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

@test integrate((1+x^3)^-1//2*(x+2^2//3)^-1, x) == :(2//9*3^(1/2)*arctan(3^(1/2)*(1+x^3)^-1//2*(1+x*2^1//3))+2//9*2^1//3*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((1+-1*x^3)^-1//2*(2^2//3+-1x)^-1, x) == :(-2//9*3^(1/2)*arctan(3^(1/2)*(1+-1*x^3)^-1//2*(1+-1*x*2^1//3))+-2//9*2^1//3*3^3//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+-1x)*Elliptic.F(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((-1+x^3)^-1//2*(2^2//3+-1x)^-1, x) == :(-2//9*3^(1/2)*arctanh(3^(1/2)*(-1+x^3)^-1//2*(1+-1*x*2^1//3))+-2//9*2^1//3*3^3//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+-1x)*Elliptic.F(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2)))
@test integrate((-1+-1*x^3)^-1//2*(x+2^2//3)^-1, x) == :(2//9*3^(1/2)*arctanh(3^(1/2)*(-1+-1*x^3)^-1//2*(1+x*2^1//3))+2//9*2^1//3*3^3//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2)))
@test integrate((a+b*x^3)^-1//2*(x*b^1//3+2^2//3*a^1//3)^-1, x) == :(2//9*3^(1/2)*a^-1//2*b^-1//3*arctan(3^(1/2)*a^1//6*(a+b*x^3)^-1//2*(a^1//3+x*2^1//3*b^1//3))+2//9*2^1//3*3^3//4*a^-1//3*b^-1//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+-1*b*x^3)^-1//2*(2^2//3*a^1//3+-1*x*b^1//3)^-1, x) == :(-2//9*3^(1/2)*a^-1//2*b^-1//3*arctan(3^(1/2)*a^1//6*(a+-1*b*x^3)^-1//2*(a^1//3+-1*x*2^1//3*b^1//3))+-2//9*2^1//3*3^3//4*a^-1//3*b^-1//3*((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+-1*b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)),-7+-4*3^(1/2)))
@test integrate((-1a+b*x^3)^-1//2*(2^2//3*a^1//3+-1*x*b^1//3)^-1, x) == :(-2//9*3^(1/2)*a^-1//2*b^-1//3*arctanh(3^(1/2)*a^1//6*(-1a+b*x^3)^-1//2*(a^1//3+-1*x*2^1//3*b^1//3))+-2//9*2^1//3*3^3//4*a^-1//3*b^-1//3*((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(-1a+b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*Elliptic.F(arcsin((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)),-7+4*3^(1/2)))
@test integrate((-1a+-1*b*x^3)^-1//2*(x*b^1//3+2^2//3*a^1//3)^-1, x) == :(2//9*3^(1/2)*a^-1//2*b^-1//3*arctanh(3^(1/2)*a^1//6*(-1a+-1*b*x^3)^-1//2*(a^1//3+x*2^1//3*b^1//3))+2//9*2^1//3*3^3//4*a^-1//3*b^-1//3*((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(-1a+-1*b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((c+d*x)^-1*(c^3+4*d^3*x^3)^-1//2, x) == :(2//9*3^(1/2)*c^-3//2*d^-1*arctan(3^(1/2)*c^(1/2)*(c^3+4*d^3*x^3)^-1//2*(c+2*d*x))+2//9*2^1//3*3^3//4*c^-1*d^-1*((c*(1+3^(1/2))+d*x*2^2//3)^-2*(c^2+2*2^1//3*d^2*x^2+-1*c*d*x*2^2//3))^(1/2)*(c*(c*(1+3^(1/2))+d*x*2^2//3)^-2*(c+d*x*2^2//3))^-1//2*(2+3^(1/2))^(1/2)*(c^3+4*d^3*x^3)^-1//2*(c+d*x*2^2//3)*Elliptic.F(arcsin((c*(1+3^(1/2))+d*x*2^2//3)^-1*(c*(1+-1*3^(1/2))+d*x*2^2//3)),-7+-4*3^(1/2)))
@test integrate((1+x^3)^-1//2*(1+x+3^(1/2))^-1, x) == :((9+6*3^(1/2))^-1//2*arctan((1+x^3)^-1//2*(3+2*3^(1/2))^(1/2)*(1+x))+1//3*3^1//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((1+-1*x^3)^-1//2*(1+3^(1/2)+-1x)^-1, x) == :(-1*(9+6*3^(1/2))^-1//2*arctan((1+-1*x^3)^-1//2*(3+2*3^(1/2))^(1/2)*(1+-1x))+-1//3*3^1//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+-1x)*Elliptic.F(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((-1+x^3)^-1//2*(1+3^(1/2)+-1x)^-1, x) == :(-1*(9+6*3^(1/2))^-1//2*arctanh((-1+x^3)^-1//2*(3+2*3^(1/2))^(1/2)*(1+-1x))+-1//3*3^1//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+-1x)*Elliptic.F(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2)))
@test integrate((-1+-1*x^3)^-1//2*(1+x+3^(1/2))^-1, x) == :((9+6*3^(1/2))^-1//2*arctanh((-1+-1*x^3)^-1//2*(3+2*3^(1/2))^(1/2)*(1+x))+1//3*3^1//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2)))
@test integrate((c+d*x)^-1*(-1*c^3+d^3*x^3)^-1//3, x) == :(-3//8*2^2//3*c^-1*d^-1*log(d*(c+-1*d*x)+d*2^2//3*(-1*c^3+d^3*x^3)^1//3)+1//8*2^2//3*c^-1*d^-1*log((c+d*x)^2*(c+-1*d*x))+1//4*2^2//3*3^(1/2)*c^-1*d^-1*arctan(1//3*3^(1/2)*(1+-1*2^1//3*(-1*c^3+d^3*x^3)^-1//3*(c+-1*d*x))))
@test integrate((c+d*x)^-1*(2*c^3+d^3*x^3)^-1//3, x) == :(-1//2*c^-1*d^-1*log(c+d*x)+-1//4*c^-1*d^-1*log((2*c^3+d^3*x^3)^1//3+-1*d*x)+3//4*c^-1*d^-1*log(d*(2c+d*x)+-1*d*(2*c^3+d^3*x^3)^1//3)+-1//2*3^(1/2)*c^-1*d^-1*arctan(1//3*3^(1/2)*(1+(2*c^3+d^3*x^3)^-1//3*(4c+2*d*x)))+1//6*3^(1/2)*c^-1*d^-1*arctan(1//3*3^(1/2)*(1+2*d*x*(2*c^3+d^3*x^3)^-1//3)))
@test integrate((1+x^3)^-1//2*(x+2^2//3)^-1*(2^2//3+-2x), x) == :(2//3*2^2//3*3^(1/2)*arctan(3^(1/2)*(1+x^3)^-1//2*(1+x*2^1//3)))
@test integrate((1+-1*x^3)^-1//2*(2^2//3+-1x)^-1*(2^2//3+2x), x) == :(-2//3*2^2//3*3^(1/2)*arctan(3^(1/2)*(1+-1*x^3)^-1//2*(1+-1*x*2^1//3)))
@test integrate((-1+x^3)^-1//2*(2^2//3+-1x)^-1*(2^2//3+2x), x) == :(-2//3*2^2//3*3^(1/2)*arctanh(3^(1/2)*(-1+x^3)^-1//2*(1+-1*x*2^1//3)))
@test integrate((-1+-1*x^3)^-1//2*(x+2^2//3)^-1*(2^2//3+-2x), x) == :(2//3*2^2//3*3^(1/2)*arctanh(3^(1/2)*(-1+-1*x^3)^-1//2*(1+x*2^1//3)))
@test integrate((a+b*x^3)^-1//2*(x*b^1//3+2^2//3*a^1//3)^-1*(2^2//3*a^1//3+-2*x*b^1//3), x) == :(2//3*2^2//3*3^(1/2)*a^-1//6*b^-1//3*arctan(3^(1/2)*a^1//6*(a+b*x^3)^-1//2*(a^1//3+x*2^1//3*b^1//3)))
@test integrate((a+-1*b*x^3)^-1//2*(2^2//3*a^1//3+-1*x*b^1//3)^-1*(2^2//3*a^1//3+2*x*b^1//3), x) == :(-2//3*2^2//3*3^(1/2)*a^-1//6*b^-1//3*arctan(3^(1/2)*a^1//6*(a+-1*b*x^3)^-1//2*(a^1//3+-1*x*2^1//3*b^1//3)))
@test integrate((-1a+b*x^3)^-1//2*(2^2//3*a^1//3+-1*x*b^1//3)^-1*(2^2//3*a^1//3+2*x*b^1//3), x) == :(-2//3*2^2//3*3^(1/2)*a^-1//6*b^-1//3*arctanh(3^(1/2)*a^1//6*(-1a+b*x^3)^-1//2*(a^1//3+-1*x*2^1//3*b^1//3)))
@test integrate((-1a+-1*b*x^3)^-1//2*(x*b^1//3+2^2//3*a^1//3)^-1*(2^2//3*a^1//3+-2*x*b^1//3), x) == :(2//3*2^2//3*3^(1/2)*a^-1//6*b^-1//3*arctanh(3^(1/2)*a^1//6*(-1a+-1*b*x^3)^-1//2*(a^1//3+x*2^1//3*b^1//3)))
@test integrate((c+d*x)^-1*(c^3+4*d^3*x^3)^-1//2*(c+-2*d*x), x) == :(2//3*3^(1/2)*c^-1//2*d^-1*arctan(3^(1/2)*c^(1/2)*(c^3+4*d^3*x^3)^-1//2*(c+2*d*x)))
@test integrate((1+x^3)^-1//2*(x+2^2//3)^-1*(2+3x), x) == :(1//9*3^(1/2)*(4+-6*2^2//3)*arctan(3^(1/2)*(1+x^3)^-1//2*(1+x*2^1//3))+2//9*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+x)*(3+2*2^1//3)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((1+-1*x^3)^-1//2*(2^2//3+-1x)^-1*(2+3x), x) == :(-1//9*3^(1/2)*(4+6*2^2//3)*arctan(3^(1/2)*(1+-1*x^3)^-1//2*(1+-1*x*2^1//3))+1//9*3^3//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+-1x)*(6+-4*2^1//3)*Elliptic.F(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((-1+x^3)^-1//2*(2^2//3+-1x)^-1*(2+3x), x) == :(-1//9*3^(1/2)*(4+6*2^2//3)*arctanh(3^(1/2)*(-1+x^3)^-1//2*(1+-1*x*2^1//3))+1//9*3^3//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+-1x)*(6+-4*2^1//3)*Elliptic.F(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2)))
@test integrate((-1+-1*x^3)^-1//2*(x+2^2//3)^-1*(2+3x), x) == :(1//9*3^(1/2)*(4+-6*2^2//3)*arctanh(3^(1/2)*(-1+-1*x^3)^-1//2*(1+x*2^1//3))+2//9*3^3//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+x)*(3+2*2^1//3)*Elliptic.F(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2)))
@test integrate((1+x^3)^-1//2*(x+2^2//3)^-1*(e+f*x), x) == :(1//9*3^(1/2)*(2*e+-2*f*2^2//3)*arctan(3^(1/2)*(1+x^3)^-1//2*(1+x*2^1//3))+2//9*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+x)*(f+e*2^1//3)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((1+-1*x^3)^-1//2*(2^2//3+-1x)^-1*(e+f*x), x) == :(-1//9*3^(1/2)*(2*e+2*f*2^2//3)*arctan(3^(1/2)*(1+-1*x^3)^-1//2*(1+-1*x*2^1//3))+-2//9*3^3//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+-1x)*(-1*f+e*2^1//3)*Elliptic.F(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((-1+x^3)^-1//2*(2^2//3+-1x)^-1*(e+f*x), x) == :(-1//9*3^(1/2)*(2*e+2*f*2^2//3)*arctanh(3^(1/2)*(-1+x^3)^-1//2*(1+-1*x*2^1//3))+-2//9*3^3//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+-1x)*(-1*f+e*2^1//3)*Elliptic.F(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2)))
@test integrate((-1+-1*x^3)^-1//2*(x+2^2//3)^-1*(e+f*x), x) == :(1//9*3^(1/2)*(2*e+-2*f*2^2//3)*arctanh(3^(1/2)*(-1+-1*x^3)^-1//2*(1+x*2^1//3))+2//9*3^3//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+x)*(f+e*2^1//3)*Elliptic.F(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2)))
@test integrate((a+b*x^3)^-1//2*(x*b^1//3+2^2//3*a^1//3)^-1*(e+f*x), x) == :(1//9*3^(1/2)*a^-1//2*b^-2//3*(2*e*b^1//3+-2*f*2^2//3*a^1//3)*arctan(3^(1/2)*a^1//6*(a+b*x^3)^-1//2*(a^1//3+x*2^1//3*b^1//3))+2//9*3^3//4*a^-1//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(f*a^1//3+e*2^1//3*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+-1*b*x^3)^-1//2*(2^2//3*a^1//3+-1*x*b^1//3)^-1*(e+f*x), x) == :(-1//9*3^(1/2)*a^-1//2*b^-2//3*(2*e*b^1//3+2*f*2^2//3*a^1//3)*arctan(3^(1/2)*a^1//6*(a+-1*b*x^3)^-1//2*(a^1//3+-1*x*2^1//3*b^1//3))+-2//9*3^3//4*a^-1//3*b^-2//3*((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+-1*b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*(-1*f*a^1//3+e*2^1//3*b^1//3)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)),-7+-4*3^(1/2)))
@test integrate((-1a+b*x^3)^-1//2*(2^2//3*a^1//3+-1*x*b^1//3)^-1*(e+f*x), x) == :(-1//9*3^(1/2)*a^-1//2*b^-2//3*(2*e*b^1//3+2*f*2^2//3*a^1//3)*arctanh(3^(1/2)*a^1//6*(-1a+b*x^3)^-1//2*(a^1//3+-1*x*2^1//3*b^1//3))+-2//9*3^3//4*a^-1//3*b^-2//3*((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(-1a+b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*(-1*f*a^1//3+e*2^1//3*b^1//3)*Elliptic.F(arcsin((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)),-7+4*3^(1/2)))
@test integrate((-1a+-1*b*x^3)^-1//2*(x*b^1//3+2^2//3*a^1//3)^-1*(e+f*x), x) == :(1//9*3^(1/2)*a^-1//2*b^-2//3*(2*e*b^1//3+-2*f*2^2//3*a^1//3)*arctanh(3^(1/2)*a^1//6*(-1a+-1*b*x^3)^-1//2*(a^1//3+x*2^1//3*b^1//3))+2//9*3^3//4*a^-1//3*b^-2//3*((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(-1a+-1*b*x^3)^-1//2*(a^1//3+x*b^1//3)*(f*a^1//3+e*2^1//3*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((c+d*x)^-1*(c^3+4*d^3*x^3)^-1//2*(e+f*x), x) == :(1//9*3^(1/2)*c^-3//2*d^-2*(-2*c*f+2*d*e)*arctan(3^(1/2)*c^(1/2)*(c^3+4*d^3*x^3)^-1//2*(c+2*d*x))+1//9*2^1//3*3^3//4*c^-1*d^-2*((c*(1+3^(1/2))+d*x*2^2//3)^-2*(c^2+2*2^1//3*d^2*x^2+-1*c*d*x*2^2//3))^(1/2)*(c*(c*(1+3^(1/2))+d*x*2^2//3)^-2*(c+d*x*2^2//3))^-1//2*(2+3^(1/2))^(1/2)*(c^3+4*d^3*x^3)^-1//2*(c+d*x*2^2//3)*(c*f+2*d*e)*Elliptic.F(arcsin((c*(1+3^(1/2))+d*x*2^2//3)^-1*(c*(1+-1*3^(1/2))+d*x*2^2//3)),-7+-4*3^(1/2)))
@test integrate(x*(1+x^3)^-1//2*(x+2^2//3)^-1, x) == :(-2//9*2^2//3*3^(1/2)*arctan(3^(1/2)*(1+x^3)^-1//2*(1+x*2^1//3))+2//9*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x*(1+-1*x^3)^-1//2*(2^2//3+-1x)^-1, x) == :(-2//9*2^2//3*3^(1/2)*arctan(3^(1/2)*(1+-1*x^3)^-1//2*(1+-1*x*2^1//3))+2//9*3^3//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+-1x)*Elliptic.F(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x*(-1+x^3)^-1//2*(2^2//3+-1x)^-1, x) == :(-2//9*2^2//3*3^(1/2)*arctanh(3^(1/2)*(-1+x^3)^-1//2*(1+-1*x*2^1//3))+2//9*3^3//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+-1x)*Elliptic.F(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2)))
@test integrate(x*(-1+-1*x^3)^-1//2*(x+2^2//3)^-1, x) == :(-2//9*2^2//3*3^(1/2)*arctanh(3^(1/2)*(-1+-1*x^3)^-1//2*(1+x*2^1//3))+2//9*3^3//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2)))
@test integrate(x*(a+b*x^3)^-1//2*(x*b^1//3+2^2//3*a^1//3)^-1, x) == :(-2//9*2^2//3*3^(1/2)*a^-1//6*b^-2//3*arctan(3^(1/2)*a^1//6*(a+b*x^3)^-1//2*(a^1//3+x*2^1//3*b^1//3))+2//9*3^3//4*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(a+-1*b*x^3)^-1//2*(2^2//3*a^1//3+-1*x*b^1//3)^-1, x) == :(-2//9*2^2//3*3^(1/2)*a^-1//6*b^-2//3*arctan(3^(1/2)*a^1//6*(a+-1*b*x^3)^-1//2*(a^1//3+-1*x*2^1//3*b^1//3))+2//9*3^3//4*b^-2//3*((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+-1*b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)),-7+-4*3^(1/2)))
@test integrate(x*(-1a+b*x^3)^-1//2*(2^2//3*a^1//3+-1*x*b^1//3)^-1, x) == :(-2//9*2^2//3*3^(1/2)*a^-1//6*b^-2//3*arctanh(3^(1/2)*a^1//6*(-1a+b*x^3)^-1//2*(a^1//3+-1*x*2^1//3*b^1//3))+2//9*3^3//4*b^-2//3*((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(-1a+b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*Elliptic.F(arcsin((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)),-7+4*3^(1/2)))
@test integrate(x*(-1a+-1*b*x^3)^-1//2*(x*b^1//3+2^2//3*a^1//3)^-1, x) == :(-2//9*2^2//3*3^(1/2)*a^-1//6*b^-2//3*arctanh(3^(1/2)*a^1//6*(-1a+-1*b*x^3)^-1//2*(a^1//3+x*2^1//3*b^1//3))+2//9*3^3//4*b^-2//3*((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(-1a+-1*b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate(x*(c+d*x)^-1*(c^3+4*d^3*x^3)^-1//2, x) == :(-2//9*3^(1/2)*c^-1//2*d^-2*arctan(3^(1/2)*c^(1/2)*(c^3+4*d^3*x^3)^-1//2*(c+2*d*x))+1//9*2^1//3*3^3//4*d^-2*((c*(1+3^(1/2))+d*x*2^2//3)^-2*(c^2+2*2^1//3*d^2*x^2+-1*c*d*x*2^2//3))^(1/2)*(c*(c*(1+3^(1/2))+d*x*2^2//3)^-2*(c+d*x*2^2//3))^-1//2*(2+3^(1/2))^(1/2)*(c^3+4*d^3*x^3)^-1//2*(c+d*x*2^2//3)*Elliptic.F(arcsin((c*(1+3^(1/2))+d*x*2^2//3)^-1*(c*(1+-1*3^(1/2))+d*x*2^2//3)),-7+-4*3^(1/2)))
@test integrate((1+x^3)^-1//2*(2+-1x)^-1*(1+x), x) == :(2//3*arctanh(1//3*(1+x)^2*(1+x^3)^-1//2))
@test integrate((1+-1*x^3)^-1//2*(2+x)^-1*(1+-1x), x) == :(-2//3*arctanh(1//3*(1+-1x)^2*(1+-1*x^3)^-1//2))
@test integrate((-1+x^3)^-1//2*(2+x)^-1*(1+-1x), x) == :(-2//3*arctan(1//3*(1+-1x)^2*(-1+x^3)^-1//2))
@test integrate((-1+-1*x^3)^-1//2*(2+-1x)^-1*(1+x), x) == :(2//3*arctan(1//3*(1+x)^2*(-1+-1*x^3)^-1//2))
@test integrate((a+b*x^3)^-1//2*(2*a^1//3+-1*x*b^1//3)^-1*(a^1//3+x*b^1//3), x) == :(2//3*a^-1//6*b^-1//3*arctanh(1//3*a^-1//6*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)^2))
@test integrate((a+-1*b*x^3)^-1//2*(2*a^1//3+x*b^1//3)^-1*(a^1//3+-1*x*b^1//3), x) == :(-2//3*a^-1//6*b^-1//3*arctanh(1//3*a^-1//6*(a+-1*b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)^2))
@test integrate((-1a+b*x^3)^-1//2*(2*a^1//3+x*b^1//3)^-1*(a^1//3+-1*x*b^1//3), x) == :(-2//3*a^-1//6*b^-1//3*arctan(1//3*a^-1//6*(a^1//3+-1*x*b^1//3)^2*(-1a+b*x^3)^-1//2))
@test integrate((-1a+-1*b*x^3)^-1//2*(2*a^1//3+-1*x*b^1//3)^-1*(a^1//3+x*b^1//3), x) == :(2//3*a^-1//6*b^-1//3*arctan(1//3*a^-1//6*(a^1//3+x*b^1//3)^2*(-1a+-1*b*x^3)^-1//2))
@test integrate((c+d*x)^-1*(c^3+-8*d^3*x^3)^-1//2*(c+-2*d*x), x) == :(-2//3*c^-1//2*d^-1*arctanh(1//3*c^-1//2*(c+-2*d*x)^2*(c^3+-8*d^3*x^3)^-1//2))
@test integrate((1+x^3)^-1//2*(2+-1x)^-1*(e+f*x), x) == :((2//9*e+4//9*f)*arctanh(1//3*(1+x)^2*(1+x^3)^-1//2)+2//9*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+x)*(e+-1*f)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((1+-1*x^3)^-1//2*(2+x)^-1*(e+f*x), x) == :((-2//9*e+4//9*f)*arctanh(1//3*(1+-1x)^2*(1+-1*x^3)^-1//2)+-2//9*3^3//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+-1x)*(e+f)*Elliptic.F(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((-1+x^3)^-1//2*(2+x)^-1*(e+f*x), x) == :((-2//9*e+4//9*f)*arctan(1//3*(1+-1x)^2*(-1+x^3)^-1//2)+-2//9*3^3//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+-1x)*(e+f)*Elliptic.F(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2)))
@test integrate((-1+-1*x^3)^-1//2*(2+-1x)^-1*(e+f*x), x) == :((2//9*e+4//9*f)*arctan(1//3*(1+x)^2*(-1+-1*x^3)^-1//2)+2//9*3^3//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+x)*(e+-1*f)*Elliptic.F(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2)))
@test integrate((a+b*x^3)^-1//2*(2*a^1//3+-1*x*b^1//3)^-1*(e+f*x), x) == :(1//9*a^-1//2*b^-2//3*(2*e*b^1//3+4*f*a^1//3)*arctanh(1//3*a^-1//6*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)^2)+2//9*3^3//4*a^-1//3*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(e*b^1//3+-1*f*a^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+-1*b*x^3)^-1//2*(2*a^1//3+x*b^1//3)^-1*(e+f*x), x) == :(-1//9*a^-1//2*b^-2//3*(-4*f*a^1//3+2*e*b^1//3)*arctanh(1//3*a^-1//6*(a+-1*b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)^2)+-2//9*3^3//4*a^-1//3*b^-2//3*((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+-1*b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*(e*b^1//3+f*a^1//3)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)),-7+-4*3^(1/2)))
@test integrate((-1a+b*x^3)^-1//2*(2*a^1//3+x*b^1//3)^-1*(e+f*x), x) == :(-1//9*a^-1//2*b^-2//3*(-4*f*a^1//3+2*e*b^1//3)*arctan(1//3*a^-1//6*(a^1//3+-1*x*b^1//3)^2*(-1a+b*x^3)^-1//2)+-2//9*3^3//4*a^-1//3*b^-2//3*((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(-1a+b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*(e*b^1//3+f*a^1//3)*Elliptic.F(arcsin((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)),-7+4*3^(1/2)))
@test integrate((-1a+-1*b*x^3)^-1//2*(2*a^1//3+-1*x*b^1//3)^-1*(e+f*x), x) == :(1//9*a^-1//2*b^-2//3*(2*e*b^1//3+4*f*a^1//3)*arctan(1//3*a^-1//6*(a^1//3+x*b^1//3)^2*(-1a+-1*b*x^3)^-1//2)+2//9*3^3//4*a^-1//3*b^-2//3*((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(-1a+-1*b*x^3)^-1//2*(a^1//3+x*b^1//3)*(e*b^1//3+-1*f*a^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate((c+d*x)^-1*(c^3+-8*d^3*x^3)^-1//2*(e+f*x), x) == :(-1//9*c^-3//2*d^-2*(-2*c*f+2*d*e)*arctanh(1//3*c^-1//2*(c+-2*d*x)^2*(c^3+-8*d^3*x^3)^-1//2)+-1//9*3^3//4*c^-1*d^-2*((c*(1+3^(1/2))+-2*d*x)^-2*(c^2+4*d^2*x^2+2*c*d*x))^(1/2)*(c*(c*(1+3^(1/2))+-2*d*x)^-2*(c+-2*d*x))^-1//2*(2+3^(1/2))^(1/2)*(c^3+-8*d^3*x^3)^-1//2*(c+-2*d*x)*(c*f+2*d*e)*Elliptic.F(arcsin((c*(1+3^(1/2))+-2*d*x)^-1*(c*(1+-1*3^(1/2))+-2*d*x)),-7+-4*3^(1/2)))
@test integrate(x*(1+x^3)^-1//2*(2+-1x)^-1, x) == :(4//9*arctanh(1//3*(1+x)^2*(1+x^3)^-1//2)+-2//9*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x*(1+-1*x^3)^-1//2*(2+x)^-1, x) == :(4//9*arctanh(1//3*(1+-1x)^2*(1+-1*x^3)^-1//2)+-2//9*3^3//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+-1x)*Elliptic.F(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x*(-1+x^3)^-1//2*(2+x)^-1, x) == :(4//9*arctan(1//3*(1+-1x)^2*(-1+x^3)^-1//2)+-2//9*3^3//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+-1x)*Elliptic.F(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2)))
@test integrate(x*(-1+-1*x^3)^-1//2*(2+-1x)^-1, x) == :(4//9*arctan(1//3*(1+x)^2*(-1+-1*x^3)^-1//2)+-2//9*3^3//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2)))
@test integrate(x*(a+b*x^3)^-1//2*(2*a^1//3+-1*x*b^1//3)^-1, x) == :(4//9*a^-1//6*b^-2//3*arctanh(1//3*a^-1//6*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)^2)+-2//9*3^3//4*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(a+-1*b*x^3)^-1//2*(2*a^1//3+x*b^1//3)^-1, x) == :(4//9*a^-1//6*b^-2//3*arctanh(1//3*a^-1//6*(a+-1*b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)^2)+-2//9*3^3//4*b^-2//3*((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+-1*b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)),-7+-4*3^(1/2)))
@test integrate(x*(-1a+b*x^3)^-1//2*(2*a^1//3+x*b^1//3)^-1, x) == :(4//9*a^-1//6*b^-2//3*arctan(1//3*a^-1//6*(a^1//3+-1*x*b^1//3)^2*(-1a+b*x^3)^-1//2)+-2//9*3^3//4*b^-2//3*((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(-1a+b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*Elliptic.F(arcsin((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)),-7+4*3^(1/2)))
@test integrate(x*(-1a+-1*b*x^3)^-1//2*(2*a^1//3+-1*x*b^1//3)^-1, x) == :(4//9*a^-1//6*b^-2//3*arctan(1//3*a^-1//6*(a^1//3+x*b^1//3)^2*(-1a+-1*b*x^3)^-1//2)+-2//9*3^3//4*b^-2//3*((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(-1a+-1*b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate(x*(c+d*x)^-1*(c^3+-8*d^3*x^3)^-1//2, x) == :(2//9*c^-1//2*d^-2*arctanh(1//3*c^-1//2*(c+-2*d*x)^2*(c^3+-8*d^3*x^3)^-1//2)+-1//9*3^3//4*d^-2*((c*(1+3^(1/2))+-2*d*x)^-2*(c^2+4*d^2*x^2+2*c*d*x))^(1/2)*(c*(c*(1+3^(1/2))+-2*d*x)^-2*(c+-2*d*x))^-1//2*(2+3^(1/2))^(1/2)*(c^3+-8*d^3*x^3)^-1//2*(c+-2*d*x)*Elliptic.F(arcsin((c*(1+3^(1/2))+-2*d*x)^-1*(c*(1+-1*3^(1/2))+-2*d*x)),-7+-4*3^(1/2)))
@test integrate((1+x^3)^-1//2*(1+x+-1*3^(1/2))^-1*(1+x+3^(1/2)), x) == :(-2*(-3+2*3^(1/2))^-1//2*arctanh((1+x^3)^-1//2*(-3+2*3^(1/2))^(1/2)*(1+x)))
@test integrate((1+-1*x^3)^-1//2*(1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x), x) == :(2*(-3+2*3^(1/2))^-1//2*arctanh((1+-1*x^3)^-1//2*(-3+2*3^(1/2))^(1/2)*(1+-1x)))
@test integrate((-1+x^3)^-1//2*(1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x), x) == :(2*(-3+2*3^(1/2))^-1//2*arctan((-1+x^3)^-1//2*(-3+2*3^(1/2))^(1/2)*(1+-1x)))
@test integrate((-1+-1*x^3)^-1//2*(1+x+-1*3^(1/2))^-1*(1+x+3^(1/2)), x) == :(-2*(-3+2*3^(1/2))^-1//2*arctan((-1+-1*x^3)^-1//2*(-3+2*3^(1/2))^(1/2)*(1+x)))
@test integrate((a+b*x^3)^-1//2*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+3^(1/2))), x) == :(-2*a^-1//6*b^-1//3*(-3+2*3^(1/2))^-1//2*arctanh(a^1//6*(-3+2*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)))
@test integrate((a+-1*b*x^3)^-1//2*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+3^(1/2))+-1*x*b^1//3), x) == :(2*a^-1//6*b^-1//3*(-3+2*3^(1/2))^-1//2*arctanh(a^1//6*(-3+2*3^(1/2))^(1/2)*(a+-1*b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)))
@test integrate((-1a+b*x^3)^-1//2*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+3^(1/2))+-1*x*b^1//3), x) == :(2*a^-1//6*b^-1//3*(-3+2*3^(1/2))^-1//2*arctan(a^1//6*(-3+2*3^(1/2))^(1/2)*(-1a+b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)))
@test integrate((-1a+-1*b*x^3)^-1//2*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+3^(1/2))), x) == :(-2*a^-1//6*b^-1//3*(-3+2*3^(1/2))^-1//2*arctan(a^1//6*(-3+2*3^(1/2))^(1/2)*(-1a+-1*b*x^3)^-1//2*(a^1//3+x*b^1//3)))
@test integrate((a+b*x^3)^-1//2*(1+-1*3^(1/2)+x*(b*a^-1)^1//3)^-1*(1+3^(1/2)+x*(b*a^-1)^1//3), x) == :(-2*a^-1//2*(b*a^-1)^-1//3*(-3+2*3^(1/2))^-1//2*arctanh(a^(1/2)*(-3+2*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(1+x*(b*a^-1)^1//3)))
@test integrate((a+-1*b*x^3)^-1//2*(1+-1*3^(1/2)+-1*x*(b*a^-1)^1//3)^-1*(1+3^(1/2)+-1*x*(b*a^-1)^1//3), x) == :(2*a^-1//2*(b*a^-1)^-1//3*(-3+2*3^(1/2))^-1//2*arctanh(a^(1/2)*(-3+2*3^(1/2))^(1/2)*(a+-1*b*x^3)^-1//2*(1+-1*x*(b*a^-1)^1//3)))
@test integrate((-1a+b*x^3)^-1//2*(1+-1*3^(1/2)+-1*x*(b*a^-1)^1//3)^-1*(1+3^(1/2)+-1*x*(b*a^-1)^1//3), x) == :(2*a^-1//2*(b*a^-1)^-1//3*(-3+2*3^(1/2))^-1//2*arctan(a^(1/2)*(-3+2*3^(1/2))^(1/2)*(-1a+b*x^3)^-1//2*(1+-1*x*(b*a^-1)^1//3)))
@test integrate((-1a+-1*b*x^3)^-1//2*(1+-1*3^(1/2)+x*(b*a^-1)^1//3)^-1*(1+3^(1/2)+x*(b*a^-1)^1//3), x) == :(-2*a^-1//2*(b*a^-1)^-1//3*(-3+2*3^(1/2))^-1//2*arctan(a^(1/2)*(-3+2*3^(1/2))^(1/2)*(-1a+-1*b*x^3)^-1//2*(1+x*(b*a^-1)^1//3)))
@test integrate((1+x^3)^-1//2*(1+x+3^(1/2))^-1*(1+x+-1*3^(1/2)), x) == :(-2*(3+2*3^(1/2))^-1//2*arctan((1+x^3)^-1//2*(3+2*3^(1/2))^(1/2)*(1+x)))
@test integrate((1+-1*x^3)^-1//2*(1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2)), x) == :(2*(3+2*3^(1/2))^-1//2*arctan((1+-1*x^3)^-1//2*(3+2*3^(1/2))^(1/2)*(1+-1x)))
@test integrate((-1+x^3)^-1//2*(1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2)), x) == :(2*(3+2*3^(1/2))^-1//2*arctanh((-1+x^3)^-1//2*(3+2*3^(1/2))^(1/2)*(1+-1x)))
@test integrate((-1+-1*x^3)^-1//2*(1+x+3^(1/2))^-1*(1+x+-1*3^(1/2)), x) == :(-2*(3+2*3^(1/2))^-1//2*arctanh((-1+-1*x^3)^-1//2*(3+2*3^(1/2))^(1/2)*(1+x)))
@test integrate((a+b*x^3)^-1//2*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2))), x) == :(-2*a^-1//6*b^-1//3*(3+2*3^(1/2))^-1//2*arctan(a^1//6*(3+2*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)))
@test integrate((a+-1*b*x^3)^-1//2*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3), x) == :(2*a^-1//6*b^-1//3*(3+2*3^(1/2))^-1//2*arctan(a^1//6*(3+2*3^(1/2))^(1/2)*(a+-1*b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)))
@test integrate((-1a+b*x^3)^-1//2*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3), x) == :(2*a^-1//6*b^-1//3*(3+2*3^(1/2))^-1//2*arctanh(a^1//6*(3+2*3^(1/2))^(1/2)*(-1a+b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)))
@test integrate((-1a+-1*b*x^3)^-1//2*(x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2))), x) == :(-2*a^-1//6*b^-1//3*(3+2*3^(1/2))^-1//2*arctanh(a^1//6*(3+2*3^(1/2))^(1/2)*(-1a+-1*b*x^3)^-1//2*(a^1//3+x*b^1//3)))
@test integrate((a+b*x^3)^-1//2*(1+3^(1/2)+x*(b*a^-1)^1//3)^-1*(1+-1*3^(1/2)+x*(b*a^-1)^1//3), x) == :(-2*a^-1//2*(b*a^-1)^-1//3*(3+2*3^(1/2))^-1//2*arctan(a^(1/2)*(3+2*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(1+x*(b*a^-1)^1//3)))
@test integrate((a+-1*b*x^3)^-1//2*(1+3^(1/2)+-1*x*(b*a^-1)^1//3)^-1*(1+-1*3^(1/2)+-1*x*(b*a^-1)^1//3), x) == :(2*a^-1//2*(b*a^-1)^-1//3*(3+2*3^(1/2))^-1//2*arctan(a^(1/2)*(3+2*3^(1/2))^(1/2)*(a+-1*b*x^3)^-1//2*(1+-1*x*(b*a^-1)^1//3)))
@test integrate((-1a+b*x^3)^-1//2*(1+3^(1/2)+-1*x*(b*a^-1)^1//3)^-1*(1+-1*3^(1/2)+-1*x*(b*a^-1)^1//3), x) == :(2*a^-1//2*(b*a^-1)^-1//3*(3+2*3^(1/2))^-1//2*arctanh(a^(1/2)*(3+2*3^(1/2))^(1/2)*(-1a+b*x^3)^-1//2*(1+-1*x*(b*a^-1)^1//3)))
@test integrate((-1a+-1*b*x^3)^-1//2*(1+3^(1/2)+x*(b*a^-1)^1//3)^-1*(1+-1*3^(1/2)+x*(b*a^-1)^1//3), x) == :(-2*a^-1//2*(b*a^-1)^-1//3*(3+2*3^(1/2))^-1//2*arctanh(a^(1/2)*(3+2*3^(1/2))^(1/2)*(-1a+-1*b*x^3)^-1//2*(1+x*(b*a^-1)^1//3)))
@test integrate((1+x^3)^-1//2*(1+x+3^(1/2))^-1*(1+x), x) == :(-1*(3+2*3^(1/2))^-1//2*arctan((1+x^3)^-1//2*(3+2*3^(1/2))^(1/2)*(1+x))+1//3*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((1+x^3)^-1//2*(1+x+-1*3^(1/2))^-1*(1+x), x) == :(-1*(-3+2*3^(1/2))^-1//2*arctanh((1+x^3)^-1//2*(-3+2*3^(1/2))^(1/2)*(1+x))+1//3*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((1+x^3)^-1//2*(1+x+3^(1/2))^-1*(e+f*x), x) == :((9+6*3^(1/2))^-1//2*(e+-1*f+-1*f*3^(1/2))*arctan((1+x^3)^-1//2*(3+2*3^(1/2))^(1/2)*(1+x))+1//3*3^1//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+x)*(e+-1*f*(1+-1*3^(1/2)))*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((1+-1*x^3)^-1//2*(1+3^(1/2)+-1x)^-1*(e+f*x), x) == :(-1*(9+6*3^(1/2))^-1//2*(e+f+f*3^(1/2))*arctan((1+-1*x^3)^-1//2*(3+2*3^(1/2))^(1/2)*(1+-1x))+-1//3*3^1//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+-1x)*(e+f*(1+-1*3^(1/2)))*Elliptic.F(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((-1+x^3)^-1//2*(1+3^(1/2)+-1x)^-1*(e+f*x), x) == :(-1*(9+6*3^(1/2))^-1//2*(e+f+f*3^(1/2))*arctanh((-1+x^3)^-1//2*(3+2*3^(1/2))^(1/2)*(1+-1x))+-1//3*3^1//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+-1x)*(e+f*(1+-1*3^(1/2)))*Elliptic.F(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2)))
@test integrate((-1+-1*x^3)^-1//2*(1+x+3^(1/2))^-1*(e+f*x), x) == :((9+6*3^(1/2))^-1//2*(e+-1*f*(1+3^(1/2)))*arctanh((-1+-1*x^3)^-1//2*(3+2*3^(1/2))^(1/2)*(1+x))+1//3*3^1//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+x)*(e+-1*f*(1+-1*3^(1/2)))*Elliptic.F(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2)))
@test integrate((a+b*x^3)^-1//2*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(e+f*x), x) == :(-1*a^-1//2*b^-2//3*(-9+6*3^(1/2))^-1//2*(e*b^1//3+-1*f*a^1//3*(1+-1*3^(1/2)))*arctanh(a^1//6*(-3+2*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3))+-1//3*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+3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*(e*b^1//3+-1*f*a^1//3*(1+3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate((a+-1*b*x^3)^-1//2*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-1*(e+f*x), x) == :(a^-1//2*b^-2//3*(-9+6*3^(1/2))^-1//2*(e*b^1//3+f*a^1//3*(1+-1*3^(1/2)))*arctanh(a^1//6*(-3+2*3^(1/2))^(1/2)*(a+-1*b*x^3)^-1//2*(a^1//3+-1*x*b^1//3))+1//3*3^1//4*a^-1//3*b^-2//3*((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+-1*b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*(e*b^1//3+f*a^1//3*(1+3^(1/2)))*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)),-7+-4*3^(1/2)))
@test integrate((-1a+b*x^3)^-1//2*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-1*(e+f*x), x) == :(a^-1//2*b^-2//3*(-9+6*3^(1/2))^-1//2*(e*b^1//3+f*a^1//3*(1+-1*3^(1/2)))*arctan(a^1//6*(-3+2*3^(1/2))^(1/2)*(-1a+b*x^3)^-1//2*(a^1//3+-1*x*b^1//3))+1//3*3^1//4*a^-1//3*b^-2//3*((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(-1a+b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*(e*b^1//3+f*a^1//3*(1+3^(1/2)))*Elliptic.F(arcsin((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)),-7+4*3^(1/2)))
@test integrate((-1a+-1*b*x^3)^-1//2*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(e+f*x), x) == :(-1*a^-1//2*b^-2//3*(-9+6*3^(1/2))^-1//2*(e*b^1//3+-1*f*a^1//3*(1+-1*3^(1/2)))*arctan(a^1//6*(-3+2*3^(1/2))^(1/2)*(-1a+-1*b*x^3)^-1//2*(a^1//3+x*b^1//3))+-1//3*3^1//4*a^-1//3*b^-2//3*((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(-1a+-1*b*x^3)^-1//2*(a^1//3+x*b^1//3)*(e*b^1//3+-1*f*a^1//3*(1+3^(1/2)))*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate(x*(1+x^3)^-1//2*(1+x+3^(1/2))^-1, x) == :(-1//3*2^(1/2)*3^1//4*arctan((1+x^3)^-1//2*(3+2*3^(1/2))^(1/2)*(1+x))+1//3*2^(1/2)*3^1//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(1+x)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x*(1+-1*x^3)^-1//2*(1+3^(1/2)+-1x)^-1, x) == :(-1//3*2^(1/2)*3^1//4*arctan((1+-1*x^3)^-1//2*(3+2*3^(1/2))^(1/2)*(1+-1x))+1//3*2^(1/2)*3^1//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(1+-1x)*Elliptic.F(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x*(-1+x^3)^-1//2*(1+3^(1/2)+-1x)^-1, x) == :(-1//3*2^(1/2)*3^1//4*arctanh((-1+x^3)^-1//2*(3+2*3^(1/2))^(1/2)*(1+-1x))+2//3*3^3//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(7//6+-2//3*3^(1/2))^(1/2)*(1+-1x)*Elliptic.F(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2)))
@test integrate(x*(-1+-1*x^3)^-1//2*(1+x+3^(1/2))^-1, x) == :(-1//3*2^(1/2)*3^1//4*arctanh((-1+-1*x^3)^-1//2*(3+2*3^(1/2))^(1/2)*(1+x))+2//3*3^3//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(7//6+-2//3*3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2)))
@test integrate(x*(1+x^3)^-1//2*(1+x+-1*3^(1/2))^-1, x) == :(-1//3*2^(1/2)*3^1//4*arctanh((1+x^3)^-1//2*(-3+2*3^(1/2))^(1/2)*(1+x))+2//3*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(7//6+2//3*3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x*(a+b*x^3)^-1//2*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-1, x) == :(-1//3*2^(1/2)*3^1//4*a^-1//6*b^-2//3*arctanh(a^1//6*(-3+2*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3))+2//3*3^3//4*b^-2//3*((x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(a^1//3*(x*b^1//3+a^1//3*(1+3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(7//6+2//3*3^(1/2))^(1/2)*(a+b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2)))
@test integrate(x*(a+-1*b*x^3)^-1//2*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-1, x) == :(-1//3*2^(1/2)*3^1//4*a^-1//6*b^-2//3*arctanh(a^1//6*(-3+2*3^(1/2))^(1/2)*(a+-1*b*x^3)^-1//2*(a^1//3+-1*x*b^1//3))+2//3*3^3//4*b^-2//3*((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(a^1//3*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(7//6+2//3*3^(1/2))^(1/2)*(a+-1*b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*Elliptic.F(arcsin((a^1//3*(1+3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)),-7+-4*3^(1/2)))
@test integrate(x*(-1a+b*x^3)^-1//2*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-1, x) == :(-1//3*2^(1/2)*3^1//4*a^-1//6*b^-2//3*arctan(a^1//6*(-3+2*3^(1/2))^(1/2)*(-1a+b*x^3)^-1//2*(a^1//3+-1*x*b^1//3))+1//3*2^(1/2)*3^1//4*b^-2//3*((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^2//3+b^2//3*x^2+x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-2*(a^1//3+-1*x*b^1//3))^-1//2*(-1a+b*x^3)^-1//2*(a^1//3+-1*x*b^1//3)*Elliptic.F(arcsin((a^1//3*(1+-1*3^(1/2))+-1*x*b^1//3)^-1*(a^1//3*(1+3^(1/2))+-1*x*b^1//3)),-7+4*3^(1/2)))
@test integrate(x*(-1a+-1*b*x^3)^-1//2*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-1, x) == :(-1//3*2^(1/2)*3^1//4*a^-1//6*b^-2//3*arctan(a^1//6*(-3+2*3^(1/2))^(1/2)*(-1a+-1*b*x^3)^-1//2*(a^1//3+x*b^1//3))+1//3*2^(1/2)*3^1//4*b^-2//3*((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^2//3+b^2//3*x^2+-1*x*a^1//3*b^1//3))^(1/2)*(-1*a^1//3*(x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-2*(a^1//3+x*b^1//3))^-1//2*(-1a+-1*b*x^3)^-1//2*(a^1//3+x*b^1//3)*Elliptic.F(arcsin((x*b^1//3+a^1//3*(1+-1*3^(1/2)))^-1*(x*b^1//3+a^1//3*(1+3^(1/2)))),-7+4*3^(1/2)))
@test integrate(x^-1*(1+x^3)^-1//2*(1+x+3^(1/2)), x) == :((-2//3+-2//3*3^(1/2))*arctanh((1+x^3)^(1/2))+2//3*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^-1*(1+-1*x^3)^-1//2*(1+3^(1/2)+-1x), x) == :((-2//3+-2//3*3^(1/2))*arctanh((1+-1*x^3)^(1/2))+2//3*3^3//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+-1x)*Elliptic.F(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^-1*(-1+x^3)^-1//2*(1+3^(1/2)+-1x), x) == :((2//3+2//3*3^(1/2))*arctan((-1+x^3)^(1/2))+2//3*3^3//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+-1x)*Elliptic.F(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2)))
@test integrate(x^-1*(-1+-1*x^3)^-1//2*(1+x+3^(1/2)), x) == :((2//3+2//3*3^(1/2))*arctan((-1+-1*x^3)^(1/2))+2//3*3^3//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2)))
@test integrate(x^-1*(1+x^3)^-1//2*(1+x+-1*3^(1/2)), x) == :((-2//3+2//3*3^(1/2))*arctanh((1+x^3)^(1/2))+2//3*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^-1*(1+-1*x^3)^-1//2*(1+-1x+-1*3^(1/2)), x) == :((-2//3+2//3*3^(1/2))*arctanh((1+-1*x^3)^(1/2))+2//3*3^3//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+-1x)*Elliptic.F(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^-1*(-1+x^3)^-1//2*(1+-1x+-1*3^(1/2)), x) == :((2//3+-2//3*3^(1/2))*arctan((-1+x^3)^(1/2))+2//3*3^3//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+-1x)*Elliptic.F(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2)))
@test integrate(x^-1*(-1+-1*x^3)^-1//2*(1+x+-1*3^(1/2)), x) == :((2//3+-2//3*3^(1/2))*arctan((-1+-1*x^3)^(1/2))+2//3*3^3//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2)))
@test integrate(x^-1*(1+x^3)^-1//2*(e+f*x), x) == :(-2//3*e*arctanh((1+x^3)^(1/2))+2//3*f*3^3//4*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^-1*(1+-1*x^3)^-1//2*(e+f*x), x) == :(-2//3*e*arctanh((1+-1*x^3)^(1/2))+-2//3*f*3^3//4*((1+3^(1/2)+-1x)^-2*(1+-1x))^-1//2*((1+3^(1/2)+-1x)^-2*(1+x+x^2))^(1/2)*(1+-1*x^3)^-1//2*(2+3^(1/2))^(1/2)*(1+-1x)*Elliptic.F(arcsin((1+3^(1/2)+-1x)^-1*(1+-1x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate(x^-1*(-1+x^3)^-1//2*(e+f*x), x) == :(2//3*e*arctan((-1+x^3)^(1/2))+-2//3*f*3^3//4*((1+-1x+-1*3^(1/2))^-2*(1+x+x^2))^(1/2)*(-1*(1+-1x+-1*3^(1/2))^-2*(1+-1x))^-1//2*(-1+x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+-1x)*Elliptic.F(arcsin((1+-1x+-1*3^(1/2))^-1*(1+3^(1/2)+-1x)),-7+4*3^(1/2)))
@test integrate(x^-1*(-1+-1*x^3)^-1//2*(e+f*x), x) == :(2//3*e*arctan((-1+-1*x^3)^(1/2))+2//3*f*3^3//4*((1+x+-1*3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(-1*(1+x+-1*3^(1/2))^-2*(1+x))^-1//2*(-1+-1*x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+x)*Elliptic.F(arcsin((1+x+-1*3^(1/2))^-1*(1+x+3^(1/2))),-7+4*3^(1/2)))
@test integrate((c+d*x)^-1*(2*c^3+d^3*x^3)^-1//3*(c+-1*d*x), x) == :(-1*d^-1*log(c+d*x)+3//2*d^-1*log(d*(2c+d*x)+-1*d*(2*c^3+d^3*x^3)^1//3)+-1*3^(1/2)*d^-1*arctan(1//3*3^(1/2)*(1+(2*c^3+d^3*x^3)^-1//3*(4c+2*d*x))))
@test integrate((c+d*x)^-1*(-1*c^3+d^3*x^3)^-1//3*(e+f*x), x) == :(-1//2*f*d^-2*log((-1*c^3+d^3*x^3)^1//3+-1*d*x)+1//3*f*3^(1/2)*d^-2*arctan(1//3*3^(1/2)*(1+2*d*x*(-1*c^3+d^3*x^3)^-1//3))+-1//8*2^2//3*c^-1*d^-2*(-3*c*f+3*d*e)*log(d*(c+-1*d*x)+d*2^2//3*(-1*c^3+d^3*x^3)^1//3)+1//8*2^2//3*c^-1*d^-2*(d*e+-1*c*f)*log((c+d*x)^2*(c+-1*d*x))+1//4*2^2//3*3^(1/2)*c^-1*d^-2*(d*e+-1*c*f)*arctan(1//3*3^(1/2)*(1+-1*2^1//3*(-1*c^3+d^3*x^3)^-1//3*(c+-1*d*x))))
@test integrate(x^2*(a+b*x)^n*(c+d*x^3), x) == :(d*b^-6*(6+n)^-1*(a+b*x)^(6+n)+b^-6*(3+n)^-1*(a+b*x)^(3+n)*(c*b^3+-10*d*a^3)+a^2*b^-6*(1+n)^-1*(a+b*x)^(1+n)*(c*b^3+-1*d*a^3)+-1*a*b^-6*(2+n)^-1*(a+b*x)^(2+n)*(-5*d*a^3+2*c*b^3)+-5*a*d*b^-6*(5+n)^-1*(a+b*x)^(5+n)+10*d*a^2*b^-6*(4+n)^-1*(a+b*x)^(4+n))
@test integrate(x*(a+b*x)^n*(c+d*x^3), x) == :(d*b^-5*(5+n)^-1*(a+b*x)^(5+n)+b^-5*(2+n)^-1*(a+b*x)^(2+n)*(c*b^3+-4*d*a^3)+-1*a*b^-5*(1+n)^-1*(a+b*x)^(1+n)*(c*b^3+-1*d*a^3)+-4*a*d*b^-5*(4+n)^-1*(a+b*x)^(4+n)+6*d*a^2*b^-5*(3+n)^-1*(a+b*x)^(3+n))
@test integrate((a+b*x)^n*(c+d*x^3), x) == :(d*b^-4*(4+n)^-1*(a+b*x)^(4+n)+b^-4*(1+n)^-1*(a+b*x)^(1+n)*(c*b^3+-1*d*a^3)+-3*a*d*b^-4*(3+n)^-1*(a+b*x)^(3+n)+3*d*a^2*b^-4*(2+n)^-1*(a+b*x)^(2+n))
@test integrate(x^2*(a+b*x)^n*(c+d*x^3)^2, x) == :(b^-9*d^2*(9+n)^-1*(a+b*x)^(9+n)+b^-9*(3+n)^-1*(a+b*x)^(3+n)*(b^6*c^2+28*a^6*d^2+-20*c*d*a^3*b^3)+a^2*b^-9*(1+n)^-1*(a+b*x)^(1+n)*(c*b^3+-1*d*a^3)^2+-8*a*b^-9*d^2*(8+n)^-1*(a+b*x)^(8+n)+2*d*b^-9*(6+n)^-1*(a+b*x)^(6+n)*(c*b^3+-28*d*a^3)+28*a^2*b^-9*d^2*(7+n)^-1*(a+b*x)^(7+n)+-10*a*d*b^-9*(5+n)^-1*(a+b*x)^(5+n)*(c*b^3+-7*d*a^3)+-2*a*b^-9*(2+n)^-1*(a+b*x)^(2+n)*(c*b^3+-1*d*a^3)*(c*b^3+-4*d*a^3)+4*d*a^2*b^-9*(4+n)^-1*(a+b*x)^(4+n)*(-14*d*a^3+5*c*b^3))
@test integrate(x*(a+b*x)^n*(c+d*x^3)^2, x) == :(b^-8*d^2*(8+n)^-1*(a+b*x)^(8+n)+d*b^-8*(5+n)^-1*(a+b*x)^(5+n)*(-35*d*a^3+2*c*b^3)+b^-8*(2+n)^-1*(a+b*x)^(2+n)*(c*b^3+-1*d*a^3)*(c*b^3+-7*d*a^3)+-1*a*b^-8*(1+n)^-1*(a+b*x)^(1+n)*(c*b^3+-1*d*a^3)^2+-7*a*b^-8*d^2*(7+n)^-1*(a+b*x)^(7+n)+21*a^2*b^-8*d^2*(6+n)^-1*(a+b*x)^(6+n)+-1*a*d*b^-8*(4+n)^-1*(a+b*x)^(4+n)*(-35*d*a^3+8*c*b^3)+3*d*a^2*b^-8*(3+n)^-1*(a+b*x)^(3+n)*(-7*d*a^3+4*c*b^3))
@test integrate((a+b*x)^n*(c+d*x^3)^2, x) == :(b^-7*d^2*(7+n)^-1*(a+b*x)^(7+n)+b^-7*(1+n)^-1*(a+b*x)^(1+n)*(c*b^3+-1*d*a^3)^2+-6*a*b^-7*d^2*(6+n)^-1*(a+b*x)^(6+n)+2*d*b^-7*(4+n)^-1*(a+b*x)^(4+n)*(c*b^3+-10*d*a^3)+15*a^2*b^-7*d^2*(5+n)^-1*(a+b*x)^(5+n)+-3*a*d*b^-7*(3+n)^-1*(a+b*x)^(3+n)*(-5*d*a^3+2*c*b^3)+6*d*a^2*b^-7*(2+n)^-1*(a+b*x)^(2+n)*(c*b^3+-1*d*a^3))
@test integrate(x^2*(a+b*x)^n*(c+d*x^3)^3, x) == :(b^-12*d^3*(12+n)^-1*(a+b*x)^(12+n)+a^2*b^-12*(1+n)^-1*(a+b*x)^(1+n)*(c*b^3+-1*d*a^3)^3+b^-12*(3+n)^-1*(a+b*x)^(3+n)*(c*b^3+-1*d*a^3)*(b^6*c^2+55*a^6*d^2+-29*c*d*a^3*b^3)+-11*a*b^-12*d^3*(11+n)^-1*(a+b*x)^(11+n)+3*d*b^-12*(6+n)^-1*(a+b*x)^(6+n)*(b^6*c^2+154*a^6*d^2+-56*c*d*a^3*b^3)+3*b^-12*d^2*(9+n)^-1*(a+b*x)^(9+n)*(c*b^3+-55*d*a^3)+55*a^2*b^-12*d^3*(10+n)^-1*(a+b*x)^(10+n)+-1*a*b^-12*(2+n)^-1*(a+b*x)^(2+n)*(c*b^3+-1*d*a^3)^2*(-11*d*a^3+2*c*b^3)+-15*a*d*b^-12*(5+n)^-1*(a+b*x)^(5+n)*(b^6*c^2+22*a^6*d^2+-14*c*d*a^3*b^3)+-6*a*b^-12*d^2*(8+n)^-1*(a+b*x)^(8+n)*(-55*d*a^3+4*c*b^3)+3*d*a^2*b^-12*(4+n)^-1*(a+b*x)^(4+n)*(10*b^6*c^2+55*a^6*d^2+-56*c*d*a^3*b^3)+42*a^2*b^-12*d^2*(7+n)^-1*(a+b*x)^(7+n)*(-11*d*a^3+2*c*b^3))
@test integrate(x*(a+b*x)^n*(c+d*x^3)^3, x) == :(b^-11*d^3*(11+n)^-1*(a+b*x)^(11+n)+b^-11*(2+n)^-1*(a+b*x)^(2+n)*(c*b^3+-1*d*a^3)^2*(c*b^3+-10*d*a^3)+-1*a*b^-11*(1+n)^-1*(a+b*x)^(1+n)*(c*b^3+-1*d*a^3)^3+-10*a*b^-11*d^3*(10+n)^-1*(a+b*x)^(10+n)+3*d*b^-11*(5+n)^-1*(a+b*x)^(5+n)*(b^6*c^2+70*a^6*d^2+-35*c*d*a^3*b^3)+3*b^-11*d^2*(8+n)^-1*(a+b*x)^(8+n)*(c*b^3+-40*d*a^3)+45*a^2*b^-11*d^3*(9+n)^-1*(a+b*x)^(9+n)+-21*a*b^-11*d^2*(7+n)^-1*(a+b*x)^(7+n)*(c*b^3+-10*d*a^3)+-3*a*d*b^-11*(4+n)^-1*(a+b*x)^(4+n)*(4*b^6*c^2+40*a^6*d^2+-35*c*d*a^3*b^3)+63*a^2*b^-11*d^2*(6+n)^-1*(a+b*x)^(6+n)*(c*b^3+-4*d*a^3)+9*d*a^2*b^-11*(3+n)^-1*(a+b*x)^(3+n)*(c*b^3+-1*d*a^3)*(-5*d*a^3+2*c*b^3))
@test integrate((a+b*x)^n*(c+d*x^3)^3, x) == :(b^-10*d^3*(10+n)^-1*(a+b*x)^(10+n)+b^-10*(1+n)^-1*(a+b*x)^(1+n)*(c*b^3+-1*d*a^3)^3+-9*a*b^-10*d^3*(9+n)^-1*(a+b*x)^(9+n)+3*d*b^-10*(4+n)^-1*(a+b*x)^(4+n)*(b^6*c^2+28*a^6*d^2+-20*c*d*a^3*b^3)+3*b^-10*d^2*(7+n)^-1*(a+b*x)^(7+n)*(c*b^3+-28*d*a^3)+36*a^2*b^-10*d^3*(8+n)^-1*(a+b*x)^(8+n)+-18*a*b^-10*d^2*(6+n)^-1*(a+b*x)^(6+n)*(c*b^3+-7*d*a^3)+9*d*a^2*b^-10*(2+n)^-1*(a+b*x)^(2+n)*(c*b^3+-1*d*a^3)^2+9*a^2*b^-10*d^2*(5+n)^-1*(a+b*x)^(5+n)*(-14*d*a^3+5*c*b^3)+-9*a*d*b^-10*(3+n)^-1*(a+b*x)^(3+n)*(c*b^3+-1*d*a^3)*(c*b^3+-4*d*a^3))
@test integrate((1+x^3)^-1//2*(2+x^2)^-1*(2+-1*x^2+-2x), x) == :(2*arctan((1+x^3)^-1//2*(1+x)))
@test integrate((1+-1*x^3)^-1//2*(2+x^2)^-1*(2+-1*x^2+2x), x) == :(-2*arctan((1+-1*x^3)^-1//2*(1+-1x)))
@test integrate((-1+x^3)^-1//2*(2+x^2)^-1*(2+-1*x^2+2x), x) == :(-2*arctanh((-1+x^3)^-1//2*(1+-1x)))
@test integrate((-1+-1*x^3)^-1//2*(2+x^2)^-1*(2+-1*x^2+-2x), x) == :(2*arctanh((-1+-1*x^3)^-1//2*(1+x)))
@test integrate((1+x^3)^-1//2*(2+d+x^2+d*x)^-1*(2+-1*x^2+-2x), x) == :(2*(1+d)^-1//2*arctan((1+d)^(1/2)*(1+x^3)^-1//2*(1+x)))
@test integrate((1+-1*x^3)^-1//2*(2+x^2+-1d+d*x)^-1*(2+-1*x^2+2x), x) == :(-2*(1+-1d)^-1//2*arctan((1+-1d)^(1/2)*(1+-1*x^3)^-1//2*(1+-1x)))
@test integrate((-1+x^3)^-1//2*(2+x^2+-1d+d*x)^-1*(2+-1*x^2+2x), x) == :(-2*(1+-1d)^-1//2*arctanh((1+-1d)^(1/2)*(-1+x^3)^-1//2*(1+-1x)))
@test integrate((-1+-1*x^3)^-1//2*(2+d+x^2+d*x)^-1*(2+-1*x^2+-2x), x) == :(2*(1+d)^-1//2*arctanh((1+d)^(1/2)*(-1+-1*x^3)^-1//2*(1+x)))
@test integrate((a+c*x^4)^(1/2)*(d+e*x)^3, x) == :(1//6*c^-1*e^3*(a+c*x^4)^3//2+1//15*d*x*(a+c*x^4)^(1/2)*(5*d^2+9*e^2*x^2)+3//4*e*d^2*x^2*(a+c*x^4)^(1/2)+3//4*a*e*c^-1//2*d^2*arctanh(c^(1/2)*x^2*(a+c*x^4)^-1//2)+6//5*a*d*x*c^-1//2*e^2*(a+c*x^4)^(1/2)*(a^(1/2)+c^(1/2)*x^2)^-1+-6//5*d*a^5//4*c^-3//4*e^2*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2)+1//15*d*a^3//4*c^-3//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(5*c^(1/2)*d^2+9*a^(1/2)*e^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate((a+c*x^4)^(1/2)*(d+e*x)^2, x) == :(1//15*x*(a+c*x^4)^(1/2)*(5*d^2+3*e^2*x^2)+(1/2)*d*e*x^2*(a+c*x^4)^(1/2)+(1/2)*a*d*e*c^-1//2*arctanh(c^(1/2)*x^2*(a+c*x^4)^-1//2)+2//5*a*x*c^-1//2*e^2*(a+c*x^4)^(1/2)*(a^(1/2)+c^(1/2)*x^2)^-1+-2//5*a^5//4*c^-3//4*e^2*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2)+1//15*a^3//4*c^-3//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(3*a^(1/2)*e^2+5*c^(1/2)*d^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate((a+c*x^4)^(1/2)*(d+e*x), x) == :(1//3*d*x*(a+c*x^4)^(1/2)+1//4*e*x^2*(a+c*x^4)^(1/2)+1//4*a*e*c^-1//2*arctanh(c^(1/2)*x^2*(a+c*x^4)^-1//2)+1//3*d*a^3//4*c^-1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate((a+c*x^4)^(1/2), x) == :(1//3*x*(a+c*x^4)^(1/2)+1//3*a^3//4*c^-1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate((a+c*x^4)^-1//2*(d+e*x)^3, x) == :((1/2)*c^-1*e^3*(a+c*x^4)^(1/2)+3//2*e*c^-1//2*d^2*arctanh(c^(1/2)*x^2*(a+c*x^4)^-1//2)+3*d*x*c^-1//2*e^2*(a+c*x^4)^(1/2)*(a^(1/2)+c^(1/2)*x^2)^-1+(1/2)*d*a^-1//4*c^-3//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(c^(1/2)*d^2+3*a^(1/2)*e^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2)+-3*d*a^1//4*c^-3//4*e^2*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate((a+c*x^4)^-1//2*(d+e*x)^2, x) == :(d*e*c^-1//2*arctanh(c^(1/2)*x^2*(a+c*x^4)^-1//2)+x*c^-1//2*e^2*(a+c*x^4)^(1/2)*(a^(1/2)+c^(1/2)*x^2)^-1+(1/2)*a^1//4*c^-3//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(e^2+a^-1//2*c^(1/2)*d^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2)+-1*a^1//4*c^-3//4*e^2*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate((a+c*x^4)^-1//2*(d+e*x), x) == :((1/2)*e*c^-1//2*arctanh(c^(1/2)*x^2*(a+c*x^4)^-1//2)+(1/2)*d*a^-1//4*c^-1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate((a+c*x^4)^-1//2, x) == :((1/2)*a^-1//4*c^-1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate((a+c*x^4)^-3//2*(d+e*x)^3, x) == :(-1//2*a^-1*c^-1*(a+c*x^4)^-1//2*(a*e^3+-1*c*x*(d^3+3*d*e^2*x^2+3*e*x*d^2))+-3//2*d*x*a^-1*c^-1//2*e^2*(a+c*x^4)^(1/2)*(a^(1/2)+c^(1/2)*x^2)^-1+1//4*d*a^-5//4*c^-3//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(c^(1/2)*d^2+-3*a^(1/2)*e^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2)+3//2*d*a^-3//4*c^-3//4*e^2*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate((a+c*x^4)^-3//2*(d+e*x)^2, x) == :((1/2)*x*a^-1*(a+c*x^4)^-1//2*(d+e*x)^2+-1//2*x*a^-1*c^-1//2*e^2*(a+c*x^4)^(1/2)*(a^(1/2)+c^(1/2)*x^2)^-1+(1/2)*a^-3//4*c^-3//4*e^2*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2)+1//4*a^-5//4*c^-3//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(c^(1/2)*d^2+-1*a^(1/2)*e^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate((a+c*x^4)^-3//2*(d+e*x), x) == :((1/2)*x*a^-1*(a+c*x^4)^-1//2*(d+e*x)+1//4*d*a^-5//4*c^-1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate((a+c*x^4)^-3//2, x) == :((1/2)*x*a^-1*(a+c*x^4)^-1//2+1//4*a^-5//4*c^-1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate((a*x^23)^(1/2)*(1+x^5)^-1//2, x) == :(-3//20*x^-9*(a*x^23)^(1/2)*(1+x^5)^(1/2)+1//10*x^-4*(a*x^23)^(1/2)*(1+x^5)^(1/2)+3//20*x^-23//2*(a*x^23)^(1/2)*arcsinh(x^5//2))
@test integrate((a*x^13)^(1/2)*(1+x^5)^-1//2, x) == :(-1//5*x^-13//2*(a*x^13)^(1/2)*arcsinh(x^5//2)+1//5*x^-4*(a*x^13)^(1/2)*(1+x^5)^(1/2))
@test integrate((a*x^3)^(1/2)*(1+x^5)^-1//2, x) == :(2//5*x^-3//2*(a*x^3)^(1/2)*arcsinh(x^5//2))
@test integrate((a*x^-7)^(1/2)*(1+x^5)^-1//2, x) == :(-2//5*x*(a*x^-7)^(1/2)*(1+x^5)^(1/2))
@test integrate((a*x^-17)^(1/2)*(1+x^5)^-1//2, x) == :(-2//15*x*(a*x^-17)^(1/2)*(1+x^5)^(1/2)+4//15*x^6*(a*x^-17)^(1/2)*(1+x^5)^(1/2))
@test integrate(x^-1*(a*x^6)^(1/2)*(1+-1*x^4)^-1, x) == :((1/2)*x^-3*(a*x^6)^(1/2)*arctanh(x)+-1//2*x^-3*(a*x^6)^(1/2)*arctan(x))
@test integrate((a*x^6)^(1/2)*(x+-1*x^5)^-1, x) == :((1/2)*x^-3*(a*x^6)^(1/2)*arctanh(x)+-1//2*x^-3*(a*x^6)^(1/2)*arctan(x))
@test integrate(x^-1*(a*x^6)^3//2*(1+-1*x^4)^-1, x) == :(-1*a*x^-2*(a*x^6)^(1/2)+-1//5*a*x^2*(a*x^6)^(1/2)+(1/2)*a*x^-3*(a*x^6)^(1/2)*arctan(x)+(1/2)*a*x^-3*(a*x^6)^(1/2)*arctanh(x))
@test integrate((1+-1*x^4)^-1+-1*x^-1*(a*x^6)^(1/2)*(1+-1*x^4)^-1, x) == :((1/2)*arctan(x)+(1/2)*arctanh(x)+(1/2)*x^-3*(a*x^6)^(1/2)*arctan(x)+-1//2*x^-3*(a*x^6)^(1/2)*arctanh(x))
@test integrate((1+-1*x^4)^-1+-1*(a*x^6)^(1/2)*(x+-1*x^5)^-1, x) == :((1/2)*arctan(x)+(1/2)*arctanh(x)+(1/2)*x^-3*(a*x^6)^(1/2)*arctan(x)+-1//2*x^-3*(a*x^6)^(1/2)*arctanh(x))
@test integrate((a*x^3)^(1/2)*(x+-1*x^3)^-1, x) == :(x^-3//2*(a*x^3)^(1/2)*arctanh(x^(1/2))+-1*x^-3//2*(a*x^3)^(1/2)*arctan(x^(1/2)))
@test integrate((a*x^4)^(1/2)*(1+x^2)^-1//2, x) == :((1/2)*x^-1*(a*x^4)^(1/2)*(1+x^2)^(1/2)+-1//2*x^-2*(a*x^4)^(1/2)*arcsinh(x))
@test integrate((a*x^3)^(1/2)*(1+x^2)^-1//2, x) == :(2//3*x^-1*(a*x^3)^(1/2)*(1+x^2)^(1/2)+-1//3*x^-3//2*(a*x^3)^(1/2)*((1+x)^-2*(1+x^2))^(1/2)*(1+x^2)^-1//2*(1+x)*Elliptic.F(2*arctan(x^(1/2)),1/2))
@test integrate((a*x^2)^(1/2)*(1+x^2)^-1//2, x) == :(x^-1*(a*x^2)^(1/2)*(1+x^2)^(1/2))
@test integrate((a*x)^(1/2)*(1+x^2)^-1//2, x) == :(2*(a*x)^(1/2)*(1+x)^-1*(1+x^2)^(1/2)+a^(1/2)*((1+x)^-2*(1+x^2))^(1/2)*(1+x^2)^-1//2*(1+x)*Elliptic.F(2*arctan(a^-1//2*(a*x)^(1/2)),1/2)+-2*a^(1/2)*((1+x)^-2*(1+x^2))^(1/2)*(1+x^2)^-1//2*(1+x)*Elliptic.E(2*arctan(a^-1//2*(a*x)^(1/2)),1/2))
@test integrate((a*x^-1)^(1/2)*(1+x^2)^-1//2, x) == :(x^(1/2)*(a*x^-1)^(1/2)*((1+x)^-2*(1+x^2))^(1/2)*(1+x^2)^-1//2*(1+x)*Elliptic.F(2*arctan(x^(1/2)),1/2))
@test integrate((a*x^-2)^(1/2)*(1+x^2)^-1//2, x) == :(-1*x*(a*x^-2)^(1/2)*arctanh((1+x^2)^(1/2)))
@test integrate((a*x^-3)^(1/2)*(1+x^2)^-1//2, x) == :(-2*x*(a*x^-3)^(1/2)*(1+x^2)^(1/2)+2*x^2*(a*x^-3)^(1/2)*(1+x)^-1*(1+x^2)^(1/2)+x^3//2*(a*x^-3)^(1/2)*((1+x)^-2*(1+x^2))^(1/2)*(1+x^2)^-1//2*(1+x)*Elliptic.F(2*arctan(x^(1/2)),1/2)+-2*x^3//2*(a*x^-3)^(1/2)*((1+x)^-2*(1+x^2))^(1/2)*(1+x^2)^-1//2*(1+x)*Elliptic.E(2*arctan(x^(1/2)),1/2))
@test integrate((a*x^-4)^(1/2)*(1+x^2)^-1//2, x) == :(-1*x*(a*x^-4)^(1/2)*(1+x^2)^(1/2))
@test integrate((a*x^4)^(1/2)*(1+x^3)^-1//2, x) == :(2//3*x^-2*(a*x^4)^(1/2)*(1+x^3)^(1/2))
@test integrate((a*x^3)^(1/2)*(1+x^3)^-1//2, x) == :(x^-1*(a*x^3)^(1/2)*(1+x^3)^(1/2)*(1+x*(1+3^(1/2)))^-1*(1+3^(1/2))+-1*3^1//4*x^-1*(a*x^3)^(1/2)*((1+x*(1+3^(1/2)))^-2*(1+x^2+-1x))^(1/2)*(x*(1+x*(1+3^(1/2)))^-2*(1+x))^-1//2*(1+x^3)^-1//2*(1+x)*Elliptic.E(arccos((1+x*(1+3^(1/2)))^-1*(1+x*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-1//6*3^3//4*x^-1*(a*x^3)^(1/2)*((1+x*(1+3^(1/2)))^-2*(1+x^2+-1x))^(1/2)*(x*(1+x*(1+3^(1/2)))^-2*(1+x))^-1//2*(1+x^3)^-1//2*(1+x)*(1+-1*3^(1/2))*Elliptic.F(arccos((1+x*(1+3^(1/2)))^-1*(1+x*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a*x^2)^(1/2)*(1+x^3)^-1//2, x) == :(2*x^-1*(a*x^2)^(1/2)*(1+x^3)^(1/2)*(1+x+3^(1/2))^-1+-1*3^1//4*x^-1*(a*x^2)^(1/2)*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+x)*Elliptic.E(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2))+2//3*2^(1/2)*3^3//4*x^-1*(a*x^2)^(1/2)*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(1+x)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((a*x)^(1/2)*(1+x^3)^-1//2, x) == :(2//3*a^(1/2)*arcsinh(a^-3//2*(a*x)^3//2))
@test integrate((a*x^-1)^(1/2)*(1+x^3)^-1//2, x) == :(1//3*x*3^3//4*(a*x^-1)^(1/2)*((1+x*(1+3^(1/2)))^-2*(1+x^2+-1x))^(1/2)*(x*(1+x*(1+3^(1/2)))^-2*(1+x))^-1//2*(1+x^3)^-1//2*(1+x)*Elliptic.F(arccos((1+x*(1+3^(1/2)))^-1*(1+x*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a*x^-2)^(1/2)*(1+x^3)^-1//2, x) == :(-2//3*x*(a*x^-2)^(1/2)*arctanh((1+x^3)^(1/2)))
@test integrate((a*x^-3)^(1/2)*(1+x^3)^-1//2, x) == :(-2*x*(a*x^-3)^(1/2)*(1+x^3)^(1/2)+x^2*(a*x^-3)^(1/2)*(1+x^3)^(1/2)*(1+x*(1+3^(1/2)))^-1*(2+2*3^(1/2))+-2*3^1//4*x^2*(a*x^-3)^(1/2)*((1+x*(1+3^(1/2)))^-2*(1+x^2+-1x))^(1/2)*(x*(1+x*(1+3^(1/2)))^-2*(1+x))^-1//2*(1+x^3)^-1//2*(1+x)*Elliptic.E(arccos((1+x*(1+3^(1/2)))^-1*(1+x*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))+-1//3*3^3//4*x^2*(a*x^-3)^(1/2)*((1+x*(1+3^(1/2)))^-2*(1+x^2+-1x))^(1/2)*(x*(1+x*(1+3^(1/2)))^-2*(1+x))^-1//2*(1+x^3)^-1//2*(1+x)*(1+-1*3^(1/2))*Elliptic.F(arccos((1+x*(1+3^(1/2)))^-1*(1+x*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2)))
@test integrate((a*x^-4)^(1/2)*(1+x^3)^-1//2, x) == :(-1*x*(a*x^-4)^(1/2)*(1+x^3)^(1/2)+x^2*(a*x^-4)^(1/2)*(1+x^3)^(1/2)*(1+x+3^(1/2))^-1+-1//2*3^1//4*x^2*(a*x^-4)^(1/2)*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(2+-1*3^(1/2))^(1/2)*(1+x)*Elliptic.E(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2))+1//3*2^(1/2)*3^3//4*x^2*(a*x^-4)^(1/2)*((1+x+3^(1/2))^-2*(1+x))^-1//2*((1+x+3^(1/2))^-2*(1+x^2+-1x))^(1/2)*(1+x^3)^-1//2*(1+x)*Elliptic.F(arcsin((1+x+3^(1/2))^-1*(1+x+-1*3^(1/2))),-7+-4*3^(1/2)))
@test integrate((a*x^(2n))^(1/2)*(1+x^n)^-1//2+2*x^(-1n)*(a*x^(2n))^(1/2)*(1+x^n)^-1//2*(2+n)^-1, x) == :(2*x^(1+-1n)*(a*x^(2n))^(1/2)*(1+x^n)^(1/2)*(2+n)^-1)
@test integrate((a*x)^(1/2)*(d+e*x)^-1//2*(e+f*x)^-1//2, x) == :(2*e^-1*f^-1//2*(a*x)^(1/2)*(e*(e^2+-1*d*f)^-1*(e+f*x))^(1/2)*(-1*e*x*d^-1)^-1//2*(e+f*x)^-1//2*(-1*e^2+d*f)^(1/2)*Elliptic.E(arcsin(f^(1/2)*(d+e*x)^(1/2)*(-1*e^2+d*f)^-1//2),1+-1*d^-1*e^2*f^-1))
@test integrate((a*x^m)^r, x) == :(x*(a*x^m)^r*(1+m*r)^-1)
@test integrate((a*x^m)^r*(b*x^n)^s, x) == :(x*(a*x^m)^r*(b*x^n)^s*(1+m*r+n*s)^-1)
@test integrate((a*x^m)^r*(b*x^n)^s*(c*x^p)^t, x) == :(x*(a*x^m)^r*(b*x^n)^s*(c*x^p)^t*(1+m*r+n*s+p*t)^-1)
@test integrate(x^2*((a+b*x)^(1/2)+(c+b*x)^(1/2))^-1, x) == :(-2//7*b^-3*(a+-1c)^-1*(c+b*x)^7//2+2//7*b^-3*(a+-1c)^-1*(a+b*x)^7//2+-4//5*a*b^-3*(a+-1c)^-1*(a+b*x)^5//2+-2//3*b^-3*c^2*(a+-1c)^-1*(c+b*x)^3//2+2//3*a^2*b^-3*(a+-1c)^-1*(a+b*x)^3//2+4//5*c*b^-3*(a+-1c)^-1*(c+b*x)^5//2)
@test integrate(x*((a+b*x)^(1/2)+(c+b*x)^(1/2))^-1, x) == :(-2//5*b^-2*(a+-1c)^-1*(c+b*x)^5//2+2//5*b^-2*(a+-1c)^-1*(a+b*x)^5//2+-2//3*a*b^-2*(a+-1c)^-1*(a+b*x)^3//2+2//3*c*b^-2*(a+-1c)^-1*(c+b*x)^3//2)
@test integrate(((a+b*x)^(1/2)+(c+b*x)^(1/2))^-1, x) == :(-2//3*b^-1*(a+-1c)^-1*(c+b*x)^3//2+2//3*b^-1*(a+-1c)^-1*(a+b*x)^3//2)
@test integrate(x^-1*((a+b*x)^(1/2)+(c+b*x)^(1/2))^-1, x) == :(-2*(a+-1c)^-1*(c+b*x)^(1/2)+2*(a+-1c)^-1*(a+b*x)^(1/2)+-2*a^(1/2)*(a+-1c)^-1*arctanh(a^-1//2*(a+b*x)^(1/2))+2*c^(1/2)*(a+-1c)^-1*arctanh(c^-1//2*(c+b*x)^(1/2)))
@test integrate(x^-2*((a+b*x)^(1/2)+(c+b*x)^(1/2))^-1, x) == :(x^-1*(a+-1c)^-1*(c+b*x)^(1/2)+-1*x^-1*(a+-1c)^-1*(a+b*x)^(1/2)+b*c^-1//2*(a+-1c)^-1*arctanh(c^-1//2*(c+b*x)^(1/2))+-1*b*a^-1//2*(a+-1c)^-1*arctanh(a^-1//2*(a+b*x)^(1/2)))
@test integrate(x^2*((a+b*x)^(1/2)+(c+b*x)^(1/2))^-2, x) == :((1/2)*b*x^4*(a+-1c)^-2+-1//32*b^-3*(-5*(a+c)^2+4*a*c)*arctanh((a+b*x)^(1/2)*(c+b*x)^-1//2)+1//3*x^3*(a+-1c)^-2*(a+c)+-1//2*x*b^-2*(a+-1c)^-2*(a+b*x)^3//2*(c+b*x)^3//2+-1//32*b^-3*(a+-1c)^-1*(a+b*x)^(1/2)*(c+b*x)^(1/2)*(-5*(a+c)^2+4*a*c)+1//12*b^-3*(a+-1c)^-2*(a+b*x)^3//2*(c+b*x)^3//2*(5a+5c)+1//16*b^-3*(a+-1c)^-2*(a+b*x)^3//2*(c+b*x)^(1/2)*(-5*(a+c)^2+4*a*c))
@test integrate(x*((a+b*x)^(1/2)+(c+b*x)^(1/2))^-2, x) == :((1/2)*x^2*(a+-1c)^-2*(a+c)+-1//4*b^-2*(a+c)*arctanh((a+b*x)^(1/2)*(c+b*x)^-1//2)+2//3*b*x^3*(a+-1c)^-2+-2//3*b^-2*(a+-1c)^-2*(a+b*x)^3//2*(c+b*x)^3//2+(1/2)*b^-2*(a+-1c)^-2*(a+b*x)^3//2*(c+b*x)^(1/2)*(a+c)+-1//4*b^-2*(a+-1c)^-1*(a+b*x)^(1/2)*(c+b*x)^(1/2)*(a+c))
@test integrate(x^-1*((a+b*x)^(1/2)+(c+b*x)^(1/2))^-2, x) == :((a+-1c)^-2*(a+c)*log(x)+-1*(a+-1c)^-2*(2a+2c)*arctanh((a+b*x)^(1/2)*(c+b*x)^-1//2)+-2*(a+-1c)^-2*(a+b*x)^(1/2)*(c+b*x)^(1/2)+2*b*x*(a+-1c)^-2+4*a^(1/2)*c^(1/2)*(a+-1c)^-2*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+b*x)^-1//2))
@test integrate(x^-2*((a+b*x)^(1/2)+(c+b*x)^(1/2))^-2, x) == :(-1*x^-1*(a+-1c)^-2*(a+c)+-4*b*(a+-1c)^-2*arctanh((a+b*x)^(1/2)*(c+b*x)^-1//2)+2*b*(a+-1c)^-2*log(x)+2*x^-1*(a+-1c)^-2*(a+b*x)^(1/2)*(c+b*x)^(1/2)+2*b*a^-1//2*c^-1//2*(a+-1c)^-2*(a+c)*arctanh(a^-1//2*c^(1/2)*(a+b*x)^(1/2)*(c+b*x)^-1//2))
@test integrate(x^2*((a+b*x)^(1/2)+(c+b*x)^(1/2))^-3, x) == :(-8//9*b^-3*(a+-1c)^-3*(c+b*x)^9//2+8//9*b^-3*(a+-1c)^-3*(a+b*x)^9//2+-24//5*b^-3*c^2*(a+-1c)^-3*(c+b*x)^5//2+-24//7*a*b^-3*(a+-1c)^-3*(a+b*x)^7//2+-8//3*a^3*b^-3*(a+-1c)^-3*(a+b*x)^3//2+-1//7*b^-3*(a+-1c)^-3*(c+b*x)^7//2*(2c+6a)+1//7*b^-3*(a+-1c)^-3*(a+b*x)^7//2*(2a+6c)+8//3*b^-3*c^3*(a+-1c)^-3*(c+b*x)^3//2+24//5*a^2*b^-3*(a+-1c)^-3*(a+b*x)^5//2+24//7*c*b^-3*(a+-1c)^-3*(c+b*x)^7//2+-4//5*a*b^-3*(a+-1c)^-3*(a+b*x)^5//2*(a+3c)+-2//3*b^-3*c^2*(a+-1c)^-3*(c+b*x)^3//2*(c+3a)+2//3*a^2*b^-3*(a+-1c)^-3*(a+b*x)^3//2*(a+3c)+4//5*c*b^-3*(a+-1c)^-3*(c+b*x)^5//2*(c+3a))
@test integrate(x*((a+b*x)^(1/2)+(c+b*x)^(1/2))^-3, x) == :(-8//7*b^-2*(a+-1c)^-3*(c+b*x)^7//2+8//7*b^-2*(a+-1c)^-3*(a+b*x)^7//2+-16//5*a*b^-2*(a+-1c)^-3*(a+b*x)^5//2+-8//3*b^-2*c^2*(a+-1c)^-3*(c+b*x)^3//2+-1//5*b^-2*(a+-1c)^-3*(c+b*x)^5//2*(2c+6a)+1//5*b^-2*(a+-1c)^-3*(a+b*x)^5//2*(2a+6c)+8//3*a^2*b^-2*(a+-1c)^-3*(a+b*x)^3//2+16//5*c*b^-2*(a+-1c)^-3*(c+b*x)^5//2+-2//3*a*b^-2*(a+-1c)^-3*(a+b*x)^3//2*(a+3c)+2//3*c*b^-2*(a+-1c)^-3*(c+b*x)^3//2*(c+3a))
@test integrate(x^-1*((a+b*x)^(1/2)+(c+b*x)^(1/2))^-3, x) == :(-8//3*(a+-1c)^-3*(c+b*x)^3//2+8//3*(a+-1c)^-3*(a+b*x)^3//2+(a+-1c)^-3*(a+b*x)^(1/2)*(2a+6c)+-1*(a+-1c)^-3*(c+b*x)^(1/2)*(2c+6a)+-2*a^(1/2)*(a+-1c)^-3*(a+3c)*arctanh(a^-1//2*(a+b*x)^(1/2))+2*c^(1/2)*(a+-1c)^-3*(c+3a)*arctanh(c^-1//2*(c+b*x)^(1/2)))
@test integrate((x^(1/2)+(1+x)^(1/2))^-1, x) == :(-2//3*x^3//2+2//3*(1+x)^3//2)
@test integrate((x^(1/2)+(-1+x)^(1/2))^-1, x) == :(-2//3*(-1+x)^3//2+2//3*x^3//2)
@test integrate(((1+x)^(1/2)+(-1+x)^(1/2))^-1, x) == :(-1//3*(-1+x)^3//2+1//3*(1+x)^3//2)
@test integrate(x^3*((1+x)^(1/2)+(1+-1x)^(1/2))^2, x) == :((1/2)*x^4+-2//3*(1+-1*x^2)^3//2+2//5*(1+-1*x^2)^5//2)
@test integrate(x^2*((1+x)^(1/2)+(1+-1x)^(1/2))^2, x) == :(1//4*arcsin(x)+2//3*x^3+(1/2)*x^3*(1+-1*x^2)^(1/2)+-1//4*x*(1+-1*x^2)^(1/2))
@test integrate(x*((1+x)^(1/2)+(1+-1x)^(1/2))^2, x) == :(x^2+-2//3*(1+-1*x^2)^3//2)
@test integrate(((1+x)^(1/2)+(1+-1x)^(1/2))^2, x) == :(2x+x*(1+-1*x^2)^(1/2)+arcsin(x))
@test integrate(x^-1*((1+x)^(1/2)+(1+-1x)^(1/2))^2, x) == :(-2*arctanh((1+-1*x^2)^(1/2))+2*(1+-1*x^2)^(1/2)+2*log(x))
@test integrate(x^-2*((1+x)^(1/2)+(1+-1x)^(1/2))^2, x) == :(-2*x^-1+-2*arcsin(x)+-2*x^-1*(1+-1*x^2)^(1/2))
@test integrate(x^-3*((1+x)^(1/2)+(1+-1x)^(1/2))^2, x) == :(-1*x^-2+-1*x^-2*(1+-1*x^2)^(1/2)+arctanh((1+-1*x^2)^(1/2)))
@test integrate(x^3*((a+b*x)^(1/2)+(a+c*x)^(1/2))^-1, x) == :(-2*c^-3*(a+c*x)^7//2*(-7c+7b)^-1+2//7*b^-3*(a+b*x)^7//2*(b+-1c)^-1+-2*a^2*c^-3*(a+c*x)^3//2*(-3c+3b)^-1+4*a*c^-3*(a+c*x)^5//2*(-5c+5b)^-1+-4//5*a*b^-3*(a+b*x)^5//2*(b+-1c)^-1+2//3*a^2*b^-3*(a+b*x)^3//2*(b+-1c)^-1)
@test integrate(x^2*((a+b*x)^(1/2)+(a+c*x)^(1/2))^-1, x) == :(-2*c^-2*(a+c*x)^5//2*(-5c+5b)^-1+2//5*b^-2*(a+b*x)^5//2*(b+-1c)^-1+2*a*c^-2*(a+c*x)^3//2*(-3c+3b)^-1+-2//3*a*b^-2*(a+b*x)^3//2*(b+-1c)^-1)
@test integrate(x*((a+b*x)^(1/2)+(a+c*x)^(1/2))^-1, x) == :(-2*c^-1*(a+c*x)^3//2*(-3c+3b)^-1+2//3*b^-1*(a+b*x)^3//2*(b+-1c)^-1)
@test integrate(((a+b*x)^(1/2)+(a+c*x)^(1/2))^-1, x) == :(-2*(a+c*x)^(1/2)*(b+-1c)^-1+2*(a+b*x)^(1/2)*(b+-1c)^-1+-2*a^(1/2)*(b+-1c)^-1*arctanh(a^-1//2*(a+b*x)^(1/2))+2*a^(1/2)*(b+-1c)^-1*arctanh(a^-1//2*(a+c*x)^(1/2)))
@test integrate(x^-1*((a+b*x)^(1/2)+(a+c*x)^(1/2))^-1, x) == :(x^-1*(a+c*x)^(1/2)*(b+-1c)^-1+-1*x^-1*(a+b*x)^(1/2)*(b+-1c)^-1+c*a^-1//2*(b+-1c)^-1*arctanh(a^-1//2*(a+c*x)^(1/2))+-1*b*a^-1//2*(b+-1c)^-1*arctanh(a^-1//2*(a+b*x)^(1/2)))
@test integrate(x^-2*((a+b*x)^(1/2)+(a+c*x)^(1/2))^-1, x) == :(x^-2*(a+c*x)^(1/2)*(-2c+2b)^-1+-1*x^-2*(a+b*x)^(1/2)*(-2c+2b)^-1+-1//4*a^-3//2*c^2*(b+-1c)^-1*arctanh(a^-1//2*(a+c*x)^(1/2))+1//4*a^-3//2*b^2*(b+-1c)^-1*arctanh(a^-1//2*(a+b*x)^(1/2))+-1//4*b*a^-1*x^-1*(a+b*x)^(1/2)*(b+-1c)^-1+1//4*c*a^-1*x^-1*(a+c*x)^(1/2)*(b+-1c)^-1)
@test integrate(x^3*((a+b*x)^(1/2)+(a+c*x)^(1/2))^-2, x) == :(a*x^2*(b+-1c)^-2+1//3*x^3*(b+-1c)^-2*(b+c)+-2//3*b^-1*c^-1*(a+b*x)^3//2*(a+c*x)^3//2*(b+-1c)^-2+-1//4*a^3*b^-5//2*c^-5//2*(b+c)*arctanh(b^-1//2*c^(1/2)*(a+b*x)^(1/2)*(a+c*x)^-1//2)+(1/2)*a*b^-2*c^-1*(a+b*x)^3//2*(a+c*x)^(1/2)*(b+-1c)^-2*(b+c)+1//4*a^2*b^-2*c^-2*(a+b*x)^(1/2)*(a+c*x)^(1/2)*(b+-1c)^-1*(b+c))
@test integrate(x^2*((a+b*x)^(1/2)+(a+c*x)^(1/2))^-2, x) == :((1/2)*x^2*(b+-1c)^-2*(b+c)+2*a*x*(b+-1c)^-2+(1/2)*a^2*b^-3//2*c^-3//2*arctanh(b^-1//2*c^(1/2)*(a+b*x)^(1/2)*(a+c*x)^-1//2)+-1*b^-1*(a+b*x)^3//2*(a+c*x)^(1/2)*(b+-1c)^-2+-1//2*a*b^-1*c^-1*(a+b*x)^(1/2)*(a+c*x)^(1/2)*(b+-1c)^-1)
@test integrate(x*((a+b*x)^(1/2)+(a+c*x)^(1/2))^-2, x) == :(x*(b+-1c)^-2*(b+c)+-2*(a+b*x)^(1/2)*(a+c*x)^(1/2)*(b+-1c)^-2+2*a*(b+-1c)^-2*log(x)+4*a*(b+-1c)^-2*arctanh((a+b*x)^(1/2)*(a+c*x)^-1//2)+-2*a*b^-1//2*c^-1//2*(b+-1c)^-2*(b+c)*arctanh(b^-1//2*c^(1/2)*(a+b*x)^(1/2)*(a+c*x)^-1//2))
@test integrate(((a+b*x)^(1/2)+(a+c*x)^(1/2))^-2, x) == :((b+-1c)^-2*(b+c)*log(x)+(b+-1c)^-2*(2b+2c)*arctanh((a+b*x)^(1/2)*(a+c*x)^-1//2)+-2*a*x^-1*(b+-1c)^-2+-4*b^(1/2)*c^(1/2)*(b+-1c)^-2*arctanh(b^-1//2*c^(1/2)*(a+b*x)^(1/2)*(a+c*x)^-1//2)+2*x^-1*(a+b*x)^(1/2)*(a+c*x)^(1/2)*(b+-1c)^-2)
@test integrate(x^-1*((a+b*x)^(1/2)+(a+c*x)^(1/2))^-2, x) == :(-1//2*a^-1*arctanh((a+b*x)^(1/2)*(a+c*x)^-1//2)+-1*a*x^-2*(b+-1c)^-2+-1*x^-1*(b+-1c)^-2*(b+c)+a^-1*x^-2*(a+b*x)^(1/2)*(a+c*x)^3//2*(b+-1c)^-2+(1/2)*a^-1*x^-1*(a+b*x)^(1/2)*(a+c*x)^(1/2)*(b+-1c)^-1)
@test integrate(x^-2*((a+b*x)^(1/2)+(a+c*x)^(1/2))^-2, x) == :(-2//3*a*x^-3*(b+-1c)^-2+-1//2*x^-2*(b+-1c)^-2*(b+c)+1//4*a^-2*(b+c)*arctanh((a+b*x)^(1/2)*(a+c*x)^-1//2)+2//3*a^-2*x^-3*(a+b*x)^3//2*(a+c*x)^3//2*(b+-1c)^-2+-1//2*a^-2*x^-2*(a+b*x)^(1/2)*(a+c*x)^3//2*(b+-1c)^-2*(b+c)+-1//4*a^-2*x^-1*(a+b*x)^(1/2)*(a+c*x)^(1/2)*(b+-1c)^-1*(b+c))
@test integrate(x^4*((a+b*x)^(1/2)+(a+c*x)^(1/2))^-3, x) == :(-8//3*a^2*b^-2*(a+b*x)^3//2*(b+-1c)^-3+-8//5*a*c^-2*(a+c*x)^5//2*(b+-1c)^-3+-1//7*c^-3*(a+c*x)^7//2*(b+-1c)^-3*(2c+6b)+1//7*b^-3*(a+b*x)^7//2*(b+-1c)^-3*(2b+6c)+8//3*a^2*c^-2*(a+c*x)^3//2*(b+-1c)^-3+8//5*a*b^-2*(a+b*x)^5//2*(b+-1c)^-3+-4//5*a*b^-3*(a+b*x)^5//2*(b+-1c)^-3*(b+3c)+-2//3*a^2*c^-3*(a+c*x)^3//2*(b+-1c)^-3*(c+3b)+2//3*a^2*b^-3*(a+b*x)^3//2*(b+-1c)^-3*(b+3c)+4//5*a*c^-3*(a+c*x)^5//2*(b+-1c)^-3*(c+3b))
@test integrate(x^3*((a+b*x)^(1/2)+(a+c*x)^(1/2))^-3, x) == :(-8//3*a*c^-1*(a+c*x)^3//2*(b+-1c)^-3+-1//5*c^-2*(a+c*x)^5//2*(b+-1c)^-3*(2c+6b)+1//5*b^-2*(a+b*x)^5//2*(b+-1c)^-3*(2b+6c)+8//3*a*b^-1*(a+b*x)^3//2*(b+-1c)^-3+-2//3*a*b^-2*(a+b*x)^3//2*(b+-1c)^-3*(b+3c)+2//3*a*c^-2*(a+c*x)^3//2*(b+-1c)^-3*(c+3b))
@test integrate(x^2*((a+b*x)^(1/2)+(a+c*x)^(1/2))^-3, x) == :(-8*a*(a+c*x)^(1/2)*(b+-1c)^-3+-8*a^3//2*(b+-1c)^-3*arctanh(a^-1//2*(a+b*x)^(1/2))+8*a*(a+b*x)^(1/2)*(b+-1c)^-3+8*a^3//2*(b+-1c)^-3*arctanh(a^-1//2*(a+c*x)^(1/2))+-1//3*c^-1*(a+c*x)^3//2*(b+-1c)^-3*(2c+6b)+1//3*b^-1*(a+b*x)^3//2*(b+-1c)^-3*(2b+6c))
@test integrate((1+-1x)^(1/2)*((1+x)^(1/2)+(1+-1x)^(1/2)), x) == :(x+(1/2)*arcsin(x)+-1//2*x^2+(1/2)*x*(1+-1*x^2)^(1/2))
@test integrate(x^3*((1+x)^(1/2)+(1+-1x)^(1/2))*(-1*(1+x)^(1/2)+-1*(1+-1x)^(1/2)), x) == :(-2//5*(1+-1*x^2)^5//2+-1//2*x^4+2//3*(1+-1*x^2)^3//2)
@test integrate(x^2*((1+x)^(1/2)+(1+-1x)^(1/2))*(-1*(1+x)^(1/2)+-1*(1+-1x)^(1/2)), x) == :(-2//3*x^3+-1//4*arcsin(x)+-1//2*x^3*(1+-1*x^2)^(1/2)+1//4*x*(1+-1*x^2)^(1/2))
@test integrate(x*((1+x)^(1/2)+(1+-1x)^(1/2))*(-1*(1+x)^(1/2)+-1*(1+-1x)^(1/2)), x) == :(-1*x^2+2//3*(1+-1*x^2)^3//2)
@test integrate(((1+x)^(1/2)+(1+-1x)^(1/2))*(-1*(1+x)^(1/2)+-1*(1+-1x)^(1/2)), x) == :(-1*arcsin(x)+-2x+-1*x*(1+-1*x^2)^(1/2))
@test integrate(x^-1*((1+x)^(1/2)+(1+-1x)^(1/2))*(-1*(1+x)^(1/2)+-1*(1+-1x)^(1/2)), x) == :(-2*(1+-1*x^2)^(1/2)+-2*log(x)+2*arctanh((1+-1*x^2)^(1/2)))
@test integrate(x^-2*((1+x)^(1/2)+(1+-1x)^(1/2))*(-1*(1+x)^(1/2)+-1*(1+-1x)^(1/2)), x) == :(2*x^-1+2*arcsin(x)+2*x^-1*(1+-1*x^2)^(1/2))
@test integrate(x^-3*((1+x)^(1/2)+(1+-1x)^(1/2))*(-1*(1+x)^(1/2)+-1*(1+-1x)^(1/2)), x) == :(x^-2+-1*arctanh((1+-1*x^2)^(1/2))+x^-2*(1+-1*x^2)^(1/2))
@test integrate(((1+x)^(1/2)+-1*(1+-1x)^(1/2))^-1*((1+x)^(1/2)+(1+-1x)^(1/2)), x) == :((1+-1*x^2)^(1/2)+-1*arctanh((1+-1*x^2)^(1/2))+log(x))
@test integrate(((1+x)^(1/2)+(-1+x)^(1/2))^-1*((1+x)^(1/2)+-1*(-1+x)^(1/2)), x) == :((1/2)*x^2+(1/2)*arccosh(x)+-1//2*x*(1+x)^(1/2)*(-1+x)^(1/2))
@test integrate((d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^3, x) == :(1//8*e^-1*(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^4+1//4*a*e^-1*f^2*(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^2+a*d*e^-1*f^2*(e*x+f*(a+e^2*f^-2*x^2)^(1/2))+-1//2*a*d^3*e^-1*f^2*(e*x+f*(a+e^2*f^-2*x^2)^(1/2))^-1+3//2*a*d^2*e^-1*f^2*log(e*x+f*(a+e^2*f^-2*x^2)^(1/2)))
@test integrate((d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^2, x) == :(1//6*e^-1*(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^3+(1/2)*a*e^-1*f^2*(e*x+f*(a+e^2*f^-2*x^2)^(1/2))+a*d*e^-1*f^2*log(e*x+f*(a+e^2*f^-2*x^2)^(1/2))+-1//2*a*d^2*e^-1*f^2*(e*x+f*(a+e^2*f^-2*x^2)^(1/2))^-1)
@test integrate(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2), x) == :(d*x+(1/2)*e*x^2+(1/2)*f*x*(a+e^2*f^-2*x^2)^(1/2)+(1/2)*a*e^-1*f^2*arctanh(e*x*f^-1*(a+e^2*f^-2*x^2)^-1//2))
@test integrate((d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^-1, x) == :((1/2)*e^-1*(1+a*d^-2*f^2)*log(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))+-1//2*a*d^-1*e^-1*f^2*(e*x+f*(a+e^2*f^-2*x^2)^(1/2))^-1+-1//2*a*d^-2*e^-1*f^2*log(e*x+f*(a+e^2*f^-2*x^2)^(1/2)))
@test integrate((d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^-2, x) == :(-1//2*e^-1*(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^-1*(1+a*d^-2*f^2)+a*d^-3*e^-1*f^2*log(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))+-1*a*d^-3*e^-1*f^2*log(e*x+f*(a+e^2*f^-2*x^2)^(1/2))+-1//2*a*d^-2*e^-1*f^2*(e*x+f*(a+e^2*f^-2*x^2)^(1/2))^-1)
@test integrate((d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^-3, x) == :(-1//4*e^-1*(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^-2*(1+a*d^-2*f^2)+-1*a*d^-3*e^-1*f^2*(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^-1+-3//2*a*d^-4*e^-1*f^2*log(e*x+f*(a+e^2*f^-2*x^2)^(1/2))+-1//2*a*d^-3*e^-1*f^2*(e*x+f*(a+e^2*f^-2*x^2)^(1/2))^-1+3//2*a*d^-4*e^-1*f^2*log(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2)))
@test integrate((d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^5//2, x) == :(1//7*e^-1*(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^7//2+1//3*a*e^-1*f^2*(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^3//2+2*a*d*e^-1*f^2*(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^(1/2)+-5//2*a*d^3//2*e^-1*f^2*arctanh(d^-1//2*(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^(1/2))+-1//2*a*d^2*e^-1*f^2*(e*x+f*(a+e^2*f^-2*x^2)^(1/2))^-1*(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^(1/2))
@test integrate((d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^3//2, x) == :(1//5*e^-1*(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^5//2+a*e^-1*f^2*(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^(1/2)+-3//2*a*d^(1/2)*e^-1*f^2*arctanh(d^-1//2*(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^(1/2))+-1//2*a*d*e^-1*f^2*(e*x+f*(a+e^2*f^-2*x^2)^(1/2))^-1*(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^(1/2))
@test integrate((d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^(1/2), x) == :(1//3*e^-1*(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^3//2+-1//2*a*d^-1//2*e^-1*f^2*arctanh(d^-1//2*(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^(1/2))+-1//2*a*e^-1*f^2*(e*x+f*(a+e^2*f^-2*x^2)^(1/2))^-1*(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^(1/2))
@test integrate((d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^-1//2, x) == :(e^-1*(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^(1/2)+(1/2)*a*d^-3//2*e^-1*f^2*arctanh(d^-1//2*(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^(1/2))+-1//2*a*d^-1*e^-1*f^2*(e*x+f*(a+e^2*f^-2*x^2)^(1/2))^-1*(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^(1/2))
@test integrate((d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^-3//2, x) == :(-1*e^-1*(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^-1//2*(1+a*d^-2*f^2)+3//2*a*d^-5//2*e^-1*f^2*arctanh(d^-1//2*(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^(1/2))+-1//2*a*d^-2*e^-1*f^2*(e*x+f*(a+e^2*f^-2*x^2)^(1/2))^-1*(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^(1/2))
@test integrate((d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^-5//2, x) == :(-1//3*e^-1*(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^-3//2*(1+a*d^-2*f^2)+-2*a*d^-3*e^-1*f^2*(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^-1//2+5//2*a*d^-7//2*e^-1*f^2*arctanh(d^-1//2*(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^(1/2))+-1//2*a*d^-3*e^-1*f^2*(e*x+f*(a+e^2*f^-2*x^2)^(1/2))^-1*(d+e*x+f*(a+e^2*f^-2*x^2)^(1/2))^(1/2))
@test integrate((x+-1*(-4+x^2)^(1/2))^(1/2), x) == :(4*(x+-1*(-4+x^2)^(1/2))^-1//2+1//3*(x+-1*(-4+x^2)^(1/2))^3//2)
@test integrate((a*x+b*(c+a^2*b^-2*x^2)^(1/2))^(1/2), x) == :(1//3*a^-1*(a*x+b*(c+a^2*b^-2*x^2)^(1/2))^3//2+-1*c*a^-1*b^2*(a*x+b*(c+a^2*b^-2*x^2)^(1/2))^-1//2)
@test integrate((1+(1+-1*x^2)^(1/2))^(1/2), x) == :(2*x*(1+(1+-1*x^2)^(1/2))^-1//2+-2//3*x^3*(1+(1+-1*x^2)^(1/2))^-3//2)
@test integrate((1+(1+x^2)^(1/2))^(1/2), x) == :(2*x*(1+(1+x^2)^(1/2))^-1//2+2//3*x^3*(1+(1+x^2)^(1/2))^-3//2)
@test integrate((5+(25+x^2)^(1/2))^(1/2), x) == :(10*x*(5+(25+x^2)^(1/2))^-1//2+2//3*x^3*(5+(25+x^2)^(1/2))^-3//2)
@test integrate((a+b*(c*x^2+a^2*b^-2)^(1/2))^(1/2), x) == :(2*a*x*(a+b*(c*x^2+a^2*b^-2)^(1/2))^-1//2+2//3*c*b^2*x^3*(a+b*(c*x^2+a^2*b^-2)^(1/2))^-3//2)
@test integrate((d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^3, x) == :(1//8*e^-1*(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^4+1//16*e^-3*f^2*(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^2*(-1*b^2*f^2+4*a*e^2)+-1//32*e^-5*f^2*(b*f^2+2*e*(e*x+f*(a+x*f^-2*(b*f^2+x*e^2))^(1/2)))^-1*(-1*b*f^2+2*d*e)^3*(-1*b^2*f^2+4*a*e^2)+1//8*e^-4*f^2*(e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))*(-1*b*f^2+2*d*e)*(-1*b^2*f^2+4*a*e^2)+3//32*e^-5*f^2*(-1*b*f^2+2*d*e)^2*(-1*b^2*f^2+4*a*e^2)*log(b*f^2+2*e*(e*x+f*(a+x*f^-2*(b*f^2+x*e^2))^(1/2))))
@test integrate((d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^2, x) == :(1//6*e^-1*(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^3+1//8*e^-3*f^2*(e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))*(-1*b^2*f^2+4*a*e^2)+-1//16*e^-4*f^2*(b*f^2+2*e*(e*x+f*(a+x*f^-2*(b*f^2+x*e^2))^(1/2)))^-1*(-1*b*f^2+2*d*e)^2*(-1*b^2*f^2+4*a*e^2)+1//8*e^-4*f^2*(-1*b*f^2+2*d*e)*(-1*b^2*f^2+4*a*e^2)*log(b*f^2+2*e*(e*x+f*(a+x*f^-2*(b*f^2+x*e^2))^(1/2))))
@test integrate(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2), x) == :(d*x+(1/2)*e*x^2+1//4*f*e^-2*(a+b*x+e^2*f^-2*x^2)^(1/2)*(b*f^2+2*x*e^2)+1//8*e^-3*f^2*(-1*b^2*f^2+4*a*e^2)*arctanh((1/2)*e^-1*f^-1*(a+b*x+e^2*f^-2*x^2)^-1//2*(b*f^2+2*x*e^2)))
@test integrate((d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^-1, x) == :((-1*b*f^2+2*d*e)^-2*(2*e*d^2+-2*b*d*f^2+2*a*e*f^2)*log(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))+-1//2*e^-1*f^2*(b*f^2+2*e*(e*x+f*(a+x*f^-2*(b*f^2+x*e^2))^(1/2)))^-1*(-1*b*f^2+2*d*e)^-1*(-1*b^2*f^2+4*a*e^2)+-1//2*e^-1*f^2*(-1*b*f^2+2*d*e)^-2*(-1*b^2*f^2+4*a*e^2)*log(b*f^2+2*e*(e*x+f*(a+x*f^-2*(b*f^2+x*e^2))^(1/2))))
@test integrate((d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^-2, x) == :(-1*(-1*b*f^2+2*d*e)^-2*(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^-1*(2*e*d^2+-2*b*d*f^2+2*a*e*f^2)+-1*f^2*(b*f^2+2*e*(e*x+f*(a+x*f^-2*(b*f^2+x*e^2))^(1/2)))^-1*(-1*b*f^2+2*d*e)^-2*(-1*b^2*f^2+4*a*e^2)+-2*f^2*(-1*b*f^2+2*d*e)^-3*(-1*b^2*f^2+4*a*e^2)*log(b*f^2+2*e*(e*x+f*(a+x*f^-2*(b*f^2+x*e^2))^(1/2)))+2*f^2*(-1*b*f^2+2*d*e)^-3*(-1*b^2*f^2+4*a*e^2)*log(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2)))
@test integrate((d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^-3, x) == :(-1*(-1*b*f^2+2*d*e)^-2*(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^-2*(e*d^2+a*e*f^2+-1*b*d*f^2)+-2*f^2*(-1*b*f^2+2*d*e)^-3*(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^-1*(-1*b^2*f^2+4*a*e^2)+-6*e*f^2*(-1*b*f^2+2*d*e)^-4*(-1*b^2*f^2+4*a*e^2)*log(b*f^2+2*e*(e*x+f*(a+x*f^-2*(b*f^2+x*e^2))^(1/2)))+-2*e*f^2*(b*f^2+2*e*(e*x+f*(a+x*f^-2*(b*f^2+x*e^2))^(1/2)))^-1*(-1*b*f^2+2*d*e)^-3*(-1*b^2*f^2+4*a*e^2)+6*e*f^2*(-1*b*f^2+2*d*e)^-4*(-1*b^2*f^2+4*a*e^2)*log(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2)))
@test integrate((d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^5//2, x) == :(1//7*e^-1*(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^7//2+1//12*e^-3*f^2*(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^3//2*(-1*b^2*f^2+4*a*e^2)+1//4*e^-4*f^2*(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^(1/2)*(-1*b*f^2+2*d*e)*(-1*b^2*f^2+4*a*e^2)+-5//32*2^(1/2)*e^-9//2*f^2*(-1*b*f^2+2*d*e)^3//2*(-1*b^2*f^2+4*a*e^2)*arctanh(2^(1/2)*e^(1/2)*(-1*b*f^2+2*d*e)^-1//2*(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^(1/2))+-1//16*e^-4*f^2*(b*f^2+2*e*(e*x+f*(a+x*f^-2*(b*f^2+x*e^2))^(1/2)))^-1*(-1*b*f^2+2*d*e)^2*(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^(1/2)*(-1*b^2*f^2+4*a*e^2))
@test integrate((d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^3//2, x) == :(1//5*e^-1*(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^5//2+1//4*e^-3*f^2*(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^(1/2)*(-1*b^2*f^2+4*a*e^2)+-3//16*2^(1/2)*e^-7//2*f^2*(-1*b*f^2+2*d*e)^(1/2)*(-1*b^2*f^2+4*a*e^2)*arctanh(2^(1/2)*e^(1/2)*(-1*b*f^2+2*d*e)^-1//2*(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^(1/2))+-1//8*e^-3*f^2*(b*f^2+2*e*(e*x+f*(a+x*f^-2*(b*f^2+x*e^2))^(1/2)))^-1*(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^(1/2)*(-1*b*f^2+2*d*e)*(-1*b^2*f^2+4*a*e^2))
@test integrate((d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^(1/2), x) == :(1//3*e^-1*(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^3//2+-1*f^2*(4*b*f^2+8*e*(e*x+f*(a+x*f^-2*(b*f^2+x*e^2))^(1/2)))^-1*(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^(1/2)*(4a+-1*b^2*e^-2*f^2)+-1//8*2^(1/2)*e^-5//2*f^2*(-1*b*f^2+2*d*e)^-1//2*(-1*b^2*f^2+4*a*e^2)*arctanh(2^(1/2)*e^(1/2)*(-1*b*f^2+2*d*e)^-1//2*(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^(1/2)))
@test integrate((d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^-1//2, x) == :(e^-1*(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^(1/2)+-1*f^2*(b*f^2+2*e*(e*x+f*(a+x*f^-2*(b*f^2+x*e^2))^(1/2)))^-1*(-2*b*f^2+4*d*e)^-1*(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^(1/2)*(4*a*e+-1*b^2*e^-1*f^2)+1//4*2^(1/2)*e^-3//2*f^2*(-1*b*f^2+2*d*e)^-3//2*(-1*b^2*f^2+4*a*e^2)*arctanh(2^(1/2)*e^(1/2)*(-1*b*f^2+2*d*e)^-1//2*(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^(1/2)))
@test integrate((d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^-3//2, x) == :(-1*(-1*b*f^2+2*d*e)^-2*(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^-1//2*(4*e*d^2+-4*b*d*f^2+4*a*e*f^2)+-1*f^2*(b*f^2+2*e*(e*x+f*(a+x*f^-2*(b*f^2+x*e^2))^(1/2)))^-1*(-1*b*f^2+2*d*e)^-2*(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^(1/2)*(-1*b^2*f^2+4*a*e^2)+3//2*2^(1/2)*e^-1//2*f^2*(-1*b*f^2+2*d*e)^-5//2*(-1*b^2*f^2+4*a*e^2)*arctanh(2^(1/2)*e^(1/2)*(-1*b*f^2+2*d*e)^-1//2*(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^(1/2)))
@test integrate((d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^-5//2, x) == :(-1//3*(-1*b*f^2+2*d*e)^-2*(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^-3//2*(4*e*d^2+-4*b*d*f^2+4*a*e*f^2)+-4*f^2*(-1*b*f^2+2*d*e)^-3*(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^-1//2*(-1*b^2*f^2+4*a*e^2)+-2*e*f^2*(b*f^2+2*e*(e*x+f*(a+x*f^-2*(b*f^2+x*e^2))^(1/2)))^-1*(-1*b*f^2+2*d*e)^-3*(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^(1/2)*(-1*b^2*f^2+4*a*e^2)+5*2^(1/2)*e^(1/2)*f^2*(-1*b*f^2+2*d*e)^-7//2*(-1*b^2*f^2+4*a*e^2)*arctanh(2^(1/2)*e^(1/2)*(-1*b*f^2+2*d*e)^-1//2*(d+e*x+f*(a+b*x+e^2*f^-2*x^2)^(1/2))^(1/2)))
@test integrate((a+x^2)^2*(x+(a+x^2)^(1/2))^n, x) == :((160+32n)^-1*(x+(a+x^2)^(1/2))^(5+n)+-1*a^5*(160+-32n)^-1*(x+(a+x^2)^(1/2))^(-5+n)+-5*a^3*(16+-16n)^-1*(x+(a+x^2)^(1/2))^(-1+n)+-5*a^4*(96+-32n)^-1*(x+(a+x^2)^(1/2))^(-3+n)+5*a*(96+32n)^-1*(x+(a+x^2)^(1/2))^(3+n)+5*a^2*(16+16n)^-1*(x+(a+x^2)^(1/2))^(1+n))
@test integrate((x+(a+x^2)^(1/2))^n*(a+x^2), x) == :((24+8n)^-1*(x+(a+x^2)^(1/2))^(3+n)+-1*a^3*(24+-8n)^-1*(x+(a+x^2)^(1/2))^(-3+n)+-3*a^2*(8+-8n)^-1*(x+(a+x^2)^(1/2))^(-1+n)+3*a*(8+8n)^-1*(x+(a+x^2)^(1/2))^(1+n))
@test integrate((x+(a+x^2)^(1/2))^n, x) == :((2+2n)^-1*(x+(a+x^2)^(1/2))^(1+n)+-1*a*(2+-2n)^-1*(x+(a+x^2)^(1/2))^(-1+n))
@test integrate((a+x^2)^2*(x+-1*(a+x^2)^(1/2))^n, x) == :((160+32n)^-1*(x+-1*(a+x^2)^(1/2))^(5+n)+-1*a^5*(160+-32n)^-1*(x+-1*(a+x^2)^(1/2))^(-5+n)+-5*a^3*(16+-16n)^-1*(x+-1*(a+x^2)^(1/2))^(-1+n)+-5*a^4*(96+-32n)^-1*(x+-1*(a+x^2)^(1/2))^(-3+n)+5*a*(96+32n)^-1*(x+-1*(a+x^2)^(1/2))^(3+n)+5*a^2*(16+16n)^-1*(x+-1*(a+x^2)^(1/2))^(1+n))
@test integrate((x+-1*(a+x^2)^(1/2))^n*(a+x^2), x) == :((24+8n)^-1*(x+-1*(a+x^2)^(1/2))^(3+n)+-1*a^3*(24+-8n)^-1*(x+-1*(a+x^2)^(1/2))^(-3+n)+-3*a^2*(8+-8n)^-1*(x+-1*(a+x^2)^(1/2))^(-1+n)+3*a*(8+8n)^-1*(x+-1*(a+x^2)^(1/2))^(1+n))
@test integrate((x+-1*(a+x^2)^(1/2))^n, x) == :((2+2n)^-1*(x+-1*(a+x^2)^(1/2))^(1+n)+-1*a*(2+-2n)^-1*(x+-1*(a+x^2)^(1/2))^(-1+n))
@test integrate((a+x^2)^5//2*(x+(a+x^2)^(1/2))^n, x) == :((384+64n)^-1*(x+(a+x^2)^(1/2))^(6+n)+-1*a^6*(384+-64n)^-1*(x+(a+x^2)^(1/2))^(-6+n)+-15*a^4*(128+-64n)^-1*(x+(a+x^2)^(1/2))^(-2+n)+-3*a^5*(128+-32n)^-1*(x+(a+x^2)^(1/2))^(-4+n)+3*a*(128+32n)^-1*(x+(a+x^2)^(1/2))^(4+n)+15*a^2*(128+64n)^-1*(x+(a+x^2)^(1/2))^(2+n)+5//16*a^3*n^-1*(x+(a+x^2)^(1/2))^n)
@test integrate((a+x^2)^3//2*(x+(a+x^2)^(1/2))^n, x) == :((64+16n)^-1*(x+(a+x^2)^(1/2))^(4+n)+a*(8+4n)^-1*(x+(a+x^2)^(1/2))^(2+n)+-1*a^3*(8+-4n)^-1*(x+(a+x^2)^(1/2))^(-2+n)+-1*a^4*(64+-16n)^-1*(x+(a+x^2)^(1/2))^(-4+n)+3//8*a^2*n^-1*(x+(a+x^2)^(1/2))^n)
@test integrate((a+x^2)^(1/2)*(x+(a+x^2)^(1/2))^n, x) == :((8+4n)^-1*(x+(a+x^2)^(1/2))^(2+n)+(1/2)*a*n^-1*(x+(a+x^2)^(1/2))^n+-1*a^2*(8+-4n)^-1*(x+(a+x^2)^(1/2))^(-2+n))
@test integrate((a+x^2)^-1//2*(x+(a+x^2)^(1/2))^n, x) == :(n^-1*(x+(a+x^2)^(1/2))^n)
@test integrate((a+x^2)^5//2*(x+-1*(a+x^2)^(1/2))^n, x) == :(-1*(384+64n)^-1*(x+-1*(a+x^2)^(1/2))^(6+n)+a^6*(384+-64n)^-1*(x+-1*(a+x^2)^(1/2))^(-6+n)+-15*a^2*(128+64n)^-1*(x+-1*(a+x^2)^(1/2))^(2+n)+-3*a*(128+32n)^-1*(x+-1*(a+x^2)^(1/2))^(4+n)+3*a^5*(128+-32n)^-1*(x+-1*(a+x^2)^(1/2))^(-4+n)+15*a^4*(128+-64n)^-1*(x+-1*(a+x^2)^(1/2))^(-2+n)+-5//16*a^3*n^-1*(x+-1*(a+x^2)^(1/2))^n)
@test integrate((a+x^2)^3//2*(x+-1*(a+x^2)^(1/2))^n, x) == :(-1*(64+16n)^-1*(x+-1*(a+x^2)^(1/2))^(4+n)+a^3*(8+-4n)^-1*(x+-1*(a+x^2)^(1/2))^(-2+n)+a^4*(64+-16n)^-1*(x+-1*(a+x^2)^(1/2))^(-4+n)+-1*a*(8+4n)^-1*(x+-1*(a+x^2)^(1/2))^(2+n)+-3//8*a^2*n^-1*(x+-1*(a+x^2)^(1/2))^n)
@test integrate((a+x^2)^(1/2)*(x+-1*(a+x^2)^(1/2))^n, x) == :(-1*(8+4n)^-1*(x+-1*(a+x^2)^(1/2))^(2+n)+a^2*(8+-4n)^-1*(x+-1*(a+x^2)^(1/2))^(-2+n)+-1//2*a*n^-1*(x+-1*(a+x^2)^(1/2))^n)
@test integrate((a+x^2)^-1//2*(x+-1*(a+x^2)^(1/2))^n, x) == :(-1*n^-1*(x+-1*(a+x^2)^(1/2))^n)
@test integrate((a+e^2*f^-2*x^2+2*d*e*x*f^-2)^2*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^n, x) == :(1//32*e^-1*f^-4*(5+n)^-1*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^(5+n)+-5//32*e^-1*f^-4*(3+-1n)^-1*(d^2+-1*a*f^2)^4*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^(-3+n)+-1//32*e^-1*f^-4*(3+n)^-1*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^(3+n)*(5*d^2+-5*a*f^2)+1//32*e^-1*f^-4*(5+-1n)^-1*(d^2+-1*a*f^2)^5*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^(-5+n)+5//16*e^-1*f^-4*(1+n)^-1*(d^2+-1*a*f^2)^2*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^(1+n)+5//16*e^-1*f^-4*(1+-1n)^-1*(d^2+-1*a*f^2)^3*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^(-1+n))
@test integrate((d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^n*(a+e^2*f^-2*x^2+2*d*e*x*f^-2), x) == :(1//8*e^-1*f^-2*(3+n)^-1*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^(3+n)+-3//8*e^-1*f^-2*(1+-1n)^-1*(d^2+-1*a*f^2)^2*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^(-1+n)+-1//8*e^-1*f^-2*(1+n)^-1*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^(1+n)*(3*d^2+-3*a*f^2)+1//8*e^-1*f^-2*(3+-1n)^-1*(d^2+-1*a*f^2)^3*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^(-3+n))
@test integrate((d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^n, x) == :((1/2)*e^-1*(1+n)^-1*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^(1+n)+(1/2)*e^-1*(1+-1n)^-1*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^(-1+n)*(d^2+-1*a*f^2))
@test integrate((d+e*x+f*(f^-2*(a*f^2+e*x*(2d+e*x)))^(1/2))^n, x) == :((1/2)*e^-1*(1+n)^-1*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^(1+n)+(1/2)*e^-1*(1+-1n)^-1*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^(-1+n)*(d^2+-1*a*f^2))
@test integrate((a+e^2*f^-2*x^2+2*d*e*x*f^-2)^3//2*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^n, x) == :(1//16*e^-1*f^-3*(4+n)^-1*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^(4+n)+-1//4*e^-1*f^-3*(2+n)^-1*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^(2+n)*(d^2+-1*a*f^2)+-1//16*e^-1*f^-3*(4+-1n)^-1*(d^2+-1*a*f^2)^4*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^(-4+n)+1//4*e^-1*f^-3*(2+-1n)^-1*(d^2+-1*a*f^2)^3*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^(-2+n)+3//8*e^-1*f^-3*n^-1*(d^2+-1*a*f^2)^2*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^n)
@test integrate((a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2)*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^n, x) == :(1//4*e^-1*f^-1*(2+n)^-1*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^(2+n)+-1//2*e^-1*f^-1*n^-1*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^n*(d^2+-1*a*f^2)+-1//4*e^-1*f^-1*(2+-1n)^-1*(d^2+-1*a*f^2)^2*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^(-2+n))
@test integrate((a+e^2*f^-2*x^2+2*d*e*x*f^-2)^-1//2*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^n, x) == :(f*e^-1*n^-1*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^n)
@test integrate((f^-2*(a*f^2+e*x*(2d+e*x)))^-1//2*(d+e*x+f*(f^-2*(a*f^2+e*x*(2d+e*x)))^(1/2))^n, x) == :(f*e^-1*n^-1*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^n)
@test integrate((d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^n*(a*g+g*e^2*f^-2*x^2+2*d*e*g*x*f^-2)^(1/2), x) == :(1//4*e^-1*f^-1*(2+n)^-1*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^-1//2*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^(2+n)*(a*g+g*e^2*f^-2*x^2+2*d*e*g*x*f^-2)^(1/2)+-1//2*e^-1*f^-1*n^-1*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^-1//2*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^n*(a*g+g*e^2*f^-2*x^2+2*d*e*g*x*f^-2)^(1/2)*(d^2+-1*a*f^2)+-1//4*e^-1*f^-1*(2+-1n)^-1*(d^2+-1*a*f^2)^2*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^-1//2*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^(-2+n)*(a*g+g*e^2*f^-2*x^2+2*d*e*g*x*f^-2)^(1/2))
@test integrate((d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^n*(a*g+g*e^2*f^-2*x^2+2*d*e*g*x*f^-2)^-1//2, x) == :(f*e^-1*n^-1*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2)*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^n*(a*g+g*e^2*f^-2*x^2+2*d*e*g*x*f^-2)^-1//2)
@test integrate((f^-2*(a*g*f^2+e*g*x*(2d+e*x)))^-1//2*(d+e*x+f*(f^-2*(a*f^2+e*x*(2d+e*x)))^(1/2))^n, x) == :(f*e^-1*n^-1*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2)*(d+e*x+f*(a+e^2*f^-2*x^2+2*d*e*x*f^-2)^(1/2))^n*(a*g+g*e^2*f^-2*x^2+2*d*e*g*x*f^-2)^-1//2)
@test integrate((e^2+4*f^2*x^4+4*d*f*x^2+4*e*f*x^2)^-1*(e+-2*f*x^2), x) == :(-1//4*f^-1//2*(-1d)^-1//2*log(e+2*f*x^2+-2*x*f^(1/2)*(-1d)^(1/2))+1//4*f^-1//2*(-1d)^-1//2*log(e+2*f*x^2+2*x*f^(1/2)*(-1d)^(1/2)))
@test integrate((e^2+4*f^2*x^4+-4*d*f*x^2+4*e*f*x^2)^-1*(e+-2*f*x^2), x) == :(-1//4*d^-1//2*f^-1//2*log(e+2*f*x^2+-2*x*d^(1/2)*f^(1/2))+1//4*d^-1//2*f^-1//2*log(e+2*f*x^2+2*x*d^(1/2)*f^(1/2)))
@test integrate((e^2+4*f^2*x^6+4*d*f*x^2+4*e*f*x^3)^-1*(e+-4*f*x^3), x) == :((1/2)*d^-1//2*f^-1//2*arctan(2*x*d^(1/2)*f^(1/2)*(e+2*f*x^3)^-1))
@test integrate((e^2+4*f^2*x^6+-4*d*f*x^2+4*e*f*x^3)^-1*(e+-4*f*x^3), x) == :((1/2)*d^-1//2*f^-1//2*arctanh(2*x*d^(1/2)*f^(1/2)*(e+2*f*x^3)^-1))
@test integrate((e^2+4*f^2*x^(2n)+4*d*f*x^2+4*e*f*x^n)^-1*(e+-2*f*x^n*(-1+n)), x) == :((1/2)*d^-1//2*f^-1//2*arctan(2*x*d^(1/2)*f^(1/2)*(e+2*f*x^n)^-1))
@test integrate((e^2+4*f^2*x^(2n)+-4*d*f*x^2+4*e*f*x^n)^-1*(e+-2*f*x^n*(-1+n)), x) == :((1/2)*d^-1//2*f^-1//2*arctanh(2*x*d^(1/2)*f^(1/2)*(e+2*f*x^n)^-1))
@test integrate(x*(e^2+4*f^2*x^4+4*d*f*x^4+4*e*f*x^2)^-1, x) == :(1//4*d^-1//2*e^-1*f^-1//2*arctan(d^-1//2*e^-1*f^(1/2)*(e+x^2*(2d+2*f))))
@test integrate(x*(e^2+4*f^2*x^4+-4*d*f*x^4+4*e*f*x^2)^-1, x) == :(-1//4*d^-1//2*e^-1*f^-1//2*arctanh(d^-1//2*e^-1*f^(1/2)*(e+-1*x^2*(-2*f+2d))))
@test integrate(x^2*(e^2+4*f^2*x^4+4*d*f*x^6+4*e*f*x^2)^-1*(3*e+2*f*x^2), x) == :((1/2)*d^-1//2*f^-1//2*arctan(2*d^(1/2)*f^(1/2)*x^3*(e+2*f*x^2)^-1))
@test integrate(x^2*(e^2+4*f^2*x^4+-4*d*f*x^6+4*e*f*x^2)^-1*(3*e+2*f*x^2), x) == :((1/2)*d^-1//2*f^-1//2*arctanh(2*d^(1/2)*f^(1/2)*x^3*(e+2*f*x^2)^-1))
@test integrate(x*(e^2+4*f^2*x^6+4*d*f*x^4+4*e*f*x^3)^-1*(2*e+-2*f*x^3), x) == :((1/2)*d^-1//2*f^-1//2*arctan(2*d^(1/2)*f^(1/2)*x^2*(e+2*f*x^3)^-1))
@test integrate(x*(e^2+4*f^2*x^6+-4*d*f*x^4+4*e*f*x^3)^-1*(2*e+-2*f*x^3), x) == :((1/2)*d^-1//2*f^-1//2*arctanh(2*d^(1/2)*f^(1/2)*x^2*(e+2*f*x^3)^-1))
@test integrate(x^2*(e^2+4*f^2*x^6+4*d*f*x^6+4*e*f*x^3)^-1, x) == :(1//6*d^-1//2*e^-1*f^-1//2*arctan(d^-1//2*e^-1*f^(1/2)*(e+x^3*(2d+2*f))))
@test integrate(x^2*(e^2+4*f^2*x^6+-4*d*f*x^6+4*e*f*x^3)^-1, x) == :(-1//6*d^-1//2*e^-1*f^-1//2*arctanh(d^-1//2*e^-1*f^(1/2)*(e+-1*x^3*(-2*f+2d))))
@test integrate(x^m*(e^2+4*f^2*x^6+4*d*f*x^(2+2m)+4*e*f*x^3)^-1*(e*(1+m)+2*f*x^3*(-2+m)), x) == :((1/2)*d^-1//2*f^-1//2*arctan(2*d^(1/2)*f^(1/2)*x^(1+m)*(e+2*f*x^3)^-1))
@test integrate(x^m*(e^2+4*f^2*x^6+-4*d*f*x^(2+2m)+4*e*f*x^3)^-1*(e*(1+m)+2*f*x^3*(-2+m)), x) == :((1/2)*d^-1//2*f^-1//2*arctanh(2*d^(1/2)*f^(1/2)*x^(1+m)*(e+2*f*x^3)^-1))
@test integrate(x^m*(e^2+4*f^2*x^(2n)+4*d*f*x^(2+2m)+4*e*f*x^n)^-1*(e*(1+m)+2*f*x^n*(1+m+-1n)), x) == :((1/2)*d^-1//2*f^-1//2*arctan(2*d^(1/2)*f^(1/2)*x^(1+m)*(e+2*f*x^n)^-1))
@test integrate(x^m*(e^2+4*f^2*x^(2n)+-4*d*f*x^(2+2m)+4*e*f*x^n)^-1*(e*(1+m)+2*f*x^n*(1+m+-1n)), x) == :((1/2)*d^-1//2*f^-1//2*arctanh(2*d^(1/2)*f^(1/2)*x^(1+m)*(e+2*f*x^n)^-1))
@test integrate(x^5*(a*c+d*(a+b*x^2)^(1/2)+b*c*x^2)^-1, x) == :(1//4*b^-3*c^-1*(a+b*x^2)^2+b^-3*c^-5*(-1*d^2+a*c^2)^2*log(d+c*(a+b*x^2)^(1/2))+-1//2*b^-2*c^-3*x^2*(-1*d^2+2*a*c^2)+-1//3*d*b^-3*c^-2*(a+b*x^2)^3//2+d*b^-3*c^-4*(a+b*x^2)^(1/2)*(-1*d^2+2*a*c^2))
@test integrate(x^3*(a*c+d*(a+b*x^2)^(1/2)+b*c*x^2)^-1, x) == :((1/2)*b^-1*c^-1*x^2+-1*d*b^-2*c^-2*(a+b*x^2)^(1/2)+-1*b^-2*c^-3*(-1*d^2+a*c^2)*log(d+c*(a+b*x^2)^(1/2)))
@test integrate(x*(a*c+d*(a+b*x^2)^(1/2)+b*c*x^2)^-1, x) == :(b^-1*c^-1*log(d+c*(a+b*x^2)^(1/2)))
@test integrate(x^-1*(a*c+d*(a+b*x^2)^(1/2)+b*c*x^2)^-1, x) == :(c*(-1*d^2+a*c^2)^-1*log(x)+-1*c*(-1*d^2+a*c^2)^-1*log(d+c*(a+b*x^2)^(1/2))+d*a^-1//2*(-1*d^2+a*c^2)^-1*arctanh(a^-1//2*(a+b*x^2)^(1/2)))
@test integrate(x^-3*(a*c+d*(a+b*x^2)^(1/2)+b*c*x^2)^-1, x) == :(b*c^3*(-1*d^2+a*c^2)^-2*log(d+c*(a+b*x^2)^(1/2))+-1*b*c^3*(-1*d^2+a*c^2)^-2*log(x)+-1//2*a^-1*x^-2*(-1*d^2+a*c^2)^-1*(a*c+-1*d*(a+b*x^2)^(1/2))+-1//2*b*d*a^-3//2*(-1*d^2+a*c^2)^-2*(-1*d^2+3*a*c^2)*arctanh(a^-1//2*(a+b*x^2)^(1/2)))
@test integrate(x^2*(a*c+d*(a+b*x^2)^(1/2)+b*c*x^2)^-1, x) == :(x*b^-1*c^-1+b^-3//2*c^-2*(-1*d^2+a*c^2)^(1/2)*arctan(d*x*b^(1/2)*(a+b*x^2)^-1//2*(-1*d^2+a*c^2)^-1//2)+-1*d*b^-3//2*c^-2*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+-1*b^-3//2*c^-2*(-1*d^2+a*c^2)^(1/2)*arctan(c*x*b^(1/2)*(-1*d^2+a*c^2)^-1//2))
@test integrate((a*c+d*(a+b*x^2)^(1/2)+b*c*x^2)^-1, x) == :(b^-1//2*(-1*d^2+a*c^2)^-1//2*arctan(c*x*b^(1/2)*(-1*d^2+a*c^2)^-1//2)+-1*b^-1//2*(-1*d^2+a*c^2)^-1//2*arctan(d*x*b^(1/2)*(a+b*x^2)^-1//2*(-1*d^2+a*c^2)^-1//2))
@test integrate(x^-2*(a*c+d*(a+b*x^2)^(1/2)+b*c*x^2)^-1, x) == :(-1*c*x^-1*(-1*d^2+a*c^2)^-1+b^(1/2)*c^2*(-1*d^2+a*c^2)^-3//2*arctan(d*x*b^(1/2)*(a+b*x^2)^-1//2*(-1*d^2+a*c^2)^-1//2)+-1*b^(1/2)*c^2*(-1*d^2+a*c^2)^-3//2*arctan(c*x*b^(1/2)*(-1*d^2+a*c^2)^-1//2)+d*a^-1*x^-1*(a+b*x^2)^(1/2)*(-1*d^2+a*c^2)^-1)
@test integrate(x^8*(a*c+d*(a+b*x^3)^(1/2)+b*c*x^3)^-1, x) == :(1//6*b^-3*c^-1*(a+b*x^3)^2+-2//9*d*b^-3*c^-2*(a+b*x^3)^3//2+-1//3*b^-2*c^-3*x^3*(-1*d^2+2*a*c^2)+2//3*b^-3*c^-5*(-1*d^2+a*c^2)^2*log(d+c*(a+b*x^3)^(1/2))+2//3*d*b^-3*c^-4*(a+b*x^3)^(1/2)*(-1*d^2+2*a*c^2))
@test integrate(x^5*(a*c+d*(a+b*x^3)^(1/2)+b*c*x^3)^-1, x) == :(1//3*b^-1*c^-1*x^3+-2//3*d*b^-2*c^-2*(a+b*x^3)^(1/2)+-1//3*b^-2*c^-3*(-2*d^2+2*a*c^2)*log(d+c*(a+b*x^3)^(1/2)))
@test integrate(x^2*(a*c+d*(a+b*x^3)^(1/2)+b*c*x^3)^-1, x) == :(2//3*b^-1*c^-1*log(d+c*(a+b*x^3)^(1/2)))
@test integrate(x^-1*(a*c+d*(a+b*x^3)^(1/2)+b*c*x^3)^-1, x) == :(c*(-1*d^2+a*c^2)^-1*log(x)+-2*c*(-3*d^2+3*a*c^2)^-1*log(d+c*(a+b*x^3)^(1/2))+2//3*d*a^-1//2*(-1*d^2+a*c^2)^-1*arctanh(a^-1//2*(a+b*x^3)^(1/2)))
@test integrate(x^-4*(a*c+d*(a+b*x^3)^(1/2)+b*c*x^3)^-1, x) == :(-1*b*c^3*(-1*d^2+a*c^2)^-2*log(x)+-1//3*a^-1*x^-3*(-1*d^2+a*c^2)^-1*(a*c+-1*d*(a+b*x^3)^(1/2))+2//3*b*c^3*(-1*d^2+a*c^2)^-2*log(d+c*(a+b*x^3)^(1/2))+-1//3*b*d*a^-3//2*(-1*d^2+a*c^2)^-2*(-1*d^2+3*a*c^2)*arctanh(a^-1//2*(a+b*x^3)^(1/2)))
@test integrate(x^(-1+n)*(a*c+d*(a+b*x^n)^(1/2)+b*c*x^n)^-1, x) == :(2*b^-1*c^-1*n^-1*log(d+c*(a+b*x^n)^(1/2)))
@test integrate((x^(1/2)+4*x^3//2)^-1, x) == :(arctan(2*x^(1/2)))
@test integrate((x^(1/2)+-1*x^5//2)^-1, x) == :(arctan(x^(1/2))+arctanh(x^(1/2)))
@test integrate((x^(1/2)+-1*x^1//4)^-1, x) == :(2*x^(1/2)+4*x^1//4+4*log(1+-1*x^1//4))
@test integrate((x^(1/2)+x^1//3)^-1, x) == :(-6*log(1+x^1//6)+-3*x^1//3+2*x^(1/2)+6*x^1//6)
@test integrate((x^(1/2)+x^1//4)^-1, x) == :(-4*x^1//4+2*x^(1/2)+4*log(1+x^1//4))
@test integrate((x^2//3+-1*x^1//3)^-1, x) == :(3*x^1//3+3*log(1+-1*x^1//3))
@test integrate((x^(1/2)+x^-1//4)^-1, x) == :(2*x^(1/2)+-2//3*log(1+x^(1/2)+-1*x^1//4)+4//3*log(1+x^1//4)+4//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x^1//4)))
@test integrate((x^1//3+x^1//4)^-1, x) == :(-12*x^1//12+-4*x^1//4+2*x^(1/2)+3*x^1//3+6*x^1//6+12*log(1+x^1//12)+-12//5*x^5//12+-12//7*x^7//12+3//2*x^2//3)
@test integrate((x^-1//3+x^-1//4)^-1, x) == :(-1x+-12*log(1+x^1//12)+-6*x^1//6+-3*x^1//3+-2*x^(1/2)+4*x^1//4+12*x^1//12+-6//5*x^5//6+-6//7*x^7//6+-3//2*x^2//3+4//3*x^3//4+4//5*x^5//4+12//5*x^5//12+12//7*x^7//12+12//11*x^11//12+12//13*x^13//12)
@test integrate((x^(1/2)+-1*x^-1//3)^-1, x) == :(2*x^(1/2)+6//5*log(1+-1*x^1//6)+-1*(3//10+-3//10*5^(1/2))*log(2+x^1//6+2*x^1//3+5^(1/2)*x^1//6)+-1*(3//10+3//10*5^(1/2))*log(2+x^1//6+2*x^1//3+-1*5^(1/2)*x^1//6)+-3//5*(10+2*5^(1/2))^(1/2)*arctan((1/2)*(1/2+1//10*5^(1/2))^(1/2)*(1+5^(1/2)+4*x^1//6))+3//5*(10+-2*5^(1/2))^(1/2)*arctan((10+2*5^(1/2))^-1//2*(1+-1*5^(1/2)+4*x^1//6)))
@test integrate(x^(1/2)*(x+x^2)^-1, x) == :(2*arctan(x^(1/2)))
@test integrate(x*(x+4*x^(1/2))^-1, x) == :(x+-8*x^(1/2)+32*log(4+x^(1/2)))
@test integrate(x^(1/2)*(x+x^1//3)^-1, x) == :(2*x^(1/2)+-3//2*2^(1/2)*arctan(1+2^(1/2)*x^1//6)+-3//4*2^(1/2)*log(1+x^1//3+-1*2^(1/2)*x^1//6)+3//2*2^(1/2)*arctan(1+-1*2^(1/2)*x^1//6)+3//4*2^(1/2)*log(1+x^1//3+2^(1/2)*x^1//6))
@test integrate(x^1//3*(x^(1/2)+x^1//4)^-1, x) == :(-12*x^1//12+-2*log(1+x^1//4)+3*x^1//3+6*log(1+x^1//12)+-12//7*x^7//12+6//5*x^5//6+-4*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x^1//12)))
@test integrate(x^(1/2)*(x^1//3+x^1//4)^-1, x) == :(x+-12*x^1//12+-4*x^1//4+2*x^(1/2)+3*x^1//3+6*x^1//6+12*log(1+x^1//12)+-12//5*x^5//12+-12//7*x^7//12+-12//11*x^11//12+-12//13*x^13//12+-4//3*x^3//4+3//2*x^2//3+6//5*x^5//6+6//7*x^7//6)
@test integrate(x^(1/2)*(x^(1/2)+-1*x^-1//3)^-1, x) == :(x+6*x^1//6+6//5*log(1+-1*x^1//6)+-1*(3//10+-3//10*5^(1/2))*log(2+x^1//6+2*x^1//3+-1*5^(1/2)*x^1//6)+-1*(3//10+3//10*5^(1/2))*log(2+x^1//6+2*x^1//3+5^(1/2)*x^1//6)+-3//5*(10+-2*5^(1/2))^(1/2)*arctan((1/2)*(1/2+1//10*5^(1/2))^(1/2)*(1+5^(1/2)+4*x^1//6))+-3//5*(10+2*5^(1/2))^(1/2)*arctan((10+2*5^(1/2))^-1//2*(1+-1*5^(1/2)+4*x^1//6)))
@test integrate(x^m*(a+-1*b*x)^-1//2*(b+-1*a*x^-1)^(1/2), x) == :(2*x^(1+m)*(1+2m)^-1*(a+-1*b*x)^-1//2*(b+-1*a*x^-1)^(1/2))
@test integrate(x^2*(a+-1*b*x)^-1//2*(b+-1*a*x^-1)^(1/2), x) == :(2//5*x^3*(a+-1*b*x)^-1//2*(b+-1*a*x^-1)^(1/2))
@test integrate(x*(a+-1*b*x)^-1//2*(b+-1*a*x^-1)^(1/2), x) == :(2//3*x^2*(a+-1*b*x)^-1//2*(b+-1*a*x^-1)^(1/2))
@test integrate((a+-1*b*x)^-1//2*(b+-1*a*x^-1)^(1/2), x) == :(2*x*(a+-1*b*x)^-1//2*(b+-1*a*x^-1)^(1/2))
@test integrate(x^-1*(a+-1*b*x)^-1//2*(b+-1*a*x^-1)^(1/2), x) == :(-2*(a+-1*b*x)^-1//2*(b+-1*a*x^-1)^(1/2))
@test integrate(x^-2*(a+-1*b*x)^-1//2*(b+-1*a*x^-1)^(1/2), x) == :(-2//3*x^-1*(a+-1*b*x)^-1//2*(b+-1*a*x^-1)^(1/2))
@test integrate(x^m*(a+-1*b*x^2)^-1//2*(b+-1*a*x^-2)^(1/2), x) == :(m^-1*x^(1+m)*(a+-1*b*x^2)^-1//2*(b+-1*a*x^-2)^(1/2))
@test integrate(x^2*(a+-1*b*x^2)^-1//2*(b+-1*a*x^-2)^(1/2), x) == :((1/2)*x^3*(a+-1*b*x^2)^-1//2*(b+-1*a*x^-2)^(1/2))
@test integrate(x*(a+-1*b*x^2)^-1//2*(b+-1*a*x^-2)^(1/2), x) == :(x^2*(a+-1*b*x^2)^-1//2*(b+-1*a*x^-2)^(1/2))
@test integrate((a+-1*b*x^2)^-1//2*(b+-1*a*x^-2)^(1/2), x) == :(x*(a+-1*b*x^2)^-1//2*(b+-1*a*x^-2)^(1/2)*log(x))
@test integrate(x^-1*(a+-1*b*x^2)^-1//2*(b+-1*a*x^-2)^(1/2), x) == :(-1*(a+-1*b*x^2)^-1//2*(b+-1*a*x^-2)^(1/2))
@test integrate(x^-2*(a+-1*b*x^2)^-1//2*(b+-1*a*x^-2)^(1/2), x) == :(-1//2*x^-1*(a+-1*b*x^2)^-1//2*(b+-1*a*x^-2)^(1/2))
@test integrate((a+b*x^-2)^-1//2*(c+d*x)^3//2, x) == :(2//5*a^-1*x^-1*(a+b*x^-2)^-1//2*(c+d*x)^3//2*(b+a*x^2)+2//5*c*a^-1*x^-1*(a+b*x^-2)^-1//2*(c+d*x)^(1/2)*(b+a*x^2)+2//5*b^(1/2)*d^-1*x^-1*(-1a)^-3//2*(a*(a*c+-1*d*b^(1/2)*(-1a)^(1/2))^-1*(c+d*x))^-1//2*(1+a*b^-1*x^2)^(1/2)*(a+b*x^-2)^-1//2*(c+d*x)^(1/2)*(a*c^2+-3*b*d^2)*Elliptic.E(arcsin((1/2)*2^(1/2)*(1+-1*x*b^-1//2*(-1a)^(1/2))^(1/2)),-2*d*b^(1/2)*(-1a)^(1/2)*(a*c+-1*d*b^(1/2)*(-1a)^(1/2))^-1)+-2//5*c*b^(1/2)*d^-1*x^-1*(-1a)^-3//2*(a*(a*c+-1*d*b^(1/2)*(-1a)^(1/2))^-1*(c+d*x))^(1/2)*(1+a*b^-1*x^2)^(1/2)*(a+b*x^-2)^-1//2*(c+d*x)^-1//2*(a*c^2+b*d^2)*Elliptic.F(arcsin((1/2)*2^(1/2)*(1+-1*x*b^-1//2*(-1a)^(1/2))^(1/2)),-2*d*b^(1/2)*(-1a)^(1/2)*(a*c+-1*d*b^(1/2)*(-1a)^(1/2))^-1))
@test integrate((x^4+-4x)^-2//3*(-1+x^3), x) == :(3//4*(x^4+-4x)^1//3)
@test integrate((-1*x^3+6x)^1//4*(2+-1*x^2), x) == :(4//15*(-1*x^3+6x)^5//4)
@test integrate((x^5+5x)^(1/2)*(1+x^4), x) == :(2//15*(x^5+5x)^3//2)
@test integrate((x^5+2x)^(1/2)*(2+5*x^4), x) == :(2//3*(x^5+2x)^3//2)
@test integrate((x^2+2*x^3)^-1//2*(x+3*x^2), x) == :((x^2+2*x^3)^(1/2))
@test integrate((3+(1+-5x)^1//3)^-1*(2+(1+-5x)^1//3), x) == :(x+-9//5*(1+-5x)^1//3+3//10*(1+-5x)^2//3+27//5*log(3+(1+-5x)^1//3))
@test integrate((-1+x^(1/2))^-1*(1+x^(1/2)), x) == :(x+4*x^(1/2)+4*log(1+-1*x^(1/2)))
@test integrate((1+(2+3x)^(1/2))^-1*(1+-1*(2+3x)^(1/2)), x) == :(-1x+-4//3*log(1+(2+3x)^(1/2))+4//3*(2+3x)^(1/2))
@test integrate((1+(a+b*x)^(1/2))^-1*(-1+(a+b*x)^(1/2)), x) == :(x+-4*b^-1*(a+b*x)^(1/2)+4*b^-1*log(1+(a+b*x)^(1/2)))
@test integrate(x^(-1n)*(b+a*x^(1+-1n))^-1*(a+b*n*x^(-1+n)), x) == :(n*log(x)+log(b+a*x^(1+-1n)))
@test integrate(x*(a+b*x+c*x^2)^m*(d+e*x+f*x^2+g*x^3)^n*(x*(3*a*e+3*b*d+a*e*n+b*d*m)+x^2*(4*a*f+4*b*e+4*c*d+b*e*m+b*e*n+2*a*f*n+2*c*d*m)+x^3*(5*a*g+5*b*f+5*c*e+b*f*m+c*e*n+2*b*f*n+2*c*e*m+3*a*g*n)+x^4*(6*b*g+6*c*f+b*g*m+2*c*f*m+2*c*f*n+3*b*g*n)+2*a*d+c*g*x^5*(7+2m+3n)), x) == :(x^2*(a+b*x+c*x^2)^(1+m)*(d+e*x+f*x^2+g*x^3)^(1+n))
@test integrate((a+b*x+c*x^2)^m*(d+e*x+f*x^2+g*x^3)^n*(a*d+x*(2*a*e+2*b*d+a*e*n+b*d*m)+x^2*(3*a*f+3*b*e+3*c*d+b*e*m+b*e*n+2*a*f*n+2*c*d*m)+x^3*(4*a*g+4*b*f+4*c*e+b*f*m+c*e*n+2*b*f*n+2*c*e*m+3*a*g*n)+x^4*(5*b*g+5*c*f+b*g*m+2*c*f*m+2*c*f*n+3*b*g*n)+c*g*x^5*(6+2m+3n)), x) == :(x*(a+b*x+c*x^2)^(1+m)*(d+e*x+f*x^2+g*x^3)^(1+n))
@test integrate((a+b*x+c*x^2)^m*(d+e*x+f*x^2+g*x^3)^n*(a*e+b*d+x*(2*a*f+2*b*e+2*c*d+b*e*m+b*e*n+2*a*f*n+2*c*d*m)+x^2*(3*a*g+3*b*f+3*c*e+b*f*m+c*e*n+2*b*f*n+2*c*e*m+3*a*g*n)+x^3*(4*b*g+4*c*f+b*g*m+2*c*f*m+2*c*f*n+3*b*g*n)+a*e*n+b*d*m+c*g*x^4*(5+2m+3n)), x) == :((a+b*x+c*x^2)^(1+m)*(d+e*x+f*x^2+g*x^3)^(1+n))
@test integrate(x^-2*(a+b*x+c*x^2)^m*(d+e*x+f*x^2+g*x^3)^n*(x*(a*e*n+b*d*m)+x^2*(a*f+b*e+c*d+b*e*m+b*e*n+2*a*f*n+2*c*d*m)+x^3*(2*a*g+2*b*f+2*c*e+b*f*m+c*e*n+2*b*f*n+2*c*e*m+3*a*g*n)+x^4*(3*b*g+3*c*f+b*g*m+2*c*f*m+2*c*f*n+3*b*g*n)+-1*a*d+c*g*x^5*(4+2m+3n)), x) == :(x^-1*(a+b*x+c*x^2)^(1+m)*(d+e*x+f*x^2+g*x^3)^(1+n))
@test integrate(x^-3*(a+b*x+c*x^2)^m*(d+e*x+f*x^2+g*x^3)^n*(x*(-1*a*e+-1*b*d+a*e*n+b*d*m)+x^2*(b*e*m+b*e*n+2*a*f*n+2*c*d*m)+x^3*(a*g+b*f+c*e+b*f*m+c*e*n+2*b*f*n+2*c*e*m+3*a*g*n)+x^4*(2*b*g+2*c*f+b*g*m+2*c*f*m+2*c*f*n+3*b*g*n)+-2*a*d+c*g*x^5*(3+2m+3n)), x) == :(x^-2*(a+b*x+c*x^2)^(1+m)*(d+e*x+f*x^2+g*x^3)^(1+n))
@test integrate(x^3*(a+b*(c+d*x)^(1/2))^2, x) == :(1//4*d^-4*(c+d*x)^4*(a^2+-3*c*b^2)+1//5*b^2*d^-4*(c+d*x)^5+(1/2)*c^2*d^-4*(c+d*x)^2*(3*a^2+-1*c*b^2)+-1*c*d^-4*(c+d*x)^3*(a^2+-1*c*b^2)+-1*x*a^2*c^3*d^-3+4//9*a*b*d^-4*(c+d*x)^9//2+-12//7*a*b*c*d^-4*(c+d*x)^7//2+-4//3*a*b*c^3*d^-4*(c+d*x)^3//2+12//5*a*b*c^2*d^-4*(c+d*x)^5//2)
@test integrate(x^2*(a+b*(c+d*x)^(1/2))^2, x) == :(1//3*d^-3*(c+d*x)^3*(a^2+-2*c*b^2)+1//4*b^2*d^-3*(c+d*x)^4+x*a^2*c^2*d^-2+-1//2*c*d^-3*(c+d*x)^2*(2*a^2+-1*c*b^2)+4//7*a*b*d^-3*(c+d*x)^7//2+-8//5*a*b*c*d^-3*(c+d*x)^5//2+4//3*a*b*c^2*d^-3*(c+d*x)^3//2)
@test integrate(x*(a+b*(c+d*x)^(1/2))^2, x) == :((1/2)*d^-2*(c+d*x)^2*(a^2+-1*c*b^2)+1//3*b^2*d^-2*(c+d*x)^3+-1*c*x*a^2*d^-1+4//5*a*b*d^-2*(c+d*x)^5//2+-4//3*a*b*c*d^-2*(c+d*x)^3//2)
@test integrate((a+b*(c+d*x)^(1/2))^2, x) == :(x*a^2+(1/2)*b^2*d^-1*(c+d*x)^2+4//3*a*b*d^-1*(c+d*x)^3//2)
@test integrate(x^-1*(a+b*(c+d*x)^(1/2))^2, x) == :((a^2+c*b^2)*log(x)+d*x*b^2+4*a*b*(c+d*x)^(1/2)+-4*a*b*c^(1/2)*arctanh(c^-1//2*(c+d*x)^(1/2)))
@test integrate(x^-2*(a+b*(c+d*x)^(1/2))^2, x) == :(-1*x^-1*(a+b*(c+d*x)^(1/2))^2+d*b^2*log(x)+-2*a*b*d*c^-1//2*arctanh(c^-1//2*(c+d*x)^(1/2)))
@test integrate(x^-3*(a+b*(c+d*x)^(1/2))^2, x) == :(-1//2*x^-2*(a+b*(c+d*x)^(1/2))^2+(1/2)*a*b*c^-3//2*d^2*arctanh(c^-1//2*(c+d*x)^(1/2))+-1//2*b*d*c^-1*x^-1*(a*(c+d*x)^(1/2)+b*c))
@test integrate(x^3*(a+b*(c+d*x)^(1/2))^(1/2), x) == :(4//17*b^-8*d^-4*(a+b*(c+d*x)^(1/2))^17//2+-28//15*a*b^-8*d^-4*(a+b*(c+d*x)^(1/2))^15//2+1//9*b^-8*d^-4*(a+b*(c+d*x)^(1/2))^9//2*(140*a^4+12*b^4*c^2+-120*c*a^2*b^2)+1//13*b^-8*d^-4*(a+b*(c+d*x)^(1/2))^13//2*(84*a^2+-12*c*b^2)+-20//11*a*b^-8*d^-4*(a+b*(c+d*x)^(1/2))^11//2*(7*a^2+-3*c*b^2)+-4//3*a*b^-8*d^-4*(a+b*(c+d*x)^(1/2))^3//2*(a^2+-1*c*b^2)^3+4//5*b^-8*d^-4*(a+b*(c+d*x)^(1/2))^5//2*(a^2+-1*c*b^2)^2*(7*a^2+-1*c*b^2)+-12//7*a*b^-8*d^-4*(a+b*(c+d*x)^(1/2))^7//2*(a^2+-1*c*b^2)*(7*a^2+-3*c*b^2))
@test integrate(x^2*(a+b*(c+d*x)^(1/2))^(1/2), x) == :(4//13*b^-6*d^-3*(a+b*(c+d*x)^(1/2))^13//2+-20//11*a*b^-6*d^-3*(a+b*(c+d*x)^(1/2))^11//2+1//5*b^-6*d^-3*(a+b*(c+d*x)^(1/2))^5//2*(20*a^4+4*b^4*c^2+-24*c*a^2*b^2)+1//9*b^-6*d^-3*(a+b*(c+d*x)^(1/2))^9//2*(40*a^2+-8*c*b^2)+-8//7*a*b^-6*d^-3*(a+b*(c+d*x)^(1/2))^7//2*(5*a^2+-3*c*b^2)+-4//3*a*b^-6*d^-3*(a+b*(c+d*x)^(1/2))^3//2*(a^2+-1*c*b^2)^2)
@test integrate(x*(a+b*(c+d*x)^(1/2))^(1/2), x) == :(4//9*b^-4*d^-2*(a+b*(c+d*x)^(1/2))^9//2+-12//7*a*b^-4*d^-2*(a+b*(c+d*x)^(1/2))^7//2+1//5*b^-4*d^-2*(a+b*(c+d*x)^(1/2))^5//2*(12*a^2+-4*c*b^2)+-4//3*a*b^-4*d^-2*(a+b*(c+d*x)^(1/2))^3//2*(a^2+-1*c*b^2))
@test integrate((a+b*(c+d*x)^(1/2))^(1/2), x) == :(4//5*b^-2*d^-1*(a+b*(c+d*x)^(1/2))^5//2+-4//3*a*b^-2*d^-1*(a+b*(c+d*x)^(1/2))^3//2)
@test integrate(x^-1*(a+b*(c+d*x)^(1/2))^(1/2), x) == :(4*(a+b*(c+d*x)^(1/2))^(1/2)+-2*(a+b*c^(1/2))^(1/2)*arctanh((a+b*c^(1/2))^-1//2*(a+b*(c+d*x)^(1/2))^(1/2))+-2*(a+-1*b*c^(1/2))^(1/2)*arctanh((a+b*(c+d*x)^(1/2))^(1/2)*(a+-1*b*c^(1/2))^-1//2))
@test integrate(x^-2*(a+b*(c+d*x)^(1/2))^(1/2), x) == :(-1*x^-1*(a+b*(c+d*x)^(1/2))^(1/2)+(1/2)*b*d*c^-1//2*(a+-1*b*c^(1/2))^-1//2*arctanh((a+b*(c+d*x)^(1/2))^(1/2)*(a+-1*b*c^(1/2))^-1//2)+-1//2*b*d*c^-1//2*(a+b*c^(1/2))^-1//2*arctanh((a+b*c^(1/2))^-1//2*(a+b*(c+d*x)^(1/2))^(1/2)))
@test integrate(x^-3*(a+b*(c+d*x)^(1/2))^(1/2), x) == :(-1//2*x^-2*(a+b*(c+d*x)^(1/2))^(1/2)+-1//16*b*c^-3//2*d^2*(a+-1*b*c^(1/2))^-3//2*(2a+-3*b*c^(1/2))*arctanh((a+b*(c+d*x)^(1/2))^(1/2)*(a+-1*b*c^(1/2))^-1//2)+1//16*b*c^-3//2*d^2*(a+b*c^(1/2))^-3//2*(2a+3*b*c^(1/2))*arctanh((a+b*c^(1/2))^-1//2*(a+b*(c+d*x)^(1/2))^(1/2))+1//8*b*d*c^-1*x^-1*(a+b*(c+d*x)^(1/2))^(1/2)*(a^2+-1*c*b^2)^-1*(b*c+-1*a*(c+d*x)^(1/2)))
@test integrate(x^3*(a+b*(c+d*x)^(1/2))^-1, x) == :(2//7*b^-1*d^-4*(c+d*x)^7//2+2*b^-7*d^-4*(c+d*x)^(1/2)*(a^2+-1*c*b^2)^3+-1//3*a*b^-2*d^-4*(c+d*x)^3+1//3*b^-5*d^-4*(c+d*x)^3//2*(2*a^4+6*b^4*c^2+-6*c*a^2*b^2)+1//5*b^-3*d^-4*(c+d*x)^5//2*(2*a^2+-6*c*b^2)+-1*a*x*b^-6*d^-3*(a^4+3*b^4*c^2+-3*c*a^2*b^2)+-2*a*b^-8*d^-4*(a^2+-1*c*b^2)^3*log(a+b*(c+d*x)^(1/2))+-1//2*a*b^-4*d^-4*(c+d*x)^2*(a^2+-3*c*b^2))
@test integrate(x^2*(a+b*(c+d*x)^(1/2))^-1, x) == :(2//5*b^-1*d^-3*(c+d*x)^5//2+2*b^-5*d^-3*(c+d*x)^(1/2)*(a^2+-1*c*b^2)^2+-1//2*a*b^-2*d^-3*(c+d*x)^2+1//3*b^-3*d^-3*(c+d*x)^3//2*(2*a^2+-4*c*b^2)+-1*a*x*b^-4*d^-2*(a^2+-2*c*b^2)+-2*a*b^-6*d^-3*(a^2+-1*c*b^2)^2*log(a+b*(c+d*x)^(1/2)))
@test integrate(x*(a+b*(c+d*x)^(1/2))^-1, x) == :(2//3*b^-1*d^-2*(c+d*x)^3//2+b^-3*d^-2*(c+d*x)^(1/2)*(2*a^2+-2*c*b^2)+-1*a*x*b^-2*d^-1+-2*a*b^-4*d^-2*(a^2+-1*c*b^2)*log(a+b*(c+d*x)^(1/2)))
@test integrate((a+b*(c+d*x)^(1/2))^-1, x) == :(2*b^-1*d^-1*(c+d*x)^(1/2)+-2*a*b^-2*d^-1*log(a+b*(c+d*x)^(1/2)))
@test integrate(x^-1*(a+b*(c+d*x)^(1/2))^-1, x) == :(a*(a^2+-1*c*b^2)^-1*log(x)+-2*a*(a^2+-1*c*b^2)^-1*log(a+b*(c+d*x)^(1/2))+2*b*c^(1/2)*(a^2+-1*c*b^2)^-1*arctanh(c^-1//2*(c+d*x)^(1/2)))
@test integrate(x^-2*(a+b*(c+d*x)^(1/2))^-1, x) == :(-1*x^-1*(a^2+-1*c*b^2)^-1*(a+-1*b*(c+d*x)^(1/2))+a*d*b^2*(a^2+-1*c*b^2)^-2*log(x)+-2*a*d*b^2*(a^2+-1*c*b^2)^-2*log(a+b*(c+d*x)^(1/2))+b*d*c^-1//2*(a^2+-1*c*b^2)^-2*(a^2+c*b^2)*arctanh(c^-1//2*(c+d*x)^(1/2)))
@test integrate(x^-3*(a+b*(c+d*x)^(1/2))^-1, x) == :(-1*x^-2*(2*a^2+-2*c*b^2)^-1*(a+-1*b*(c+d*x)^(1/2))+a*b^4*d^2*(a^2+-1*c*b^2)^-3*log(x)+-2*a*b^4*d^2*(a^2+-1*c*b^2)^-3*log(a+b*(c+d*x)^(1/2))+-1//4*b*d*c^-1*x^-1*(a^2+-1*c*b^2)^-2*(-1*(c+d*x)^(1/2)*(a^2+3*c*b^2)+4*a*b*c)+-1//4*b*c^-3//2*d^2*(a^2+-1*c*b^2)^-3*(a^4+-3*b^4*c^2+-6*c*a^2*b^2)*arctanh(c^-1//2*(c+d*x)^(1/2)))
@test integrate(x^3*(a+b*(c+d*x)^(1/2))^-2, x) == :(1//3*b^-2*d^-4*(c+d*x)^3+x*b^-6*d^-3*(5*a^4+3*b^4*c^2+-9*c*a^2*b^2)+(1/2)*b^-4*d^-4*(c+d*x)^2*(3*a^2+-3*c*b^2)+-4//5*a*b^-3*d^-4*(c+d*x)^5//2+-12*a*b^-7*d^-4*(c+d*x)^(1/2)*(a^2+-1*c*b^2)^2+2*a*b^-8*d^-4*(a+b*(c+d*x)^(1/2))^-1*(a^2+-1*c*b^2)^3+2*b^-8*d^-4*(a^2+-1*c*b^2)^2*(7*a^2+-1*c*b^2)*log(a+b*(c+d*x)^(1/2))+-4//3*a*b^-5*d^-4*(c+d*x)^3//2*(2*a^2+-3*c*b^2))
@test integrate(x^2*(a+b*(c+d*x)^(1/2))^-2, x) == :((1/2)*b^-2*d^-3*(c+d*x)^2+x*b^-4*d^-2*(3*a^2+-2*c*b^2)+b^-6*d^-3*(10*a^4+2*b^4*c^2+-12*c*a^2*b^2)*log(a+b*(c+d*x)^(1/2))+-4//3*a*b^-3*d^-3*(c+d*x)^3//2+-8*a*b^-5*d^-3*(c+d*x)^(1/2)*(a^2+-1*c*b^2)+2*a*b^-6*d^-3*(a+b*(c+d*x)^(1/2))^-1*(a^2+-1*c*b^2)^2)
@test integrate(x*(a+b*(c+d*x)^(1/2))^-2, x) == :(x*b^-2*d^-1+b^-4*d^-2*(6*a^2+-2*c*b^2)*log(a+b*(c+d*x)^(1/2))+-4*a*b^-3*d^-2*(c+d*x)^(1/2)+2*a*b^-4*d^-2*(a+b*(c+d*x)^(1/2))^-1*(a^2+-1*c*b^2))
@test integrate((a+b*(c+d*x)^(1/2))^-2, x) == :(2*b^-2*d^-1*log(a+b*(c+d*x)^(1/2))+2*a*b^-2*d^-1*(a+b*(c+d*x)^(1/2))^-1)
@test integrate(x^-1*(a+b*(c+d*x)^(1/2))^-2, x) == :((a^2+-1*c*b^2)^-2*(a^2+c*b^2)*log(x)+-1*(a^2+-1*c*b^2)^-2*(2*a^2+2*c*b^2)*log(a+b*(c+d*x)^(1/2))+2*a*(a+b*(c+d*x)^(1/2))^-1*(a^2+-1*c*b^2)^-1+4*a*b*c^(1/2)*(a^2+-1*c*b^2)^-2*arctanh(c^-1//2*(c+d*x)^(1/2)))
@test integrate(x^-2*(a+b*(c+d*x)^(1/2))^-2, x) == :(-1*x^-1*(a+b*(c+d*x)^(1/2))^-1*(a^2+-1*c*b^2)^-1*(a+-1*b*(c+d*x)^(1/2))+d*b^2*(a^2+-1*c*b^2)^-3*(3*a^2+c*b^2)*log(x)+-2*d*b^2*(a^2+-1*c*b^2)^-3*(3*a^2+c*b^2)*log(a+b*(c+d*x)^(1/2))+4*a*d*b^2*(a+b*(c+d*x)^(1/2))^-1*(a^2+-1*c*b^2)^-2+2*a*b*d*c^-1//2*(a^2+-1*c*b^2)^-3*(a^2+3*c*b^2)*arctanh(c^-1//2*(c+d*x)^(1/2)))
@test integrate(x^-3*(a+b*(c+d*x)^(1/2))^-2, x) == :(-1*x^-2*(a+b*(c+d*x)^(1/2))^-1*(2*a^2+-2*c*b^2)^-1*(a+-1*b*(c+d*x)^(1/2))+b^4*d^2*(a^2+-1*c*b^2)^-4*(5*a^2+c*b^2)*log(x)+-2*b^4*d^2*(a^2+-1*c*b^2)^-4*(5*a^2+c*b^2)*log(a+b*(c+d*x)^(1/2))+(1/2)*a*b^2*c^-1*d^2*(a+b*(c+d*x)^(1/2))^-1*(a^2+-1*c*b^2)^-3*(a^2+11*c*b^2)+-1//2*a*b*c^-3//2*d^2*(a^2+-1*c*b^2)^-4*(a^4+-15*b^4*c^2+-10*c*a^2*b^2)*arctanh(c^-1//2*(c+d*x)^(1/2))+-1//2*b*d*c^-1*x^-1*(a+b*(c+d*x)^(1/2))^-1*(a^2+-1*c*b^2)^-2*(-1*(c+d*x)^(1/2)*(a^2+2*c*b^2)+3*a*b*c))
@test integrate(x^3*(a+b*(c+d*x)^(1/2))^-1//2, x) == :(4//15*b^-8*d^-4*(a+b*(c+d*x)^(1/2))^15//2+-28//13*a*b^-8*d^-4*(a+b*(c+d*x)^(1/2))^13//2+1//7*b^-8*d^-4*(a+b*(c+d*x)^(1/2))^7//2*(140*a^4+12*b^4*c^2+-120*c*a^2*b^2)+1//11*b^-8*d^-4*(a+b*(c+d*x)^(1/2))^11//2*(84*a^2+-12*c*b^2)+-4*a*b^-8*d^-4*(a+b*(c+d*x)^(1/2))^(1/2)*(a^2+-1*c*b^2)^3+-20//9*a*b^-8*d^-4*(a+b*(c+d*x)^(1/2))^9//2*(7*a^2+-3*c*b^2)+4//3*b^-8*d^-4*(a+b*(c+d*x)^(1/2))^3//2*(a^2+-1*c*b^2)^2*(7*a^2+-1*c*b^2)+-12//5*a*b^-8*d^-4*(a+b*(c+d*x)^(1/2))^5//2*(a^2+-1*c*b^2)*(7*a^2+-3*c*b^2))
@test integrate(x^2*(a+b*(c+d*x)^(1/2))^-1//2, x) == :(4//11*b^-6*d^-3*(a+b*(c+d*x)^(1/2))^11//2+-20//9*a*b^-6*d^-3*(a+b*(c+d*x)^(1/2))^9//2+1//3*b^-6*d^-3*(a+b*(c+d*x)^(1/2))^3//2*(20*a^4+4*b^4*c^2+-24*c*a^2*b^2)+1//7*b^-6*d^-3*(a+b*(c+d*x)^(1/2))^7//2*(40*a^2+-8*c*b^2)+-4*a*b^-6*d^-3*(a+b*(c+d*x)^(1/2))^(1/2)*(a^2+-1*c*b^2)^2+-8//5*a*b^-6*d^-3*(a+b*(c+d*x)^(1/2))^5//2*(5*a^2+-3*c*b^2))
@test integrate(x*(a+b*(c+d*x)^(1/2))^-1//2, x) == :(4//7*b^-4*d^-2*(a+b*(c+d*x)^(1/2))^7//2+-12//5*a*b^-4*d^-2*(a+b*(c+d*x)^(1/2))^5//2+1//3*b^-4*d^-2*(a+b*(c+d*x)^(1/2))^3//2*(12*a^2+-4*c*b^2)+-4*a*b^-4*d^-2*(a+b*(c+d*x)^(1/2))^(1/2)*(a^2+-1*c*b^2))
@test integrate((a+b*(c+d*x)^(1/2))^-1//2, x) == :(4//3*b^-2*d^-1*(a+b*(c+d*x)^(1/2))^3//2+-4*a*b^-2*d^-1*(a+b*(c+d*x)^(1/2))^(1/2))
@test integrate(x^-1*(a+b*(c+d*x)^(1/2))^-1//2, x) == :(-2*(a+b*c^(1/2))^-1//2*arctanh((a+b*c^(1/2))^-1//2*(a+b*(c+d*x)^(1/2))^(1/2))+-2*(a+-1*b*c^(1/2))^-1//2*arctanh((a+b*(c+d*x)^(1/2))^(1/2)*(a+-1*b*c^(1/2))^-1//2))
@test integrate(x^-2*(a+b*(c+d*x)^(1/2))^-1//2, x) == :(-1*x^-1*(a+b*(c+d*x)^(1/2))^(1/2)*(a^2+-1*c*b^2)^-1*(a+-1*b*(c+d*x)^(1/2))+(1/2)*b*d*c^-1//2*(a+b*c^(1/2))^-3//2*arctanh((a+b*c^(1/2))^-1//2*(a+b*(c+d*x)^(1/2))^(1/2))+-1//2*b*d*c^-1//2*(a+-1*b*c^(1/2))^-3//2*arctanh((a+b*(c+d*x)^(1/2))^(1/2)*(a+-1*b*c^(1/2))^-1//2))
@test integrate(x^-3*(a+b*(c+d*x)^(1/2))^-1//2, x) == :(-1*x^-2*(a+b*(c+d*x)^(1/2))^(1/2)*(2*a^2+-2*c*b^2)^-1*(a+-1*b*(c+d*x)^(1/2))+-1//16*b*c^-3//2*d^2*(a+b*c^(1/2))^-5//2*(2a+5*b*c^(1/2))*arctanh((a+b*c^(1/2))^-1//2*(a+b*(c+d*x)^(1/2))^(1/2))+1//16*b*c^-3//2*d^2*(a+-1*b*c^(1/2))^-5//2*(2a+-5*b*c^(1/2))*arctanh((a+b*(c+d*x)^(1/2))^(1/2)*(a+-1*b*c^(1/2))^-1//2)+-1//8*b*d*c^-1*x^-1*(a+b*(c+d*x)^(1/2))^(1/2)*(a^2+-1*c*b^2)^-2*(-1*(c+d*x)^(1/2)*(a^2+5*c*b^2)+6*a*b*c))
@test integrate(x^3*(a+b*(c+d*x)^(1/2))^p, x) == :(2*b^-8*d^-4*(8+p)^-1*(a+b*(c+d*x)^(1/2))^(8+p)+b^-8*d^-4*(4+p)^-1*(a+b*(c+d*x)^(1/2))^(4+p)*(70*a^4+6*b^4*c^2+-60*c*a^2*b^2)+b^-8*d^-4*(6+p)^-1*(a+b*(c+d*x)^(1/2))^(6+p)*(42*a^2+-6*c*b^2)+-14*a*b^-8*d^-4*(7+p)^-1*(a+b*(c+d*x)^(1/2))^(7+p)+-10*a*b^-8*d^-4*(5+p)^-1*(a+b*(c+d*x)^(1/2))^(5+p)*(7*a^2+-3*c*b^2)+-2*a*b^-8*d^-4*(1+p)^-1*(a+b*(c+d*x)^(1/2))^(1+p)*(a^2+-1*c*b^2)^3+2*b^-8*d^-4*(2+p)^-1*(a+b*(c+d*x)^(1/2))^(2+p)*(a^2+-1*c*b^2)^2*(7*a^2+-1*c*b^2)+-6*a*b^-8*d^-4*(3+p)^-1*(a+b*(c+d*x)^(1/2))^(3+p)*(a^2+-1*c*b^2)*(7*a^2+-3*c*b^2))
@test integrate(x^2*(a+b*(c+d*x)^(1/2))^p, x) == :(2*b^-6*d^-3*(6+p)^-1*(a+b*(c+d*x)^(1/2))^(6+p)+b^-6*d^-3*(2+p)^-1*(a+b*(c+d*x)^(1/2))^(2+p)*(10*a^4+2*b^4*c^2+-12*c*a^2*b^2)+b^-6*d^-3*(4+p)^-1*(a+b*(c+d*x)^(1/2))^(4+p)*(20*a^2+-4*c*b^2)+-10*a*b^-6*d^-3*(5+p)^-1*(a+b*(c+d*x)^(1/2))^(5+p)+-4*a*b^-6*d^-3*(3+p)^-1*(a+b*(c+d*x)^(1/2))^(3+p)*(5*a^2+-3*c*b^2)+-2*a*b^-6*d^-3*(1+p)^-1*(a+b*(c+d*x)^(1/2))^(1+p)*(a^2+-1*c*b^2)^2)
@test integrate(x*(a+b*(c+d*x)^(1/2))^p, x) == :(2*b^-4*d^-2*(4+p)^-1*(a+b*(c+d*x)^(1/2))^(4+p)+b^-4*d^-2*(2+p)^-1*(a+b*(c+d*x)^(1/2))^(2+p)*(6*a^2+-2*c*b^2)+-6*a*b^-4*d^-2*(3+p)^-1*(a+b*(c+d*x)^(1/2))^(3+p)+-2*a*b^-4*d^-2*(1+p)^-1*(a+b*(c+d*x)^(1/2))^(1+p)*(a^2+-1*c*b^2))
@test integrate((a+b*(c+d*x)^(1/2))^p, x) == :(2*b^-2*d^-1*(2+p)^-1*(a+b*(c+d*x)^(1/2))^(2+p)+-2*a*b^-2*d^-1*(1+p)^-1*(a+b*(c+d*x)^(1/2))^(1+p))
@test integrate(x^-1*(a+b*(c*x)^n)^5//2, x) == :(2//5*n^-1*(a+b*(c*x)^n)^5//2+-2*a^5//2*n^-1*arctanh(a^-1//2*(a+b*(c*x)^n)^(1/2))+2*a^2*n^-1*(a+b*(c*x)^n)^(1/2)+2//3*a*n^-1*(a+b*(c*x)^n)^3//2)
@test integrate(x^-1*(a+b*(c*x)^n)^3//2, x) == :(2//3*n^-1*(a+b*(c*x)^n)^3//2+-2*a^3//2*n^-1*arctanh(a^-1//2*(a+b*(c*x)^n)^(1/2))+2*a*n^-1*(a+b*(c*x)^n)^(1/2))
@test integrate(x^-1*(a+b*(c*x)^n)^(1/2), x) == :(2*n^-1*(a+b*(c*x)^n)^(1/2)+-2*a^(1/2)*n^-1*arctanh(a^-1//2*(a+b*(c*x)^n)^(1/2)))
@test integrate(x^-1*(a+b*(c*x)^n)^-1//2, x) == :(-2*a^-1//2*n^-1*arctanh(a^-1//2*(a+b*(c*x)^n)^(1/2)))
@test integrate(x^-1*(a+b*(c*x)^n)^-3//2, x) == :(-2*a^-3//2*n^-1*arctanh(a^-1//2*(a+b*(c*x)^n)^(1/2))+2*a^-1*n^-1*(a+b*(c*x)^n)^-1//2)
@test integrate(x^-1*(a+b*(c*x)^n)^-5//2, x) == :(-2*a^-5//2*n^-1*arctanh(a^-1//2*(a+b*(c*x)^n)^(1/2))+2*a^-2*n^-1*(a+b*(c*x)^n)^-1//2+2//3*a^-1*n^-1*(a+b*(c*x)^n)^-3//2)
@test integrate(x^-1*(-1a+b*(c*x)^n)^5//2, x) == :(2//5*n^-1*(-1a+b*(c*x)^n)^5//2+-2*a^5//2*n^-1*arctan(a^-1//2*(-1a+b*(c*x)^n)^(1/2))+2*a^2*n^-1*(-1a+b*(c*x)^n)^(1/2)+-2//3*a*n^-1*(-1a+b*(c*x)^n)^3//2)
@test integrate(x^-1*(-1a+b*(c*x)^n)^3//2, x) == :(2//3*n^-1*(-1a+b*(c*x)^n)^3//2+-2*a*n^-1*(-1a+b*(c*x)^n)^(1/2)+2*a^3//2*n^-1*arctan(a^-1//2*(-1a+b*(c*x)^n)^(1/2)))
@test integrate(x^-1*(-1a+b*(c*x)^n)^(1/2), x) == :(2*n^-1*(-1a+b*(c*x)^n)^(1/2)+-2*a^(1/2)*n^-1*arctan(a^-1//2*(-1a+b*(c*x)^n)^(1/2)))
@test integrate(x^-1*(-1a+b*(c*x)^n)^-1//2, x) == :(2*a^-1//2*n^-1*arctan(a^-1//2*(-1a+b*(c*x)^n)^(1/2)))
@test integrate(x^-1*(-1a+b*(c*x)^n)^-3//2, x) == :(-2*a^-1*n^-1*(-1a+b*(c*x)^n)^-1//2+-2*a^-3//2*n^-1*arctan(a^-1//2*(-1a+b*(c*x)^n)^(1/2)))
@test integrate(x^-1*(-1a+b*(c*x)^n)^-5//2, x) == :(2*a^-2*n^-1*(-1a+b*(c*x)^n)^-1//2+2*a^-5//2*n^-1*arctan(a^-1//2*(-1a+b*(c*x)^n)^(1/2))+-2//3*a^-1*n^-1*(-1a+b*(c*x)^n)^-3//2)
@test integrate(x^-1*(a+b*x)^-1//2, x) == :(-2*a^-1//2*arctanh(a^-1//2*(a+b*x)^(1/2)))
@test integrate(x^-1*(a+b*(c*x)^m)^-1//2, x) == :(-2*a^-1//2*m^-1*arctanh(a^-1//2*(a+b*(c*x)^m)^(1/2)))
@test integrate(x^-1*(a+b*(c*(d*x)^m)^n)^-1//2, x) == :(-2*a^-1//2*m^-1*n^-1*arctanh(a^-1//2*(a+b*(c*(d*x)^m)^n)^(1/2)))
@test integrate(x^-1*(a+b*(c*(d*(e*x)^m)^n)^p)^-1//2, x) == :(-2*a^-1//2*m^-1*n^-1*p^-1*arctanh(a^-1//2*(a+b*(c*(d*(e*x)^m)^n)^p)^(1/2)))
@test integrate(x^-1*(a+b*(c*(d*(e*(f*x)^m)^n)^p)^q)^-1//2, x) == :(-2*a^-1//2*m^-1*n^-1*p^-1*q^-1*arctanh(a^-1//2*(a+b*(c*(d*(e*(f*x)^m)^n)^p)^q)^(1/2)))
@test integrate(x^-1*(-1+x^-2)^(1/2)*(-1+x^2)^3, x) == :(-35//16*arctan((-1+x^-2)^(1/2))+35//16*(-1+x^-2)^(1/2)+-35//48*x^2*(-1+x^-2)^3//2+-7//24*x^4*(-1+x^-2)^5//2+-1//6*x^6*(-1+x^-2)^7//2)
@test integrate(x^-1*(-1+x^-2)^(1/2)*(-1+x^2)^2, x) == :(-15//8*(-1+x^-2)^(1/2)+15//8*arctan((-1+x^-2)^(1/2))+1//4*x^4*(-1+x^-2)^5//2+5//8*x^2*(-1+x^-2)^3//2)
@test integrate(x^-1*(-1+x^-2)^(1/2)*(-1+x^2), x) == :(-3//2*arctan((-1+x^-2)^(1/2))+3//2*(-1+x^-2)^(1/2)+-1//2*x^2*(-1+x^-2)^3//2)
@test integrate(x^-1*(-1+x^-2)^(1/2)*(-1+x^2)^-1, x) == :((-1+x^-2)^(1/2))
@test integrate(x^-1*(-1+x^-2)^(1/2)*(-1+x^2)^-2, x) == :((-1+x^-2)^-1//2+-1*(-1+x^-2)^(1/2))
@test integrate(x^-1*(-1+x^-2)^(1/2)*(-1+x^2)^-3, x) == :((-1+x^-2)^(1/2)+-2*(-1+x^-2)^-1//2+-1//3*(-1+x^-2)^-3//2)
@test integrate(x*(1+x^-2)^(1/2)*(1+x^2)^-2, x) == :((1+x^-2)^-1//2)
@test integrate(x^-1*(1+x^-2)^-1//2*(1+x^2)^-1, x) == :((1+x^-2)^-1//2)
@test integrate(x*(a+(a+b*x^2)^(1/2)+b*x^2)^-1, x) == :(b^-1*log(1+(a+b*x^2)^(1/2)))
@test integrate(x*(x^2+-1*(x^2)^1//3)^-1, x) == :(3//4*log(1+-1*(x^2)^2//3))
@test integrate(x*(1+x^2)^3*(2+x^4+2*x^2)^(1/2), x) == :(-1//15*(2+x^4+2*x^2)^3//2+1//10*(1+x^2)^2*(2+x^4+2*x^2)^3//2)
@test integrate(x*((1+x^2)^-1*(1+-1*x^2))^(1/2), x) == :(-1*arctan(((1+x^2)^-1*(1+-1*x^2))^(1/2))+(1/2)*((1+x^2)^-1*(1+-1*x^2))^(1/2)*(1+x^2))
@test integrate(x*((7+5*x^2)^-1*(5+-7*x^2))^(1/2), x) == :(-37//175*35^(1/2)*arctan(1//7*35^(1/2)*((7+5*x^2)^-1*(5+-7*x^2))^(1/2))+1//10*((7+5*x^2)^-1*(5+-7*x^2))^(1/2)*(7+5*x^2))
@test integrate(x^2*((1+x^3)^-1*(1+-1*x^3))^(1/2), x) == :(-2//3*arctan(((1+x^3)^-1*(1+-1*x^3))^(1/2))+1//3*((1+x^3)^-1*(1+-1*x^3))^(1/2)*(1+x^3))
@test integrate(x^5*(1+x^9)^2*(1+-1*x^3)^(1/2), x) == :(-74//33*(1+-1*x^3)^11//2+-22//7*(1+-1*x^3)^7//2+-14//45*(1+-1*x^3)^15//2+-8//9*(1+-1*x^3)^3//2+2//51*(1+-1*x^3)^17//2+14//13*(1+-1*x^3)^13//2+32//15*(1+-1*x^3)^5//2+86//27*(1+-1*x^3)^9//2)
@test integrate(x^8*((1+x^3)^-1*(1+-1*x^3))^(1/2), x) == :(-1//3*arctan(((1+x^3)^-1*(1+-1*x^3))^(1/2))+(1/2)*((1+x^3)^-1*(1+-1*x^3))^(1/2)*(1+x^3)+-1//6*((1+x^3)^-1*(1+-1*x^3))^(1/2)*(1+x^3)^2+-1//9*((1+x^3)^-1*(1+-1*x^3))^3//2*(1+x^3)^3)
@test integrate(x^9*((7+5*x^5)^-1*(5+-7*x^5))^(1/2), x) == :(-27//350*((7+5*x^5)^-1*(5+-7*x^5))^(1/2)*(7+5*x^5)+1//250*((7+5*x^5)^-1*(5+-7*x^5))^(1/2)*(7+5*x^5)^2+2257//30625*35^(1/2)*arctan(1//7*35^(1/2)*((7+5*x^5)^-1*(5+-7*x^5))^(1/2)))
@test integrate(x*(a+b*x^2)^-3//2+x*(1+x^2)^-1*(a+b*x^2)^-1//2, x) == :(-1*b^-1*(a+b*x^2)^-1//2+-1*(a+-1b)^-1//2*arctanh((a+-1b)^-1//2*(a+b*x^2)^(1/2)))
@test integrate(x*(1+x^2)^-1*(a+b*x^2)^-3//2*(1+a+x^2+b*x^2), x) == :(-1*b^-1*(a+b*x^2)^-1//2+-1*(a+-1b)^-1//2*arctanh((a+-1b)^-1//2*(a+b*x^2)^(1/2)))
@test integrate(x*(a+b*x^2)^-5//2+x*(a+b*x^2)^-3//2+x*(1+x^2)^-1*(a+b*x^2)^-1//2, x) == :(-1*b^-1*(a+b*x^2)^-1//2+-1*(a+-1b)^-1//2*arctanh((a+-1b)^-1//2*(a+b*x^2)^(1/2))+-1//3*b^-1*(a+b*x^2)^-3//2)
@test integrate(x*(1+x^2)^-1*(a+b*x^2)^-5//2*(1+a+a^2+x^2+a*x^2+b*x^2+b*x^4+b^2*x^4+2*a*b*x^2), x) == :(-1*b^-1*(a+b*x^2)^-1//2+-1*(a+-1b)^-1//2*arctanh((a+-1b)^-1//2*(a+b*x^2)^(1/2))+-1//3*b^-1*(a+b*x^2)^-3//2)
@test integrate((x+x^(1/2))^-1//2, x) == :(-2*arctanh(x^(1/2)*(x+x^(1/2))^-1//2)+2*(x+x^(1/2))^(1/2))
@test integrate((x+x^(1/2))^(1/2), x) == :(-1//4*(x+x^(1/2))^(1/2)+1//4*arctanh(x^(1/2)*(x+x^(1/2))^-1//2)+1//6*x^(1/2)*(x+x^(1/2))^(1/2)+2//3*x*(x+x^(1/2))^(1/2))
@test integrate((-1x)^(1/2)*(x+(-1x)^(1/2)), x) == :(-1//2*x^2+2//5*(-1x)^5//2)
@test integrate((-6+x)^-1*(5+x^1//4), x) == :(4*x^1//4+5*log(6+-1x)+-2*6^1//4*arctan(1//6*6^3//4*x^1//4)+-2*6^1//4*arctanh(1//6*6^3//4*x^1//4))
@test integrate((4+(4+-1x)^(1/2)+-1x)^-1, x) == :(-2*log(1+(4+-1x)^(1/2)))
@test integrate((1+x+-1*(2+x)^(1/2))^-1, x) == :((1+-1//5*5^(1/2))*log(1+-1*5^(1/2)+-2*(2+x)^(1/2))+(1+1//5*5^(1/2))*log(1+5^(1/2)+-2*(2+x)^(1/2)))
@test integrate((4+x+(1+x)^(1/2))^-1, x) == :(-2//11*11^(1/2)*arctan(1//11*11^(1/2)*(1+2*(1+x)^(1/2)))+log(4+x+(1+x)^(1/2)))
@test integrate((x+-1*(1+x)^(1/2))^-1, x) == :((1+-1//5*5^(1/2))*log(1+-1*5^(1/2)+-2*(1+x)^(1/2))+(1+1//5*5^(1/2))*log(1+5^(1/2)+-2*(1+x)^(1/2)))
@test integrate((x+-1*(2+x)^(1/2))^-1, x) == :(2//3*log(1+(2+x)^(1/2))+4//3*log(2+-1*(2+x)^(1/2)))
@test integrate((x+-1*(1+-1x)^(1/2))^-1, x) == :((1+-1//5*5^(1/2))*log(1+-1*5^(1/2)+2*(1+-1x)^(1/2))+(1+1//5*5^(1/2))*log(1+5^(1/2)+2*(1+-1x)^(1/2)))
@test integrate((1+x+x^(1/2))^(1/2), x) == :(-3//8*arcsinh(1//3*3^(1/2)*(1+2*x^(1/2)))+2//3*(1+x+x^(1/2))^3//2+(1+x+x^(1/2))^(1/2)*(-1//4+-1//2*x^(1/2)))
@test integrate((1+x+(1+x)^(1/2))^(1/2), x) == :(1//4*arctanh((1+x)^(1/2)*(1+x+(1+x)^(1/2))^-1//2)+2//3*(1+x+(1+x)^(1/2))^3//2+-1//4*(1+x+(1+x)^(1/2))^(1/2)*(1+2*(1+x)^(1/2)))
@test integrate((x+(-1+x)^(1/2))^(1/2), x) == :(-3//8*arcsinh(1//3*3^(1/2)*(1+2*(-1+x)^(1/2)))+2//3*(x+(-1+x)^(1/2))^3//2+(x+(-1+x)^(1/2))^(1/2)*(-1//4+-1//2*(-1+x)^(1/2)))
@test integrate(((-1+2x)^(1/2)+2x)^(1/2), x) == :(-3//16*arcsinh(1//3*3^(1/2)*(1+2*(-1+2x)^(1/2)))+1//3*((-1+2x)^(1/2)+2x)^3//2+-1//8*((-1+2x)^(1/2)+2x)^(1/2)*(1+2*(-1+2x)^(1/2)))
@test integrate(((-7+8x)^(1/2)+3x)^(1/2), x) == :(-47//216*6^(1/2)*arcsinh(1//47*47^(1/2)*(4+3*(-7+8x)^(1/2)))+1//144*2^(1/2)*(8*(-7+8x)^(1/2)+24x)^3//2+-1//72*2^(1/2)*(8*(-7+8x)^(1/2)+24x)^(1/2)*(4+3*(-7+8x)^(1/2)))
@test integrate((x+(1+x)^(1/2))^-1//2, x) == :(-1*arctanh((1/2)*(x+(1+x)^(1/2))^-1//2*(1+2*(1+x)^(1/2)))+2*(x+(1+x)^(1/2))^(1/2))
@test integrate((4+x+(-9+6x)^(1/2))^-1*(1+x), x) == :(x+3*log(4+x+3^(1/2)*(-3+2x)^(1/2))+-2*3^(1/2)*(-3+2x)^(1/2)+4*6^(1/2)*arctan(1//12*6^(1/2)*(3+(-9+6x)^(1/2))))
@test integrate((4+x+(-9+6x)^(1/2))^-1*(12+-1x), x) == :(-1x+10*log(4+x+3^(1/2)*(-3+2x)^(1/2))+2*3^(1/2)*(-3+2x)^(1/2)+-21//2*6^(1/2)*arctan(1//12*6^(1/2)*(3+(-9+6x)^(1/2))))
@test integrate(x^-1//2*(1+x^2)^-1*(-1+x^3), x) == :(2//3*x^3//2+2^(1/2)*arctan(1+-1*2^(1/2)*x^(1/2))+-1*2^(1/2)*arctan(1+2^(1/2)*x^(1/2)))
@test integrate((1/2)*(-1+x)^-1//2*(x+-1*(-1+x)^(1/2))^-1//2, x) == :(-1*arcsinh(1//3*3^(1/2)*(1+-2*(-1+x)^(1/2))))
@test integrate(((-1+2x)^(1/2)+(-1+2x)^1//3)^-1*(4+2x), x) == :(-1x+-18*log(1+(-1+2x)^1//6)+-9*(-1+2x)^1//3+6*(-1+2x)^(1/2)+18*(-1+2x)^1//6+-3//4*(-1+2x)^2//3+-3//8*(-1+2x)^4//3+1//3*(-1+2x)^3//2+3//5*(-1+2x)^5//6+3//7*(-1+2x)^7//6)
@test integrate((2+(1+x^(1/2))^(1/2))^-1//2, x) == :(-48*(2+(1+x^(1/2))^(1/2))^(1/2)+-48//5*(2+(1+x^(1/2))^(1/2))^5//2+8//7*(2+(1+x^(1/2))^(1/2))^7//2+88//3*(2+(1+x^(1/2))^(1/2))^3//2)
@test integrate((2+(4+x^(1/2))^(1/2))^(1/2), x) == :(-48//7*(2+(4+x^(1/2))^(1/2))^7//2+8//9*(2+(4+x^(1/2))^(1/2))^9//2+64//5*(2+(4+x^(1/2))^(1/2))^5//2)
@test integrate((2+-1*(4+(-9+5x)^(1/2))^(1/2))^(1/2), x) == :(-48//35*(2+-1*(4+(-9+5x)^(1/2))^(1/2))^7//2+8//45*(2+-1*(4+(-9+5x)^(1/2))^(1/2))^9//2+64//25*(2+-1*(4+(-9+5x)^(1/2))^(1/2))^5//2)
@test integrate((2+(1+x^(1/2))^(1/2))^-1//2, x) == :(-48*(2+(1+x^(1/2))^(1/2))^(1/2)+-48//5*(2+(1+x^(1/2))^(1/2))^5//2+8//7*(2+(1+x^(1/2))^(1/2))^7//2+88//3*(2+(1+x^(1/2))^(1/2))^3//2)
@test integrate((1+(1+(1+x^(1/2))^(1/2))^(1/2))^(1/2), x) == :(-320//11*(1+(1+(1+x^(1/2))^(1/2))^(1/2))^11//2+-112//15*(1+(1+(1+x^(1/2))^(1/2))^(1/2))^15//2+-32//5*(1+(1+(1+x^(1/2))^(1/2))^(1/2))^5//2+16//17*(1+(1+(1+x^(1/2))^(1/2))^(1/2))^17//2+48//7*(1+(1+(1+x^(1/2))^(1/2))^(1/2))^7//2+112//9*(1+(1+(1+x^(1/2))^(1/2))^(1/2))^9//2+288//13*(1+(1+(1+x^(1/2))^(1/2))^(1/2))^13//2)
@test integrate((2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^(1/2), x) == :(-760//11*(2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^11//2+-480//7*(2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^7//2+-56//15*(2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^15//2+-16//3*(2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^3//2+4//17*(2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^17//2+136//5*(2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^5//2+300//13*(2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^13//2+304//3*(2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^9//2)
@test integrate(x*(1+(1+(-1+x)^(1/2))^(1/2))^(1/2), x) == :(8*(1+(1+(-1+x)^(1/2))^(1/2))^9//2+-160//11*(1+(1+(-1+x)^(1/2))^(1/2))^11//2+-56//15*(1+(1+(-1+x)^(1/2))^(1/2))^15//2+-24//7*(1+(1+(-1+x)^(1/2))^(1/2))^7//2+8//17*(1+(1+(-1+x)^(1/2))^(1/2))^17//2+16//5*(1+(1+(-1+x)^(1/2))^(1/2))^5//2+144//13*(1+(1+(-1+x)^(1/2))^(1/2))^13//2)
@test integrate((-1+x)^-1//2*(x+-1*(-1+x)^(1/2))^-1//2, x) == :(-2*arcsinh(1//3*3^(1/2)*(1+-2*(-1+x)^(1/2))))
@test integrate((b+a*x)^-1//2*(f+(b+a*x)^(1/2))^-1*(q+p*x), x) == :(p*x*a^-1+-1*a^-2*(-2*a*q+-2*p*f^2+2*b*p)*log(f+(b+a*x)^(1/2))+-2*f*p*a^-2*(b+a*x)^(1/2))
@test integrate((1+-1x+-1*x^(1/2))^(1/2), x) == :(-5//8*arcsin(1//5*5^(1/2)*(1+2*x^(1/2)))+-2//3*(1+-1x+-1*x^(1/2))^3//2+(1+-1x+-1*x^(1/2))^(1/2)*(-1//4+-1//2*x^(1/2)))
@test integrate((x+4*x^(1/2))^-1*(9+x+6*x^(1/2)), x) == :(x+2*log(4+x^(1/2))+4*x^(1/2))
@test integrate((5+-9*x^(1/2))^-1*(6+-8*x^7//2), x) == :(-280728140//387420489*log(5+-9*x^(1/2))+-56145628//43046721*x^(1/2)+2//9*x^4+80//567*x^7//2+200//2187*x^3+400//6561*x^5//2+2500//59049*x^2+50000//1594323*x^3//2+125000//4782969*x)
@test integrate(x^-1//2*(-1+x)^-1*(-1+x+-1*x^(1/2))^(1/2), x) == :(-1*arctanh((1/2)*(-1+x+-1*x^(1/2))^-1//2*(1+3*x^(1/2)))+-2*arctanh((1/2)*(-1+x+-1*x^(1/2))^-1//2*(1+-2*x^(1/2)))+arctan((1/2)*(-1+x+-1*x^(1/2))^-1//2*(3+-1*x^(1/2))))
@test integrate(x^-1*(1+x)^-1//2*(x+(1+x)^(1/2))^-1//2*(1+2*(1+x)^(1/2)), x) == :(-1*arctan((1/2)*(x+(1+x)^(1/2))^-1//2*(3+(1+x)^(1/2)))+3*arctanh((1/2)*(x+(1+x)^(1/2))^-1//2*(1+-3*(1+x)^(1/2))))
@test integrate(x^-1//2*(1+x)^-1//2, x) == :(2*arcsinh(x^(1/2)))
@test integrate(x^-1*(x*(1+x)^-1)^(1/2), x) == :(2*arcsinh(x^(1/2)))
@test integrate(x^(1/2)*(1+x)^-1//2, x) == :(-1*arcsinh(x^(1/2))+x^(1/2)*(1+x)^(1/2))
@test integrate((x*(1+x)^-1)^(1/2), x) == :(-1*arcsinh(x^(1/2))+x^(1/2)*(1+x)^(1/2))
@test integrate(x^-2*(1+x)^-1//2*(-1+x)^(1/2), x) == :(-1*x^-1*(1+x)^(1/2)*(-1+x)^(1/2)+arctan((1+x)^(1/2)*(-1+x)^(1/2)))
@test integrate(x^-2*((1+x)^-1*(-1+x))^(1/2), x) == :(-1*x^-1*(1+x)^(1/2)*(-1+x)^(1/2)+arctan((1+x)^(1/2)*(-1+x)^(1/2)))
@test integrate(x^3*(1+x)^-1//2*(-1+x)^(1/2), x) == :(3//8*arccosh(x)+-3//8*(1+x)^(1/2)*(-1+x)^(1/2)+(1+x)^(1/2)*(-1+x)^3//2*(7//24+-1//12*x)+1//4*x^2*(1+x)^(1/2)*(-1+x)^3//2)
@test integrate(x^3*((1+x)^-1*(-1+x))^(1/2), x) == :(3//8*arccosh(x)+-3//8*(1+x)^(1/2)*(-1+x)^(1/2)+(1+x)^(1/2)*(-1+x)^3//2*(7//24+-1//12*x)+1//4*x^2*(1+x)^(1/2)*(-1+x)^3//2)
@test integrate(x^-1*(-1*x*(1+x)^-1)^(1/2), x) == :(2*arctan((-1*x*(1+x)^-1)^(1/2)))
@test integrate(((1+x)^-1*(1+-1x))^(1/2)*(-1+x)^-1, x) == :(2*arctan(((1+x)^-1*(1+-1x))^(1/2)))
@test integrate(((c+-1*b*x)^-1*(a+b*x))^(1/2)*(a+b*x)^-1, x) == :(2*b^-1*arctan(((c+-1*b*x)^-1*(a+b*x))^(1/2)))
@test integrate(((c+d*x)^-1*(a+b*x))^(1/2)*(a+b*x)^-1, x) == :(2*b^-1//2*d^-1//2*arctanh(b^-1//2*d^(1/2)*((c+d*x)^-1*(a+b*x))^(1/2)))
@test integrate((-1*x*(1+x)^-1)^(1/2), x) == :(-1*arctan((-1*x*(1+x)^-1)^(1/2))+(-1*x*(1+x)^-1)^(1/2)*(1+x))
@test integrate(((1+x)^-1*(1+-1x))^(1/2), x) == :(-2*arctan(((1+x)^-1*(1+-1x))^(1/2))+((1+x)^-1*(1+-1x))^(1/2)*(1+x))
@test integrate(((a+-1x)^-1*(a+x))^(1/2), x) == :(-1*((a+-1x)^-1*(a+x))^(1/2)*(a+-1x)+2*a*arctan(((a+-1x)^-1*(a+x))^(1/2)))
@test integrate(((a+x)^-1*(x+-1a))^(1/2), x) == :((-1*(a+x)^-1*(a+-1x))^(1/2)*(a+x)+-2*a*arctanh((-1*(a+x)^-1*(a+-1x))^(1/2)))
@test integrate(((c+d*x)^-1*(a+b*x))^(1/2), x) == :(d^-1*((c+d*x)^-1*(a+b*x))^(1/2)*(c+d*x)+-1*b^-1//2*d^-3//2*(b*c+-1*a*d)*arctanh(b^-1//2*d^(1/2)*((c+d*x)^-1*(a+b*x))^(1/2)))
@test integrate(((5+3x)^-1*(-1+x))^(1/2), x) == :(-8//9*3^(1/2)*arcsinh(1//4*6^(1/2)*(-1+x)^(1/2))+1//3*(-1+x)^(1/2)*(5+3x)^(1/2))
@test integrate(x^-2*((1+7x)^-1*(-1+5x))^(1/2), x) == :(-12*arctan((1+7x)^(1/2)*(-1+5x)^-1//2)+-1*x^-1*(1+7x)^(1/2)*(-1+5x)^(1/2))
@test integrate(x*((1+x)^-1*(1+-1x))^-1//2*(1+x)^-1, x) == :(-1*((1+x)^-1*(1+-1x))^(1/2)*(1+x))
@test integrate(x*(1+x)^-1*(-1+2*(1+x)^-1)^-1//2, x) == :(-1*(-1+2*(1+x)^-1)^(1/2)*(1+x))
@test integrate(x*((3+x)^-1*(2+x))^-1//2*(1+x)^-1, x) == :(-1*arcsinh((2+x)^(1/2))+(2+x)^(1/2)*(3+x)^(1/2)+2*2^(1/2)*arctanh(2^(1/2)*(2+x)^(1/2)*(3+x)^-1//2))
@test integrate((1+x)^-2*(1+x^-1)^(1/2), x) == :(2*(1+x^-1)^-1//2)
@test integrate((1+x^-1)^(1/2)*(1+-1*x^2)^-1//2, x) == :(-1*x^(1/2)*(1+x)^-1//2*(1+x^-1)^(1/2)*arcsin(1+-2x))
@test integrate((x+(3+-1*x^2+-2x)^(1/2))^-1, x) == :(-1//2*log(-1*x^-2*(3+-1x+-1*3^(1/2)*(3+-1*x^2+-2x)^(1/2)))+(1/2+-1//14*7^(1/2))*log(1+3^(1/2)+7^(1/2)+-1*3^(1/2)*x^-1*(3^(1/2)+-1*(3+-1*x^2+-2x)^(1/2)))+(1/2+1//14*7^(1/2))*log(1+3^(1/2)+-1*7^(1/2)+-1*3^(1/2)*x^-1*(3^(1/2)+-1*(3+-1*x^2+-2x)^(1/2)))+arctan(x^-1*(3^(1/2)+-1*(3+-1*x^2+-2x)^(1/2))))
@test integrate((x+(3+-1*x^2+-2x)^(1/2))^-2, x) == :((14+-7*3^(1/2)+-7*x^-1*(2+2*3^(1/2))*(3^(1/2)+-1*(3+-1*x^2+-2x)^(1/2))+7*3^(1/2)*x^-2*(3^(1/2)+-1*(3+-1*x^2+-2x)^(1/2))^2)^-1*(8+-2*3^(1/2)+2*x^-1*(-3*(3+-1*x^2+-2x)^(1/2)+3*3^(1/2)))+8//49*7^(1/2)*arctanh(1//7*7^(1/2)*x^-1*(3+-1x+-1*x*3^(1/2)+-1*3^(1/2)*(3+-1*x^2+-2x)^(1/2))))
@test integrate((x+(3+-1*x^2+-2x)^(1/2))^-3, x) == :((294+-147*3^(1/2)+-147*x^-1*(2+2*3^(1/2))*(3^(1/2)+-1*(3+-1*x^2+-2x)^(1/2))+147*3^(1/2)*x^-2*(3^(1/2)+-1*(3+-1*x^2+-2x)^(1/2))^2)^-1*(36+-86*3^(1/2)+-2*x^-1*(18+49*3^(1/2))*(3^(1/2)+-1*(3+-1*x^2+-2x)^(1/2)))+-1//21*(2+-1*3^(1/2)+3^(1/2)*x^-2*(3^(1/2)+-1*(3+-1*x^2+-2x)^(1/2))^2+-1*x^-1*(2+2*3^(1/2))*(3^(1/2)+-1*(3+-1*x^2+-2x)^(1/2)))^-2*(36+-20*3^(1/2)+4*x^-1*(21+5*3^(1/2))*(3^(1/2)+-1*(3+-1*x^2+-2x)^(1/2)))+12//343*7^(1/2)*arctanh(1//7*7^(1/2)*x^-1*(3+-1x+-1*x*3^(1/2)+-1*3^(1/2)*(3+-1*x^2+-2x)^(1/2))))
@test integrate((x+(-3+x^2+-2x)^(1/2))^-1, x) == :(-2*(1+-1x+-1*(-3+x^2+-2x)^(1/2))^-1+2*log(1+-1x+-1*(-3+x^2+-2x)^(1/2))+-3//2*log(x+(-3+x^2+-2x)^(1/2)))
@test integrate((x+(-3+x^2+-2x)^(1/2))^-2, x) == :(-4*log(x+(-3+x^2+-2x)^(1/2))+-2*(1+-1x+-1*(-3+x^2+-2x)^(1/2))^-1+3*(2x+2*(-3+x^2+-2x)^(1/2))^-1+4*log(1+-1x+-1*(-3+x^2+-2x)^(1/2)))
@test integrate((x+(-3+x^2+-2x)^(1/2))^-3, x) == :(-6*log(x+(-3+x^2+-2x)^(1/2))+-2*(1+-1x+-1*(-3+x^2+-2x)^(1/2))^-1+4*(x+(-3+x^2+-2x)^(1/2))^-1+6*log(1+-1x+-1*(-3+x^2+-2x)^(1/2))+3//4*(x+(-3+x^2+-2x)^(1/2))^-2)
@test integrate((x+(-3+-1*x^2+-4x)^(1/2))^-1, x) == :((1/2)*log((3+x)^-3//2*(3*(-1+-1x)^(1/2)+x*(-1+-1x)^(1/2)+x*(3+x)^(1/2)))+(1/2)*log(3+x)+-1*arctan((-1+-1x)^(1/2)*(3+x)^-1//2)+-1*2^(1/2)*arctan((1/2)*2^(1/2)*(1+-3*(-1+-1x)^(1/2)*(3+x)^-1//2)))
@test integrate((x+(-3+-1*x^2+-4x)^(1/2))^-2, x) == :((1+-1*(3+x)^-1*(3+3x)+-2*(-1+-1x)^(1/2)*(3+x)^-1//2)^-1*(1+-1*(-1+-1x)^(1/2)*(3+x)^-1//2)+(1/2)*2^(1/2)*arctan((1/2)*2^(1/2)*(1+-3*(-1+-1x)^(1/2)*(3+x)^-1//2)))
@test integrate((x+(-3+-1*x^2+-4x)^(1/2))^-3, x) == :(-1*(18+-36*(-1+-1x)^(1/2)*(3+x)^-1//2+-18*(3+x)^-1*(3+3x))^-1*(13+-27*(-1+-1x)^(1/2)*(3+x)^-1//2)+-3//4*2^(1/2)*arctan((1/2)*2^(1/2)*(1+-3*(-1+-1x)^(1/2)*(3+x)^-1//2))+-1//9*(1+-1*(3+x)^-1*(3+3x)+-2*(-1+-1x)^(1/2)*(3+x)^-1//2)^-2*(4+-2*(-1+-1x)^(1/2)*(3+x)^-1//2))
@test integrate((-1*x^4+-8*x^2+4*x^3+8x)^3//2, x) == :(-176//35*3^(1/2)*Elliptic.F(arcsin(1+-1x),-1//3)+1//7*(3+-1*(-1+x)^4+-2*(-1+x)^2)^3//2*(-1+x)+16//5*3^(1/2)*Elliptic.E(arcsin(1+-1x),-1//3)+(3+-1*(-1+x)^4+-2*(-1+x)^2)^(1/2)*(-1+x)*(26//35+-6//35*(-1+x)^2))
@test integrate((-1*x^4+-8*x^2+4*x^3+8x)^(1/2), x) == :(-4//3*3^(1/2)*Elliptic.F(arcsin(1+-1x),-1//3)+1//3*(3+-1*(-1+x)^4+-2*(-1+x)^2)^(1/2)*(-1+x)+2//3*3^(1/2)*Elliptic.E(arcsin(1+-1x),-1//3))
@test integrate((-1*x^4+-8*x^2+4*x^3+8x)^-1//2, x) == :(-1//3*3^(1/2)*Elliptic.F(arcsin(1+-1x),-1//3))
@test integrate((-1*x^4+-8*x^2+4*x^3+8x)^-3//2, x) == :(-1//12*3^(1/2)*Elliptic.F(arcsin(1+-1x),-1//3)+1//24*3^(1/2)*Elliptic.E(arcsin(1+-1x),-1//3)+1//24*(3+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(-1+x)*(5+(-1+x)^2))
@test integrate((-1*x^4+-8*x^2+4*x^3+8x)^-5//2, x) == :(-11//432*3^(1/2)*Elliptic.F(arcsin(1+-1x),-1//3)+7//432*3^(1/2)*Elliptic.E(arcsin(1+-1x),-1//3)+1//72*(3+-1*(-1+x)^4+-2*(-1+x)^2)^-3//2*(-1+x)*(5+(-1+x)^2)+1//432*(3+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(-1+x)*(26+7*(-1+x)^2))
@test integrate((x*(2+-1x)*(4+x^2+-2x))^3//2, x) == :(-176//35*3^(1/2)*Elliptic.F(arcsin(1+-1x),-1//3)+1//7*(3+-1*(-1+x)^4+-2*(-1+x)^2)^3//2*(-1+x)+16//5*3^(1/2)*Elliptic.E(arcsin(1+-1x),-1//3)+(3+-1*(-1+x)^4+-2*(-1+x)^2)^(1/2)*(-1+x)*(26//35+-6//35*(-1+x)^2))
@test integrate((x*(2+-1x)*(4+x^2+-2x))^(1/2), x) == :(-4//3*3^(1/2)*Elliptic.F(arcsin(1+-1x),-1//3)+1//3*(3+-1*(-1+x)^4+-2*(-1+x)^2)^(1/2)*(-1+x)+2//3*3^(1/2)*Elliptic.E(arcsin(1+-1x),-1//3))
@test integrate((x*(2+-1x)*(4+x^2+-2x))^-1//2, x) == :(-1//3*3^(1/2)*Elliptic.F(arcsin(1+-1x),-1//3))
@test integrate((x*(2+-1x)*(4+x^2+-2x))^-3//2, x) == :(-1//12*3^(1/2)*Elliptic.F(arcsin(1+-1x),-1//3)+1//24*3^(1/2)*Elliptic.E(arcsin(1+-1x),-1//3)+1//24*(3+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(-1+x)*(5+(-1+x)^2))
@test integrate((x*(2+-1x)*(4+x^2+-2x))^-5//2, x) == :(-11//432*3^(1/2)*Elliptic.F(arcsin(1+-1x),-1//3)+7//432*3^(1/2)*Elliptic.E(arcsin(1+-1x),-1//3)+1//72*(3+-1*(-1+x)^4+-2*(-1+x)^2)^-3//2*(-1+x)*(5+(-1+x)^2)+1//432*(3+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(-1+x)*(26+7*(-1+x)^2))
@test integrate((d^2*x^4+4*a*c+4*c^2*x^2+4*c*d*x^3)^3//2, x) == :((d^2*x^4+4*a*c+4*c^2*x^2+4*c*d*x^3)^3//2*(1//7*x+1//7*c*d^-1)+2//35*c*d^-2*(d^2*x^4+4*a*c+4*c^2*x^2+4*c*d*x^3)^(1/2)*(x+c*d^-1)*(7*c^3+20*a*d^2+-3*c*d^2*(x+c*d^-1)^2)+-16//35*c^3*d^-2*(c^(1/2)+d^2*(x+c*d^-1)^2*(c^3+4*a*d^2)^-1//2)^-1*(c^3+4*a*d^2)^-1//2*(d^2*x^4+4*a*c+4*c^2*x^2+4*c*d*x^3)^(1/2)*(x+c*d^-1)*(c^3+8*a*d^2)+8//35*c^7//4*d^-5*(d^2*(c^(1/2)+d^2*(x+c*d^-1)^2*(c^3+4*a*d^2)^-1//2)^-2*(c^3+4*a*d^2)^-1*(d^2*x^4+4*a*c+4*c^2*x^2+4*c*d*x^3))^(1/2)*(c^3+4*a*d^2)^3//4*(d^2*x^4+4*a*c+4*c^2*x^2+4*c*d*x^3)^-1//2*(c^(1/2)+d^2*(x+c*d^-1)^2*(c^3+4*a*d^2)^-1//2)*((c^3+4*a*d^2)^(1/2)*(c^3+5*a*d^2)+-1*c^3//2*(c^3+8*a*d^2))*Elliptic.F(2*arctan(c^-1//4*(c^3+4*a*d^2)^-1//4*(c+d*x)),1/2+(1/2)*c^3//2*(c^3+4*a*d^2)^-1//2)+16//35*c^13//4*d^-5*(d^2*(c^(1/2)+d^2*(x+c*d^-1)^2*(c^3+4*a*d^2)^-1//2)^-2*(c^3+4*a*d^2)^-1*(d^2*x^4+4*a*c+4*c^2*x^2+4*c*d*x^3))^(1/2)*(c^3+4*a*d^2)^3//4*(d^2*x^4+4*a*c+4*c^2*x^2+4*c*d*x^3)^-1//2*(c^(1/2)+d^2*(x+c*d^-1)^2*(c^3+4*a*d^2)^-1//2)*(c^3+8*a*d^2)*Elliptic.E(2*arctan(c^-1//4*(c^3+4*a*d^2)^-1//4*(c+d*x)),1/2+(1/2)*c^3//2*(c^3+4*a*d^2)^-1//2))
@test integrate((d^2*x^4+4*a*c+4*c^2*x^2+4*c*d*x^3)^(1/2), x) == :((d^2*x^4+4*a*c+4*c^2*x^2+4*c*d*x^3)^(1/2)*(1//3*x+1//3*c*d^-1)+-2//3*c^2*(c^(1/2)+d^2*(x+c*d^-1)^2*(c^3+4*a*d^2)^-1//2)^-1*(c^3+4*a*d^2)^-1//2*(d^2*x^4+4*a*c+4*c^2*x^2+4*c*d*x^3)^(1/2)*(x+c*d^-1)+2//3*c^9//4*d^-3*(d^2*(c^(1/2)+d^2*(x+c*d^-1)^2*(c^3+4*a*d^2)^-1//2)^-2*(c^3+4*a*d^2)^-1*(d^2*x^4+4*a*c+4*c^2*x^2+4*c*d*x^3))^(1/2)*(c^3+4*a*d^2)^3//4*(d^2*x^4+4*a*c+4*c^2*x^2+4*c*d*x^3)^-1//2*(c^(1/2)+d^2*(x+c*d^-1)^2*(c^3+4*a*d^2)^-1//2)*Elliptic.E(2*arctan(c^-1//4*(c^3+4*a*d^2)^-1//4*(c+d*x)),1/2+(1/2)*c^3//2*(c^3+4*a*d^2)^-1//2)+1//3*c^3//4*d^-3*(d^2*(c^(1/2)+d^2*(x+c*d^-1)^2*(c^3+4*a*d^2)^-1//2)^-2*(c^3+4*a*d^2)^-1*(d^2*x^4+4*a*c+4*c^2*x^2+4*c*d*x^3))^(1/2)*(c^3+4*a*d^2)^1//4*(d^2*x^4+4*a*c+4*c^2*x^2+4*c*d*x^3)^-1//2*(c^(1/2)+d^2*(x+c*d^-1)^2*(c^3+4*a*d^2)^-1//2)*(c^3+-1*c^3//2*(c^3+4*a*d^2)^(1/2)+4*a*d^2)*Elliptic.F(2*arctan(c^-1//4*(c^3+4*a*d^2)^-1//4*(c+d*x)),1/2+(1/2)*c^3//2*(c^3+4*a*d^2)^-1//2))
@test integrate((d^2*x^4+4*a*c+4*c^2*x^2+4*c*d*x^3)^-1//2, x) == :((1/2)*c^-1//4*d^-1*(d^2*(c^(1/2)+d^2*(x+c*d^-1)^2*(c^3+4*a*d^2)^-1//2)^-2*(c^3+4*a*d^2)^-1*(d^2*x^4+4*a*c+4*c^2*x^2+4*c*d*x^3))^(1/2)*(c^3+4*a*d^2)^1//4*(d^2*x^4+4*a*c+4*c^2*x^2+4*c*d*x^3)^-1//2*(c^(1/2)+d^2*(x+c*d^-1)^2*(c^3+4*a*d^2)^-1//2)*Elliptic.F(2*arctan(c^-1//4*(c^3+4*a*d^2)^-1//4*(c+d*x)),1/2+(1/2)*c^3//2*(c^3+4*a*d^2)^-1//2))
@test integrate((d^2*x^4+4*a*c+4*c^2*x^2+4*c*d*x^3)^-3//2, x) == :(-1//8*a^-1*c^-1*(c^3+4*a*d^2)^-1*(d^2*x^4+4*a*c+4*c^2*x^2+4*c*d*x^3)^-1//2*(x+c*d^-1)*(c^3+-4*a*d^2+-1*c*d^2*(x+c*d^-1)^2)+-1//8*a^-1*d^2*(c^(1/2)+d^2*(x+c*d^-1)^2*(c^3+4*a*d^2)^-1//2)^-1*(c^3+4*a*d^2)^-3//2*(d^2*x^4+4*a*c+4*c^2*x^2+4*c*d*x^3)^(1/2)*(x+c*d^-1)+1//8*a^-1*c^1//4*d^-1*(d^2*(c^(1/2)+d^2*(x+c*d^-1)^2*(c^3+4*a*d^2)^-1//2)^-2*(c^3+4*a*d^2)^-1*(d^2*x^4+4*a*c+4*c^2*x^2+4*c*d*x^3))^(1/2)*(c^3+4*a*d^2)^-1//4*(d^2*x^4+4*a*c+4*c^2*x^2+4*c*d*x^3)^-1//2*(c^(1/2)+d^2*(x+c*d^-1)^2*(c^3+4*a*d^2)^-1//2)*Elliptic.E(2*arctan(c^-1//4*(c^3+4*a*d^2)^-1//4*(c+d*x)),1/2+(1/2)*c^3//2*(c^3+4*a*d^2)^-1//2)+1//16*a^-1*c^-5//4*d^-1*(d^2*(c^(1/2)+d^2*(x+c*d^-1)^2*(c^3+4*a*d^2)^-1//2)^-2*(c^3+4*a*d^2)^-1*(d^2*x^4+4*a*c+4*c^2*x^2+4*c*d*x^3))^(1/2)*(c^3+4*a*d^2)^-3//4*(d^2*x^4+4*a*c+4*c^2*x^2+4*c*d*x^3)^-1//2*(c^(1/2)+d^2*(x+c*d^-1)^2*(c^3+4*a*d^2)^-1//2)*(c^3+-1*c^3//2*(c^3+4*a*d^2)^(1/2)+4*a*d^2)*Elliptic.F(2*arctan(c^-1//4*(c^3+4*a*d^2)^-1//4*(c+d*x)),1/2+(1/2)*c^3//2*(c^3+4*a*d^2)^-1//2))
@test integrate((-1*x*d^3+8*a*e^2+8*e^3*x^4+8*d*e^2*x^3)^(1/2), x) == :((-1*x*d^3+8*a*e^2+8*e^3*x^4+8*d*e^2*x^3)^(1/2)*(1//3*x+1//12*d*e^-1)+-2*d^2*(1+16*e^2*(x+1//4*d*e^-1)^2*(5*d^4+256*a*e^3)^-1//2)^-1*(5*d^4+256*a*e^3)^-1//2*(-1*x*d^3+8*a*e^2+8*e^3*x^4+8*d*e^2*x^3)^(1/2)*(x+1//4*d*e^-1)+1//16*2^(1/2)*d^2*e^-2*(e*(1+16*e^2*(x+1//4*d*e^-1)^2*(5*d^4+256*a*e^3)^-1//2)^-2*(5*d^4+256*a*e^3)^-1*(-1*x*d^3+8*a*e^2+8*e^3*x^4+8*d*e^2*x^3))^(1/2)*(5*d^4+256*a*e^3)^3//4*(-1*x*d^3+8*a*e^2+8*e^3*x^4+8*d*e^2*x^3)^-1//2*(1+16*e^2*(x+1//4*d*e^-1)^2*(5*d^4+256*a*e^3)^-1//2)*Elliptic.E(2*arctan((5*d^4+256*a*e^3)^-1//4*(d+4*e*x)),1/2+3//2*d^2*(5*d^4+256*a*e^3)^-1//2)+1//96*2^(1/2)*e^-2*(e*(1+16*e^2*(x+1//4*d*e^-1)^2*(5*d^4+256*a*e^3)^-1//2)^-2*(5*d^4+256*a*e^3)^-1*(-1*x*d^3+8*a*e^2+8*e^3*x^4+8*d*e^2*x^3))^(1/2)*(5*d^4+256*a*e^3)^1//4*(-1*x*d^3+8*a*e^2+8*e^3*x^4+8*d*e^2*x^3)^-1//2*(1+16*e^2*(x+1//4*d*e^-1)^2*(5*d^4+256*a*e^3)^-1//2)*(5*d^4+-3*d^2*(5*d^4+256*a*e^3)^(1/2)+256*a*e^3)*Elliptic.F(2*arctan((5*d^4+256*a*e^3)^-1//4*(d+4*e*x)),1/2+3//2*d^2*(5*d^4+256*a*e^3)^-1//2))
@test integrate((-1*x*d^3+8*a*e^2+8*e^3*x^4+8*d*e^2*x^3)^-1//2, x) == :((1/2)*2^(1/2)*e^-1*(e*(1+16*e^2*(x+1//4*d*e^-1)^2*(5*d^4+256*a*e^3)^-1//2)^-2*(5*d^4+256*a*e^3)^-1*(-1*x*d^3+8*a*e^2+8*e^3*x^4+8*d*e^2*x^3))^(1/2)*(5*d^4+256*a*e^3)^1//4*(-1*x*d^3+8*a*e^2+8*e^3*x^4+8*d*e^2*x^3)^-1//2*(1+16*e^2*(x+1//4*d*e^-1)^2*(5*d^4+256*a*e^3)^-1//2)*Elliptic.F(2*arctan((5*d^4+256*a*e^3)^-1//4*(d+4*e*x)),1/2+3//2*d^2*(5*d^4+256*a*e^3)^-1//2))
@test integrate((-1*x*d^3+8*a*e^2+8*e^3*x^4+8*d*e^2*x^3)^-3//2, x) == :(4*e*(5*d^8+-16384*a^2*e^6+-64*a*d^4*e^3)^-1*(-1*x*d^3+8*a*e^2+8*e^3*x^4+8*d*e^2*x^3)^-1//2*(x+1//4*d*e^-1)*(13*d^4+-256*a*e^3+-48*d^2*e^2*(x+1//4*d*e^-1)^2)+384*d^2*e^2*(1+16*e^2*(x+1//4*d*e^-1)^2*(5*d^4+256*a*e^3)^-1//2)^-1*(d^4+-64*a*e^3)^-1*(5*d^4+256*a*e^3)^-3//2*(-1*x*d^3+8*a*e^2+8*e^3*x^4+8*d*e^2*x^3)^(1/2)*(x+1//4*d*e^-1)+-12*2^(1/2)*d^2*(e*(1+16*e^2*(x+1//4*d*e^-1)^2*(5*d^4+256*a*e^3)^-1//2)^-2*(5*d^4+256*a*e^3)^-1*(-1*x*d^3+8*a*e^2+8*e^3*x^4+8*d*e^2*x^3))^(1/2)*(d^4+-64*a*e^3)^-1*(5*d^4+256*a*e^3)^-1//4*(-1*x*d^3+8*a*e^2+8*e^3*x^4+8*d*e^2*x^3)^-1//2*(1+16*e^2*(x+1//4*d*e^-1)^2*(5*d^4+256*a*e^3)^-1//2)*Elliptic.E(2*arctan((5*d^4+256*a*e^3)^-1//4*(d+4*e*x)),1/2+3//2*d^2*(5*d^4+256*a*e^3)^-1//2)+-2*2^(1/2)*(e*(1+16*e^2*(x+1//4*d*e^-1)^2*(5*d^4+256*a*e^3)^-1//2)^-2*(5*d^4+256*a*e^3)^-1*(-1*x*d^3+8*a*e^2+8*e^3*x^4+8*d*e^2*x^3))^(1/2)*(d^4+-64*a*e^3)^-1*(5*d^4+256*a*e^3)^-3//4*(-1*x*d^3+8*a*e^2+8*e^3*x^4+8*d*e^2*x^3)^-1//2*(1+16*e^2*(x+1//4*d*e^-1)^2*(5*d^4+256*a*e^3)^-1//2)*(5*d^4+-3*d^2*(5*d^4+256*a*e^3)^(1/2)+256*a*e^3)*Elliptic.F(2*arctan((5*d^4+256*a*e^3)^-1//4*(d+4*e*x)),1/2+3//2*d^2*(5*d^4+256*a*e^3)^-1//2))
@test integrate((a+-1*x^4+-8*x^2+4*x^3+8x)^3//2, x) == :(1//7*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^3//2*(-1+x)+(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^(1/2)*(-1+x)*(26//35+-6//35*(-1+x)^2+2//7*a)+-1//35*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+-1*(4+a)^(1/2))*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2)*(-1+x)*(112+32a)+1//35*((1+(1+(4+a)^(1/2))^-1*(-1+x)^2)^-1*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2))^-1//2*(1+(4+a)^(1/2))^(1/2)*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+-1*(4+a)^(1/2))*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2)*(112+32a)*Elliptic.E(arctan((1+(4+a)^(1/2))^-1//2*(-1+x)),-2*(1+-1*(4+a)^(1/2))^-1*(4+a)^(1/2))+1//35*((1+(1+(4+a)^(1/2))^-1*(-1+x)^2)^-1*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2))^-1//2*(1+(4+a)^(1/2))^(1/2)*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2)*(12+4a)*(16+5a)*Elliptic.F(arctan((1+(4+a)^(1/2))^-1//2*(-1+x)),-2*(1+-1*(4+a)^(1/2))^-1*(4+a)^(1/2)))
@test integrate((a+-1*x^4+-8*x^2+4*x^3+8x)^(1/2), x) == :(1//3*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^(1/2)*(-1+x)+-1//3*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2)*(-1+x)*(2+-2*(4+a)^(1/2))+1//3*((1+(1+(4+a)^(1/2))^-1*(-1+x)^2)^-1*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2))^-1//2*(1+(4+a)^(1/2))^(1/2)*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2)*(2+-2*(4+a)^(1/2))*Elliptic.E(arctan((1+(4+a)^(1/2))^-1//2*(-1+x)),-2*(1+-1*(4+a)^(1/2))^-1*(4+a)^(1/2))+1//3*((1+(1+(4+a)^(1/2))^-1*(-1+x)^2)^-1*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2))^-1//2*(1+(4+a)^(1/2))^(1/2)*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2)*(6+2a)*Elliptic.F(arctan((1+(4+a)^(1/2))^-1//2*(-1+x)),-2*(1+-1*(4+a)^(1/2))^-1*(4+a)^(1/2)))
@test integrate((a+-1*x^4+-8*x^2+4*x^3+8x)^-1//2, x) == :(((1+(1+(4+a)^(1/2))^-1*(-1+x)^2)^-1*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2))^-1//2*(1+(4+a)^(1/2))^(1/2)*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2)*Elliptic.F(arctan((1+(4+a)^(1/2))^-1//2*(-1+x)),-2*(1+-1*(4+a)^(1/2))^-1*(4+a)^(1/2)))
@test integrate(x*(a+-1*x^4+-8*x^2+4*x^3+8x)^3//2, x) == :((3+a+-1*(-1+x)^4+-2*(-1+x)^2)^3//2*(1//8+1//8*(-1+x)^2)+1//7*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^3//2*(-1+x)+3//16*(4+a)^2*arctan((3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+(-1+x)^2))+(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^(1/2)*(1+(-1+x)^2)*(3//4+3//16*a)+(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^(1/2)*(-1+x)*(26//35+-6//35*(-1+x)^2+2//7*a)+-1//35*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+-1*(4+a)^(1/2))*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2)*(-1+x)*(112+32a)+1//35*((1+(1+(4+a)^(1/2))^-1*(-1+x)^2)^-1*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2))^-1//2*(1+(4+a)^(1/2))^(1/2)*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+-1*(4+a)^(1/2))*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2)*(112+32a)*Elliptic.E(arctan((1+(4+a)^(1/2))^-1//2*(-1+x)),-2*(1+-1*(4+a)^(1/2))^-1*(4+a)^(1/2))+1//35*((1+(1+(4+a)^(1/2))^-1*(-1+x)^2)^-1*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2))^-1//2*(1+(4+a)^(1/2))^(1/2)*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2)*(12+4a)*(16+5a)*Elliptic.F(arctan((1+(4+a)^(1/2))^-1//2*(-1+x)),-2*(1+-1*(4+a)^(1/2))^-1*(4+a)^(1/2)))
@test integrate(x*(a+-1*x^4+-8*x^2+4*x^3+8x)^(1/2), x) == :((3+a+-1*(-1+x)^4+-2*(-1+x)^2)^(1/2)*(1//4+1//4*(-1+x)^2)+(1+1//4*a)*arctan((3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+(-1+x)^2))+1//3*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^(1/2)*(-1+x)+-1//3*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2)*(-1+x)*(2+-2*(4+a)^(1/2))+1//3*((1+(1+(4+a)^(1/2))^-1*(-1+x)^2)^-1*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2))^-1//2*(1+(4+a)^(1/2))^(1/2)*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2)*(2+-2*(4+a)^(1/2))*Elliptic.E(arctan((1+(4+a)^(1/2))^-1//2*(-1+x)),-2*(1+-1*(4+a)^(1/2))^-1*(4+a)^(1/2))+1//3*((1+(1+(4+a)^(1/2))^-1*(-1+x)^2)^-1*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2))^-1//2*(1+(4+a)^(1/2))^(1/2)*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2)*(6+2a)*Elliptic.F(arctan((1+(4+a)^(1/2))^-1//2*(-1+x)),-2*(1+-1*(4+a)^(1/2))^-1*(4+a)^(1/2)))
@test integrate(x*(a+-1*x^4+-8*x^2+4*x^3+8x)^-1//2, x) == :((1/2)*arctan((3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+(-1+x)^2))+((1+(1+(4+a)^(1/2))^-1*(-1+x)^2)^-1*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2))^-1//2*(1+(4+a)^(1/2))^(1/2)*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2)*Elliptic.F(arctan((1+(4+a)^(1/2))^-1//2*(-1+x)),-2*(1+-1*(4+a)^(1/2))^-1*(4+a)^(1/2)))
@test integrate(x^2*(a+-1*x^4+-8*x^2+4*x^3+8x)^3//2, x) == :((3+a+-1*(-1+x)^4+-2*(-1+x)^2)^3//2*(1//4+1//4*(-1+x)^2)+3//8*(4+a)^2*arctan((3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+(-1+x)^2))+(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^(1/2)*(1+(-1+x)^2)*(3//2+3//8*a)+(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^(1/2)*(-1+x)*(64//63+12//35*a+2//315*(-1+x)^2*(60+21a))+(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^3//2*(-1+x)*(5//21+1//9*(-1+x)^2)+1//315*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+-1*(4+a)^(1/2))*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2)*(-1+x)*(560+84*a^2+444a)+-1//315*((1+(1+(4+a)^(1/2))^-1*(-1+x)^2)^-1*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2))^-1//2*(1+(4+a)^(1/2))^(1/2)*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+-1*(4+a)^(1/2))*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2)*(560+84*a^2+444a)*Elliptic.E(arctan((1+(4+a)^(1/2))^-1//2*(-1+x)),-2*(1+-1*(4+a)^(1/2))^-1*(4+a)^(1/2))+1//315*((1+(1+(4+a)^(1/2))^-1*(-1+x)^2)^-1*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2))^-1//2*(1+(4+a)^(1/2))^(1/2)*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2)*(12+4a)*(100+33a)*Elliptic.F(arctan((1+(4+a)^(1/2))^-1//2*(-1+x)),-2*(1+-1*(4+a)^(1/2))^-1*(4+a)^(1/2)))
@test integrate(x^2*(a+-1*x^4+-8*x^2+4*x^3+8x)^(1/2), x) == :((3+a+-1*(-1+x)^4+-2*(-1+x)^2)^(1/2)*(1/2+(1/2)*(-1+x)^2)+(2+(1/2)*a)*arctan((3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+(-1+x)^2))+(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^(1/2)*(-1+x)*(7//15+1//5*(-1+x)^2)+1//15*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+-1*(4+a)^(1/2))*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2)*(-1+x)*(16+6a)+1//15*((1+(1+(4+a)^(1/2))^-1*(-1+x)^2)^-1*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2))^-1//2*(1+(4+a)^(1/2))^(1/2)*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2)*(24+8a)*Elliptic.F(arctan((1+(4+a)^(1/2))^-1//2*(-1+x)),-2*(1+-1*(4+a)^(1/2))^-1*(4+a)^(1/2))+-1//15*((1+(1+(4+a)^(1/2))^-1*(-1+x)^2)^-1*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2))^-1//2*(1+(4+a)^(1/2))^(1/2)*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+-1*(4+a)^(1/2))*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2)*(16+6a)*Elliptic.E(arctan((1+(4+a)^(1/2))^-1//2*(-1+x)),-2*(1+-1*(4+a)^(1/2))^-1*(4+a)^(1/2)))
@test integrate(x^2*(a+-1*x^4+-8*x^2+4*x^3+8x)^-1//2, x) == :((3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+-1*(4+a)^(1/2))*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2)*(-1+x)+((1+(1+(4+a)^(1/2))^-1*(-1+x)^2)^-1*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2))^-1//2*(1+(4+a)^(1/2))^(1/2)*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2)*Elliptic.F(arctan((1+(4+a)^(1/2))^-1//2*(-1+x)),-2*(1+-1*(4+a)^(1/2))^-1*(4+a)^(1/2))+-1*((1+(1+(4+a)^(1/2))^-1*(-1+x)^2)^-1*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2))^-1//2*(1+(4+a)^(1/2))^(1/2)*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+-1*(4+a)^(1/2))*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2)*Elliptic.E(arctan((1+(4+a)^(1/2))^-1//2*(-1+x)),-2*(1+-1*(4+a)^(1/2))^-1*(4+a)^(1/2))+arctan((3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+(-1+x)^2)))
@test integrate(x^2*(a+-1*x^4+-8*x^2+4*x^3+8x)^-3//2, x) == :((4+a)^-1*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+(-1+x)^2)+(24+2*a^2+14a)^-1*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(-1+x)*(2+(-1+x)^2)*(4+a)+-1*(6+2a)^-1*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+-1*(4+a)^(1/2))*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2)*(-1+x)+((1+(1+(4+a)^(1/2))^-1*(-1+x)^2)^-1*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2))^-1//2*(1+(4+a)^(1/2))^(1/2)*(6+2a)^-1*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+-1*(4+a)^(1/2))*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2)*Elliptic.E(arctan((1+(4+a)^(1/2))^-1//2*(-1+x)),-2*(1+-1*(4+a)^(1/2))^-1*(4+a)^(1/2)))
@test integrate(x^2*(a+-1*x^4+-8*x^2+4*x^3+8x)^-5//2, x) == :((12+3a)^-1*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-3//2*(1+(-1+x)^2)+1//3*(4+a)^-2*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(2+2*(-1+x)^2)+(72+6*a^2+42a)^-1*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-3//2*(-1+x)*(2+(-1+x)^2)*(4+a)+1//12*(3+a)^-2*(4+a)^-1*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(-1+x)*(29+7a+(-1+x)^2*(13+3a))+((1+(1+(4+a)^(1/2))^-1*(-1+x)^2)^-1*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2))^-1//2*(1+(4+a)^(1/2))^(1/2)*(144+12*a^2+84a)^-1*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2)*Elliptic.F(arctan((1+(4+a)^(1/2))^-1//2*(-1+x)),-2*(1+-1*(4+a)^(1/2))^-1*(4+a)^(1/2))+-1//12*(3+a)^-2*(4+a)^-1*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+-1*(4+a)^(1/2))*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2)*(-1+x)*(13+3a)+1//12*((1+(1+(4+a)^(1/2))^-1*(-1+x)^2)^-1*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2))^-1//2*(1+(4+a)^(1/2))^(1/2)*(3+a)^-2*(4+a)^-1*(3+a+-1*(-1+x)^4+-2*(-1+x)^2)^-1//2*(1+-1*(4+a)^(1/2))*(1+(1+-1*(4+a)^(1/2))^-1*(-1+x)^2)*(13+3a)*Elliptic.E(arctan((1+(4+a)^(1/2))^-1//2*(-1+x)),-2*(1+-1*(4+a)^(1/2))^-1*(4+a)^(1/2)))
@test integrate((8+-1*x^3+8x+8*x^4)^-1//2, x) == :(-1//696*3^(1/2)*29^3//4*x^2*((87+29^(1/2)*x^-2*(4+x)^2)^-2*(261+(1+4*x^-1)^4+-6*(1+4*x^-1)^2))^(1/2)*(8+-1*x^3+8x+8*x^4)^-1//2*(87+29^(1/2)*x^-2*(4+x)^2)*Elliptic.F(2*arctan(1//87*3^(1/2)*29^3//4*x^-1*(4+x)),1/2+1//58*29^(1/2)))
@test integrate((8+-1*x^3+8x+8*x^4)^-3//2, x) == :(-1//1008*x^2*(8+-1*x^3+8x+8*x^4)^-1//2*(66+-1*(1+4*x^-1)^2)+1//12528*x^2*(8+-1*x^3+8x+8*x^4)^-1//2*(1+4*x^-1)*(216+-7*(1+4*x^-1)^2)+1//12528*29^(1/2)*x^2*(87+29^(1/2)*x^-2*(4+x)^2)^-1*(8+-1*x^3+8x+8*x^4)^-1//2*(1+4*x^-1)*(1827+-42*(1+4*x^-1)^2+7*(1+4*x^-1)^4)+-7//12528*3^(1/2)*29^1//4*x^2*((87+29^(1/2)*x^-2*(4+x)^2)^-2*(261+(1+4*x^-1)^4+-6*(1+4*x^-1)^2))^(1/2)*(8+-1*x^3+8x+8*x^4)^-1//2*(87+29^(1/2)*x^-2*(4+x)^2)*Elliptic.E(2*arctan(1//87*3^(1/2)*29^3//4*x^-1*(4+x)),1/2+1//58*29^(1/2))+1//50112*3^(1/2)*29^1//4*x^2*((87+29^(1/2)*x^-2*(4+x)^2)^-2*(261+(1+4*x^-1)^4+-6*(1+4*x^-1)^2))^(1/2)*(8+-1*x^3+8x+8*x^4)^-1//2*(14+-5*29^(1/2))*(87+29^(1/2)*x^-2*(4+x)^2)*Elliptic.F(2*arctan(1//87*3^(1/2)*29^3//4*x^-1*(4+x)),1/2+1//58*29^(1/2)))
@test integrate((1+4x+4*x^2+4*x^4)^-1//2, x) == :(-1//10*5^3//4*x^2*((5^(1/2)+(1+x^-1)^2)^-2*(5+(1+x^-1)^4+-2*(1+x^-1)^2))^(1/2)*(1+4x+4*x^2+4*x^4)^-1//2*(5^(1/2)+(1+x^-1)^2)*Elliptic.F(2*arctan(1//5*5^3//4*(1+x^-1)),1/2+1//10*5^(1/2)))
@test integrate((1+4x+4*x^2+4*x^4)^-3//2, x) == :(-1*x^2*(1+4x+4*x^2+4*x^4)^-1//2*(3+-1*(1+x^-1)^2)+1//10*x^2*(1+4x+4*x^2+4*x^4)^-1//2*(1+x^-1)*(13+-9*(1+x^-1)^2)+x^2*(10*5^(1/2)+10*(1+x^-1)^2)^-1*(1+4x+4*x^2+4*x^4)^-1//2*(1+x^-1)*(45+-18*(1+x^-1)^2+9*(1+x^-1)^4)+-1//10*5^1//4*x^2*((5^(1/2)+(1+x^-1)^2)^-2*(5+(1+x^-1)^4+-2*(1+x^-1)^2))^(1/2)*(1+4x+4*x^2+4*x^4)^-1//2*(9*5^(1/2)+9*(1+x^-1)^2)*Elliptic.E(2*arctan(1//5*5^3//4*(1+x^-1)),1/2+1//10*5^(1/2))+1//20*5^1//4*x^2*((5^(1/2)+(1+x^-1)^2)^-2*(5+(1+x^-1)^4+-2*(1+x^-1)^2))^(1/2)*(1+4x+4*x^2+4*x^4)^-1//2*(9+-3*5^(1/2))*(5^(1/2)+(1+x^-1)^2)*Elliptic.F(2*arctan(1//5*5^3//4*(1+x^-1)),1/2+1//10*5^(1/2)))
@test integrate((8+-15*x^3+8*x^2+8*x^4+24x)^-1//2, x) == :(-1//4136*517^3//4*x^2*((517^(1/2)+(3+4*x^-1)^2)^-2*(517+(3+4*x^-1)^4+-38*(3+4*x^-1)^2))^(1/2)*(8+-15*x^3+8*x^2+8*x^4+24x)^-1//2*(517^(1/2)+(3+4*x^-1)^2)*Elliptic.F(2*arctan(1//517*517^3//4*x^-1*(4+3x)),1/2+19//1034*517^(1/2)))
@test integrate((8+-15*x^3+8*x^2+8*x^4+24x)^-3//2, x) == :(-1//208*x^2*(8+-15*x^3+8*x^2+8*x^4+24x)^-1//2*(172+-7*(3+4*x^-1)^2)+1//322608*x^2*(8+-15*x^3+8*x^2+8*x^4+24x)^-1//2*(3+4*x^-1)*(50896+-2455*(3+4*x^-1)^2)+x^2*(322608*517^(1/2)+322608*(3+4*x^-1)^2)^-1*(8+-15*x^3+8*x^2+8*x^4+24x)^-1//2*(3+4*x^-1)*(1269235+-93290*(3+4*x^-1)^2+2455*(3+4*x^-1)^4)+-1//322608*517^1//4*x^2*((517^(1/2)+(3+4*x^-1)^2)^-2*(517+(3+4*x^-1)^4+-38*(3+4*x^-1)^2))^(1/2)*(8+-15*x^3+8*x^2+8*x^4+24x)^-1//2*(2455*517^(1/2)+2455*(3+4*x^-1)^2)*Elliptic.E(2*arctan(1//517*517^3//4*x^-1*(4+3x)),1/2+19//1034*517^(1/2))+1//1290432*517^1//4*x^2*((517^(1/2)+(3+4*x^-1)^2)^-2*(517+(3+4*x^-1)^4+-38*(3+4*x^-1)^2))^(1/2)*(8+-15*x^3+8*x^2+8*x^4+24x)^-1//2*(4910+-203*517^(1/2))*(517^(1/2)+(3+4*x^-1)^2)*Elliptic.F(2*arctan(1//517*517^3//4*x^-1*(4+3x)),1/2+19//1034*517^(1/2)))
@test integrate((8+-15*x^3+8*x^2+8*x^4+24x)^-5//2, x) == :(-1//97344*x^2*(8+-15*x^3+8*x^2+8*x^4+24x)^-1//2*(124415+-6308*(3+4*x^-1)^2)+-1*x^2*(322608+-23712*(3+4*x^-1)^2+624*(3+4*x^-1)^4)^-1*(8+-15*x^3+8*x^2+8*x^4+24x)^-1//2*(64489+-1399*(3+4*x^-1)^2)+1//78056941248*x^2*(8+-15*x^3+8*x^2+8*x^4+24x)^-1//2*(3+4*x^-1)*(18932921731+-1086525994*(3+4*x^-1)^2)+x^2*(39028470624*517^(1/2)+39028470624*(3+4*x^-1)^2)^-1*(8+-15*x^3+8*x^2+8*x^4+24x)^-1//2*(3+4*x^-1)*(280866969449+-20643993886*(3+4*x^-1)^2+543262997*(3+4*x^-1)^4)+x^2*(250182504+-18388656*(3+4*x^-1)^2+483912*(3+4*x^-1)^4)^-1*(8+-15*x^3+8*x^2+8*x^4+24x)^-1//2*(3+4*x^-1)*(11921698+-359497*(3+4*x^-1)^2)+-1//39028470624*517^1//4*x^2*((517^(1/2)+(3+4*x^-1)^2)^-2*(517+(3+4*x^-1)^4+-38*(3+4*x^-1)^2))^(1/2)*(8+-15*x^3+8*x^2+8*x^4+24x)^-1//2*(543262997*517^(1/2)+543262997*(3+4*x^-1)^2)*Elliptic.E(2*arctan(1//517*517^3//4*x^-1*(4+3x)),1/2+19//1034*517^(1/2))+1//624455529984*517^1//4*x^2*((517^(1/2)+(3+4*x^-1)^2)^-2*(517+(3+4*x^-1)^4+-38*(3+4*x^-1)^2))^(1/2)*(8+-15*x^3+8*x^2+8*x^4+24x)^-1//2*(4346103976+-175318963*517^(1/2))*(517^(1/2)+(3+4*x^-1)^2)*Elliptic.F(2*arctan(1//517*517^3//4*x^-1*(4+3x)),1/2+19//1034*517^(1/2)))
@test integrate((9+-44*x^2+-6x+3*x^4+15*x^3)^-1//2, x) == :(-1//7356*613^3//4*x^2*((613^(1/2)+x^-2*(6+-1x)^2)^-2*(613+(-1+6*x^-1)^4+-182*(1+-6*x^-1)^2))^(1/2)*(9+-44*x^2+-6x+3*x^4+15*x^3)^-1//2*(613^(1/2)+x^-2*(6+-1x)^2)*Elliptic.F(2*arctan(1//613*613^3//4*x^-1*(6+-1x)),1/2+91//1226*613^(1/2)))
@test integrate((9+-44*x^2+-6x+3*x^4+15*x^3)^-3//2, x) == :(-1//51759*x^2*(9+-44*x^2+-6x+3*x^4+15*x^3)^-1//2*(176+-23*(1+-6*x^-1)^2)+1//31728267*x^2*(9+-44*x^2+-6x+3*x^4+15*x^3)^-1//2*(1+-6*x^-1)*(45401+-3722*(1+-6*x^-1)^2)+x^2*(31728267*613^(1/2)+31728267*x^-2*(6+-1x)^2)^-1*(9+-44*x^2+-6x+3*x^4+15*x^3)^-1//2*(1+-6*x^-1)*(2281586+-677404*(1+-6*x^-1)^2+3722*(-1+6*x^-1)^4)+3722//31728267*613^1//4*x^2*((613^(1/2)+x^-2*(6+-1x)^2)^-2*(613+(-1+6*x^-1)^4+-182*(1+-6*x^-1)^2))^(1/2)*(9+-44*x^2+-6x+3*x^4+15*x^3)^-1//2*(613^(1/2)+x^-2*(6+-1x)^2)*Elliptic.E(2*arctan(1//613*613^3//4*x^-1*(6+-1x)),1/2+91//1226*613^(1/2))+-1//126913068*613^1//4*x^2*((613^(1/2)+x^-2*(6+-1x)^2)^-2*(613+(-1+6*x^-1)^4+-182*(1+-6*x^-1)^2))^(1/2)*(9+-44*x^2+-6x+3*x^4+15*x^3)^-1//2*(7444+-145*613^(1/2))*(613^(1/2)+x^-2*(6+-1x)^2)*Elliptic.F(2*arctan(1//613*613^3//4*x^-1*(6+-1x)),1/2+91//1226*613^(1/2)))
@test integrate(x^-1*(2*(3+-1x)^(1/2)+3*(1+x)^-1//2)^2, x) == :(-9*log(1+x)+-4x+12*arcsin(1/2+-1//2*x)+21*log(x)+-24*3^(1/2)*arctanh(3^(1/2)*(1+x)^(1/2)*(3+-1x)^-1//2))
@test integrate((1+(1+x^2)^(1/2))^-1*(-1+x+x^2), x) == :((1+x^2)^(1/2)+-1x+-1*x^-1+-1*log(1+(1+x^2)^(1/2))+-1//2*arcsinh(x)+x^-1*(1+x^2)^(1/2)+(1/2)*x*(1+x^2)^(1/2))
@test integrate(x^-1*(-1+x)^-1//2*(x+2*(-1+x)^(1/2)), x) == :(2*(-1+x)^(1/2)+2*log(x))
@test integrate((a+b*x^2//3+c*x^(1/2))^2, x) == :(x*a^2+(1/2)*c^2*x^2+3//7*b^2*x^7//3+4//3*a*c*x^3//2+6//5*a*b*x^5//3+12//13*b*c*x^13//6)
@test integrate((a+b*x^2//3+c*x^(1/2))^3, x) == :(x*a^3+1//3*b^3*x^3+2//5*c^3*x^5//2+2*c*a^2*x^3//2+3//2*a*c^2*x^2+9//5*b*a^2*x^5//3+9//7*a*b^2*x^7//3+9//8*b*c^2*x^8//3+18//17*c*b^2*x^17//6+36//13*a*b*c*x^13//6)
@test integrate(x^-3*(a+-1b+b*x^-2)^-1//2*(-1+x^2), x) == :(b^-1*(a+-1*b*(1+-1*x^-2))^(1/2)+(a+-1b)^-1//2*arctanh((a+-1b)^-1//2*(a+-1*b*(1+-1*x^-2))^(1/2)))
@test integrate(x^-3*(a+b*(-1+x^-2))^-1//2*(-1+x^2), x) == :(b^-1*(a+-1*b*(1+-1*x^-2))^(1/2)+(a+-1b)^-1//2*arctanh((a+-1b)^-1//2*(a+-1*b*(1+-1*x^-2))^(1/2)))
@test integrate((4+x^2)^-1*(9+x^2)^-1//2*(1+x), x) == :(-1//5*5^(1/2)*arctanh(1//5*5^(1/2)*(9+x^2)^(1/2))+1//10*5^(1/2)*arctan((1/2)*x*5^(1/2)*(9+x^2)^-1//2))
@test integrate(x*(1+(1+-1*x^2)^(1/2)), x) == :((1/2)*x^2+-1//3*(1+-1*x^2)^3//2)
@test integrate(x*(1+(1+x)^(1/2)*(1+-1x)^(1/2)), x) == :((1/2)*x^2+-1//3*(1+-1*x^2)^3//2)
@test integrate(x*(1+(2+x)^-1//2*(3+x)^-1//2), x) == :((1/2)*x^2+-5*arcsinh((2+x)^(1/2))+(2+x)^(1/2)*(3+x)^(1/2))
@test integrate(x^-1*(1+-1*x^4)^-1*(x+-1*(x^6)^(1/2)), x) == :((1/2)*arctan(x)+(1/2)*arctanh(x)+(1/2)*x^-3*(x^6)^(1/2)*arctan(x)+-1//2*x^-3*(x^6)^(1/2)*arctanh(x))
@test integrate((1+-1*x^4)^-1*(1+-1*x^-1*(x^6)^(1/2)), x) == :((1/2)*arctan(x)+(1/2)*arctanh(x)+(1/2)*x^-3*(x^6)^(1/2)*arctan(x)+-1//2*x^-3*(x^6)^(1/2)*arctanh(x))
@test integrate((x+-1*x^5)^-1*(x+-1*(x^6)^(1/2)), x) == :((1/2)*arctan(x)+(1/2)*arctanh(x)+(1/2)*x^-3*(x^6)^(1/2)*arctan(x)+-1//2*x^-3*(x^6)^(1/2)*arctanh(x))
@test integrate(x*(x+(x^6)^(1/2))^-1, x) == :((1/2)*arctan(x)+(1/2)*arctanh(x)+(1/2)*x^-3*(x^6)^(1/2)*arctan(x)+-1//2*x^-3*(x^6)^(1/2)*arctanh(x))
@test integrate((x+-1*x^3)^-1*(x^(1/2)+-1*(x^3)^(1/2)), x) == :(x^-3//2*(x^3)^(1/2)*arctan(x^(1/2))+-1*x^-3//2*(x^3)^(1/2)*arctanh(x^(1/2))+arctan(x^(1/2))+arctanh(x^(1/2)))
@test integrate((x^(1/2)+(x^3)^(1/2))^-1, x) == :(x^-3//2*(x^3)^(1/2)*arctan(x^(1/2))+-1*x^-3//2*(x^3)^(1/2)*arctanh(x^(1/2))+arctan(x^(1/2))+arctanh(x^(1/2)))
@test integrate((((-1+x)^3)^(1/2)+(-1+x)^(1/2))^-1, x) == :(((-1+x)^3)^(1/2)*(-1+x)^-3//2*arctan((-1+x)^(1/2))+-1*((-1+x)^3)^(1/2)*(-1+x)^-3//2*arctanh((-1+x)^(1/2))+arctan((-1+x)^(1/2))+arctanh((-1+x)^(1/2)))
@test integrate(-3*(4+5x)^-2+-1*(1+-1*x^2)^-1//2*(4+5x)^-2*(5+4x), x) == :(3*(20+25x)^-1+(1+-1*x^2)^(1/2)*(4+5x)^-1)
@test integrate((1+-1*x^2)^-1//2*(4+5x)^-2*(-5+-4x+-3*(1+-1*x^2)^(1/2)), x) == :(3*(20+25x)^-1+(1+-1*x^2)^(1/2)*(4+5x)^-1)
@test integrate((3+-3*x^2+(1+-1*x^2)^(1/2)*(-5+-4x))^-1, x) == :(3*(20+25x)^-1+(1+-1*x^2)^(1/2)*(4+5x)^-1)
@test integrate((3+-5*(1+-1*x^2)^(1/2)+-3*x^2+-4*x*(1+-1*x^2)^(1/2))^-1, x) == :(3*(20+25x)^-1+(1+-1*x^2)^(1/2)*(4+5x)^-1)
@test integrate((1+-1*x^2)^-1//2*(2+x+-2*(1+-1*x^2)^(1/2))^-2*(-1+(1+-1*x^2)^(1/2)), x) == :(3*(20+25x)^-1+(1+-1*x^2)^(1/2)*(4+5x)^-1)
@test integrate((c*x+d*x^n)^-1*(a+b*x^(-1+n)), x) == :(b*d^-1*log(x)+-1*c^-1*d^-1*(1+-1n)^-1*(b*c+-1*a*d)*log(d+c*x^(1+-1n)))
@test integrate((1+(1+2*x^2)^(1/2))^-1*(1+2*x^2)^(1/2), x) == :(x+-1//2*x^-1+(1/2)*x^-1*(1+2*x^2)^(1/2)+-1//2*2^(1/2)*arcsinh(x*2^(1/2)))
@test integrate((-1+4*x^2)^(1/2)*(x+(-1+4*x^2)^(1/2))^-1, x) == :(-1//3*(-1+4*x^2)^(1/2)+4//3*x+-1//9*3^(1/2)*arctanh(x*3^(1/2))+1//9*3^(1/2)*arctanh(3^(1/2)*(-1+4*x^2)^(1/2)))
@test integrate((-1+x^2)^-1//2*(d+e*x)^-3*(a+b*x+c*x^2), x) == :(-1//2*(d^2+-1*e^2)^-5//2*(-1*a*(e^2+2*d^2)+-1*c*(d^2+2*e^2)+3*b*d*e)*arctanh((-1+x^2)^-1//2*(d^2+-1*e^2)^-1//2*(e+d*x))+(1/2)*e^-1*(-1+x^2)^(1/2)*(d+e*x)^-1*(d^2+-1*e^2)^-2*(c*(d^3+-4*d*e^2)+-1*e*(-1*b*(d^2+2*e^2)+3*a*d*e))+-1//2*e^-1*(-1+x^2)^(1/2)*(d+e*x)^-2*(d^2+-1*e^2)^-1*(a*e^2+c*d^2+-1*b*d*e))
@test integrate(x^-1*(1+x^8)^-3//2*(1+2*x^8), x) == :(-1//4*(1+x^8)^-1//2+-1//4*arctanh((1+x^8)^(1/2)))
@test integrate((1+x^8)^(1/2)*(x+x^17+2*x^9)^-1*(1+2*x^8), x) == :(-1//4*(1+x^8)^-1//2+-1//4*arctanh((1+x^8)^(1/2)))
@test integrate(1+-9*x^2+x*(1+-9*x^2)^-1//2, x) == :(x+-3*x^3+-1//9*(1+-9*x^2)^(1/2))
@test integrate((1+-9*x^2)^-1//2*(x+(1+-9*x^2)^3//2), x) == :(x+-3*x^3+-1//9*(1+-9*x^2)^(1/2))
@test integrate(x^-1//2*(x+-3*x^(1/2))^2//3*(-3+2*x^(1/2)), x) == :(6//5*(x+-3*x^(1/2))^5//3)
@test integrate((x+-3*x^(1/2))^-1//3*(9+-9*x^(1/2)+2x), x) == :(6//5*(x+-3*x^(1/2))^5//3)
@test integrate((4+-9*x^2)^-1//2, x) == :(1//3*arcsin(3//2*x))
@test integrate((2+-3x)^-1//2*(2+3x)^-1//2, x) == :(1//3*arcsin(3//2*x))
@test integrate(((2+-3x)*(2+3x))^-1//2, x) == :(1//3*arcsin(3//2*x))
@test integrate((15+-1*x^2+-2x)^-1//2, x) == :(-1*arcsin(-1//4+-1//4*x))
@test integrate((3+-1x)^-1//2*(5+x)^-1//2, x) == :(-1*arcsin(-1//4+-1//4*x))
@test integrate(((3+-1x)*(5+x))^-1//2, x) == :(-1*arcsin(-1//4+-1//4*x))
@test integrate((-15+-1*x^2+-8x)^-1//2, x) == :(arcsin(4+x))
@test integrate((-3+-1x)^-1//2*(5+x)^-1//2, x) == :(arcsin(4+x))
@test integrate(((-3+-1x)*(5+x))^-1//2, x) == :(arcsin(4+x))
@test integrate(1+-1*x^(1/2), x) == :(x+-2//3*x^3//2)
@test integrate((1+x^(1/2))^-1*(1+-1x), x) == :(x+-2//3*x^3//2)
@test integrate(((1+-1*x^2)^-1)^(1/2), x) == :(((1+-1*x^2)^-1)^(1/2)*(1+-1*x^2)^(1/2)*arcsin(x))
@test integrate(((1+-1*x^4)^-1*(1+x^2))^(1/2), x) == :(((1+-1*x^2)^-1)^(1/2)*(1+-1*x^2)^(1/2)*arcsin(x))
@test integrate(((-1+x^2)^-1)^(1/2), x) == :(((-1+x^2)^-1)^(1/2)*(-1+x^2)^(1/2)*arctanh(x*(-1+x^2)^-1//2))
@test integrate(((-1+x^4)^-1*(1+x^2))^(1/2), x) == :(((-1+x^2)^-1)^(1/2)*(-1+x^2)^(1/2)*arctanh(x*(-1+x^2)^-1//2))
@test integrate((1+-1x)^-1//2, x) == :(-2*(1+-1x)^(1/2))
@test integrate((1+x)^(1/2)*(1+-1*x^2)^-1//2, x) == :(-2*(1+-1x)^(1/2))
@test integrate((1+x)^-1//2, x) == :(2*(1+x)^(1/2))
@test integrate((1+-1x)^(1/2)*(1+-1*x^2)^-1//2, x) == :(2*(1+x)^(1/2))
@test integrate((1+-1x)^(1/2), x) == :(-2//3*(1+-1x)^3//2)
@test integrate((1+x)^-1//2*(1+-1*x^2)^(1/2), x) == :(-2//3*(1+-1x)^3//2)
@test integrate((1+x)^(1/2), x) == :(2//3*(1+x)^3//2)
@test integrate((1+-1x)^-1//2*(1+-1*x^2)^(1/2), x) == :(2//3*(1+x)^3//2)
@test integrate((1+x)^-1//2*(2+3x)^(1/2), x) == :((1+x)^(1/2)*(2+3x)^(1/2)+-1//3*3^(1/2)*arcsinh((2+3x)^(1/2)))
@test integrate((1+-1x)^(1/2)*(1+-1*x^2)^-1//2*(2+3x)^(1/2), x) == :((1+x)^(1/2)*(2+3x)^(1/2)+-1//3*3^(1/2)*arcsinh((2+3x)^(1/2)))
@test integrate(x^-1*(1+x)^3//2*(1+-1x)^-3//2, x) == :(-1*arcsin(x)+-1*arctanh((1+x)^(1/2)*(1+-1x)^(1/2))+4*(1+x)^(1/2)*(1+-1x)^-1//2)
@test integrate(x^-1*(1+x)^3*(1+-1*x^2)^-3//2, x) == :(-1*arcsin(x)+-1*arctanh((1+-1*x^2)^(1/2))+(1+-1*x^2)^-1//2*(4+4x))
@test integrate(x^-1*(1+a*x)^3//2*(1+-1*a*x)^-3//2, x) == :(-1*arcsin(a*x)+-1*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2))+4*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2)
@test integrate(x^-1*(1+a*x)^3*(1+-1*a^2*x^2)^-3//2, x) == :(-1*arcsin(a*x)+-1*arctanh((1+-1*a^2*x^2)^(1/2))+(1+-1*a^2*x^2)^-1//2*(4+4*a*x))
@test integrate((1+-1*x^2)^-1//2, x) == :(arcsin(x))
@test integrate((1+x^2)^(1/2)*(1+-1*x^4)^-1//2, x) == :(arcsin(x))
@test integrate((1+x^2)^-1//2, x) == :(arcsinh(x))
@test integrate((1+-1*x^2)^(1/2)*(1+-1*x^4)^-1//2, x) == :(arcsinh(x))
@test integrate((1+-1*x^2)^(1/2), x) == :((1/2)*arcsin(x)+(1/2)*x*(1+-1*x^2)^(1/2))
@test integrate((1+x^2)^-1//2*(1+-1*x^4)^(1/2), x) == :((1/2)*arcsin(x)+(1/2)*x*(1+-1*x^2)^(1/2))
@test integrate((1+x^2)^(1/2), x) == :((1/2)*arcsinh(x)+(1/2)*x*(1+x^2)^(1/2))
@test integrate((1+-1*x^2)^-1//2*(1+-1*x^4)^(1/2), x) == :((1/2)*arcsinh(x)+(1/2)*x*(1+x^2)^(1/2))
@test integrate((x+-1*(1+x^2)^(1/2))^-1, x) == :(-1//2*x^2+-1//2*arcsinh(x)+-1//2*x*(1+x^2)^(1/2))
@test integrate((x+-1*(1+-1*x^2)^(1/2))^-1, x) == :(-1//2*arcsin(x)+-1//2*arctanh(x*(1+-1*x^2)^-1//2)+1//4*log(1+-2*x^2))
@test integrate((x+-1*(1+2*x^2)^(1/2))^-1, x) == :(-1//2*log(1+x^2)+-1*2^(1/2)*arcsinh(x*2^(1/2))+arctanh(x*(1+2*x^2)^-1//2))
@test integrate((-2+2*x^2)^-1*(-1*x^3+2x+x^2*(2+-1*x^2)^(1/2)), x) == :(-1//2*arctanh(x*(2+-1*x^2)^-1//2)+-1//4*x^2+1//4*log(1+-1*x^2)+1//4*x*(2+-1*x^2)^(1/2))
@test integrate(x*(2+-1*x^2)^(1/2)*(x+-1*(2+-1*x^2)^(1/2))^-1, x) == :(-1//2*arctanh(x*(2+-1*x^2)^-1//2)+-1//4*x^2+1//4*log(1+x)+1//4*log(1+-1x)+1//4*x*(2+-1*x^2)^(1/2))
@test integrate(x*((-1*x^2+2x)^(1/2)+-1x)^-1, x) == :((1/2)*arctanh((-1*x^2+2x)^(1/2))+-1//2*x+-1//2*(-1*x^2+2x)^(1/2)+-1//2*log(1+-1x))
@test integrate((2+-2x)^-1*(x+(-1*x^2+2x)^(1/2)), x) == :((1/2)*arctanh((-1*x^2+2x)^(1/2))+-1//2*x+-1//2*(-1*x^2+2x)^(1/2)+-1//2*log(1+-1x))
@test integrate((2+-2x)^-1*(x+x^(1/2)*(2+-1x)^(1/2)), x) == :((1/2)*arctanh((-1*x^2+2x)^(1/2))+-1//2*x+-1//2*(-1*x^2+2x)^(1/2)+-1//2*log(1+-1x))
@test integrate(x^(1/2)*((2+-1x)^(1/2)+-1*x^(1/2))^-1, x) == :((1/2)*arctanh(x^(1/2)*(2+-1x)^(1/2))+-1//2*x+-1//2*log(1+-1x)+-1//2*x^(1/2)*(2+-1x)^(1/2))
@test integrate((x^2*(-1+x^2)^-1)^(1/2)*(1+x^2)^-1, x) == :((1/2)*2^(1/2)*x^-1*(-1*x^2*(1+-1*x^2)^-1)^(1/2)*(-1+x^2)^(1/2)*arctan((1/2)*2^(1/2)*(-1+x^2)^(1/2)))
@test integrate((x^2*(-1+a+x^2*(1+a))^-1)^(1/2)*(1+x^2)^-1, x) == :((1/2)*2^(1/2)*x^-1*(-1*x^2*(1+-1a+-1*x^2*(1+a))^-1)^(1/2)*(-1+a+x^2*(1+a))^(1/2)*arctan((1/2)*2^(1/2)*(-1+a+x^2*(1+a))^(1/2)))
@test integrate((x*(1+x^2))^-1//2*(1+x^2)^-1*(-1+x^2), x) == :(-2*x*(x*(1+x^2))^-1//2)
@test integrate((1+x^2)^-1*(x+x^3)^-1//2*(-1+x^2), x) == :(-2*x*(x+x^3)^-1//2)
@test integrate((x^-1*(1+x^2)^-1*(-1+x^2)^2)^(1/2)*(1+x^2)^-1, x) == :(2*x*(x^-1*(1+x^2)^-1*(1+-1*x^2)^2)^(1/2)*(1+-1*x^2)^-1)
@test integrate(((-1+x^2)^2*(x+x^3)^-1)^(1/2)*(1+x^2)^-1, x) == :(2*x*((1+-1*x^2)^2*(x+x^3)^-1)^(1/2)*(1+-1*x^2)^-1)
@test integrate((a+b*x^-2)^-1//2*(c+d*x^2)^-1//2, x) == :(a^-1//2*d^-1//2*x^-1*(a+b*x^-2)^-1//2*(b+a*x^2)^(1/2)*arctanh(a^-1//2*d^(1/2)*(b+a*x^2)^(1/2)*(c+d*x^2)^-1//2))
@test integrate((-1+x^2)^-1*(2+x^2)^-1*(x^4+-2*x^2)^(1/2), x) == :(-1//3*x^-1*(-2+x^2)^-1//2*(x^4+-2*x^2)^(1/2)*arctan((-2+x^2)^(1/2))+2//3*x^-1*(-2+x^2)^-1//2*(x^4+-2*x^2)^(1/2)*arctan((1/2)*(-2+x^2)^(1/2)))
@test integrate(((-1+x^2)^-2*(x^4+-2*x^2))^(1/2)*(2+x^2)^-1, x) == :(-1//3*x^-1*(-1*(1+-1*x^2)^-2*(-1*x^4+2*x^2))^(1/2)*(-2+x^2)^-1//2*(2+-2*x^2)*arctan((1/2)*(-2+x^2)^(1/2))+1//3*x^-1*(-1*(1+-1*x^2)^-2*(-1*x^4+2*x^2))^(1/2)*(-2+x^2)^-1//2*(1+-1*x^2)*arctan((-2+x^2)^(1/2)))
@test integrate((1+2*x*(1+x^2)^-1)^5//2, x) == :((1+2*x*(1+x^2)^-1)^(1/2)*(1+x)*(-4//3+8//3*x)+-1*(1+x)^-1*(1+2*x*(1+x^2)^-1)^(1/2)*(1+x^2)*(4+3x)+-1*(1+x)^3*(1+2*x*(1+x^2)^-1)^(1/2)*(3+3*x^2)^-1*(1+-1x)+5*(1+x)^-1*(1+x^2)^(1/2)*(1+2*x*(1+x^2)^-1)^(1/2)*arcsinh(x))
@test integrate((1+2*x*(1+x^2)^-1)^3//2, x) == :(-1*(1+2*x*(1+x^2)^-1)^(1/2)*(1+x)*(1+-1x)+-1*x*(1+x)^-1*(1+2*x*(1+x^2)^-1)^(1/2)*(1+x^2)+3*(1+x)^-1*(1+x^2)^(1/2)*(1+2*x*(1+x^2)^-1)^(1/2)*arcsinh(x))
@test integrate((1+2*x*(1+x^2)^-1)^(1/2), x) == :((1+x)^-1*(1+2*x*(1+x^2)^-1)^(1/2)*(1+x^2)+(1+x)^-1*(1+x^2)^(1/2)*(1+2*x*(1+x^2)^-1)^(1/2)*arcsinh(x))
@test integrate((1+2*x*(1+x^2)^-1)^-1//2, x) == :((1+2*x*(1+x^2)^-1)^-1//2*(1+x)+-1*(1+x^2)^-1//2*(1+2*x*(1+x^2)^-1)^-1//2*(1+x)*arcsinh(x)+-1*2^(1/2)*(1+x^2)^-1//2*(1+2*x*(1+x^2)^-1)^-1//2*(1+x)*arctanh((1/2)*2^(1/2)*(1+x^2)^-1//2*(1+-1x)))
@test integrate((1+2*x*(1+x^2)^-1)^-3//2, x) == :((1/2)*(1+2*x*(1+x^2)^-1)^-1//2*(6+3x)+-1*(1+2*x*(1+x^2)^-1)^-1//2*(2+2x)^-1*(1+x^2)+-1*(1+x^2)^-1//2*(1+2*x*(1+x^2)^-1)^-1//2*(3+3x)*arcsinh(x)+-1//4*2^(1/2)*(1+x^2)^-1//2*(1+2*x*(1+x^2)^-1)^-1//2*(9+9x)*arctanh((1/2)*2^(1/2)*(1+x^2)^-1//2*(1+-1x)))
@test integrate((1+x^2)^-1*(1+2*x*(1+x^2)^-1)^(1/2), x) == :(-1*(1+x)^-1*(1+2*x*(1+x^2)^-1)^(1/2)*(1+-1x))
@test integrate(x^2*(c*(a+b*x^2)^-1)^3//2, x) == :(-1*c*x*b^-1*(c*(a+b*x^2)^-1)^(1/2)+c*b^-3//2*(c*(a+b*x^2)^-1)^(1/2)*(a+b*x^2)^(1/2)*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2))
@test integrate(x*(c*(a+b*x^2)^-1)^3//2, x) == :(-1*c*b^-1*(c*(a+b*x^2)^-1)^(1/2))
@test integrate((c*(a+b*x^2)^-1)^3//2, x) == :(c*x*a^-1*(c*(a+b*x^2)^-1)^(1/2))
@test integrate(x^-1*(c*(a+b*x^2)^-1)^3//2, x) == :(c*a^-1*(c*(a+b*x^2)^-1)^(1/2)+-1*c*a^-3//2*(c*(a+b*x^2)^-1)^(1/2)*(a+b*x^2)^(1/2)*arctanh(a^-1//2*(a+b*x^2)^(1/2)))
@test integrate(x^-2*(c*(a+b*x^2)^-1)^3//2, x) == :(-1*c*a^-1*x^-1*(c*(a+b*x^2)^-1)^(1/2)+-2*b*c*x*a^-2*(c*(a+b*x^2)^-1)^(1/2))
@test integrate(x^-3*(c*(a+b*x^2)^-1)^3//2, x) == :(-3//2*b*c*a^-2*(c*(a+b*x^2)^-1)^(1/2)+-1//2*c*a^-1*x^-2*(c*(a+b*x^2)^-1)^(1/2)+3//2*b*c*a^-5//2*(c*(a+b*x^2)^-1)^(1/2)*(a+b*x^2)^(1/2)*arctanh(a^-1//2*(a+b*x^2)^(1/2)))
@test integrate(x^2*(c*(a+b*x^2)^3)^3//2, x) == :(1//12*c*x^3*(c*(a+b*x^2)^3)^(1/2)*(a+b*x^2)^3+7//128*c*a^3*x^3*(c*(a+b*x^2)^3)^(1/2)+21*c*a^4*x^3*(c*(a+b*x^2)^3)^(1/2)*(512a+512*b*x^2)^-1+3//40*a*c*x^3*(c*(a+b*x^2)^3)^(1/2)*(a+b*x^2)^2+21//320*c*a^2*x^3*(c*(a+b*x^2)^3)^(1/2)*(a+b*x^2)+-21//1024*c*a^6*b^-3//2*(c*(a+b*x^2)^3)^(1/2)*(a+b*x^2)^-3//2*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+21//1024*c*x*a^5*b^-1*(c*(a+b*x^2)^3)^(1/2)*(a+b*x^2)^-1)
@test integrate(x*(c*(a+b*x^2)^3)^3//2, x) == :(1//11*c*b^-1*(c*(a+b*x^2)^3)^(1/2)*(a+b*x^2)^4)
@test integrate((c*(a+b*x^2)^3)^3//2, x) == :(1//10*c*x*(c*(a+b*x^2)^3)^(1/2)*(a+b*x^2)^3+21//128*c*x*a^3*(c*(a+b*x^2)^3)^(1/2)+63*c*x*a^4*(c*(a+b*x^2)^3)^(1/2)*(256a+256*b*x^2)^-1+9//80*a*c*x*(c*(a+b*x^2)^3)^(1/2)*(a+b*x^2)^2+21//160*c*x*a^2*(c*(a+b*x^2)^3)^(1/2)*(a+b*x^2)+63//256*c*a^5*b^-1//2*(c*(a+b*x^2)^3)^(1/2)*(a+b*x^2)^-3//2*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2))
@test integrate(x^-1*(c*(a+b*x^2)^3)^3//2, x) == :(1//3*c*a^3*(c*(a+b*x^2)^3)^(1/2)+1//9*c*(c*(a+b*x^2)^3)^(1/2)*(a+b*x^2)^3+c*a^4*(c*(a+b*x^2)^3)^(1/2)*(a+b*x^2)^-1+1//5*c*a^2*(c*(a+b*x^2)^3)^(1/2)*(a+b*x^2)+1//7*a*c*(c*(a+b*x^2)^3)^(1/2)*(a+b*x^2)^2+-1*c*a^9//2*(c*(a+b*x^2)^3)^(1/2)*(a+b*x^2)^-3//2*arctanh(a^-1//2*(a+b*x^2)^(1/2)))
@test integrate(x^-2*(c*(a+b*x^2)^3)^3//2, x) == :(-1*c*x^-1*(c*(a+b*x^2)^3)^(1/2)*(a+b*x^2)^3+9//8*b*c*x*(c*(a+b*x^2)^3)^(1/2)*(a+b*x^2)^2+105//64*b*c*x*a^2*(c*(a+b*x^2)^3)^(1/2)+315*b*c*x*a^3*(c*(a+b*x^2)^3)^(1/2)*(128a+128*b*x^2)^-1+21//16*a*b*c*x*(c*(a+b*x^2)^3)^(1/2)*(a+b*x^2)+315//128*c*a^4*b^(1/2)*(c*(a+b*x^2)^3)^(1/2)*(a+b*x^2)^-3//2*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2))
@test integrate(x^-3*(c*(a+b*x^2)^3)^3//2, x) == :(-1//2*c*x^-2*(c*(a+b*x^2)^3)^(1/2)*(a+b*x^2)^3+3//2*b*c*a^2*(c*(a+b*x^2)^3)^(1/2)+9//14*b*c*(c*(a+b*x^2)^3)^(1/2)*(a+b*x^2)^2+9*b*c*a^3*(c*(a+b*x^2)^3)^(1/2)*(2a+2*b*x^2)^-1+9//10*a*b*c*(c*(a+b*x^2)^3)^(1/2)*(a+b*x^2)+-9//2*b*c*a^7//2*(c*(a+b*x^2)^3)^(1/2)*(a+b*x^2)^-3//2*arctanh(a^-1//2*(a+b*x^2)^(1/2)))
@test integrate((a+b^2*x^4)^-1//2*((a+b^2*x^4)^(1/2)+b*x^2)^(1/2), x) == :((1/2)*2^(1/2)*b^-1//2*arctanh(x*2^(1/2)*b^(1/2)*((a+b^2*x^4)^(1/2)+b*x^2)^-1//2))
@test integrate((a+b^2*x^4)^-1//2*((a+b^2*x^4)^(1/2)+-1*b*x^2)^(1/2), x) == :((1/2)*2^(1/2)*b^-1//2*arctan(x*2^(1/2)*b^(1/2)*((a+b^2*x^4)^(1/2)+-1*b*x^2)^-1//2))
@test integrate((3+4*x^4)^-1//2*(c+d*x)^-1*((3+4*x^4)^(1/2)+2*x^2)^(1/2), x) == :((-1*3^(1/2)*d^2+2*im*c^2)^-1//2*(1/2+-1//2*im)*arctan((3^(1/2)+-2*im*x^2)^-1//2*(-1*3^(1/2)*d^2+2*im*c^2)^-1//2*(d*3^(1/2)+2*im*c*x))+-1*(3^(1/2)*d^2+2*im*c^2)^-1//2*(1/2+(1/2)*im)*arctanh((3^(1/2)+2*im*x^2)^-1//2*(3^(1/2)*d^2+2*im*c^2)^-1//2*(d*3^(1/2)+-2*im*c*x)))
@test integrate((3+4*x^4)^-1//2*(c+d*x)^-2*((3+4*x^4)^(1/2)+2*x^2)^(1/2), x) == :(c*(3^(1/2)*d^2+2*im*c^2)^-3//2*(1+-1im)*arctanh((3^(1/2)+2*im*x^2)^-1//2*(3^(1/2)*d^2+2*im*c^2)^-1//2*(d*3^(1/2)+-2*im*c*x))+c*(-1*3^(1/2)*d^2+2*im*c^2)^-3//2*(1+im)*arctan((3^(1/2)+-2*im*x^2)^-1//2*(-1*3^(1/2)*d^2+2*im*c^2)^-1//2*(d*3^(1/2)+2*im*c*x))+d*(c+d*x)^-1*(3^(1/2)+-2*im*x^2)^(1/2)*(-1*3^(1/2)*d^2+2*im*c^2)^-1*(1/2+-1//2*im)+-1*d*(c+d*x)^-1*(3^(1/2)+2*im*x^2)^(1/2)*(3^(1/2)*d^2+2*im*c^2)^-1*(1/2+(1/2)*im))
@test integrate(x^-1//2*(1+x^1//3)^-1*(-4+x), x) == :(-30*x^1//6+2*x^(1/2)+30*arctan(x^1//6)+-6//5*x^5//6+6//7*x^7//6)
@test integrate((x^5//6+x^7//6)^-1*(1+x^(1/2)), x) == :(-3*log(1+x^1//3)+3*x^1//3+6*arctan(x^1//6))
@test integrate(x^-1//2*(1+x^1//3)^-1*(1+x^(1/2)), x) == :(-6*arctan(x^1//6)+-3*x^1//3+3*log(1+x^1//3)+6*x^1//6+3//2*x^2//3)
@test integrate((2+b*x^-2)^(1/2)*(b+2*x^2)^-1, x) == :(-1*b^-1//2*arccsch(x*2^(1/2)*b^-1//2))
@test integrate((2+-1*b*x^-2)^(1/2)*(-1b+2*x^2)^-1, x) == :(-1*b^-1//2*arccsc(x*2^(1/2)*b^-1//2))
@test integrate((a+c*x^-2)^(1/2)*(d+e*x)^-1, x) == :(a^(1/2)*e^-1*arctanh(a^-1//2*(a+c*x^-2)^(1/2))+-1*c^(1/2)*d^-1*arctanh(c^(1/2)*x^-1*(a+c*x^-2)^-1//2)+-1*d^-1*e^-1*(a*d^2+c*e^2)^(1/2)*arctanh((a+c*x^-2)^-1//2*(a*d^2+c*e^2)^-1//2*(a*d+-1*c*e*x^-1)))
@test integrate((d+e*x)^-1*(a+b*x^-1+c*x^-2)^(1/2), x) == :(a^(1/2)*e^-1*arctanh((1/2)*a^-1//2*(a+b*x^-1+c*x^-2)^-1//2*(2a+b*x^-1))+-1*c^(1/2)*d^-1*arctanh((1/2)*c^-1//2*(a+b*x^-1+c*x^-2)^-1//2*(b+2*c*x^-1))+-1*d^-1*e^-1*(a*d^2+-1*e*(b*d+-1*c*e))^(1/2)*arctanh((1/2)*(a*d^2+-1*e*(b*d+-1*c*e))^-1//2*(a+b*x^-1+c*x^-2)^-1//2*(x^-1*(b*d+-2*c*e)+-1*b*e+2*a*d)))
@test integrate(x^-1//2*(x^1//6+(x^3)^1//5), x) == :(3//2*x^2//3+10//11*x^(1/2)*(x^3)^1//5)
@test integrate((-1*x^2+4x)^-1//2*(2+x), x) == :(-1*(-1*x^2+4x)^(1/2)+-4*arcsin(1+-1//2*x))
@test integrate((x^2+6x)^-1//3*(3+x), x) == :(3//4*(x^2+6x)^2//3)
@test integrate((-1*x^2+6x)^-3//2*(4+x), x) == :(-1//9*(-1*x^2+6x)^-1//2*(12+-7x))
@test integrate((1+x)^-1*(x^2+2x)^-1//2, x) == :(arctan((x^2+2x)^(1/2)))
@test integrate((1+2x)^-1*(x+x^2)^-1//2, x) == :(arctan(2*(x+x^2)^(1/2)))
@test integrate((-1*x^2+2x)^-1//2*(-1+x), x) == :(-1*(-1*x^2+2x)^(1/2))
@test integrate((1+x)^-1*(x+-1*x^2)^(1/2), x) == :((x+-1*x^2)^(1/2)+-3//2*arcsin(1+-2x)+2^(1/2)*arctan(1//4*2^(1/2)*(x+-1*x^2)^-1//2*(1+-3x)))
@test integrate((x+x^1//4)^(1/2), x) == :(-1//3*arctanh(x^(1/2)*(x+x^1//4)^-1//2)+1//3*x^1//4*(x+x^1//4)^(1/2)+2//3*x*(x+x^1//4)^(1/2))
@test integrate((x+x^3//2)^(1/2), x) == :(-16//35*x^-1*(x+x^3//2)^3//2+4//7*x^-1//2*(x+x^3//2)^3//2+32//105*x^-3//2*(x+x^3//2)^3//2)
@test integrate(x*(x+x^3//2)^(1/2), x) == :(-32//99*(x+x^3//2)^3//2+-256//1155*x^-1*(x+x^3//2)^3//2+4//11*x^(1/2)*(x+x^3//2)^3//2+64//231*x^-1//2*(x+x^3//2)^3//2+512//3465*x^-3//2*(x+x^3//2)^3//2)
@test integrate(((2+-1*x^2)^-1)^(1/2)*(1+-1*x^2), x) == :((1/2)*x*((2+-1*x^2)^-1)^-1//2)
@test integrate((x^2+x^3+-1*x^4)^(1/2), x) == :(-1//3*x^-1*(x^2+x^3+-1*x^4)^(1/2)*(1+x+-1*x^2)+-1//8*x^-1*(x^2+x^3+-1*x^4)^(1/2)*(1+-2x)+-5//16*x^-1*(1+x+-1*x^2)^-1//2*(x^2+x^3+-1*x^4)^(1/2)*arcsin(1//5*5^(1/2)*(1+-2x)))
@test integrate(((a^2+x^2)^3)^-1//2, x) == :(x*a^-2*((a^2+x^2)^3)^-1//2*(a^2+x^2))
@test integrate(x^(1/2)*(1+x+x^(1/2))^-1, x) == :(-1*log(1+x+x^(1/2))+2*x^(1/2)+-2//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*x^(1/2))))
@test integrate(x*(1+x+x^(1/2))^-1, x) == :(x+-2*x^(1/2)+4//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*x^(1/2))))
@test integrate(x^-1//2*(1+x+x^(1/2))^-7//2, x) == :(1//15*(1+x+x^(1/2))^-5//2*(4+8*x^(1/2))+1//135*(1+x+x^(1/2))^-3//2*(64+128*x^(1/2))+1//405*(1+x+x^(1/2))^-1//2*(512+1024*x^(1/2)))
@test integrate((1+(1+x^2)^(1/2))^-1*(-1+x), x) == :((1+x^2)^(1/2)+-1*x^-1+-1*arcsinh(x)+-1*log(1+(1+x^2)^(1/2))+x^-1*(1+x^2)^(1/2))
@test integrate((1+x)^-2//3*(-1+x^2)^-2//3, x) == :(3//2*(1+x)^-2//3*(-1+x^2)^1//3)
@test integrate((1+-1*x^6)^2//3+x^-6*(1+-1*x^6)^2//3, x) == :(-1//5*x^-5*(1+-1*x^6)^2//3+1//5*x*(1+-1*x^6)^2//3)
@test integrate((1/2)*x^(-1+m)*(a+b*x^n)^-3//2*(2*a*m+b*x^n*(-1n+2m)), x) == :(x^m*(a+b*x^n)^-1//2)
@test integrate((2+3x)^-1//2*(x+-2*x^3), x) == :(-10//81*(2+3x)^3//2+-4//81*(2+3x)^(1/2)+-4//567*(2+3x)^7//2+8//135*(2+3x)^5//2)
@test integrate(((1+x)^(1/2)+(1+x)^1//4)^-1, x) == :(-4*(1+x)^1//4+2*(1+x)^(1/2)+4*log(1+(1+x)^1//4))
@test integrate((x+x^2)^-1//2*(1+2x), x) == :(2*(x+x^2)^(1/2))
@test integrate((1/2)*x^-1//2*(1+x)^-1, x) == :(arctan(x^(1/2)))
@test integrate(x^-1*(-1*x^2+6x)^-1//2, x) == :(-1//3*x^-1*(-1*x^2+6x)^(1/2))
@test integrate(x^(1/2)*(1+x^(1/2)), x) == :((1/2)*x^2+2//3*x^3//2)
@test integrate(x^-1//3*(1+-1*x^(1/2)), x) == :(-6//7*x^7//6+3//2*x^2//3)
@test integrate(x^(1/2)*(1+x^1//3)^-1, x) == :(-6*x^1//6+2*x^(1/2)+6*arctan(x^1//6)+-6//5*x^5//6+6//7*x^7//6)
@test integrate(x^-1*(1+x^(1/2))^1//3, x) == :(3*log(1+-1*(1+x^(1/2))^1//3)+6*(1+x^(1/2))^1//3+-1//2*log(x)+-2*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*(1+x^(1/2))^1//3)))
@test integrate(1+-1*x^(1/2), x) == :(x+-2//3*x^3//2)
@test integrate(1+-1*x^1//4, x) == :(x+-4//5*x^5//4)
@test integrate((1+x^1//4)^-1*(1+-1*x^(1/2)), x) == :(x+-4//5*x^5//4)
@test integrate(((a+b*x)*(c+d*x))^-1//2, x) == :(b^-1//2*d^-1//2*arctanh((1/2)*b^-1//2*d^-1//2*(a*c+x*(a*d+b*c)+b*d*x^2)^-1//2*(a*d+b*c+2*b*d*x)))
@test integrate(((a+b*x)*(c+-1*d*x))^-1//2, x) == :(-1*b^-1//2*d^-1//2*arctan((1/2)*b^-1//2*d^-1//2*(a*c+x*(b*c+-1*a*d)+-1*b*d*x^2)^-1//2*(b*c+-1*a*d+-2*b*d*x)))
@test integrate(x^-1//2*(1+-1*x^2)^-1, x) == :(arctan(x^(1/2))+arctanh(x^(1/2)))
@test integrate(x^(1/2)*(x+-1*x^3)^-1, x) == :(arctan(x^(1/2))+arctanh(x^(1/2)))
@test integrate(x*(2+x^2+-1*3^(1/2)+x*(1+3^(1/2)))^-1, x) == :((1/2)*log(2+x^2+-1*3^(1/2)+x*(1+3^(1/2)))+(13//23+8//23*3^(1/2))^(1/2)*arctanh((-4+6*3^(1/2))^-1//2*(1+3^(1/2)+2x)))
@test integrate((x^2+x^3)^(1/2), x) == :(-4//15*x^-3*(x^2+x^3)^3//2+2//5*x^-2*(x^2+x^3)^3//2)
@test integrate((1+x)^-1*(x^2+2x)^-1//2, x) == :(arctan((x^2+2x)^(1/2)))
@test integrate(x^(1/2)*(1+-1x+-1*x^(1/2))^(1/2), x) == :(5//12*(1+-1x+-1*x^(1/2))^3//2+45//64*arcsin(1//5*5^(1/2)*(1+2*x^(1/2)))+(1+-1x+-1*x^(1/2))^(1/2)*(9//32+9//16*x^(1/2))+-1//2*x^(1/2)*(1+-1x+-1*x^(1/2))^3//2)
@test integrate((1+(-3+x)^(1/2))^1//3, x) == :(-3//2*(1+(-3+x)^(1/2))^4//3+6//7*(1+(-3+x)^(1/2))^7//3)
@test integrate((3+(-1+2x)^(1/2))^-1//2, x) == :(-6*(3+(-1+2x)^(1/2))^(1/2)+2//3*(3+(-1+2x)^(1/2))^3//2)
@test integrate((1+x^(1/2))^-1*(1+-1x)^(1/2), x) == :(-1*arcsin(x^(1/2))+-1*(1+-1x)^(1/2)*(2+-1*x^(1/2)))
@test integrate((1+-1x)^(1/2)*(1+-1*x^(1/2))^-1, x) == :(-1*(1+-1x)^(1/2)*(2+x^(1/2))+arcsin(x^(1/2)))
@test integrate(x*(x+-1*(1+x^2)^(1/2))^-1, x) == :(-1//3*x^3+-1//3*(1+x^2)^3//2)
@test integrate(x*(x+-1*(1+-1*x^2)^(1/2))^-1, x) == :((1/2)*x+(1/2)*(1+-1*x^2)^(1/2)+-1//4*2^(1/2)*arctanh(x*2^(1/2))+-1//4*2^(1/2)*arctanh(2^(1/2)*(1+-1*x^2)^(1/2)))
@test integrate(x*(x+-1*(1+2*x^2)^(1/2))^-1, x) == :(-1x+-1*(1+2*x^2)^(1/2)+arctan(x)+arctan((1+2*x^2)^(1/2)))
@test integrate(x^(1/2)*(x+x^(1/2))^(1/2), x) == :(-5//12*(x+x^(1/2))^3//2+-5//32*arctanh(x^(1/2)*(x+x^(1/2))^-1//2)+(x+x^(1/2))^(1/2)*(5//32+5//16*x^(1/2))+(1/2)*x^(1/2)*(x+x^(1/2))^3//2)
@test integrate((1+x^(1/2))^-1*(1+x^1//3), x) == :(-1*log(1+x^1//3+-1*x^1//6)+-4*log(1+x^1//6)+-3*x^1//3+2*x^(1/2)+6//5*x^5//6+-2*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x^1//6)))
@test integrate((1+x^1//4)^-1*(1+x^1//3), x) == :(-8*log(1+x^1//12)+-3*x^1//3+-2*x^(1/2)+-2*log(1+x^1//6+-1*x^1//12)+4*x^1//4+12*x^1//12+-6//5*x^5//6+4//3*x^3//4+12//7*x^7//12+12//13*x^13//12+4*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x^1//12)))
@test integrate(x^2*(-1+x^2+(1+-1*x^2)^(1/2))^-1, x) == :(x+arcsin(x))
@test integrate((x^-1*(1+x))^(1/2), x) == :(x*(1+x^-1)^(1/2)+arctanh((1+x^-1)^(1/2)))
@test integrate((x^-1*(1+-1x))^(1/2), x) == :(-1*arctan((-1+x^-1)^(1/2))+x*(-1+x^-1)^(1/2))
@test integrate(x^-1*(x^-1*(1+x))^(1/2), x) == :(-2*(1+x^-1)^(1/2)+2*arctanh((1+x^-1)^(1/2)))
@test integrate((x*(1+x)^-1)^(1/2), x) == :(-1*arcsinh(x^(1/2))+x^(1/2)*(1+x)^(1/2))
@test integrate((x^-1*(-1+-1x))^-1//2, x) == :(-1*x*(-1*x^-1*(1+x))^(1/2)+arctan((-1*x^-1*(1+x))^(1/2)))
@test integrate((x*(4+-1x))^(1/2), x) == :(-2*arcsin(1+-1//2*x)+(-1*x^2+4x)^(1/2)*(-1+(1/2)*x))
@test integrate((x*(1+-1x))^-1//2, x) == :(-1*arcsin(1+-2x))
@test integrate(x*(x*(2+x))^-3//2, x) == :(x*(x^2+2x)^-1//2)
@test integrate((1+x^-1)^(1/2)*(1+-1*x^2)^-1, x) == :(2^(1/2)*arctanh((1/2)*2^(1/2)*(1+x^-1)^(1/2)))
@test integrate((1+5^(1/2)+-1*x^2+5^(1/2)*x^2)^-1, x) == :((1/2)*arctan(x*(3//2+-1//2*5^(1/2))^(1/2)))
@test integrate(((b+-1x)*(x+-1a))^(1/2), x) == :((-1*x^2+x*(a+b)+-1*a*b)^(1/2)*((1/2)*x+-1//4*a+-1//4*b)+-1//8*(a+-1b)^2*arctan((1/2)*(-1*x^2+x*(a+b)+-1*a*b)^-1//2*(a+b+-2x)))
@test integrate(((b+-1x)*(x+-1a))^-1//2, x) == :(-1*arctan((1/2)*(-1*x^2+x*(a+b)+-1*a*b)^-1//2*(a+b+-2x)))
@test integrate(((1+-1*x^2)*(3+x^2))^(1/2), x) == :(-2//3*3^(1/2)*Elliptic.E(arcsin(x),-1//3)+1//3*x*(3+-1*x^4+-2*x^2)^(1/2)+4//3*3^(1/2)*Elliptic.F(arcsin(x),-1//3))
@test integrate(((1+-1*x^2)*(3+x^2))^-1//2, x) == :(1//3*3^(1/2)*Elliptic.F(arcsin(x),-1//3))
@test integrate((a*x+b*x^2)^-1//2, x) == :(2*b^-1//2*arctanh(x*b^(1/2)*(a*x+b*x^2)^-1//2))
@test integrate((x*(a+b*x))^-1//2, x) == :(2*b^-1//2*arctanh(x*b^(1/2)*(a*x+b*x^2)^-1//2))
@test integrate((x^2*(b+a*x^-1))^-1//2, x) == :(2*b^-1//2*arctanh(x*b^(1/2)*(a*x+b*x^2)^-1//2))
@test integrate((x^3*(a*x^-2+b*x^-1))^-1//2, x) == :(2*b^-1//2*arctanh(x*b^(1/2)*(a*x+b*x^2)^-1//2))
@test integrate((x^-1*(a*x^2+b*x^3))^-1//2, x) == :(2*b^-1//2*arctanh(x*b^(1/2)*(a*x+b*x^2)^-1//2))
@test integrate((x^-2*(a*x^3+b*x^4))^-1//2, x) == :(2*b^-1//2*arctanh(x*b^(1/2)*(a*x+b*x^2)^-1//2))
@test integrate((a*c*x+b*c*x^2)^-1//2, x) == :(2*b^-1//2*c^-1//2*arctanh(x*b^(1/2)*c^(1/2)*(a*c*x+b*c*x^2)^-1//2))
@test integrate((c*(a*x+b*x^2))^-1//2, x) == :(2*b^-1//2*c^-1//2*arctanh(x*b^(1/2)*c^(1/2)*(a*c*x+b*c*x^2)^-1//2))
@test integrate((c*x*(a+b*x))^-1//2, x) == :(2*b^-1//2*c^-1//2*arctanh(x*b^(1/2)*c^(1/2)*(a*c*x+b*c*x^2)^-1//2))
@test integrate((c*x^2*(b+a*x^-1))^-1//2, x) == :(2*b^-1//2*c^-1//2*arctanh(x*b^(1/2)*c^(1/2)*(a*c*x+b*c*x^2)^-1//2))
@test integrate((1+-1*x^2+x*(-1+x^2)^(1/2))^(1/2), x) == :((1+-1*x^2+x*(-1+x^2)^(1/2))^(1/2)*(1//4*(-1+x^2)^(1/2)+3//4*x)+3//8*2^(1/2)*arcsin(x+-1*(-1+x^2)^(1/2)))
@test integrate((1+x)^-1//2*(-1x+x^(1/2)*(1+x)^(1/2))^(1/2), x) == :((-1x+x^(1/2)*(1+x)^(1/2))^(1/2)*((1/2)*x^(1/2)+3//2*(1+x)^(1/2))+-3//4*2^(1/2)*arcsin(x^(1/2)+-1*(1+x)^(1/2)))
@test integrate(-1*(x+x^3+(1+x^2)^(1/2))^-1*(x+2*(1+x^2)^(1/2)), x) == :((-2+2*5^(1/2))^(1/2)*arctanh((2+5^(1/2))^(1/2)*(x+(1+x^2)^(1/2)))+-1*(2+2*5^(1/2))^(1/2)*arctan((-2+5^(1/2))^(1/2)*(x+(1+x^2)^(1/2))))
@test integrate((1+x^2)^-1*(2+x^2+2x)^-1//2*(1+2x), x) == :(-1*(1/2+(1/2)*5^(1/2))^(1/2)*arctan((10+10*5^(1/2))^-1//2*(2+x^2+2x)^-1//2*(2*5^(1/2)+-1*x*(5+5^(1/2))))+-1*(-1//2+(1/2)*5^(1/2))^(1/2)*arctanh((-10+10*5^(1/2))^-1//2*(2+x^2+2x)^-1//2*(2*5^(1/2)+x*(5+-1*5^(1/2)))))
@test integrate((1+x^4)^-1*((1+x^4)^(1/2)+-1*x^2)^-1//2, x) == :(arctan(x*((1+x^4)^(1/2)+-1*x^2)^-1//2))
@test integrate((a+b*x^4)^-1*(c*x^2+d*(a+b*x^4)^(1/2))^-1//2, x) == :(a^-1*c^-1//2*arctanh(x*c^(1/2)*(c*x^2+d*(a+b*x^4)^(1/2))^-1//2))
@test integrate((a+b*x^4)^-1*(d*(a+b*x^4)^(1/2)+-1*c*x^2)^-1//2, x) == :(a^-1*c^-1//2*arctan(x*c^(1/2)*(d*(a+b*x^4)^(1/2)+-1*c*x^2)^-1//2))
@test integrate(x*(a+b*c^4+b*d^4*x^4+4*b*c*d^3*x^3+4*b*d*x*c^3+6*b*c^2*d^2*x^2)^-1//2, x) == :((1/2)*b^-1//2*d^-2*arctanh(b^(1/2)*d^2*(a+b*d^4*(x+c*d^-1)^4)^-1//2*(x+c*d^-1)^2)+-1//2*c*a^-1//4*b^-1//4*d^-2*((a^(1/2)+b^(1/2)*d^2*(x+c*d^-1)^2)^-2*(a+b*d^4*(x+c*d^-1)^4))^(1/2)*(a+b*d^4*(x+c*d^-1)^4)^-1//2*(a^(1/2)+b^(1/2)*d^2*(x+c*d^-1)^2)*Elliptic.F(2*arctan(a^-1//4*b^1//4*(c+d*x)),1/2))
@test integrate((a+b*c^4+b*d^4*x^4+4*b*c*d^3*x^3+4*b*d*x*c^3+6*b*c^2*d^2*x^2)^-1//2, x) == :((1/2)*a^-1//4*b^-1//4*d^-1*((a^(1/2)+b^(1/2)*d^2*(x+c*d^-1)^2)^-2*(a+b*d^4*(x+c*d^-1)^4))^(1/2)*(a+b*d^4*(x+c*d^-1)^4)^-1//2*(a^(1/2)+b^(1/2)*d^2*(x+c*d^-1)^2)*Elliptic.F(2*arctan(a^-1//4*b^1//4*(c+d*x)),1/2))
@test integrate((a+b*x^2+c*x^4)^-1//2*(a*d+a*e*x^2+c*d*x^4)^-1*(a+-1*c*x^4), x) == :(d^-1//2*(b*d+-1*a*e)^-1//2*arctanh(x*d^-1//2*(b*d+-1*a*e)^(1/2)*(a+b*x^2+c*x^4)^-1//2))
@test integrate((a+c*x^4+-1*b*x^2)^-1//2*(a*d+a*e*x^2+c*d*x^4)^-1*(a+-1*c*x^4), x) == :(d^-1//2*(a*e+b*d)^-1//2*arctan(x*d^-1//2*(a*e+b*d)^(1/2)*(a+c*x^4+-1*b*x^2)^-1//2))
@test integrate((8+x^3)^-1*(5+x^2+-2x)^-1//2, x) == :(1//12*arctanh((5+x^2+-2x)^(1/2))+-1//12*3^(1/2)*arctan(1//3*3^(1/2)*(5+x^2+-2x)^-1//2*(1+-1x))+-1//156*13^(1/2)*arctanh(1//13*13^(1/2)*(5+x^2+-2x)^-1//2*(7+-3x)))
@test integrate((x^2*(1+x^2)^-1)^(1/2), x) == :(x^-1*(x^2)^(1/2)*(1+x^2)^(1/2))
@test integrate((a*d+a*d*x^2+b*d*x)^-1*(a+a*x^4+b*x+b*x^3+c*x^2)^-1//2*(e*f+-1*e*f*x^2), x) == :(e*f*a^-1*d^-1*(-1c+2a)^-1//2*arctan((1/2)*a^-1*(-1c+2a)^-1//2*(a+a*x^4+b*x+b*x^3+c*x^2)^-1//2*(a*b+x*(b^2+4*a^2+-2*a*c)+a*b*x^2)))
@test integrate((-1*a*d+b*d*x+-1*a*d*x^2)^-1*(-1a+b*x+b*x^3+c*x^2+-1*a*x^4)^-1//2*(e*f+-1*e*f*x^2), x) == :(e*f*a^-1*d^-1*(c+2a)^-1//2*arctanh((1/2)*a^-1*(c+2a)^-1//2*(-1a+b*x+b*x^3+c*x^2+-1*a*x^4)^-1//2*(a*b+-1*x*(b^2+4*a^2+2*a*c)+a*b*x^2)))
@test integrate(x^-1*(a*x^2+b*x*(-1*a*b^-2+a^2*b^-2*x^2)^(1/2))^(1/2)*(-1*a*b^-2+a^2*b^-2*x^2)^-1//2, x) == :(b*2^(1/2)*a^-1//2*arcsinh(a^-1//2*(a*x+b*(-1*a*b^-2+a^2*b^-2*x^2)^(1/2))))
@test integrate(x^-1*(a*b^-2+a^2*b^-2*x^2)^-1//2*(-1*a*x^2+b*x*(a*b^-2+a^2*b^-2*x^2)^(1/2))^(1/2), x) == :(b*2^(1/2)*a^-1//2*arcsin(a^-1//2*(a*x+-1*b*(a*b^-2+a^2*b^-2*x^2)^(1/2))))
@test integrate(x^-1*(x*(a*x+b*(-1*a*b^-2+a^2*b^-2*x^2)^(1/2)))^(1/2)*(-1*a*b^-2+a^2*b^-2*x^2)^-1//2, x) == :(b*2^(1/2)*a^-1//2*arcsinh(a^-1//2*(a*x+b*(-1*a*b^-2+a^2*b^-2*x^2)^(1/2))))
@test integrate(x^-1*(x*(b*(a*b^-2+a^2*b^-2*x^2)^(1/2)+-1*a*x))^(1/2)*(a*b^-2+a^2*b^-2*x^2)^-1//2, x) == :(b*2^(1/2)*a^-1//2*arcsin(a^-1//2*(a*x+-1*b*(a*b^-2+a^2*b^-2*x^2)^(1/2))))
@test integrate((1+(-1+x)^(1/2)+(-4+x)^(1/2))^-1*(4+x^2+-5x)^-1*(-1*(-4+x)^(1/2)+-4*(-1+x)^(1/2)+x*(-1+x)^(1/2)+x*(-4+x)^(1/2)), x) == :(2*log(1+(-1+x)^(1/2)+(-4+x)^(1/2)))
@test integrate(x^-1*(3+x^2+3x)^-1*(3+x^3+3x+3*x^2)^-1//3, x) == :(-1//3*3^1//6*arctan(1//3*3^(1/2)+1//3*3^5//6*(2+(1+x)^3)^-1//3*(2+2x))+-1//18*3^2//3*log(1+3^1//3*(2+(1+x)^3)^-1//3*(1+x)+3^2//3*(1+x)^2*(2+(1+x)^3)^-2//3)+1//9*3^2//3*log(1+-1*3^1//3*(2+(1+x)^3)^-1//3*(1+x)))
@test integrate((1+-1*x^3)^-2//3*(1+x^2+-1x)^-1*(1+-1*x^2), x) == :(-1//4*2^1//3*log(1+-1*x^3+2*(1+-1x)^3)+3//4*2^1//3*log((1+-1*x^3)^1//3+2^1//3*(1+-1x))+(1/2)*2^1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*2^1//3*(1+-1*x^3)^-1//3*(1+-1x))))
@test integrate(x^2*(1+x^4)^-1*(-1+x^4)^-1//2, x) == :(-1//4*arctan(x^-1*(-1+x^4)^-1//2*(1+x^2))+-1//4*arctanh(x^-1*(-1+x^4)^-1//2*(1+-1*x^2)))
@test integrate((d+e*x^2)^-1*(a*e+c*d*x^2)^-1*(a+b*x^2+c*x^4)^-1//2*(a+-1*c*x^4), x) == :(d^-1//2*e^-1//2*(a*e^2+c*d^2+-1*b*d*e)^-1//2*arctan(x*d^-1//2*e^-1//2*(a+b*x^2+c*x^4)^-1//2*(a*e^2+c*d^2+-1*b*d*e)^(1/2)))
@test integrate(((2+-1*x^2*(-2+3^(1/2)))*(-4+x^2+2*3^(1/2)))^-1//2*(1+x+3^(1/2))^-1*(1+x+-1*3^(1/2)), x) == :(1//3*3^1//4*arctanh(1//3*3^1//4*((2+-1*x^2*(-2+3^(1/2)))*(-4+x^2+2*3^(1/2)))^-1//2*(1+x+-1*3^(1/2))^2))
@test integrate(x+(1+x)^-1*(1+-1*x^2), x) == :(x)
@test integrate((x^-1+(1+-1*x^2)^(1/2))^-1, x) == :(-1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*x^2))+-1//3*3^(1/2)*arctan(x*(-1*(im+3^(1/2))^-1*(im+-1*3^(1/2)))^(1/2)*(1+-1*x^2)^-1//2)+-1//3*3^(1/2)*arctan(x*(-1*(im+3^(1/2))^-1*(im+-1*3^(1/2)))^-1//2*(1+-1*x^2)^-1//2)+arcsin(x))
@test integrate((1+-1*x^4)^n*(1+x+x^2+x^3)^(-1n), x) == :(-1*(1+n)^-1*(1+-1*x^4)^n*(1+x+x^2+x^3)^(-1n)*(1+-1x))
@test integrate(x*(-44375*b^4+5308416*c^4*x^4+576000*c*x*b^3+576000*b^2*c^2*x^2)^-1//2, x) == :(1//18432*c^-2*log(5308416*(-44375*b^4+5308416*c^4*x^4+576000*c*x*b^3+576000*b^2*c^2*x^2)^(1/2)*(12203125*b^6*c^4+12230590464*c^10*x^6+38880000*b^4*c^6*x^2+79200000*x*b^5*c^5+1105920000*b^3*c^7*x^3+1990656000*b^2*c^8*x^4)+20738073600000000*b^8*c^4+149587343098087735296*c^12*x^8+597005697024000000*b^6*c^6*x^2+951050714480640000*b^4*c^8*x^4+2583100705996800000*b^5*c^7*x^3+21641687369515008000*b^3*c^9*x^5+32462531054272512000*b^2*c^10*x^6))

max_stars_repo_path: test/1 Algebraic functions/1.3 Miscellaneous/1.3.2 Algebraic functions.jl