(a^(1/2)*x^(1/2)*(a*x+b*x^(1/2))^-1//2)+-21//4*b*x*a^-3*(a*x+b*x^(1/2))^(1/2)+105//16*a^-4*b^2*x^(1/2)*(a*x+b*x^(1/2))^(1/2))
@test integrate(x^3//2*(a*x+b*x^(1/2))^-3//2, x) == :(-4*a^-1*x^3//2*(a*x+b*x^(1/2))^-1//2+5*a^-2*x^(1/2)*(a*x+b*x^(1/2))^(1/2)+-15//2*b*a^-3*(a*x+b*x^(1/2))^(1/2)+15//2*a^-7//2*b^2*arctanh(a^(1/2)*x^(1/2)*(a*x+b*x^(1/2))^-1//2))
@test integrate(x^(1/2)*(a*x+b*x^(1/2))^-3//2, x) == :(4*a^-3//2*arctanh(a^(1/2)*x^(1/2)*(a*x+b*x^(1/2))^-1//2)+-4*a^-1*x^(1/2)*(a*x+b*x^(1/2))^-1//2)
@test integrate(x^-1//2*(a*x+b*x^(1/2))^-3//2, x) == :(-1*b^-2*(a*x+b*x^(1/2))^-1//2*(4b+8*a*x^(1/2)))
@test integrate(x^-3//2*(a*x+b*x^(1/2))^-3//2, x) == :(4*b^-1*x^-1*(a*x+b*x^(1/2))^-1//2+-24//5*b^-2*x^-3//2*(a*x+b*x^(1/2))^(1/2)+-64//5*a^2*b^-4*x^-1//2*(a*x+b*x^(1/2))^(1/2)+32//5*a*b^-3*x^-1*(a*x+b*x^(1/2))^(1/2))
@test integrate(x^-5//2*(a*x+b*x^(1/2))^-3//2, x) == :(4*b^-1*x^-2*(a*x+b*x^(1/2))^-1//2+-40//9*b^-2*x^-5//2*(a*x+b*x^(1/2))^(1/2)+-1024//63*a^4*b^-6*x^-1//2*(a*x+b*x^(1/2))^(1/2)+-128//21*a^2*b^-4*x^-3//2*(a*x+b*x^(1/2))^(1/2)+320//63*a*b^-3*x^-2*(a*x+b*x^(1/2))^(1/2)+512//63*a^3*b^-5*x^-1*(a*x+b*x^(1/2))^(1/2))
@test integrate(x^-7//2*(a*x+b*x^(1/2))^-3//2, x) == :(4*b^-1*x^-3*(a*x+b*x^(1/2))^-1//2+-56//13*b^-2*x^-7//2*(a*x+b*x^(1/2))^(1/2)+-8192//429*a^6*b^-8*x^-1//2*(a*x+b*x^(1/2))^(1/2)+-2240//429*a^2*b^-4*x^-5//2*(a*x+b*x^(1/2))^(1/2)+-1024//143*a^4*b^-6*x^-3//2*(a*x+b*x^(1/2))^(1/2)+672//143*a*b^-3*x^-3*(a*x+b*x^(1/2))^(1/2)+2560//429*a^3*b^-5*x^-2*(a*x+b*x^(1/2))^(1/2)+4096//429*a^5*b^-7*x^-1*(a*x+b*x^(1/2))^(1/2))
@test integrate(x^3*(a*x+b*x^1//3)^(1/2), x) == :(2//9*x^4*(a*x+b*x^1//3)^(1/2)+-884//14421*a^-6*b^6*(a*x+b*x^1//3)^(1/2)+-6188//216315*a^-4*b^4*x^4//3*(a*x+b*x^1//3)^(1/2)+-28//1311*a^-2*b^2*x^8//3*(a*x+b*x^1//3)^(1/2)+4//207*b*a^-1*x^10//3*(a*x+b*x^1//3)^(1/2)+476//19665*a^-3*b^3*x^2*(a*x+b*x^1//3)^(1/2)+884//24035*a^-5*b^5*x^2//3*(a*x+b*x^1//3)^(1/2)+442//14421*a^-25//4*b^27//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x^2*(a*x+b*x^1//3)^(1/2), x) == :(2//7*x^3*(a*x+b*x^1//3)^(1/2)+-60//1547*a^-2*b^2*x^5//3*(a*x+b*x^1//3)^(1/2)+-44//663*a^-4*b^4*x^1//3*(a*x+b*x^1//3)^(1/2)+4//119*b*a^-1*x^7//3*(a*x+b*x^1//3)^(1/2)+220//4641*x*a^-3*b^3*(a*x+b*x^1//3)^(1/2)+44//221*a^-9//2*b^5*x^1//3*(b^(1/2)+a^(1/2)*x^1//3)^-1*(a*x+b*x^1//3)^-1//2*(b+a*x^2//3)+-44//221*a^-19//4*b^21//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.E(2*arctan(a^1//4*b^-1//4*x^1//6),1/2)+22//221*a^-19//4*b^21//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x*(a*x+b*x^1//3)^(1/2), x) == :(2//5*x^2*(a*x+b*x^1//3)^(1/2)+12//77*a^-3*b^3*(a*x+b*x^1//3)^(1/2)+-36//385*a^-2*b^2*x^2//3*(a*x+b*x^1//3)^(1/2)+4//55*b*a^-1*x^4//3*(a*x+b*x^1//3)^(1/2)+-6//77*a^-13//4*b^15//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate((a*x+b*x^1//3)^(1/2), x) == :(2//3*x*(a*x+b*x^1//3)^(1/2)+4//15*b*a^-1*x^1//3*(a*x+b*x^1//3)^(1/2)+-4//5*a^-3//2*b^2*x^1//3*(b^(1/2)+a^(1/2)*x^1//3)^-1*(a*x+b*x^1//3)^-1//2*(b+a*x^2//3)+-2//5*a^-7//4*b^9//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2)+4//5*a^-7//4*b^9//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.E(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x^-1*(a*x+b*x^1//3)^(1/2), x) == :(2*(a*x+b*x^1//3)^(1/2)+2*a^-1//4*b^3//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x^-2*(a*x+b*x^1//3)^(1/2), x) == :(-6//5*x^-1*(a*x+b*x^1//3)^(1/2)+-12//5*a*b^-1*x^-1//3*(a*x+b*x^1//3)^(1/2)+12//5*a^3//2*b^-1*x^1//3*(b^(1/2)+a^(1/2)*x^1//3)^-1*(a*x+b*x^1//3)^-1//2*(b+a*x^2//3)+-12//5*a^5//4*b^-3//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.E(2*arctan(a^1//4*b^-1//4*x^1//6),1/2)+6//5*a^5//4*b^-3//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x^-3*(a*x+b*x^1//3)^(1/2), x) == :(-6//11*x^-2*(a*x+b*x^1//3)^(1/2)+-12//77*a*b^-1*x^-4//3*(a*x+b*x^1//3)^(1/2)+20//77*a^2*b^-2*x^-2//3*(a*x+b*x^1//3)^(1/2)+10//77*a^11//4*b^-9//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x^-4*(a*x+b*x^1//3)^(1/2), x) == :(-6//17*x^-3*(a*x+b*x^1//3)^(1/2)+-308//3315*a^3*b^-3*x^-1*(a*x+b*x^1//3)^(1/2)+-12//221*a*b^-1*x^-7//3*(a*x+b*x^1//3)^(1/2)+44//663*a^2*b^-2*x^-5//3*(a*x+b*x^1//3)^(1/2)+308//1105*a^4*b^-4*x^-1//3*(a*x+b*x^1//3)^(1/2)+-308//1105*a^9//2*b^-4*x^1//3*(b^(1/2)+a^(1/2)*x^1//3)^-1*(a*x+b*x^1//3)^-1//2*(b+a*x^2//3)+-154//1105*a^17//4*b^-15//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2)+308//1105*a^17//4*b^-15//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.E(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x^-5*(a*x+b*x^1//3)^(1/2), x) == :(-6//23*x^-4*(a*x+b*x^1//3)^(1/2)+-2652//33649*a^5*b^-5*x^-2//3*(a*x+b*x^1//3)^(1/2)+-884//24035*a^3*b^-3*x^-2*(a*x+b*x^1//3)^(1/2)+-12//437*a*b^-1*x^-10//3*(a*x+b*x^1//3)^(1/2)+68//2185*a^2*b^-2*x^-8//3*(a*x+b*x^1//3)^(1/2)+7956//168245*a^4*b^-4*x^-4//3*(a*x+b*x^1//3)^(1/2)+-1326//33649*a^23//4*b^-21//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x^2*(a*x+b*x^1//3)^3//2, x) == :(2//9*x^3*(a*x+b*x^1//3)^3//2+4//69*b*x^10//3*(a*x+b*x^1//3)^(1/2)+1768//100947*a^-5*b^6*(a*x+b*x^1//3)^(1/2)+-1768//168245*a^-4*b^5*x^2//3*(a*x+b*x^1//3)^(1/2)+-136//19665*a^-2*b^3*x^2*(a*x+b*x^1//3)^(1/2)+8//1311*a^-1*b^2*x^8//3*(a*x+b*x^1//3)^(1/2)+1768//216315*a^-3*b^4*x^4//3*(a*x+b*x^1//3)^(1/2)+-884//100947*a^-21//4*b^27//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x*(a*x+b*x^1//3)^3//2, x) == :(2//7*x^2*(a*x+b*x^1//3)^3//2+12//119*b*x^7//3*(a*x+b*x^1//3)^(1/2)+-88//4641*x*a^-2*b^3*(a*x+b*x^1//3)^(1/2)+24//1547*a^-1*b^2*x^5//3*(a*x+b*x^1//3)^(1/2)+88//3315*a^-3*b^4*x^1//3*(a*x+b*x^1//3)^(1/2)+-88//1105*a^-7//2*b^5*x^1//3*(b^(1/2)+a^(1/2)*x^1//3)^-1*(a*x+b*x^1//3)^-1//2*(b+a*x^2//3)+-44//1105*a^-15//4*b^21//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2)+88//1105*a^-15//4*b^21//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.E(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate((a*x+b*x^1//3)^3//2, x) == :(2//5*x*(a*x+b*x^1//3)^3//2+-8//77*a^-2*b^3*(a*x+b*x^1//3)^(1/2)+12//55*b*x^4//3*(a*x+b*x^1//3)^(1/2)+24//385*a^-1*b^2*x^2//3*(a*x+b*x^1//3)^(1/2)+4//77*a^-9//4*b^15//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x^-1*(a*x+b*x^1//3)^3//2, x) == :(2//3*(a*x+b*x^1//3)^3//2+4//5*b*x^1//3*(a*x+b*x^1//3)^(1/2)+8//5*a^-1//2*b^2*x^1//3*(b^(1/2)+a^(1/2)*x^1//3)^-1*(a*x+b*x^1//3)^-1//2*(b+a*x^2//3)+-8//5*a^-3//4*b^9//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.E(2*arctan(a^1//4*b^-1//4*x^1//6),1/2)+4//5*a^-3//4*b^9//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x^-2*(a*x+b*x^1//3)^3//2, x) == :(-2*x^-1*(a*x+b*x^1//3)^3//2+4*a*(a*x+b*x^1//3)^(1/2)+4*a^3//4*b^3//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x^-3*(a*x+b*x^1//3)^3//2, x) == :(-2//3*x^-2*(a*x+b*x^1//3)^3//2+-4//5*a*x^-1*(a*x+b*x^1//3)^(1/2)+-8//5*a^2*b^-1*x^-1//3*(a*x+b*x^1//3)^(1/2)+8//5*a^5//2*b^-1*x^1//3*(b^(1/2)+a^(1/2)*x^1//3)^-1*(a*x+b*x^1//3)^-1//2*(b+a*x^2//3)+-8//5*a^9//4*b^-3//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.E(2*arctan(a^1//4*b^-1//4*x^1//6),1/2)+4//5*a^9//4*b^-3//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x^-4*(a*x+b*x^1//3)^3//2, x) == :(-2//5*x^-3*(a*x+b*x^1//3)^3//2+-12//55*a*x^-2*(a*x+b*x^1//3)^(1/2)+-24//385*a^2*b^-1*x^-4//3*(a*x+b*x^1//3)^(1/2)+8//77*a^3*b^-2*x^-2//3*(a*x+b*x^1//3)^(1/2)+4//77*a^15//4*b^-9//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x^-5*(a*x+b*x^1//3)^3//2, x) == :(-2//7*x^-4*(a*x+b*x^1//3)^3//2+-12//119*a*x^-3*(a*x+b*x^1//3)^(1/2)+-88//3315*a^4*b^-3*x^-1*(a*x+b*x^1//3)^(1/2)+-24//1547*a^2*b^-1*x^-7//3*(a*x+b*x^1//3)^(1/2)+88//1105*a^5*b^-4*x^-1//3*(a*x+b*x^1//3)^(1/2)+88//4641*a^3*b^-2*x^-5//3*(a*x+b*x^1//3)^(1/2)+-88//1105*a^11//2*b^-4*x^1//3*(b^(1/2)+a^(1/2)*x^1//3)^-1*(a*x+b*x^1//3)^-1//2*(b+a*x^2//3)+-44//1105*a^21//4*b^-15//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2)+88//1105*a^21//4*b^-15//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.E(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x^-6*(a*x+b*x^1//3)^3//2, x) == :(-2//9*x^-5*(a*x+b*x^1//3)^3//2+-4//69*a*x^-4*(a*x+b*x^1//3)^(1/2)+-1768//100947*a^6*b^-5*x^-2//3*(a*x+b*x^1//3)^(1/2)+-1768//216315*a^4*b^-3*x^-2*(a*x+b*x^1//3)^(1/2)+-8//1311*a^2*b^-1*x^-10//3*(a*x+b*x^1//3)^(1/2)+136//19665*a^3*b^-2*x^-8//3*(a*x+b*x^1//3)^(1/2)+1768//168245*a^5*b^-4*x^-4//3*(a*x+b*x^1//3)^(1/2)+-884//100947*a^27//4*b^-21//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x^4*(a*x+b*x^1//3)^-1//2, x) == :(2//9*a^-1*x^4*(a*x+b*x^1//3)^(1/2)+11050//14421*a^-7*b^6*(a*x+b*x^1//3)^(1/2)+-2210//4807*a^-6*b^5*x^2//3*(a*x+b*x^1//3)^(1/2)+-1190//3933*a^-4*b^3*x^2*(a*x+b*x^1//3)^(1/2)+-50//207*b*a^-2*x^10//3*(a*x+b*x^1//3)^(1/2)+350//1311*a^-3*b^2*x^8//3*(a*x+b*x^1//3)^(1/2)+15470//43263*a^-5*b^4*x^4//3*(a*x+b*x^1//3)^(1/2)+-5525//14421*a^-29//4*b^27//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x^3*(a*x+b*x^1//3)^-1//2, x) == :(2//7*a^-1*x^3*(a*x+b*x^1//3)^(1/2)+-2090//4641*x*a^-4*b^3*(a*x+b*x^1//3)^(1/2)+-38//119*b*a^-2*x^7//3*(a*x+b*x^1//3)^(1/2)+418//663*a^-5*b^4*x^1//3*(a*x+b*x^1//3)^(1/2)+570//1547*a^-3*b^2*x^5//3*(a*x+b*x^1//3)^(1/2)+-418//221*a^-11//2*b^5*x^1//3*(b^(1/2)+a^(1/2)*x^1//3)^-1*(a*x+b*x^1//3)^-1//2*(b+a*x^2//3)+-209//221*a^-23//4*b^21//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2)+418//221*a^-23//4*b^21//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.E(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x^2*(a*x+b*x^1//3)^-1//2, x) == :(-78//77*a^-4*b^3*(a*x+b*x^1//3)^(1/2)+2//5*a^-1*x^2*(a*x+b*x^1//3)^(1/2)+-26//55*b*a^-2*x^4//3*(a*x+b*x^1//3)^(1/2)+234//385*a^-3*b^2*x^2//3*(a*x+b*x^1//3)^(1/2)+39//77*a^-17//4*b^15//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x*(a*x+b*x^1//3)^-1//2, x) == :(2//3*x*a^-1*(a*x+b*x^1//3)^(1/2)+-14//15*b*a^-2*x^1//3*(a*x+b*x^1//3)^(1/2)+14//5*a^-5//2*b^2*x^1//3*(b^(1/2)+a^(1/2)*x^1//3)^-1*(a*x+b*x^1//3)^-1//2*(b+a*x^2//3)+-14//5*a^-11//4*b^9//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.E(2*arctan(a^1//4*b^-1//4*x^1//6),1/2)+7//5*a^-11//4*b^9//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate((a*x+b*x^1//3)^-1//2, x) == :(2*a^-1*(a*x+b*x^1//3)^(1/2)+-1*a^-5//4*b^3//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x^-1*(a*x+b*x^1//3)^-1//2, x) == :(-6*b^-1*x^-1//3*(a*x+b*x^1//3)^(1/2)+6*a^(1/2)*b^-1*x^1//3*(b^(1/2)+a^(1/2)*x^1//3)^-1*(a*x+b*x^1//3)^-1//2*(b+a*x^2//3)+-6*a^1//4*b^-3//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.E(2*arctan(a^1//4*b^-1//4*x^1//6),1/2)+3*a^1//4*b^-3//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x^-2*(a*x+b*x^1//3)^-1//2, x) == :(-6//7*b^-1*x^-4//3*(a*x+b*x^1//3)^(1/2)+10//7*a*b^-2*x^-2//3*(a*x+b*x^1//3)^(1/2)+5//7*a^7//4*b^-9//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x^-3*(a*x+b*x^1//3)^-1//2, x) == :(-6//13*b^-1*x^-7//3*(a*x+b*x^1//3)^(1/2)+-154//195*a^2*b^-3*x^-1*(a*x+b*x^1//3)^(1/2)+22//39*a*b^-2*x^-5//3*(a*x+b*x^1//3)^(1/2)+154//65*a^3*b^-4*x^-1//3*(a*x+b*x^1//3)^(1/2)+-154//65*a^7//2*b^-4*x^1//3*(b^(1/2)+a^(1/2)*x^1//3)^-1*(a*x+b*x^1//3)^-1//2*(b+a*x^2//3)+-77//65*a^13//4*b^-15//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2)+154//65*a^13//4*b^-15//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.E(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x^-4*(a*x+b*x^1//3)^-1//2, x) == :(-6//19*b^-1*x^-10//3*(a*x+b*x^1//3)^(1/2)+-1326//1463*a^4*b^-5*x^-2//3*(a*x+b*x^1//3)^(1/2)+-442//1045*a^2*b^-3*x^-2*(a*x+b*x^1//3)^(1/2)+34//95*a*b^-2*x^-8//3*(a*x+b*x^1//3)^(1/2)+3978//7315*a^3*b^-4*x^-4//3*(a*x+b*x^1//3)^(1/2)+-663//1463*a^19//4*b^-21//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x^4*(a*x+b*x^1//3)^-3//2, x) == :(-3*a^-1*x^4*(a*x+b*x^1//3)^-1//2+23//7*a^-2*x^3*(a*x+b*x^1//3)^(1/2)+-24035//4641*x*a^-5*b^3*(a*x+b*x^1//3)^(1/2)+-437//119*b*a^-3*x^7//3*(a*x+b*x^1//3)^(1/2)+4807//663*a^-6*b^4*x^1//3*(a*x+b*x^1//3)^(1/2)+6555//1547*a^-4*b^2*x^5//3*(a*x+b*x^1//3)^(1/2)+-4807//221*a^-13//2*b^5*x^1//3*(b^(1/2)+a^(1/2)*x^1//3)^-1*(a*x+b*x^1//3)^-1//2*(b+a*x^2//3)+-4807//442*a^-27//4*b^21//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2)+4807//221*a^-27//4*b^21//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.E(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x^3*(a*x+b*x^1//3)^-3//2, x) == :(-3*a^-1*x^3*(a*x+b*x^1//3)^-1//2+-663//77*a^-5*b^3*(a*x+b*x^1//3)^(1/2)+17//5*a^-2*x^2*(a*x+b*x^1//3)^(1/2)+-221//55*b*a^-3*x^4//3*(a*x+b*x^1//3)^(1/2)+1989//385*a^-4*b^2*x^2//3*(a*x+b*x^1//3)^(1/2)+663//154*a^-21//4*b^15//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x^2*(a*x+b*x^1//3)^-3//2, x) == :(-3*a^-1*x^2*(a*x+b*x^1//3)^-1//2+11//3*x*a^-2*(a*x+b*x^1//3)^(1/2)+-77//15*b*a^-3*x^1//3*(a*x+b*x^1//3)^(1/2)+77//5*a^-7//2*b^2*x^1//3*(b^(1/2)+a^(1/2)*x^1//3)^-1*(a*x+b*x^1//3)^-1//2*(b+a*x^2//3)+-77//5*a^-15//4*b^9//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.E(2*arctan(a^1//4*b^-1//4*x^1//6),1/2)+77//10*a^-15//4*b^9//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x*(a*x+b*x^1//3)^-3//2, x) == :(5*a^-2*(a*x+b*x^1//3)^(1/2)+-3*x*a^-1*(a*x+b*x^1//3)^-1//2+-5//2*a^-9//4*b^3//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate((a*x+b*x^1//3)^-3//2, x) == :(3*b^-1*x^2//3*(a*x+b*x^1//3)^-1//2+-1*a^-1//2*b^-1*x^1//3*(b^(1/2)+a^(1/2)*x^1//3)^-1*(a*x+b*x^1//3)^-1//2*(3b+3*a*x^2//3)+a^-3//4*b^-3//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(3*b^(1/2)+3*a^(1/2)*x^1//3)*Elliptic.E(2*arctan(a^1//4*b^-1//4*x^1//6),1/2)+-1//2*a^-3//4*b^-3//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(3*b^(1/2)+3*a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x^-1*(a*x+b*x^1//3)^-3//2, x) == :(-5*b^-2*x^-2//3*(a*x+b*x^1//3)^(1/2)+3*b^-1*x^-1//3*(a*x+b*x^1//3)^-1//2+-5//2*a^3//4*b^-9//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x^-2*(a*x+b*x^1//3)^-3//2, x) == :(3*b^-1*x^-4//3*(a*x+b*x^1//3)^-1//2+-11//3*b^-2*x^-5//3*(a*x+b*x^1//3)^(1/2)+-77//5*a^2*b^-4*x^-1//3*(a*x+b*x^1//3)^(1/2)+77//15*a*b^-3*x^-1*(a*x+b*x^1//3)^(1/2)+77//5*a^5//2*b^-4*x^1//3*(b^(1/2)+a^(1/2)*x^1//3)^-1*(a*x+b*x^1//3)^-1//2*(b+a*x^2//3)+-77//5*a^9//4*b^-15//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.E(2*arctan(a^1//4*b^-1//4*x^1//6),1/2)+77//10*a^9//4*b^-15//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x^-3*(a*x+b*x^1//3)^-3//2, x) == :(3*b^-1*x^-7//3*(a*x+b*x^1//3)^-1//2+-17//5*b^-2*x^-8//3*(a*x+b*x^1//3)^(1/2)+-1989//385*a^2*b^-4*x^-4//3*(a*x+b*x^1//3)^(1/2)+221//55*a*b^-3*x^-2*(a*x+b*x^1//3)^(1/2)+663//77*a^3*b^-5*x^-2//3*(a*x+b*x^1//3)^(1/2)+663//154*a^15//4*b^-21//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x^-4*(a*x+b*x^1//3)^-3//2, x) == :(3*b^-1*x^-10//3*(a*x+b*x^1//3)^-1//2+-23//7*b^-2*x^-11//3*(a*x+b*x^1//3)^(1/2)+-6555//1547*a^2*b^-4*x^-7//3*(a*x+b*x^1//3)^(1/2)+-4807//663*a^4*b^-6*x^-1*(a*x+b*x^1//3)^(1/2)+437//119*a*b^-3*x^-3*(a*x+b*x^1//3)^(1/2)+4807//221*a^5*b^-7*x^-1//3*(a*x+b*x^1//3)^(1/2)+24035//4641*a^3*b^-5*x^-5//3*(a*x+b*x^1//3)^(1/2)+-4807//221*a^11//2*b^-7*x^1//3*(b^(1/2)+a^(1/2)*x^1//3)^-1*(a*x+b*x^1//3)^-1//2*(b+a*x^2//3)+-4807//442*a^21//4*b^-27//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.F(2*arctan(a^1//4*b^-1//4*x^1//6),1/2)+4807//221*a^21//4*b^-27//4*x^1//6*((b^(1/2)+a^(1/2)*x^1//3)^-2*(b+a*x^2//3))^(1/2)*(a*x+b*x^1//3)^-1//2*(b^(1/2)+a^(1/2)*x^1//3)*Elliptic.E(2*arctan(a^1//4*b^-1//4*x^1//6),1/2))
@test integrate(x^3*(a*x+b*x^2//3)^(1/2), x) == :(-524288//4345965*a^-10*b^9*(a*x+b*x^2//3)^3//2+2//9*a^-1*x^3*(a*x+b*x^2//3)^3//2+-4194304//50702925*a^-12*b^11*x^-2//3*(a*x+b*x^2//3)^3//2+-360448//2414425*a^-8*b^7*x^2//3*(a*x+b*x^2//3)^3//2+-45056//260015*a^-6*b^5*x^4//3*(a*x+b*x^2//3)^3//2+-1408//7245*a^-4*b^3*x^2*(a*x+b*x^2//3)^3//2+-16//75*b*a^-2*x^8//3*(a*x+b*x^2//3)^3//2+352//1725*a^-3*b^2*x^7//3*(a*x+b*x^2//3)^3//2+2816//15295*a^-5*b^4*x^5//3*(a*x+b*x^2//3)^3//2+65536//482885*a^-9*b^8*x^1//3*(a*x+b*x^2//3)^3//2+90112//557175*x*a^-7*b^6*(a*x+b*x^2//3)^3//2+1048576//10140585*a^-11*b^10*x^-1//3*(a*x+b*x^2//3)^3//2+8388608//152108775*a^-13*b^12*x^-1*(a*x+b*x^2//3)^3//2)
@test integrate(x^2*(a*x+b*x^2//3)^(1/2), x) == :(2//7*a^-1*x^2*(a*x+b*x^2//3)^3//2+8192//46189*a^-7*b^6*(a*x+b*x^2//3)^3//2+-131072//1616615*a^-10*b^9*x^-1*(a*x+b*x^2//3)^3//2+-49152//323323*a^-8*b^7*x^-1//3*(a*x+b*x^2//3)^3//2+-9216//46189*a^-6*b^5*x^1//3*(a*x+b*x^2//3)^3//2+-384//1615*x*a^-4*b^3*(a*x+b*x^2//3)^3//2+-36//133*b*a^-2*x^5//3*(a*x+b*x^2//3)^3//2+576//2261*a^-3*b^2*x^4//3*(a*x+b*x^2//3)^3//2+4608//20995*a^-5*b^4*x^2//3*(a*x+b*x^2//3)^3//2+196608//1616615*a^-9*b^8*x^-2//3*(a*x+b*x^2//3)^3//2)
@test integrate(x*(a*x+b*x^2//3)^(1/2), x) == :(-128//429*a^-4*b^3*(a*x+b*x^2//3)^3//2+2//5*x*a^-1*(a*x+b*x^2//3)^3//2+-1024//5005*a^-6*b^5*x^-2//3*(a*x+b*x^2//3)^3//2+-24//65*b*a^-2*x^2//3*(a*x+b*x^2//3)^3//2+48//143*a^-3*b^2*x^1//3*(a*x+b*x^2//3)^3//2+256//1001*a^-5*b^4*x^-1//3*(a*x+b*x^2//3)^3//2+2048//15015*a^-7*b^6*x^-1*(a*x+b*x^2//3)^3//2)
@test integrate((a*x+b*x^2//3)^(1/2), x) == :(2//3*a^-1*(a*x+b*x^2//3)^3//2+-32//105*a^-4*b^3*x^-1*(a*x+b*x^2//3)^3//2+-4//7*b*a^-2*x^-1//3*(a*x+b*x^2//3)^3//2+16//35*a^-3*b^2*x^-2//3*(a*x+b*x^2//3)^3//2)
@test integrate(x^-1*(a*x+b*x^2//3)^(1/2), x) == :(2*a^-1*x^-1*(a*x+b*x^2//3)^3//2)
@test integrate(x^-2*(a*x+b*x^2//3)^(1/2), x) == :(-3//2*x^-1*(a*x+b*x^2//3)^(1/2)+3//4*a^2*b^-3//2*arctanh(b^(1/2)*x^1//3*(a*x+b*x^2//3)^-1//2)+-3//4*a*b^-1*x^-2//3*(a*x+b*x^2//3)^(1/2))
@test integrate(x^-3*(a*x+b*x^2//3)^(1/2), x) == :(-3//5*x^-2*(a*x+b*x^2//3)^(1/2)+-21//128*a^5*b^-9//2*arctanh(b^(1/2)*x^1//3*(a*x+b*x^2//3)^-1//2)+-7//64*a^3*b^-3*x^-1*(a*x+b*x^2//3)^(1/2)+-3//40*a*b^-1*x^-5//3*(a*x+b*x^2//3)^(1/2)+7//80*a^2*b^-2*x^-4//3*(a*x+b*x^2//3)^(1/2)+21//128*a^4*b^-4*x^-2//3*(a*x+b*x^2//3)^(1/2))
@test integrate(x^-4*(a*x+b*x^2//3)^(1/2), x) == :(-3//8*x^-3*(a*x+b*x^2//3)^(1/2)+1287//16384*a^8*b^-15//2*arctanh(b^(1/2)*x^1//3*(a*x+b*x^2//3)^-1//2)+-1287//16384*a^7*b^-7*x^-2//3*(a*x+b*x^2//3)^(1/2)+-429//10240*a^5*b^-5*x^-4//3*(a*x+b*x^2//3)^(1/2)+-143//4480*a^3*b^-3*x^-2*(a*x+b*x^2//3)^(1/2)+-3//112*a*b^-1*x^-8//3*(a*x+b*x^2//3)^(1/2)+13//448*a^2*b^-2*x^-7//3*(a*x+b*x^2//3)^(1/2)+429//8192*a^6*b^-6*x^-1*(a*x+b*x^2//3)^(1/2)+1287//35840*a^4*b^-4*x^-5//3*(a*x+b*x^2//3)^(1/2))
@test integrate(x^-5*(a*x+b*x^2//3)^(1/2), x) == :(-3//11*x^-4*(a*x+b*x^2//3)^(1/2)+-12597//262144*a^11*b^-21//2*arctanh(b^(1/2)*x^1//3*(a*x+b*x^2//3)^-1//2)+-12597//573440*a^7*b^-7*x^-5//3*(a*x+b*x^2//3)^(1/2)+-4199//131072*a^9*b^-9*x^-1*(a*x+b*x^2//3)^(1/2)+-4199//236544*a^5*b^-5*x^-7//3*(a*x+b*x^2//3)^(1/2)+-323//21120*a^3*b^-3*x^-3*(a*x+b*x^2//3)^(1/2)+-3//220*a*b^-1*x^-11//3*(a*x+b*x^2//3)^(1/2)+19//1320*a^2*b^-2*x^-10//3*(a*x+b*x^2//3)^(1/2)+323//19712*a^4*b^-4*x^-8//3*(a*x+b*x^2//3)^(1/2)+4199//163840*a^8*b^-8*x^-4//3*(a*x+b*x^2//3)^(1/2)+4199//215040*a^6*b^-6*x^-2*(a*x+b*x^2//3)^(1/2)+12597//262144*a^10*b^-10*x^-2//3*(a*x+b*x^2//3)^(1/2))
@test integrate(x^2*(a*x+b*x^2//3)^3//2, x) == :(2//9*a^-1*x^2*(a*x+b*x^2//3)^5//2+45056//557175*a^-7*b^6*(a*x+b*x^2//3)^5//2+-1048576//152108775*a^-12*b^11*x^-5//3*(a*x+b*x^2//3)^5//2+-131072//4345965*a^-10*b^9*x^-1*(a*x+b*x^2//3)^5//2+-90112//1448655*a^-8*b^7*x^-1//3*(a*x+b*x^2//3)^5//2+-11264//111435*a^-6*b^5*x^1//3*(a*x+b*x^2//3)^5//2+-352//2415*x*a^-4*b^3*(a*x+b*x^2//3)^5//2+-44//225*b*a^-2*x^5//3*(a*x+b*x^2//3)^5//2+176//1035*a^-3*b^2*x^4//3*(a*x+b*x^2//3)^5//2+5632//45885*a^-5*b^4*x^2//3*(a*x+b*x^2//3)^5//2+65536//1448655*a^-9*b^8*x^-2//3*(a*x+b*x^2//3)^5//2+524288//30421755*a^-11*b^10*x^-4//3*(a*x+b*x^2//3)^5//2)
@test integrate(x*(a*x+b*x^2//3)^3//2, x) == :(-256//1615*a^-4*b^3*(a*x+b*x^2//3)^5//2+2//7*x*a^-1*(a*x+b*x^2//3)^5//2+-32768//969969*a^-8*b^7*x^-4//3*(a*x+b*x^2//3)^5//2+-4096//46189*a^-6*b^5*x^-2//3*(a*x+b*x^2//3)^5//2+-32//133*b*a^-2*x^2//3*(a*x+b*x^2//3)^5//2+64//323*a^-3*b^2*x^1//3*(a*x+b*x^2//3)^5//2+512//4199*a^-5*b^4*x^-1//3*(a*x+b*x^2//3)^5//2+8192//138567*a^-7*b^6*x^-1*(a*x+b*x^2//3)^5//2+65536//4849845*a^-9*b^8*x^-5//3*(a*x+b*x^2//3)^5//2)
@test integrate((a*x+b*x^2//3)^3//2, x) == :(2//5*a^-1*(a*x+b*x^2//3)^5//2+-512//15015*a^-6*b^5*x^-5//3*(a*x+b*x^2//3)^5//2+-64//429*a^-4*b^3*x^-1*(a*x+b*x^2//3)^5//2+-4//13*b*a^-2*x^-1//3*(a*x+b*x^2//3)^5//2+32//143*a^-3*b^2*x^-2//3*(a*x+b*x^2//3)^5//2+256//3003*a^-5*b^4*x^-4//3*(a*x+b*x^2//3)^5//2)
@test integrate(x^-1*(a*x+b*x^2//3)^3//2, x) == :(2//3*a^-1*x^-1*(a*x+b*x^2//3)^5//2+-8//21*b*a^-2*x^-4//3*(a*x+b*x^2//3)^5//2+16//105*a^-3*b^2*x^-5//3*(a*x+b*x^2//3)^5//2)
@test integrate(x^-2*(a*x+b*x^2//3)^3//2, x) == :(-6*b^3//2*arctanh(b^(1/2)*x^1//3*(a*x+b*x^2//3)^-1//2)+2*x^-1*(a*x+b*x^2//3)^3//2+6*b*x^-1//3*(a*x+b*x^2//3)^(1/2))
@test integrate(x^-3*(a*x+b*x^2//3)^3//2, x) == :(-1*x^-2*(a*x+b*x^2//3)^3//2+-3//4*a*x^-1*(a*x+b*x^2//3)^(1/2)+3//8*a^3*b^-3//2*arctanh(b^(1/2)*x^1//3*(a*x+b*x^2//3)^-1//2)+-3//8*a^2*b^-1*x^-2//3*(a*x+b*x^2//3)^(1/2))
@test integrate(x^-4*(a*x+b*x^2//3)^3//2, x) == :(-1//2*x^-3*(a*x+b*x^2//3)^3//2+-21//512*a^6*b^-9//2*arctanh(b^(1/2)*x^1//3*(a*x+b*x^2//3)^-1//2)+-3//20*a*x^-2*(a*x+b*x^2//3)^(1/2)+-7//256*a^4*b^-3*x^-1*(a*x+b*x^2//3)^(1/2)+-3//160*a^2*b^-1*x^-5//3*(a*x+b*x^2//3)^(1/2)+7//320*a^3*b^-2*x^-4//3*(a*x+b*x^2//3)^(1/2)+21//512*a^5*b^-4*x^-2//3*(a*x+b*x^2//3)^(1/2))
@test integrate(x^-5*(a*x+b*x^2//3)^3//2, x) == :(-1//3*x^-4*(a*x+b*x^2//3)^3//2+-1//16*a*x^-3*(a*x+b*x^2//3)^(1/2)+429//32768*a^9*b^-15//2*arctanh(b^(1/2)*x^1//3*(a*x+b*x^2//3)^-1//2)+-429//32768*a^8*b^-7*x^-2//3*(a*x+b*x^2//3)^(1/2)+-143//20480*a^6*b^-5*x^-4//3*(a*x+b*x^2//3)^(1/2)+-143//26880*a^4*b^-3*x^-2*(a*x+b*x^2//3)^(1/2)+-1//224*a^2*b^-1*x^-8//3*(a*x+b*x^2//3)^(1/2)+13//2688*a^3*b^-2*x^-7//3*(a*x+b*x^2//3)^(1/2)+143//16384*a^7*b^-6*x^-1*(a*x+b*x^2//3)^(1/2)+429//71680*a^5*b^-4*x^-5//3*(a*x+b*x^2//3)^(1/2))
@test integrate(x^-6*(a*x+b*x^2//3)^3//2, x) == :(-1//4*x^-5*(a*x+b*x^2//3)^3//2+-12597//2097152*a^12*b^-21//2*arctanh(b^(1/2)*x^1//3*(a*x+b*x^2//3)^-1//2)+-3//88*a*x^-4*(a*x+b*x^2//3)^(1/2)+-12597//4587520*a^8*b^-7*x^-5//3*(a*x+b*x^2//3)^(1/2)+-4199//1048576*a^10*b^-9*x^-1*(a*x+b*x^2//3)^(1/2)+-4199//1892352*a^6*b^-5*x^-7//3*(a*x+b*x^2//3)^(1/2)+-323//168960*a^4*b^-3*x^-3*(a*x+b*x^2//3)^(1/2)+-3//1760*a^2*b^-1*x^-11//3*(a*x+b*x^2//3)^(1/2)+19//10560*a^3*b^-2*x^-10//3*(a*x+b*x^2//3)^(1/2)+323//157696*a^5*b^-4*x^-8//3*(a*x+b*x^2//3)^(1/2)+4199//1310720*a^9*b^-8*x^-4//3*(a*x+b*x^2//3)^(1/2)+4199//1720320*a^7*b^-6*x^-2*(a*x+b*x^2//3)^(1/2)+12597//2097152*a^11*b^-10*x^-2//3*(a*x+b*x^2//3)^(1/2))
@test integrate(x^4*(a*x+b*x^2//3)^-1//2, x) == :(2//9*a^-1*x^4*(a*x+b*x^2//3)^(1/2)+8388608//11700675*a^-13*b^12*(a*x+b*x^2//3)^(1/2)+-16777216//11700675*a^-14*b^13*x^-1//3*(a*x+b*x^2//3)^(1/2)+-2097152//3900225*a^-12*b^11*x^1//3*(a*x+b*x^2//3)^(1/2)+-180224//557175*a^-8*b^7*x^5//3*(a*x+b*x^2//3)^(1/2)+-131072//334305*x*a^-10*b^9*(a*x+b*x^2//3)^(1/2)+-73216//260015*a^-6*b^5*x^7//3*(a*x+b*x^2//3)^(1/2)+-9152//36225*a^-4*b^3*x^3*(a*x+b*x^2//3)^(1/2)+-52//225*b*a^-2*x^11//3*(a*x+b*x^2//3)^(1/2)+416//1725*a^-3*b^2*x^10//3*(a*x+b*x^2//3)^(1/2)+36608//137655*a^-5*b^4*x^8//3*(a*x+b*x^2//3)^(1/2)+65536//185725*a^-9*b^8*x^4//3*(a*x+b*x^2//3)^(1/2)+1048576//2340135*a^-11*b^10*x^2//3*(a*x+b*x^2//3)^(1/2)+1171456//3900225*a^-7*b^6*x^2*(a*x+b*x^2//3)^(1/2))
@test integrate(x^3*(a*x+b*x^2//3)^-1//2, x) == :(-262144//323323*a^-10*b^9*(a*x+b*x^2//3)^(1/2)+2//7*a^-1*x^3*(a*x+b*x^2//3)^(1/2)+-163840//323323*a^-8*b^7*x^2//3*(a*x+b*x^2//3)^(1/2)+-18432//46189*a^-6*b^5*x^4//3*(a*x+b*x^2//3)^(1/2)+-768//2261*a^-4*b^3*x^2*(a*x+b*x^2//3)^(1/2)+-40//133*b*a^-2*x^8//3*(a*x+b*x^2//3)^(1/2)+720//2261*a^-3*b^2*x^7//3*(a*x+b*x^2//3)^(1/2)+1536//4199*a^-5*b^4*x^5//3*(a*x+b*x^2//3)^(1/2)+20480//46189*x*a^-7*b^6*(a*x+b*x^2//3)^(1/2)+196608//323323*a^-9*b^8*x^1//3*(a*x+b*x^2//3)^(1/2)+524288//323323*a^-11*b^10*x^-1//3*(a*x+b*x^2//3)^(1/2))
@test integrate(x^2*(a*x+b*x^2//3)^-1//2, x) == :(2//5*a^-1*x^2*(a*x+b*x^2//3)^(1/2)+2048//2145*a^-7*b^6*(a*x+b*x^2//3)^(1/2)+-4096//2145*a^-8*b^7*x^-1//3*(a*x+b*x^2//3)^(1/2)+-512//715*a^-6*b^5*x^1//3*(a*x+b*x^2//3)^(1/2)+-224//429*x*a^-4*b^3*(a*x+b*x^2//3)^(1/2)+-28//65*b*a^-2*x^5//3*(a*x+b*x^2//3)^(1/2)+256//429*a^-5*b^4*x^2//3*(a*x+b*x^2//3)^(1/2)+336//715*a^-3*b^2*x^4//3*(a*x+b*x^2//3)^(1/2))
@test integrate(x*(a*x+b*x^2//3)^-1//2, x) == :(-128//105*a^-4*b^3*(a*x+b*x^2//3)^(1/2)+2//3*x*a^-1*(a*x+b*x^2//3)^(1/2)+-16//21*b*a^-2*x^2//3*(a*x+b*x^2//3)^(1/2)+32//35*a^-3*b^2*x^1//3*(a*x+b*x^2//3)^(1/2)+256//105*a^-5*b^4*x^-1//3*(a*x+b*x^2//3)^(1/2))
@test integrate((a*x+b*x^2//3)^-1//2, x) == :(2*a^-1*(a*x+b*x^2//3)^(1/2)+-4*b*a^-2*x^-1//3*(a*x+b*x^2//3)^(1/2))
@test integrate(x^-1*(a*x+b*x^2//3)^-1//2, x) == :(-3*b^-1*x^-2//3*(a*x+b*x^2//3)^(1/2)+3*a*b^-3//2*arctanh(b^(1/2)*x^1//3*(a*x+b*x^2//3)^-1//2))
@test integrate(x^-2*(a*x+b*x^2//3)^-1//2, x) == :(-105//64*a^4*b^-9//2*arctanh(b^(1/2)*x^1//3*(a*x+b*x^2//3)^-1//2)+-3//4*b^-1*x^-5//3*(a*x+b*x^2//3)^(1/2)+-35//32*a^2*b^-3*x^-1*(a*x+b*x^2//3)^(1/2)+7//8*a*b^-2*x^-4//3*(a*x+b*x^2//3)^(1/2)+105//64*a^3*b^-4*x^-2//3*(a*x+b*x^2//3)^(1/2))
@test integrate(x^-3*(a*x+b*x^2//3)^-1//2, x) == :(-3//7*b^-1*x^-8//3*(a*x+b*x^2//3)^(1/2)+1287//1024*a^7*b^-15//2*arctanh(b^(1/2)*x^1//3*(a*x+b*x^2//3)^-1//2)+-1287//1024*a^6*b^-7*x^-2//3*(a*x+b*x^2//3)^(1/2)+-429//640*a^4*b^-5*x^-4//3*(a*x+b*x^2//3)^(1/2)+-143//280*a^2*b^-3*x^-2*(a*x+b*x^2//3)^(1/2)+13//28*a*b^-2*x^-7//3*(a*x+b*x^2//3)^(1/2)+429//512*a^5*b^-6*x^-1*(a*x+b*x^2//3)^(1/2)+1287//2240*a^3*b^-4*x^-5//3*(a*x+b*x^2//3)^(1/2))
@test integrate(x^-4*(a*x+b*x^2//3)^-1//2, x) == :(-138567//131072*a^10*b^-21//2*arctanh(b^(1/2)*x^1//3*(a*x+b*x^2//3)^-1//2)+-3//10*b^-1*x^-11//3*(a*x+b*x^2//3)^(1/2)+-138567//286720*a^6*b^-7*x^-5//3*(a*x+b*x^2//3)^(1/2)+-46189//65536*a^8*b^-9*x^-1*(a*x+b*x^2//3)^(1/2)+-4199//10752*a^4*b^-5*x^-7//3*(a*x+b*x^2//3)^(1/2)+-323//960*a^2*b^-3*x^-3*(a*x+b*x^2//3)^(1/2)+19//60*a*b^-2*x^-10//3*(a*x+b*x^2//3)^(1/2)+323//896*a^3*b^-4*x^-8//3*(a*x+b*x^2//3)^(1/2)+46189//81920*a^7*b^-8*x^-4//3*(a*x+b*x^2//3)^(1/2)+46189//107520*a^5*b^-6*x^-2*(a*x+b*x^2//3)^(1/2)+138567//131072*a^9*b^-10*x^-2//3*(a*x+b*x^2//3)^(1/2))
@test integrate(x^4*(a*x+b*x^2//3)^-3//2, x) == :(-6*a^-1*x^4*(a*x+b*x^2//3)^-1//2+-524288//29393*a^-11*b^9*(a*x+b*x^2//3)^(1/2)+44//7*a^-2*x^3*(a*x+b*x^2//3)^(1/2)+-327680//29393*a^-9*b^7*x^2//3*(a*x+b*x^2//3)^(1/2)+-36864//4199*a^-7*b^5*x^4//3*(a*x+b*x^2//3)^(1/2)+-16896//2261*a^-5*b^3*x^2*(a*x+b*x^2//3)^(1/2)+-880//133*b*a^-3*x^8//3*(a*x+b*x^2//3)^(1/2)+15840//2261*a^-4*b^2*x^7//3*(a*x+b*x^2//3)^(1/2)+33792//4199*a^-6*b^4*x^5//3*(a*x+b*x^2//3)^(1/2)+40960//4199*x*a^-8*b^6*(a*x+b*x^2//3)^(1/2)+393216//29393*a^-10*b^8*x^1//3*(a*x+b*x^2//3)^(1/2)+1048576//29393*a^-12*b^10*x^-1//3*(a*x+b*x^2//3)^(1/2))
@test integrate(x^3*(a*x+b*x^2//3)^-3//2, x) == :(-6*a^-1*x^3*(a*x+b*x^2//3)^-1//2+32//5*a^-2*x^2*(a*x+b*x^2//3)^(1/2)+32768//2145*a^-8*b^6*(a*x+b*x^2//3)^(1/2)+-65536//2145*a^-9*b^7*x^-1//3*(a*x+b*x^2//3)^(1/2)+-8192//715*a^-7*b^5*x^1//3*(a*x+b*x^2//3)^(1/2)+-3584//429*x*a^-5*b^3*(a*x+b*x^2//3)^(1/2)+-448//65*b*a^-3*x^5//3*(a*x+b*x^2//3)^(1/2)+4096//429*a^-6*b^4*x^2//3*(a*x+b*x^2//3)^(1/2)+5376//715*a^-4*b^2*x^4//3*(a*x+b*x^2//3)^(1/2))
@test integrate(x^2*(a*x+b*x^2//3)^-3//2, x) == :(-6*a^-1*x^2*(a*x+b*x^2//3)^-1//2+-256//21*a^-5*b^3*(a*x+b*x^2//3)^(1/2)+20//3*x*a^-2*(a*x+b*x^2//3)^(1/2)+-160//21*b*a^-3*x^2//3*(a*x+b*x^2//3)^(1/2)+64//7*a^-4*b^2*x^1//3*(a*x+b*x^2//3)^(1/2)+512//21*a^-6*b^4*x^-1//3*(a*x+b*x^2//3)^(1/2))
@test integrate(x*(a*x+b*x^2//3)^-3//2, x) == :(8*a^-2*(a*x+b*x^2//3)^(1/2)+-6*x*a^-1*(a*x+b*x^2//3)^-1//2+-16*b*a^-3*x^-1//3*(a*x+b*x^2//3)^(1/2))
@test integrate((a*x+b*x^2//3)^-3//2, x) == :(-6*b^-3//2*arctanh(b^(1/2)*x^1//3*(a*x+b*x^2//3)^-1//2)+6*b^-1*x^1//3*(a*x+b*x^2//3)^-1//2)
@test integrate(x^-1*(a*x+b*x^2//3)^-3//2, x) == :(-7*b^-2*x^-4//3*(a*x+b*x^2//3)^(1/2)+6*b^-1*x^-2//3*(a*x+b*x^2//3)^-1//2+105//8*a^3*b^-9//2*arctanh(b^(1/2)*x^1//3*(a*x+b*x^2//3)^-1//2)+-105//8*a^2*b^-4*x^-2//3*(a*x+b*x^2//3)^(1/2)+35//4*a*b^-3*x^-1*(a*x+b*x^2//3)^(1/2))
@test integrate(x^-2*(a*x+b*x^2//3)^-3//2, x) == :(6*b^-1*x^-5//3*(a*x+b*x^2//3)^-1//2+-9009//512*a^6*b^-15//2*arctanh(b^(1/2)*x^1//3*(a*x+b*x^2//3)^-1//2)+-13//2*b^-2*x^-7//3*(a*x+b*x^2//3)^(1/2)+-3003//256*a^4*b^-6*x^-1*(a*x+b*x^2//3)^(1/2)+-1287//160*a^2*b^-4*x^-5//3*(a*x+b*x^2//3)^(1/2)+143//20*a*b^-3*x^-2*(a*x+b*x^2//3)^(1/2)+3003//320*a^3*b^-5*x^-4//3*(a*x+b*x^2//3)^(1/2)+9009//512*a^5*b^-7*x^-2//3*(a*x+b*x^2//3)^(1/2))
@test integrate(x^-3*(a*x+b*x^2//3)^-3//2, x) == :(6*b^-1*x^-8//3*(a*x+b*x^2//3)^-1//2+-19//3*b^-2*x^-10//3*(a*x+b*x^2//3)^(1/2)+692835//32768*a^9*b^-21//2*arctanh(b^(1/2)*x^1//3*(a*x+b*x^2//3)^-1//2)+-692835//32768*a^8*b^-10*x^-2//3*(a*x+b*x^2//3)^(1/2)+-46189//4096*a^6*b^-8*x^-4//3*(a*x+b*x^2//3)^(1/2)+-46189//5376*a^4*b^-6*x^-2*(a*x+b*x^2//3)^(1/2)+-1615//224*a^2*b^-4*x^-8//3*(a*x+b*x^2//3)^(1/2)+323//48*a*b^-3*x^-3*(a*x+b*x^2//3)^(1/2)+20995//2688*a^3*b^-5*x^-7//3*(a*x+b*x^2//3)^(1/2)+138567//14336*a^5*b^-7*x^-5//3*(a*x+b*x^2//3)^(1/2)+230945//16384*a^7*b^-9*x^-1*(a*x+b*x^2//3)^(1/2))
@test integrate(x^-4*(a*x+b*x^2//3)^-3//2, x) == :(6*b^-1*x^-11//3*(a*x+b*x^2//3)^-1//2+-50702925//2097152*a^12*b^-27//2*arctanh(b^(1/2)*x^1//3*(a*x+b*x^2//3)^-1//2)+-25//4*b^-2*x^-13//3*(a*x+b*x^2//3)^(1/2)+-16900975//1048576*a^10*b^-12*x^-1*(a*x+b*x^2//3)^(1/2)+-2414425//270336*a^6*b^-8*x^-7//3*(a*x+b*x^2//3)^(1/2)+-1448655//131072*a^8*b^-10*x^-5//3*(a*x+b*x^2//3)^(1/2)+-260015//33792*a^4*b^-6*x^-3*(a*x+b*x^2//3)^(1/2)+-2415//352*a^2*b^-4*x^-11//3*(a*x+b*x^2//3)^(1/2)+575//88*a*b^-3*x^-4*(a*x+b*x^2//3)^(1/2)+15295//2112*a^3*b^-5*x^-10//3*(a*x+b*x^2//3)^(1/2)+185725//22528*a^5*b^-7*x^-8//3*(a*x+b*x^2//3)^(1/2)+482885//49152*a^7*b^-9*x^-2*(a*x+b*x^2//3)^(1/2)+3380195//262144*a^9*b^-11*x^-4//3*(a*x+b*x^2//3)^(1/2)+50702925//2097152*a^11*b^-13*x^-2//3*(a*x+b*x^2//3)^(1/2))
@test integrate(x^2*(a*x^2+b*x^3), x) == :(1//5*a*x^5+1//6*b*x^6)
@test integrate(x*(a*x^2+b*x^3), x) == :(1//4*a*x^4+1//5*b*x^5)
@test integrate(a*x^2+b*x^3, x) == :(1//3*a*x^3+1//4*b*x^4)
@test integrate(x^-1*(a*x^2+b*x^3), x) == :((1/2)*a*x^2+1//3*b*x^3)
@test integrate(x^-2*(a*x^2+b*x^3), x) == :(a*x+(1/2)*b*x^2)
@test integrate(x^2*(a*x^2+b*x^3)^2, x) == :(1//7*a^2*x^7+1//9*b^2*x^9+1//4*a*b*x^8)
@test integrate(x*(a*x^2+b*x^3)^2, x) == :(1//6*a^2*x^6+1//8*b^2*x^8+2//7*a*b*x^7)
@test integrate((a*x^2+b*x^3)^2, x) == :(1//5*a^2*x^5+1//7*b^2*x^7+1//3*a*b*x^6)
@test integrate(x^-1*(a*x^2+b*x^3)^2, x) == :(1//4*a^2*x^4+1//6*b^2*x^6+2//5*a*b*x^5)
@test integrate(x^-2*(a*x^2+b*x^3)^2, x) == :(1//3*a^2*x^3+1//5*b^2*x^5+(1/2)*a*b*x^4)
@test integrate(x^6*(a*x^2+b*x^3)^-1, x) == :(1//4*b^-1*x^4+a^4*b^-5*log(a+b*x)+(1/2)*a^2*b^-3*x^2+-1*x*a^3*b^-4+-1//3*a*b^-2*x^3)
@test integrate(x^5*(a*x^2+b*x^3)^-1, x) == :(1//3*b^-1*x^3+x*a^2*b^-3+-1*a^3*b^-4*log(a+b*x)+-1//2*a*b^-2*x^2)
@test integrate(x^4*(a*x^2+b*x^3)^-1, x) == :((1/2)*b^-1*x^2+a^2*b^-3*log(a+b*x)+-1*a*x*b^-2)
@test integrate(x^3*(a*x^2+b*x^3)^-1, x) == :(x*b^-1+-1*a*b^-2*log(a+b*x))
@test integrate(x^2*(a*x^2+b*x^3)^-1, x) == :(b^-1*log(a+b*x))
@test integrate(x*(a*x^2+b*x^3)^-1, x) == :(a^-1*log(x)+-1*a^-1*log(a+b*x))
@test integrate((a*x^2+b*x^3)^-1, x) == :(-1*a^-1*x^-1+b*a^-2*log(a+b*x)+-1*b*a^-2*log(x))
@test integrate(x^-1*(a*x^2+b*x^3)^-1, x) == :(-1//2*a^-1*x^-2+b*a^-2*x^-1+a^-3*b^2*log(x)+-1*a^-3*b^2*log(a+b*x))
@test integrate(x^-2*(a*x^2+b*x^3)^-1, x) == :(-1//3*a^-1*x^-3+a^-4*b^3*log(a+b*x)+(1/2)*b*a^-2*x^-2+-1*a^-4*b^3*log(x)+-1*a^-3*b^2*x^-1)
@test integrate(x^8*(a*x^2+b*x^3)^-2, x) == :(1//3*b^-2*x^3+-1*a*b^-3*x^2+-1*a^4*b^-5*(a+b*x)^-1+-4*a^3*b^-5*log(a+b*x)+3*x*a^2*b^-4)
@test integrate(x^7*(a*x^2+b*x^3)^-2, x) == :((1/2)*b^-2*x^2+a^3*b^-4*(a+b*x)^-1+-2*a*x*b^-3+3*a^2*b^-4*log(a+b*x))
@test integrate(x^6*(a*x^2+b*x^3)^-2, x) == :(x*b^-2+-1*a^2*b^-3*(a+b*x)^-1+-2*a*b^-3*log(a+b*x))
@test integrate(x^5*(a*x^2+b*x^3)^-2, x) == :(b^-2*log(a+b*x)+a*b^-2*(a+b*x)^-1)
@test integrate(x^4*(a*x^2+b*x^3)^-2, x) == :(-1*b^-1*(a+b*x)^-1)
@test integrate(x^3*(a*x^2+b*x^3)^-2, x) == :(a^-1*(a+b*x)^-1+a^-2*log(x)+-1*a^-2*log(a+b*x))
@test integrate(x^2*(a*x^2+b*x^3)^-2, x) == :(-1*a^-2*x^-1+-1*b*a^-2*(a+b*x)^-1+-2*b*a^-3*log(x)+2*b*a^-3*log(a+b*x))
@test integrate(x*(a*x^2+b*x^3)^-2, x) == :(-1//2*a^-2*x^-2+a^-3*b^2*(a+b*x)^-1+-3*a^-4*b^2*log(a+b*x)+2*b*a^-3*x^-1+3*a^-4*b^2*log(x))
@test integrate((a*x^2+b*x^3)^-2, x) == :(-1//3*a^-2*x^-3+b*a^-3*x^-2+-1*a^-4*b^3*(a+b*x)^-1+-4*a^-5*b^3*log(x)+-3*a^-4*b^2*x^-1+4*a^-5*b^3*log(a+b*x))
@test integrate(x^-1*(a*x^2+b*x^3)^-2, x) == :(-1//4*a^-2*x^-4+a^-5*b^4*(a+b*x)^-1+-5*a^-6*b^4*log(a+b*x)+4*a^-5*b^3*x^-1+5*a^-6*b^4*log(x)+-3//2*a^-4*b^2*x^-2+2//3*b*a^-3*x^-3)
@test integrate(x^2*(a*x^2+b*x^3)^(1/2), x) == :(2//9*b^-1*(a*x^2+b*x^3)^3//2+-32//315*a^3*b^-4*x^-3*(a*x^2+b*x^3)^3//2+-4//21*a*b^-2*x^-1*(a*x^2+b*x^3)^3//2+16//105*a^2*b^-3*x^-2*(a*x^2+b*x^3)^3//2)
@test integrate(x*(a*x^2+b*x^3)^(1/2), x) == :(2//7*b^-1*x^-1*(a*x^2+b*x^3)^3//2+-8//35*a*b^-2*x^-2*(a*x^2+b*x^3)^3//2+16//105*a^2*b^-3*x^-3*(a*x^2+b*x^3)^3//2)
@test integrate((a*x^2+b*x^3)^(1/2), x) == :(2//5*b^-1*x^-2*(a*x^2+b*x^3)^3//2+-4//15*a*b^-2*x^-3*(a*x^2+b*x^3)^3//2)
@test integrate(x^-1*(a*x^2+b*x^3)^(1/2), x) == :(2//3*b^-1*x^-3*(a*x^2+b*x^3)^3//2)
@test integrate(x^-2*(a*x^2+b*x^3)^(1/2), x) == :(-2*a^(1/2)*arctanh(x*a^(1/2)*(a*x^2+b*x^3)^-1//2)+2*x^-1*(a*x^2+b*x^3)^(1/2))
@test integrate(x^-3*(a*x^2+b*x^3)^(1/2), x) == :(-1*x^-2*(a*x^2+b*x^3)^(1/2)+-1*b*a^-1//2*arctanh(x*a^(1/2)*(a*x^2+b*x^3)^-1//2))
@test integrate(x^-4*(a*x^2+b*x^3)^(1/2), x) == :(-1//2*x^-3*(a*x^2+b*x^3)^(1/2)+1//4*a^-3//2*b^2*arctanh(x*a^(1/2)*(a*x^2+b*x^3)^-1//2)+-1//4*b*a^-1*x^-2*(a*x^2+b*x^3)^(1/2))
@test integrate(x^-5*(a*x^2+b*x^3)^(1/2), x) == :(-1//3*x^-4*(a*x^2+b*x^3)^(1/2)+-1//8*a^-5//2*b^3*arctanh(x*a^(1/2)*(a*x^2+b*x^3)^-1//2)+-1//12*b*a^-1*x^-3*(a*x^2+b*x^3)^(1/2)+1//8*a^-2*b^2*x^-2*(a*x^2+b*x^3)^(1/2))
@test integrate(x^2*(a*x^2+b*x^3)^3//2, x) == :(2//15*b^-1*(a*x^2+b*x^3)^5//2+-512//45045*a^5*b^-6*x^-5*(a*x^2+b*x^3)^5//2+-64//1287*a^3*b^-4*x^-3*(a*x^2+b*x^3)^5//2+-4//39*a*b^-2*x^-1*(a*x^2+b*x^3)^5//2+32//429*a^2*b^-3*x^-2*(a*x^2+b*x^3)^5//2+256//9009*a^4*b^-5*x^-4*(a*x^2+b*x^3)^5//2)
@test integrate(x*(a*x^2+b*x^3)^3//2, x) == :(2//13*b^-1*x^-1*(a*x^2+b*x^3)^5//2+-128//3003*a^3*b^-4*x^-4*(a*x^2+b*x^3)^5//2+-16//143*a*b^-2*x^-2*(a*x^2+b*x^3)^5//2+32//429*a^2*b^-3*x^-3*(a*x^2+b*x^3)^5//2+256//15015*a^4*b^-5*x^-5*(a*x^2+b*x^3)^5//2)
@test integrate((a*x^2+b*x^3)^3//2, x) == :(2//11*b^-1*x^-2*(a*x^2+b*x^3)^5//2+-32//1155*a^3*b^-4*x^-5*(a*x^2+b*x^3)^5//2+-4//33*a*b^-2*x^-3*(a*x^2+b*x^3)^5//2+16//231*a^2*b^-3*x^-4*(a*x^2+b*x^3)^5//2)
@test integrate(x^-1*(a*x^2+b*x^3)^3//2, x) == :(2//9*b^-1*x^-3*(a*x^2+b*x^3)^5//2+-8//63*a*b^-2*x^-4*(a*x^2+b*x^3)^5//2+16//315*a^2*b^-3*x^-5*(a*x^2+b*x^3)^5//2)
@test integrate(x^-2*(a*x^2+b*x^3)^3//2, x) == :(2//7*b^-1*x^-4*(a*x^2+b*x^3)^5//2+-4//35*a*b^-2*x^-5*(a*x^2+b*x^3)^5//2)
@test integrate(x^-3*(a*x^2+b*x^3)^3//2, x) == :(2//5*b^-1*x^-5*(a*x^2+b*x^3)^5//2)
@test integrate(x^-4*(a*x^2+b*x^3)^3//2, x) == :(-2*a^3//2*arctanh(x*a^(1/2)*(a*x^2+b*x^3)^-1//2)+2//3*x^-3*(a*x^2+b*x^3)^3//2+2*a*x^-1*(a*x^2+b*x^3)^(1/2))
@test integrate(x^-5*(a*x^2+b*x^3)^3//2, x) == :(-1*x^-4*(a*x^2+b*x^3)^3//2+-3*b*a^(1/2)*arctanh(x*a^(1/2)*(a*x^2+b*x^3)^-1//2)+3*b*x^-1*(a*x^2+b*x^3)^(1/2))
@test integrate(x^-6*(a*x^2+b*x^3)^3//2, x) == :(-1//2*x^-5*(a*x^2+b*x^3)^3//2+-3//4*b*x^-2*(a*x^2+b*x^3)^(1/2)+-3//4*a^-1//2*b^2*arctanh(x*a^(1/2)*(a*x^2+b*x^3)^-1//2))
@test integrate(x^-7*(a*x^2+b*x^3)^3//2, x) == :(-1//3*x^-6*(a*x^2+b*x^3)^3//2+-1//4*b*x^-3*(a*x^2+b*x^3)^(1/2)+1//8*a^-3//2*b^3*arctanh(x*a^(1/2)*(a*x^2+b*x^3)^-1//2)+-1//8*a^-1*b^2*x^-2*(a*x^2+b*x^3)^(1/2))
@test integrate(x^-8*(a*x^2+b*x^3)^3//2, x) == :(-1//4*x^-7*(a*x^2+b*x^3)^3//2+-3//64*a^-5//2*b^4*arctanh(x*a^(1/2)*(a*x^2+b*x^3)^-1//2)+-1//8*b*x^-4*(a*x^2+b*x^3)^(1/2)+-1//32*a^-1*b^2*x^-3*(a*x^2+b*x^3)^(1/2)+3//64*a^-2*b^3*x^-2*(a*x^2+b*x^3)^(1/2))
@test integrate(x^-9*(a*x^2+b*x^3)^3//2, x) == :(-1//5*x^-8*(a*x^2+b*x^3)^3//2+-3//40*b*x^-5*(a*x^2+b*x^3)^(1/2)+3//128*a^-7//2*b^5*arctanh(x*a^(1/2)*(a*x^2+b*x^3)^-1//2)+-3//128*a^-3*b^4*x^-2*(a*x^2+b*x^3)^(1/2)+-1//80*a^-1*b^2*x^-4*(a*x^2+b*x^3)^(1/2)+1//64*a^-2*b^3*x^-3*(a*x^2+b*x^3)^(1/2))
@test integrate(x^4*(a*x^2+b*x^3)^-1//2, x) == :(2//7*b^-1*x^2*(a*x^2+b*x^3)^(1/2)+16//35*a^2*b^-3*(a*x^2+b*x^3)^(1/2)+-32//35*a^3*b^-4*x^-1*(a*x^2+b*x^3)^(1/2)+-12//35*a*x*b^-2*(a*x^2+b*x^3)^(1/2))
@test integrate(x^3*(a*x^2+b*x^3)^-1//2, x) == :(-8//15*a*b^-2*(a*x^2+b*x^3)^(1/2)+2//5*x*b^-1*(a*x^2+b*x^3)^(1/2)+16//15*a^2*b^-3*x^-1*(a*x^2+b*x^3)^(1/2))
@test integrate(x^2*(a*x^2+b*x^3)^-1//2, x) == :(2//3*b^-1*(a*x^2+b*x^3)^(1/2)+-4//3*a*b^-2*x^-1*(a*x^2+b*x^3)^(1/2))
@test integrate(x*(a*x^2+b*x^3)^-1//2, x) == :(2*b^-1*x^-1*(a*x^2+b*x^3)^(1/2))
@test integrate((a*x^2+b*x^3)^-1//2, x) == :(-2*a^-1//2*arctanh(x*a^(1/2)*(a*x^2+b*x^3)^-1//2))
@test integrate(x^-1*(a*x^2+b*x^3)^-1//2, x) == :(b*a^-3//2*arctanh(x*a^(1/2)*(a*x^2+b*x^3)^-1//2)+-1*a^-1*x^-2*(a*x^2+b*x^3)^(1/2))
@test integrate(x^-2*(a*x^2+b*x^3)^-1//2, x) == :(-3//4*a^-5//2*b^2*arctanh(x*a^(1/2)*(a*x^2+b*x^3)^-1//2)+-1//2*a^-1*x^-3*(a*x^2+b*x^3)^(1/2)+3//4*b*a^-2*x^-2*(a*x^2+b*x^3)^(1/2))
@test integrate(x^-3*(a*x^2+b*x^3)^-1//2, x) == :(-1//3*a^-1*x^-4*(a*x^2+b*x^3)^(1/2)+5//8*a^-7//2*b^3*arctanh(x*a^(1/2)*(a*x^2+b*x^3)^-1//2)+-5//8*a^-3*b^2*x^-2*(a*x^2+b*x^3)^(1/2)+5//12*b*a^-2*x^-3*(a*x^2+b*x^3)^(1/2))
@test integrate(x^6*(a*x^2+b*x^3)^-3//2, x) == :(-2*b^-1*x^4*(a*x^2+b*x^3)^-1//2+-16//5*a*b^-3*(a*x^2+b*x^3)^(1/2)+12//5*x*b^-2*(a*x^2+b*x^3)^(1/2)+32//5*a^2*b^-4*x^-1*(a*x^2+b*x^3)^(1/2))
@test integrate(x^5*(a*x^2+b*x^3)^-3//2, x) == :(8//3*b^-2*(a*x^2+b*x^3)^(1/2)+-2*b^-1*x^3*(a*x^2+b*x^3)^-1//2+-16//3*a*b^-3*x^-1*(a*x^2+b*x^3)^(1/2))
@test integrate(x^4*(a*x^2+b*x^3)^-3//2, x) == :(-2*b^-1*x^2*(a*x^2+b*x^3)^-1//2+4*b^-2*x^-1*(a*x^2+b*x^3)^(1/2))
@test integrate(x^3*(a*x^2+b*x^3)^-3//2, x) == :(-2*x*b^-1*(a*x^2+b*x^3)^-1//2)
@test integrate(x^2*(a*x^2+b*x^3)^-3//2, x) == :(-2*a^-3//2*arctanh(x*a^(1/2)*(a*x^2+b*x^3)^-1//2)+2*x*a^-1*(a*x^2+b*x^3)^-1//2)
@test integrate(x*(a*x^2+b*x^3)^-3//2, x) == :(2*a^-1*(a*x^2+b*x^3)^-1//2+-3*a^-2*x^-2*(a*x^2+b*x^3)^(1/2)+3*b*a^-5//2*arctanh(x*a^(1/2)*(a*x^2+b*x^3)^-1//2))
@test integrate((a*x^2+b*x^3)^-3//2, x) == :(2*a^-1*x^-1*(a*x^2+b*x^3)^-1//2+-15//4*a^-7//2*b^2*arctanh(x*a^(1/2)*(a*x^2+b*x^3)^-1//2)+-5//2*a^-2*x^-3*(a*x^2+b*x^3)^(1/2)+15//4*b*a^-3*x^-2*(a*x^2+b*x^3)^(1/2))
@test integrate(x^-1*(a*x^2+b*x^3)^-3//2, x) == :(2*a^-1*x^-2*(a*x^2+b*x^3)^-1//2+-7//3*a^-2*x^-4*(a*x^2+b*x^3)^(1/2)+35//8*a^-9//2*b^3*arctanh(x*a^(1/2)*(a*x^2+b*x^3)^-1//2)+-35//8*a^-4*b^2*x^-2*(a*x^2+b*x^3)^(1/2)+35//12*b*a^-3*x^-3*(a*x^2+b*x^3)^(1/2))
@test integrate(x^-2*(a*x^2+b*x^3)^-3//2, x) == :(2*a^-1*x^-3*(a*x^2+b*x^3)^-1//2+-315//64*a^-11//2*b^4*arctanh(x*a^(1/2)*(a*x^2+b*x^3)^-1//2)+-9//4*a^-2*x^-5*(a*x^2+b*x^3)^(1/2)+-105//32*a^-4*b^2*x^-3*(a*x^2+b*x^3)^(1/2)+21//8*b*a^-3*x^-4*(a*x^2+b*x^3)^(1/2)+315//64*a^-5*b^3*x^-2*(a*x^2+b*x^3)^(1/2))
@test integrate(x^7//2*(a*x^2+b*x^3)^-1//2, x) == :(-5//8*a^3*b^-7//2*arctanh(b^(1/2)*x^3//2*(a*x^2+b*x^3)^-1//2)+1//3*b^-1*x^3//2*(a*x^2+b*x^3)^(1/2)+-5//12*a*b^-2*x^(1/2)*(a*x^2+b*x^3)^(1/2)+5//8*a^2*b^-3*x^-1//2*(a*x^2+b*x^3)^(1/2))
@test integrate(x^5//2*(a*x^2+b*x^3)^-1//2, x) == :((1/2)*b^-1*x^(1/2)*(a*x^2+b*x^3)^(1/2)+3//4*a^2*b^-5//2*arctanh(b^(1/2)*x^3//2*(a*x^2+b*x^3)^-1//2)+-3//4*a*b^-2*x^-1//2*(a*x^2+b*x^3)^(1/2))
@test integrate(x^3//2*(a*x^2+b*x^3)^-1//2, x) == :(b^-1*x^-1//2*(a*x^2+b*x^3)^(1/2)+-1*a*b^-3//2*arctanh(b^(1/2)*x^3//2*(a*x^2+b*x^3)^-1//2))
@test integrate(x^(1/2)*(a*x^2+b*x^3)^-1//2, x) == :(2*b^-1//2*arctanh(b^(1/2)*x^3//2*(a*x^2+b*x^3)^-1//2))
@test integrate(x^-1//2*(a*x^2+b*x^3)^-1//2, x) == :(-2*a^-1*x^-3//2*(a*x^2+b*x^3)^(1/2))
@test integrate(x^-3//2*(a*x^2+b*x^3)^-1//2, x) == :(-2//3*a^-1*x^-5//2*(a*x^2+b*x^3)^(1/2)+4//3*b*a^-2*x^-3//2*(a*x^2+b*x^3)^(1/2))
@test integrate(x^-5//2*(a*x^2+b*x^3)^-1//2, x) == :(-2//5*a^-1*x^-7//2*(a*x^2+b*x^3)^(1/2)+-16//15*a^-3*b^2*x^-3//2*(a*x^2+b*x^3)^(1/2)+8//15*b*a^-2*x^-5//2*(a*x^2+b*x^3)^(1/2))
@test integrate(x^-7//2*(a*x^2+b*x^3)^-1//2, x) == :(-2//7*a^-1*x^-9//2*(a*x^2+b*x^3)^(1/2)+-16//35*a^-3*b^2*x^-5//2*(a*x^2+b*x^3)^(1/2)+12//35*b*a^-2*x^-7//2*(a*x^2+b*x^3)^(1/2)+32//35*a^-4*b^3*x^-3//2*(a*x^2+b*x^3)^(1/2))
@test integrate(x^(-2+-3n)*(a*x^2+b*x^3)^n, x) == :(-1*a^-1*x^(-3+-3n)*(1+n)^-1*(a*x^2+b*x^3)^(1+n))
@test integrate(x^(-3+-3n)*(a*x^2+b*x^3)^n, x) == :(-1*a^-1*x^(-4+-3n)*(2+n)^-1*(a*x^2+b*x^3)^(1+n)+b*a^-2*x^(-3+-3n)*(1+n)^-1*(2+n)^-1*(a*x^2+b*x^3)^(1+n))
@test integrate(x^11*(a*x^2+b*x^5)^-3, x) == :(1//6*a^-1*x^6*(a+b*x^3)^-2)
@test integrate(x^9*(a*x^2+b*x^5)^-1//2, x) == :(2//15*b^-1*x^5*(a*x^2+b*x^5)^(1/2)+-8//45*a*b^-2*x^2*(a*x^2+b*x^5)^(1/2)+16//45*a^2*b^-3*x^-1*(a*x^2+b*x^5)^(1/2))
@test integrate(x^6*(a*x^2+b*x^5)^-1//2, x) == :(2//9*b^-1*x^2*(a*x^2+b*x^5)^(1/2)+-4//9*a*b^-2*x^-1*(a*x^2+b*x^5)^(1/2))
@test integrate(x^3*(a*x^2+b*x^5)^-1//2, x) == :(2//3*b^-1*x^-1*(a*x^2+b*x^5)^(1/2))
@test integrate((a*x^2+b*x^5)^-1//2, x) == :(-2//3*a^-1//2*arctanh(x*a^(1/2)*(a*x^2+b*x^5)^-1//2))
@test integrate(x^-3*(a*x^2+b*x^5)^-1//2, x) == :(-1//3*a^-1*x^-4*(a*x^2+b*x^5)^(1/2)+1//3*b*a^-3//2*arctanh(x*a^(1/2)*(a*x^2+b*x^5)^-1//2))
@test integrate(x^4*(a*x^2+b*x^5)^-1//2, x) == :(2//5*b^-1*(a*x^2+b*x^5)^(1/2)+-4//15*a*x*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*x^2+b*x^5)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(a*x^2+b*x^5)^-1//2, x) == :(2//3*x*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*x^2+b*x^5)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-2*(a*x^2+b*x^5)^-1//2, x) == :(-1//2*a^-1*x^-3*(a*x^2+b*x^5)^(1/2)+-1//6*x*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*x^2+b*x^5)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^5*(a*x^2+b*x^5)^-1//2, x) == :(2//7*x*b^-1*(a*x^2+b*x^5)^(1/2)+-8//7*a*x*b^-5//3*(a*x^2+b*x^5)^-1//2*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(a+b*x^3)+-8//21*x*2^(1/2)*3^3//4*a^4//3*b^-5//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a*x^2+b*x^5)^-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))+4//7*x*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*x^2+b*x^5)^-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*x^2+b*x^5)^-1//2, x) == :(2*x*b^-2//3*(a*x^2+b*x^5)^-1//2*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(a+b*x^3)+-1*x*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*x^2+b*x^5)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))+2//3*x*2^(1/2)*3^3//4*a^1//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a*x^2+b*x^5)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^-1*(a*x^2+b*x^5)^-1//2, x) == :(-1*a^-1*x^-2*(a*x^2+b*x^5)^(1/2)+x*a^-1*b^1//3*(a*x^2+b*x^5)^-1//2*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(a+b*x^3)+-1//2*x*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*x^2+b*x^5)^-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*x*2^(1/2)*3^3//4*a^-2//3*b^1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a*x^2+b*x^5)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x^13//2*(a*x^2+b*x^5)^-1//2, x) == :(1//5*b^-1*x^5//2*(a*x^2+b*x^5)^(1/2)+-7//20*a*b^-2*x^-1//2*(a*x^2+b*x^5)^(1/2)+7//120*3^3//4*a^5//3*b^-2*x^3//2*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a*x^2+b*x^5)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate(x^11//2*(a*x^2+b*x^5)^-1//2, x) == :(1//4*b^-1*x^3//2*(a*x^2+b*x^5)^(1/2)+-1//8*a*b^-5//3*x^3//2*(a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a*x^2+b*x^5)^-1//2*(5+5*3^(1/2))*(a+b*x^3)+5//8*3^1//4*a^4//3*b^-5//3*x^3//2*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a*x^2+b*x^5)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+1//48*3^3//4*a^4//3*b^-5//3*x^3//2*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a*x^2+b*x^5)^-1//2*(5+-5*3^(1/2))*(a^1//3+x*b^1//3)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate(x^9//2*(a*x^2+b*x^5)^-1//2, x) == :(-1//3*a*b^-3//2*arctanh(b^(1/2)*x^5//2*(a*x^2+b*x^5)^-1//2)+1//3*b^-1*x^(1/2)*(a*x^2+b*x^5)^(1/2))
@test integrate(x^7//2*(a*x^2+b*x^5)^-1//2, x) == :((1/2)*b^-1*x^-1//2*(a*x^2+b*x^5)^(1/2)+-1//12*3^3//4*a^2//3*b^-1*x^3//2*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a*x^2+b*x^5)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate(x^5//2*(a*x^2+b*x^5)^-1//2, x) == :(b^-2//3*x^3//2*(a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a*x^2+b*x^5)^-1//2*(1+3^(1/2))*(a+b*x^3)+-1*3^1//4*a^1//3*b^-2//3*x^3//2*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a*x^2+b*x^5)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-1//6*3^3//4*a^1//3*b^-2//3*x^3//2*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a*x^2+b*x^5)^-1//2*(1+-1*3^(1/2))*(a^1//3+x*b^1//3)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate(x^3//2*(a*x^2+b*x^5)^-1//2, x) == :(2//3*b^-1//2*arctanh(b^(1/2)*x^5//2*(a*x^2+b*x^5)^-1//2))
@test integrate(x^(1/2)*(a*x^2+b*x^5)^-1//2, x) == :(1//3*3^3//4*a^-1//3*x^3//2*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a*x^2+b*x^5)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate(x^-1//2*(a*x^2+b*x^5)^-1//2, x) == :(-2*a^-1*x^-3//2*(a*x^2+b*x^5)^(1/2)+a^-1*b^1//3*x^3//2*(a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a*x^2+b*x^5)^-1//2*(2+2*3^(1/2))*(a+b*x^3)+-2*3^1//4*a^-2//3*b^1//3*x^3//2*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a*x^2+b*x^5)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-1//3*3^3//4*a^-2//3*b^1//3*x^3//2*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a*x^2+b*x^5)^-1//2*(1+-1*3^(1/2))*(a^1//3+x*b^1//3)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate(x^-3//2*(a*x^2+b*x^5)^-1//2, x) == :(-2//3*a^-1*x^-5//2*(a*x^2+b*x^5)^(1/2))
@test integrate(x^-5//2*(a*x^2+b*x^5)^-1//2, x) == :(-2//5*a^-1*x^-7//2*(a*x^2+b*x^5)^(1/2)+-2//15*b*3^3//4*a^-4//3*x^3//2*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a*x^2+b*x^5)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate(x^-7//2*(a*x^2+b*x^5)^-1//2, x) == :(-2//7*a^-1*x^-9//2*(a*x^2+b*x^5)^(1/2)+8//7*b*a^-2*x^-3//2*(a*x^2+b*x^5)^(1/2)+-1//7*a^-2*b^4//3*x^3//2*(a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a*x^2+b*x^5)^-1//2*(8+8*3^(1/2))*(a+b*x^3)+8//7*3^1//4*a^-5//3*b^4//3*x^3//2*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a*x^2+b*x^5)^-1//2*(a^1//3+x*b^1//3)*Elliptic.E(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+1//21*3^3//4*a^-5//3*b^4//3*x^3//2*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a*x^2+b*x^5)^-1//2*(4+-4*3^(1/2))*(a^1//3+x*b^1//3)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate(x^-9//2*(a*x^2+b*x^5)^-1//2, x) == :(-2//9*a^-1*x^-11//2*(a*x^2+b*x^5)^(1/2)+4//9*b*a^-2*x^-5//2*(a*x^2+b*x^5)^(1/2))
@test integrate(x^-11//2*(a*x^2+b*x^5)^-1//2, x) == :(-2//11*a^-1*x^-13//2*(a*x^2+b*x^5)^(1/2)+16//55*b*a^-2*x^-7//2*(a*x^2+b*x^5)^(1/2)+16//165*3^3//4*a^-7//3*b^2*x^3//2*((a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(x*b^1//3*(a^1//3+x*b^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(a*x^2+b*x^5)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arccos((a^1//3+x*b^1//3*(1+3^(1/2)))^-1*(a^1//3+x*b^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate(x*(a*x^3+b*x^4)^-1, x) == :(-1*a^-1*x^-1+b*a^-2*log(a+b*x)+-1*b*a^-2*log(x))
@test integrate((a*x^3+b*x^4)^-1, x) == :(-1//2*a^-1*x^-2+b*a^-2*x^-1+a^-3*b^2*log(x)+-1*a^-3*b^2*log(a+b*x))
@test integrate(x^4*(a*x^3+b*x^4)^-1//2, x) == :(-5//8*a^3*b^-7//2*arctanh(b^(1/2)*x^2*(a*x^3+b*x^4)^-1//2)+-5//12*a*b^-2*(a*x^3+b*x^4)^(1/2)+1//3*x*b^-1*(a*x^3+b*x^4)^(1/2)+5//8*a^2*b^-3*x^-1*(a*x^3+b*x^4)^(1/2))
@test integrate(x^3*(a*x^3+b*x^4)^-1//2, x) == :((1/2)*b^-1*(a*x^3+b*x^4)^(1/2)+3//4*a^2*b^-5//2*arctanh(b^(1/2)*x^2*(a*x^3+b*x^4)^-1//2)+-3//4*a*b^-2*x^-1*(a*x^3+b*x^4)^(1/2))
@test integrate(x^2*(a*x^3+b*x^4)^-1//2, x) == :(b^-1*x^-1*(a*x^3+b*x^4)^(1/2)+-1*a*b^-3//2*arctanh(b^(1/2)*x^2*(a*x^3+b*x^4)^-1//2))
@test integrate(x*(a*x^3+b*x^4)^-1//2, x) == :(2*b^-1//2*arctanh(b^(1/2)*x^2*(a*x^3+b*x^4)^-1//2))
@test integrate((a*x^3+b*x^4)^-1//2, x) == :(-2*a^-1*x^-2*(a*x^3+b*x^4)^(1/2))
@test integrate(x^-1*(a*x^3+b*x^4)^-1//2, x) == :(-2//3*a^-1*x^-3*(a*x^3+b*x^4)^(1/2)+4//3*b*a^-2*x^-2*(a*x^3+b*x^4)^(1/2))
@test integrate(x^-2*(a*x^3+b*x^4)^-1//2, x) == :(-2//5*a^-1*x^-4*(a*x^3+b*x^4)^(1/2)+-16//15*a^-3*b^2*x^-2*(a*x^3+b*x^4)^(1/2)+8//15*b*a^-2*x^-3*(a*x^3+b*x^4)^(1/2))
@test integrate(x^-3*(a*x^3+b*x^4)^-1//2, x) == :(-2//7*a^-1*x^-5*(a*x^3+b*x^4)^(1/2)+-16//35*a^-3*b^2*x^-3*(a*x^3+b*x^4)^(1/2)+12//35*b*a^-2*x^-4*(a*x^3+b*x^4)^(1/2)+32//35*a^-4*b^3*x^-2*(a*x^3+b*x^4)^(1/2))
@test integrate(x^-4*(a*x^3+b*x^4)^-1//2, x) == :(-2//9*a^-1*x^-6*(a*x^3+b*x^4)^(1/2)+-256//315*a^-5*b^4*x^-2*(a*x^3+b*x^4)^(1/2)+-32//105*a^-3*b^2*x^-4*(a*x^3+b*x^4)^(1/2)+16//63*b*a^-2*x^-5*(a*x^3+b*x^4)^(1/2)+128//315*a^-4*b^3*x^-3*(a*x^3+b*x^4)^(1/2))
@test integrate((x^3+b*x^5)^-1, x) == :(-1//2*x^-2+(1/2)*b*log(1+b*x^2)+-1*b*log(x))
@test integrate((-1*x^3+b*x^5)^-1, x) == :((1/2)*x^-2+(1/2)*b*log(1+-1*b*x^2)+-1*b*log(x))
@test integrate((a*x+b*x)^-1, x) == :((a+b)^-1*log(x))
@test integrate((a*x+b*x)^-2, x) == :(-1*x^-1*(a+b)^-2)
@test integrate((a*x+b*x)^-3, x) == :(-1//2*x^-2*(a+b)^-3)
@test integrate((a*x^2+b*x^2)^-1, x) == :(-1*x^-1*(a+b)^-1)
@test integrate((a*x^n+b*x^n)^-1, x) == :(x^(1+-1n)*(1+-1n)^-1*(a+b)^-1)
@test integrate((a*x^n+b*x^n)^-2, x) == :(x^(1+-2n)*(1+-2n)^-1*(a+b)^-2)
@test integrate((a*x^n+b*x^n)^-3, x) == :(x^(1+-3n)*(1+-3n)^-1*(a+b)^-3)
@test integrate((a*x+b*x^14)^12, x) == :(1//169*b^-1*(a+b*x^13)^13)
@test integrate(x^12*(a*x+b*x^26)^12, x) == :(1//325*b^-1*(a+b*x^25)^13)
@test integrate(x^24*(a*x+b*x^38)^12, x) == :(1//481*b^-1*(a+b*x^37)^13)
@test integrate(x^(-12+12m)*(a*x+b*x^(2+12m))^12, x) == :(1//13*b^-1*(1+12m)^-1*(a+b*x^(1+12m))^13)
@test integrate((a*x+b*x^14)^12, x) == :(1//169*b^-1*(a+b*x^13)^13)
@test integrate((a*x^2+b*x^27)^12, x) == :(1//325*b^-1*(a+b*x^25)^13)
@test integrate((a*x^3+b*x^40)^12, x) == :(1//481*b^-1*(a+b*x^37)^13)
@test integrate((a*x^m+b*x^(1+13m))^12, x) == :(1//13*b^-1*(1+12m)^-1*(a+b*x^(1+12m))^13)
@test integrate((a*x^m+b*x^(1+6m))^5, x) == :(1//6*b^-1*(1+5m)^-1*(a+b*x^(1+5m))^6)
@test integrate((a*x^m+b*x^(1+-2m))^-3, x) == :(-1//2*b^-1*(1+-3m)^-1*(a+b*x^(1+-3m))^-2)
@test integrate((a*x+b*x^-1)^-1, x) == :((1/2)*a^-1*log(b+a*x^2))
@test integrate((a*x+b*x^-2)^-1, x) == :(1//3*a^-1*log(b+a*x^3))
@test integrate((a*x+b*x^-3)^-1, x) == :(1//4*a^-1*log(b+a*x^4))
@test integrate((a*x+b*x^-1)^-3, x) == :(1//4*b^-1*x^4*(b+a*x^2)^-2)
@test integrate((a*x^2+b*x^-3)^-3, x) == :(1//10*b^-1*x^10*(b+a*x^5)^-2)
@test integrate((a*x^3+b*x^-5)^-3, x) == :(1//16*b^-1*x^16*(b+a*x^8)^-2)
@test integrate((a*x^-1+b*x)^2, x) == :(-1*a^2*x^-1+1//3*b^2*x^3+2*a*b*x)
@test integrate((a*x^-1+b*x)^3, x) == :(-1//2*a^3*x^-2+1//4*b^3*x^4+3*b*a^2*log(x)+3//2*a*b^2*x^2)
@test integrate((a*x^-1+b*x)^4, x) == :(-1//3*a^4*x^-3+1//5*b^4*x^5+-4*b*a^3*x^-1+6*x*a^2*b^2+4//3*a*b^3*x^3)
@test integrate((x^-2+x^3)^-1, x) == :(1//5*log(1+x)+-1*(1//20+-1//20*5^(1/2))*log(1+x^2+-1*x*(1/2+(1/2)*5^(1/2)))+-1*(1//20+1//20*5^(1/2))*log(1+x^2+-1*x*(1/2+-1//2*5^(1/2)))+-1//5*(5//2+(1/2)*5^(1/2))^(1/2)*arctan((1+2//5*5^(1/2))^(1/2)+-1*x*(2+2//5*5^(1/2))^(1/2))+-1//5*(5//2+-1//2*5^(1/2))^(1/2)*arctan((1+-2//5*5^(1/2))^(1/2)+2*x*2^(1/2)*(5+5^(1/2))^-1//2))
@test integrate(x^p*(a*x^n+b*x^(1+p+13n))^12, x) == :(1//13*b^-1*(a+b*x^(1+p+12n))^13*(1+p+12n)^-1)
@test integrate(x^12*(a+b*x^13)^12, x) == :(1//169*b^-1*(a+b*x^13)^13)
@test integrate(x^12*(a*x+b*x^26)^12, x) == :(1//325*b^-1*(a+b*x^25)^13)
@test integrate(x^12*(a*x^2+b*x^39)^12, x) == :(1//481*b^-1*(a+b*x^37)^13)
@test integrate(x^24*(a+b*x^25)^12, x) == :(1//325*b^-1*(a+b*x^25)^13)
@test integrate(x^24*(a*x+b*x^38)^12, x) == :(1//481*b^-1*(a+b*x^37)^13)
@test integrate(x^36*(a+b*x^37)^12, x) == :(1//481*b^-1*(a+b*x^37)^13)
@test integrate((a*x+b*x^n)^-1, x) == :(a^-1*(1+-1n)^-1*log(b+a*x^(1+-1n)))
@test integrate((a*x+b*x^(1+n))^-1, x) == :(a^-1*log(x)+-1*a^-1*n^-1*log(a+b*x^n))
@test integrate((a*x+b*x^(1+-1n))^-1, x) == :(a^-1*n^-1*log(b+a*x^n))
@test integrate((2x+3*x^(1+n))^-1, x) == :((1/2)*log(x)+-1//2*n^-1*log(2+3*x^n))
@test integrate((2x+3*x^(1+-1n))^-1, x) == :((1/2)*n^-1*log(3+2*x^n))
@test integrate((x+-1*x^(1/2))^-1, x) == :(2*log(1+-1*x^(1/2)))
@test integrate((x+-1*x^3//5)^-1, x) == :(5//2*log(1+-1*x^2//5))
@test integrate((x+x^-1//3)^-1, x) == :(3//4*log(1+x^4//3))
@test integrate((x+x^(2^(1/2)))^-1, x) == :(-1*(1+2^(1/2))*log(1+x^(-1+2^(1/2)))+log(x))
@test integrate(x^(-1+-1//2*j)*(a*x^j+b*x^n)^(1/2), x) == :(-2*x^(-1//2*j)*(j+-1n)^-1*(a*x^j+b*x^n)^(1/2)+2*a^(1/2)*(j+-1n)^-1*arctanh(a^(1/2)*x^((1/2)*j)*(a*x^j+b*x^n)^-1//2))
@test integrate((c*x)^(-1+-1//2*j)*(a*x^j+b*x^n)^(1/2), x) == :(-2*c^-1*(c*x)^(-1//2*j)*(j+-1n)^-1*(a*x^j+b*x^n)^(1/2)+2*a^(1/2)*c^-1*x^((1/2)*j)*(c*x)^(-1//2*j)*(j+-1n)^-1*arctanh(a^(1/2)*x^((1/2)*j)*(a*x^j+b*x^n)^-1//2))
@test integrate((c*x)^-5//2*(a*x^3+b*x^n)^(1/2), x) == :(-2*c^-1*(c*x)^-3//2*(3+-1n)^-1*(a*x^3+b*x^n)^(1/2)+2*a^(1/2)*c^-3*x^-1//2*(c*x)^(1/2)*(3+-1n)^-1*arctanh(a^(1/2)*x^3//2*(a*x^3+b*x^n)^-1//2))
@test integrate(c^-2*x^-2*(a*x^2+b*x^n)^(1/2), x) == :(-2*c^-2*x^-1*(2+-1n)^-1*(a*x^2+b*x^n)^(1/2)+2*a^(1/2)*c^-2*(2+-1n)^-1*arctanh(x*a^(1/2)*(a*x^2+b*x^n)^-1//2))
@test integrate((c*x)^-3//2*(a*x+b*x^n)^(1/2), x) == :(-2*c^-1*(c*x)^-1//2*(1+-1n)^-1*(a*x+b*x^n)^(1/2)+2*a^(1/2)*c^-1*x^(1/2)*(c*x)^-1//2*(1+-1n)^-1*arctanh(a^(1/2)*x^(1/2)*(a*x+b*x^n)^-1//2))
@test integrate(c^-1*x^-1*(a+b*x^n)^(1/2), x) == :(2*c^-1*n^-1*(a+b*x^n)^(1/2)+-2*a^(1/2)*c^-1*n^-1*arctanh(a^-1//2*(a+b*x^n)^(1/2)))
@test integrate((c*x)^-1//2*(a*x^-1+b*x^n)^(1/2), x) == :(2*c^-1*(c*x)^(1/2)*(1+n)^-1*(a*x^-1+b*x^n)^(1/2)+-2*a^(1/2)*x^(1/2)*(c*x)^-1//2*(1+n)^-1*arctanh(a^(1/2)*x^-1//2*(a*x^-1+b*x^n)^-1//2))
@test integrate((a*x^-2+b*x^n)^(1/2), x) == :(-2*a^(1/2)*(2+n)^-1*arctanh(a^(1/2)*x^-1*(a*x^-2+b*x^n)^-1//2)+2*x*(2+n)^-1*(a*x^-2+b*x^n)^(1/2))
@test integrate((c*x)^(1/2)*(a*x^-3+b*x^n)^(1/2), x) == :(2*c^-1*(c*x)^3//2*(3+n)^-1*(a*x^-3+b*x^n)^(1/2)+-2*c*a^(1/2)*x^(1/2)*(c*x)^-1//2*(3+n)^-1*arctanh(a^(1/2)*x^-3//2*(a*x^-3+b*x^n)^-1//2))
@test integrate((c*x)^(-1+-3//2*j)*(a*x^j+b*x^n)^3//2, x) == :(-2//3*c^-1*(c*x)^(-3//2*j)*(j+-1n)^-1*(a*x^j+b*x^n)^3//2+-2*a*c^-1*x^j*(c*x)^(-3//2*j)*(j+-1n)^-1*(a*x^j+b*x^n)^(1/2)+2*a^3//2*c^-1*x^(3//2*j)*(c*x)^(-3//2*j)*(j+-1n)^-1*arctanh(a^(1/2)*x^((1/2)*j)*(a*x^j+b*x^n)^-1//2))
@test integrate((c*x)^-11//2*(a*x^3+b*x^n)^3//2, x) == :(-2//3*c^-1*(c*x)^-9//2*(3+-1n)^-1*(a*x^3+b*x^n)^3//2+-2*a*c^-4*(c*x)^-3//2*(3+-1n)^-1*(a*x^3+b*x^n)^(1/2)+2*a^3//2*c^-6*x^-1//2*(c*x)^(1/2)*(3+-1n)^-1*arctanh(a^(1/2)*x^3//2*(a*x^3+b*x^n)^-1//2))
@test integrate(c^-4*x^-4*(a*x^2+b*x^n)^3//2, x) == :(2*a^3//2*c^-4*(2+-1n)^-1*arctanh(x*a^(1/2)*(a*x^2+b*x^n)^-1//2)+-2//3*c^-4*x^-3*(2+-1n)^-1*(a*x^2+b*x^n)^3//2+-2*a*c^-4*x^-1*(2+-1n)^-1*(a*x^2+b*x^n)^(1/2))
@test integrate((c*x)^-5//2*(a*x+b*x^n)^3//2, x) == :(-2//3*c^-1*(c*x)^-3//2*(1+-1n)^-1*(a*x+b*x^n)^3//2+-2*a*c^-2*(c*x)^-1//2*(1+-1n)^-1*(a*x+b*x^n)^(1/2)+2*a^3//2*c^-2*x^(1/2)*(c*x)^-1//2*(1+-1n)^-1*arctanh(a^(1/2)*x^(1/2)*(a*x+b*x^n)^-1//2))
@test integrate(c^-1*x^-1*(a+b*x^n)^3//2, x) == :(2//3*c^-1*n^-1*(a+b*x^n)^3//2+-2*a^3//2*c^-1*n^-1*arctanh(a^-1//2*(a+b*x^n)^(1/2))+2*a*c^-1*n^-1*(a+b*x^n)^(1/2))
@test integrate((c*x)^(1/2)*(a*x^-1+b*x^n)^3//2, x) == :(2*a*(c*x)^(1/2)*(1+n)^-1*(a*x^-1+b*x^n)^(1/2)+2//3*c^-1*(c*x)^3//2*(1+n)^-1*(a*x^-1+b*x^n)^3//2+-2*c*a^3//2*x^(1/2)*(c*x)^-1//2*(1+n)^-1*arctanh(a^(1/2)*x^-1//2*(a*x^-1+b*x^n)^-1//2))
@test integrate(c^2*x^2*(a*x^-2+b*x^n)^3//2, x) == :(-2*a^3//2*c^2*(2+n)^-1*arctanh(a^(1/2)*x^-1*(a*x^-2+b*x^n)^-1//2)+2*c^2*x^3*(6+3n)^-1*(a*x^-2+b*x^n)^3//2+2*a*x*c^2*(2+n)^-1*(a*x^-2+b*x^n)^(1/2))
@test integrate((c*x)^7//2*(a*x^-3+b*x^n)^3//2, x) == :(2//3*c^-1*(c*x)^9//2*(3+n)^-1*(a*x^-3+b*x^n)^3//2+2*a*c^2*(c*x)^3//2*(3+n)^-1*(a*x^-3+b*x^n)^(1/2)+-2*a^3//2*c^4*x^(1/2)*(c*x)^-1//2*(3+n)^-1*arctanh(a^(1/2)*x^-3//2*(a*x^-3+b*x^n)^-1//2))
@test integrate(c^5*x^5*(a*x^-4+b*x^n)^3//2, x) == :(-2*a^3//2*c^5*(4+n)^-1*arctanh(a^(1/2)*x^-2*(a*x^-4+b*x^n)^-1//2)+2*c^5*x^6*(12+3n)^-1*(a*x^-4+b*x^n)^3//2+2*a*c^5*x^2*(4+n)^-1*(a*x^-4+b*x^n)^(1/2))
@test integrate((x^-2*(a+b*x))^(1/2), x) == :(-2*a^(1/2)*arctanh(a^(1/2)*x^-1*(a*x^-2+b*x^-1)^-1//2)+2*x*(a*x^-2+b*x^-1)^(1/2))
@test integrate((x^-2*(a+b*x^2))^(1/2), x) == :(x*(b+a*x^-2)^(1/2)+-1*a^(1/2)*arctanh(a^(1/2)*x^-1*(b+a*x^-2)^-1//2))
@test integrate((x^-2*(a+b*x^3))^(1/2), x) == :(-2//3*a^(1/2)*arctanh(a^(1/2)*x^-1*(a*x^-2+b*x)^-1//2)+2//3*x*(a*x^-2+b*x)^(1/2))
@test integrate((x^-2*(a+b*x^n))^(1/2), x) == :(-2*a^(1/2)*n^-1*arctanh(a^(1/2)*x^-1*(a*x^-2+b*x^(-2+n))^-1//2)+2*x*n^-1*(a*x^-2+b*x^(-2+n))^(1/2))
@test integrate((x^-2*(-1a+b*x))^(1/2), x) == :(2*x*(b*x^-1+-1*a*x^-2)^(1/2)+2*a^(1/2)*arctan(a^(1/2)*x^-1*(b*x^-1+-1*a*x^-2)^-1//2))
@test integrate((x^-2*(-1a+b*x^2))^(1/2), x) == :(x*(b+-1*a*x^-2)^(1/2)+a^(1/2)*arctan(a^(1/2)*x^-1*(b+-1*a*x^-2)^-1//2))
@test integrate((x^-2*(-1a+b*x^3))^(1/2), x) == :(2//3*x*(b*x+-1*a*x^-2)^(1/2)+2//3*a^(1/2)*arctan(a^(1/2)*x^-1*(b*x+-1*a*x^-2)^-1//2))
@test integrate((x^-2*(-1a+b*x^n))^(1/2), x) == :(2*x*n^-1*(b*x^(-2+n)+-1*a*x^-2)^(1/2)+2*a^(1/2)*n^-1*arctan(a^(1/2)*x^-1*(b*x^(-2+n)+-1*a*x^-2)^-1//2))
@test integrate((c*x)^(-1+(1/2)*j)*(a*x^j+b*x^n)^-1//2, x) == :(2*a^-1//2*c^-1*x^(-1//2*j)*(c*x)^((1/2)*j)*(j+-1n)^-1*arctanh(a^(1/2)*x^((1/2)*j)*(a*x^j+b*x^n)^-1//2))
@test integrate((c*x)^(1/2)*(a*x^3+b*x^n)^-1//2, x) == :(2*a^-1//2*x^-1//2*(c*x)^(1/2)*(3+-1n)^-1*arctanh(a^(1/2)*x^3//2*(a*x^3+b*x^n)^-1//2))
@test integrate((a*x^2+b*x^n)^-1//2, x) == :(2*a^-1//2*(2+-1n)^-1*arctanh(x*a^(1/2)*(a*x^2+b*x^n)^-1//2))
@test integrate((c*x)^-1//2*(a*x+b*x^n)^-1//2, x) == :(2*a^-1//2*x^(1/2)*(c*x)^-1//2*(1+-1n)^-1*arctanh(a^(1/2)*x^(1/2)*(a*x+b*x^n)^-1//2))
@test integrate(c^-1*x^-1*(a+b*x^n)^-1//2, x) == :(-2*a^-1//2*c^-1*n^-1*arctanh(a^-1//2*(a+b*x^n)^(1/2)))
@test integrate((c*x)^-3//2*(a*x^-1+b*x^n)^-1//2, x) == :(-2*a^-1//2*c^-1*x^(1/2)*(c*x)^-1//2*(1+n)^-1*arctanh(a^(1/2)*x^-1//2*(a*x^-1+b*x^n)^-1//2))
@test integrate(c^-2*x^-2*(a*x^-2+b*x^n)^-1//2, x) == :(-2*a^-1//2*c^-2*(2+n)^-1*arctanh(a^(1/2)*x^-1*(a*x^-2+b*x^n)^-1//2))
@test integrate((c*x)^-5//2*(a*x^-3+b*x^n)^-1//2, x) == :(-2*a^-1//2*c^-2*x^(1/2)*(c*x)^-1//2*(3+n)^-1*arctanh(a^(1/2)*x^-3//2*(a*x^-3+b*x^n)^-1//2))
@test integrate((c*x)^(-1+3//2*j)*(a*x^j+b*x^n)^-3//2, x) == :(-2*a^-1*c^-1*x^(-1j)*(c*x)^(3//2*j)*(j+-1n)^-1*(a*x^j+b*x^n)^-1//2+2*a^-3//2*c^-1*x^(-3//2*j)*(c*x)^(3//2*j)*(j+-1n)^-1*arctanh(a^(1/2)*x^((1/2)*j)*(a*x^j+b*x^n)^-1//2))
@test integrate((c*x)^7//2*(a*x^3+b*x^n)^-3//2, x) == :(-2*a^-1*c^2*(c*x)^3//2*(3+-1n)^-1*(a*x^3+b*x^n)^-1//2+2*a^-3//2*c^3*x^-1//2*(c*x)^(1/2)*(3+-1n)^-1*arctanh(a^(1/2)*x^3//2*(a*x^3+b*x^n)^-1//2))
@test integrate(c^2*x^2*(a*x^2+b*x^n)^-3//2, x) == :(2*a^-3//2*c^2*(2+-1n)^-1*arctanh(x*a^(1/2)*(a*x^2+b*x^n)^-1//2)+-2*x*a^-1*c^2*(2+-1n)^-1*(a*x^2+b*x^n)^-1//2)
@test integrate((c*x)^(1/2)*(a*x+b*x^n)^-3//2, x) == :(-2*a^-1*(c*x)^(1/2)*(1+-1n)^-1*(a*x+b*x^n)^-1//2+2*c*a^-3//2*x^(1/2)*(c*x)^-1//2*(1+-1n)^-1*arctanh(a^(1/2)*x^(1/2)*(a*x+b*x^n)^-1//2))
@test integrate(c^-1*x^-1*(a+b*x^n)^-3//2, x) == :(-2*a^-3//2*c^-1*n^-1*arctanh(a^-1//2*(a+b*x^n)^(1/2))+2*a^-1*c^-1*n^-1*(a+b*x^n)^-1//2)
@test integrate((c*x)^-5//2*(a*x^-1+b*x^n)^-3//2, x) == :(2*a^-1*c^-2*(c*x)^-1//2*(1+n)^-1*(a*x^-1+b*x^n)^-1//2+-2*a^-3//2*c^-2*x^(1/2)*(c*x)^-1//2*(1+n)^-1*arctanh(a^(1/2)*x^-1//2*(a*x^-1+b*x^n)^-1//2))
@test integrate(c^-4*x^-4*(a*x^-2+b*x^n)^-3//2, x) == :(-2*a^-3//2*c^-4*(2+n)^-1*arctanh(a^(1/2)*x^-1*(a*x^-2+b*x^n)^-1//2)+2*a^-1*c^-4*x^-1*(2+n)^-1*(a*x^-2+b*x^n)^-1//2)
@test integrate((c*x)^-11//2*(a*x^-3+b*x^n)^-3//2, x) == :(2*a^-1*c^-4*(c*x)^-3//2*(3+n)^-1*(a*x^-3+b*x^n)^-1//2+-2*a^-3//2*c^-5*x^(1/2)*(c*x)^-1//2*(3+n)^-1*arctanh(a^(1/2)*x^-3//2*(a*x^-3+b*x^n)^-1//2))
@test integrate(c^-7*x^-7*(a*x^-4+b*x^n)^-3//2, x) == :(-2*a^-3//2*c^-7*(4+n)^-1*arctanh(a^(1/2)*x^-2*(a*x^-4+b*x^n)^-1//2)+2*a^-1*c^-7*x^-2*(4+n)^-1*(a*x^-4+b*x^n)^-1//2)
@test integrate((x^-1*(a+b*x^3))^-1//2, x) == :(2//3*b^-1//2*arctanh(x*b^(1/2)*(a*x^-1+b*x^2)^-1//2))
@test integrate((x^-2*(a+b*x^4))^-1//2, x) == :((1/2)*b^-1//2*arctanh(x*b^(1/2)*(a*x^-2+b*x^2)^-1//2))
@test integrate((x^-3*(a+b*x^5))^-1//2, x) == :(2//5*b^-1//2*arctanh(x*b^(1/2)*(a*x^-3+b*x^2)^-1//2))
@test integrate((x^(2+-1n)*(a+b*x^n))^-1//2, x) == :(2*b^-1//2*n^-1*arctanh(x*b^(1/2)*(a*x^(2+-1n)+b*x^2)^-1//2))
@test integrate((x^-1*(a+-1*b*x^3))^-1//2, x) == :(2//3*b^-1//2*arctan(x*b^(1/2)*(a*x^-1+-1*b*x^2)^-1//2))
@test integrate((x^-2*(a+-1*b*x^4))^-1//2, x) == :((1/2)*b^-1//2*arctan(x*b^(1/2)*(a*x^-2+-1*b*x^2)^-1//2))
@test integrate((x^-3*(a+-1*b*x^5))^-1//2, x) == :(2//5*b^-1//2*arctan(x*b^(1/2)*(a*x^-3+-1*b*x^2)^-1//2))
@test integrate((x^(2+-1n)*(a+-1*b*x^n))^-1//2, x) == :(2*b^-1//2*n^-1*arctan(x*b^(1/2)*(a*x^(2+-1n)+-1*b*x^2)^-1//2))
@test integrate((x^n*(a+b*x^(2+-1n)))^-1//2, x) == :(2*b^-1//2*(2+-1n)^-1*arctanh(x*b^(1/2)*(a*x^n+b*x^2)^-1//2))
@test integrate((x^2*(b+a*x^(-2+n)))^-1//2, x) == :(2*b^-1//2*(2+-1n)^-1*arctanh(x*b^(1/2)*(a*x^n+b*x^2)^-1//2))
@test integrate((x*(a*x^(-1+n)+b*x))^-1//2, x) == :(2*b^-1//2*(2+-1n)^-1*arctanh(x*b^(1/2)*(a*x^n+b*x^2)^-1//2))
@test integrate((x^n*(a+-1*b*x^(2+-1n)))^-1//2, x) == :(2*b^-1//2*(2+-1n)^-1*arctan(x*b^(1/2)*(a*x^n+-1*b*x^2)^-1//2))
@test integrate((x^2*(-1b+a*x^(-2+n)))^-1//2, x) == :(2*b^-1//2*(2+-1n)^-1*arctan(x*b^(1/2)*(a*x^n+-1*b*x^2)^-1//2))
@test integrate((x*(a*x^(-1+n)+-1*b*x))^-1//2, x) == :(2*b^-1//2*(2+-1n)^-1*arctan(x*b^(1/2)*(a*x^n+-1*b*x^2)^-1//2))
@test integrate((x^-5*(1+x))^(1/2), x) == :(-2//3*x^6*(x^-5+x^-4)^3//2)
@test integrate((x+x^5//2)^(1/2), x) == :(4//9*x^-3//2*(x+x^5//2)^3//2)
@test integrate((x^(1/2)+x^3//2)^-1, x) == :(2*arctan(x^(1/2)))
@test integrate(x*(x^2*(a+b*x^3))^(1/2), x) == :(2//9*b^-1*x^-3*(x^2*(a+b*x^3))^3//2)
@test integrate(x*(a*x^2+b*x^5)^(1/2), x) == :(2//9*b^-1*x^-3*(a*x^2+b*x^5)^3//2)
@test integrate((x^4*(a+b*x^3))^(1/2), x) == :(2//9*b^-1*x^-6*(a*x^4+b*x^7)^3//2)
@test integrate((a*x^1//3+b*x^2//3)^-1//3, x) == :(1//7*b^-1*x^2//3*(a*x^1//3+b*x^2//3)^-1//3*(9a+9*b*x^1//3)+-45//28*a*b^-2*x^1//3*(a*x^1//3+b*x^2//3)^-1//3*(a+b*x^1//3)+-45//28*2^2//3*a^2*b^-3*(-1*b*a^-2*(a*x^1//3+b*x^2//3))^1//3*(a*x^1//3+b*x^2//3)^-1//3*(1+-1*3^(1/2)+-1*2^2//3*(-1*b*a^-2*x^1//3*(a+b*x^1//3))^1//3)^-1*(a+2*b*x^1//3)+15//14*2^1//6*3^3//4*a^4*b^-3*((1+-1*3^(1/2)+-1*2^2//3*(-1*b*a^-2*x^1//3*(a+b*x^1//3))^1//3)^-2*(1+2^2//3*(-1*b*a^-2*x^1//3*(a+b*x^1//3))^1//3+2*2^1//3*(-1*b*a^-2*x^1//3*(a+b*x^1//3))^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*2^2//3*(-1*b*a^-2*x^1//3*(a+b*x^1//3))^1//3)^-2*(1+-1*2^2//3*(-1*b*a^-2*x^1//3*(a+b*x^1//3))^1//3))^-1//2*(-1*b*a^-2*(a*x^1//3+b*x^2//3))^1//3*(a+2*b*x^1//3)^-1*(a*x^1//3+b*x^2//3)^-1//3*(1+-1*2^2//3*(-1*b*a^-2*x^1//3*(a+b*x^1//3))^1//3)*Elliptic.F(arcsin((1+-1*3^(1/2)+-1*2^2//3*(-1*b*a^-2*x^1//3*(a+b*x^1//3))^1//3)^-1*(1+3^(1/2)+-1*2^2//3*(-1*b*a^-2*x^1//3*(a+b*x^1//3))^1//3)),-7+4*3^(1/2))+-45//56*2^2//3*3^1//4*a^4*b^-3*((1+-1*3^(1/2)+-1*2^2//3*(-1*b*a^-2*x^1//3*(a+b*x^1//3))^1//3)^-2*(1+2^2//3*(-1*b*a^-2*x^1//3*(a+b*x^1//3))^1//3+2*2^1//3*(-1*b*a^-2*x^1//3*(a+b*x^1//3))^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*2^2//3*(-1*b*a^-2*x^1//3*(a+b*x^1//3))^1//3)^-2*(1+-1*2^2//3*(-1*b*a^-2*x^1//3*(a+b*x^1//3))^1//3))^-1//2*(-1*b*a^-2*(a*x^1//3+b*x^2//3))^1//3*(2+3^(1/2))^(1/2)*(a+2*b*x^1//3)^-1*(a*x^1//3+b*x^2//3)^-1//3*(1+-1*2^2//3*(-1*b*a^-2*x^1//3*(a+b*x^1//3))^1//3)*Elliptic.E(arcsin((1+-1*3^(1/2)+-1*2^2//3*(-1*b*a^-2*x^1//3*(a+b*x^1//3))^1//3)^-1*(1+3^(1/2)+-1*2^2//3*(-1*b*a^-2*x^1//3*(a+b*x^1//3))^1//3)),-7+4*3^(1/2)))
@test integrate((a*x^1//3+b*x^2//3)^-2//3, x) == :(1//5*b^-1*x^2//3*(a*x^1//3+b*x^2//3)^-2//3*(9a+9*b*x^1//3)+-18//5*a*b^-2*x^1//3*(a*x^1//3+b*x^2//3)^-2//3*(a+b*x^1//3)+6//5*2^1//3*3^3//4*a^4*b^-3*((1+-1*3^(1/2)+-1*2^2//3*(-1*b*a^-2*x^1//3*(a+b*x^1//3))^1//3)^-2*(1+2^2//3*(-1*b*a^-2*x^1//3*(a+b*x^1//3))^1//3+2*2^1//3*(-1*b*a^-2*x^1//3*(a+b*x^1//3))^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*2^2//3*(-1*b*a^-2*x^1//3*(a+b*x^1//3))^1//3)^-2*(1+-1*2^2//3*(-1*b*a^-2*x^1//3*(a+b*x^1//3))^1//3))^-1//2*(-1*b*a^-2*(a*x^1//3+b*x^2//3))^2//3*(2+-1*3^(1/2))^(1/2)*(a+2*b*x^1//3)^-1*(a*x^1//3+b*x^2//3)^-2//3*(1+-1*2^2//3*(-1*b*a^-2*x^1//3*(a+b*x^1//3))^1//3)*Elliptic.F(arcsin((1+-1*3^(1/2)+-1*2^2//3*(-1*b*a^-2*x^1//3*(a+b*x^1//3))^1//3)^-1*(1+3^(1/2)+-1*2^2//3*(-1*b*a^-2*x^1//3*(a+b*x^1//3))^1//3)),-7+4*3^(1/2)))
@test integrate((a*x^m+b*x^(1+m+m*p))^p, x) == :(b^-1*x^(-1*m*(1+p))*(1+p)^-1*(1+m*p)^-1*(a*x^m+b*x^(1+m+m*p))^(1+p))
@test integrate((x^m*(a+b*x^(1+m*p)))^p, x) == :(b^-1*x^(-1*m*(1+p))*(1+p)^-1*(1+m*p)^-1*(a*x^m+b*x^(1+m+m*p))^(1+p))
@test integrate(x^n*(x^m*(a+b*x^(1+n+m*p)))^p, x) == :(b^-1*x^(-1*m*(1+p))*(1+p)^-1*(a*x^m+b*x^(1+m+n+m*p))^(1+p)*(1+n+m*p)^-1)
@test integrate(x^n*(a*x^m+b*x^(1+m+n+m*p))^p, x) == :(b^-1*x^(-1*m*(1+p))*(1+p)^-1*(a*x^m+b*x^(1+m+n+m*p))^(1+p)*(1+n+m*p)^-1)
@test integrate((x^(-2+2n)*(a+b*x^n))^(1/2), x) == :(2//3*b^-1*n^-1*x^(3+-3n)*(a*x^(-2+2n)+b*x^(-2+3n))^3//2)
@test integrate((x^(-3+3n)*(a+b*x^n))^1//3, x) == :(3//4*b^-1*n^-1*x^(4+-4n)*(a*x^(-3+3n)+b*x^(-3+4n))^4//3)
@test integrate((x^(-4+4n)*(a+b*x^n))^1//4, x) == :(4//5*b^-1*n^-1*x^(5+-5n)*(a*x^(-4+4n)+b*x^(-4+5n))^5//4)
@test integrate((x^(p*(-1+n))*(a+b*x^n))^(p^-1), x) == :(p*b^-1*n^-1*x^((1+p)*(1+-1n))*(1+p)^-1*(a*x^(-1*p*(1+-1n))+b*x^(n+-1*p*(1+-1n)))^(1+p^-1))
@test integrate((x^(p^-1*(-1+n))*(a+b*x^n))^p, x) == :(b^-1*n^-1*x^(p^-1*(1+p)*(1+-1n))*(1+p)^-1*(a*x^(-1*p^-1*(1+-1n))+b*x^(n+-1*p^-1*(1+-1n)))^(1+p))
@test integrate(x^(-1+n+-1*p*(1+q))*(a*x^n+b*x^p)^q, x) == :(a^-1*x^(-1*p*(1+q))*(1+q)^-1*(n+-1p)^-1*(a*x^n+b*x^p)^(1+q))
@test integrate(x^(-1+-1*n*q+-1*p*(1+q))*(x^n*(a+b*x^p))^q, x) == :(-1*a^-1*p^-1*x^(-1*(1+q)*(n+p))*(1+q)^-1*(a*x^n+b*x^(n+p))^(1+q))

max_stars_repo_path: test/1 Algebraic functions/1.1 Binomial products/1.1.4 Improper/1.1.4.2 (c x)^m (a x^j+b x^n)^p.jl