text:
@testset "1.1.3.8 P(x) (c x)^m (a+b x^n)^p" begin
    (A, B, C, a, b, c, d, e, f, g, h, i, j, m, n, p, x, ) = @variables A B C a b c d e f g h i j m n p x

    #= ::Package:: =#

    #= ::Title::Closed:: =#
    #=Integrands*of*the*form*Pq(x)*(a+b*x^n)^p=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*Pq(x)*(a+b*x^1)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*P(x)*(a+b*x)^(m/2)=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [(c + d*x + e*x^2)^1/sqrt(a + b*x), x, 2, (2*(b^2*c - a*b*d + a^2*e)*sqrt(a + b*x))/b^3 + (2*(b*d - 2*a*e)*(a + b*x)^(3/2))/(3*b^3) + (2*e*(a + b*x)^(5/2))/(5*b^3)]
    @test_int [(c + d*x + e*x^2)^2/sqrt(a + b*x), x, 2, (2*(b^2*c - a*b*d + a^2*e)^2*sqrt(a + b*x))/b^5 + (4*(b*d - 2*a*e)*(b^2*c - a*b*d + a^2*e)*(a + b*x)^(3/2))/(3*b^5) - (2*(6*a*b*d*e - 6*a^2*e^2 - b^2*(d^2 + 2*c*e))*(a + b*x)^(5/2))/(5*b^5) + (4*e*(b*d - 2*a*e)*(a + b*x)^(7/2))/(7*b^5) + (2*e^2*(a + b*x)^(9/2))/(9*b^5)]
    @test_int [(c + d*x + e*x^2)^3/sqrt(a + b*x), x, 2, (2*(b^2*c - a*b*d + a^2*e)^3*sqrt(a + b*x))/b^7 + (2*(b*d - 2*a*e)*(b^2*c - a*b*d + a^2*e)^2*(a + b*x)^(3/2))/b^7 - (6*(b^2*c - a*b*d + a^2*e)*(5*a*b*d*e - 5*a^2*e^2 - b^2*(d^2 + c*e))*(a + b*x)^(5/2))/(5*b^7) - (2*(b*d - 2*a*e)*(10*a*b*d*e - 10*a^2*e^2 - b^2*(d^2 + 6*c*e))*(a + b*x)^(7/2))/(7*b^7) - (2*e*(5*a*b*d*e - 5*a^2*e^2 - b^2*(d^2 + c*e))*(a + b*x)^(9/2))/(3*b^7) + (6*e^2*(b*d - 2*a*e)*(a + b*x)^(11/2))/(11*b^7) + (2*e^3*(a + b*x)^(13/2))/(13*b^7)]

    @test_int [(c + d*x + e*x^2 + f*x^3)^1/sqrt(a + b*x), x, 2, (2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*sqrt(a + b*x))/b^4 + (2*(b^2*d - 2*a*b*e + 3*a^2*f)*(a + b*x)^(3/2))/(3*b^4) + (2*(b*e - 3*a*f)*(a + b*x)^(5/2))/(5*b^4) + (2*f*(a + b*x)^(7/2))/(7*b^4)]
    @test_int [(c + d*x + e*x^2 + f*x^3)^2/sqrt(a + b*x), x, 2, (2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)^2*sqrt(a + b*x))/b^7 + (4*(b^2*d - 2*a*b*e + 3*a^2*f)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*(a + b*x)^(3/2))/(3*b^7) + (2*(b^4*(d^2 + 2*c*e) - 20*a^3*b*e*f + 15*a^4*f^2 - 6*a*b^3*(d*e + c*f) + 6*a^2*b^2*(e^2 + 2*d*f))*(a + b*x)^(5/2))/(5*b^7) + (4*(10*a^2*b*e*f - 10*a^3*f^2 + b^3*(d*e + c*f) - 2*a*b^2*(e^2 + 2*d*f))*(a + b*x)^(7/2))/(7*b^7) - (2*(10*a*b*e*f - 15*a^2*f^2 - b^2*(e^2 + 2*d*f))*(a + b*x)^(9/2))/(9*b^7) + (4*f*(b*e - 3*a*f)*(a + b*x)^(11/2))/(11*b^7) + (2*f^2*(a + b*x)^(13/2))/(13*b^7)]
    @test_int [(c + d*x + e*x^2 + f*x^3)^3/sqrt(a + b*x), x, 2, (2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)^3*sqrt(a + b*x))/b^10 + (2*(b^2*d - 2*a*b*e + 3*a^2*f)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)^2*(a + b*x)^(3/2))/b^10 + (6*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*(b^4*(d^2 + c*e) - 16*a^3*b*e*f + 12*a^4*f^2 - a*b^3*(5*d*e + 3*c*f) + a^2*b^2*(5*e^2 + 9*d*f))*(a + b*x)^(5/2))/(5*b^10) - (2*(168*a^5*b*e*f^2 - 84*a^6*f^3 - b^6*(d^3 + 6*c*d*e + 3*c^2*f) - 105*a^4*b^2*f*(e^2 + d*f) + 12*a*b^5*(d^2*e + c*e^2 + 2*c*d*f) - 30*a^2*b^4*(d*e^2 + d^2*f + 2*c*e*f) + 20*a^3*b^3*(e^3 + 6*d*e*f + 3*c*f^2))*(a + b*x)^(7/2))/(7*b^10) + (2*(70*a^4*b*e*f^2 - 42*a^5*f^3 - 35*a^3*b^2*f*(e^2 + d*f) + b^5*(d^2*e + c*e^2 + 2*c*d*f) - 5*a*b^4*(d*e^2 + d^2*f + 2*c*e*f) + 5*a^2*b^3*(e^3 + 6*d*e*f + 3*c*f^2))*(a + b*x)^(9/2))/(3*b^10) - (6*(56*a^3*b*e*f^2 - 42*a^4*f^3 - 21*a^2*b^2*f*(e^2 + d*f) - b^4*(d*e^2 + d^2*f + 2*c*e*f) + 2*a*b^3*(e^3 + 6*d*e*f + 3*c*f^2))*(a + b*x)^(11/2))/(11*b^10) + (2*(84*a^2*b*e*f^2 - 84*a^3*f^3 - 21*a*b^2*f*(e^2 + d*f) + b^3*(e^3 + 6*d*e*f + 3*c*f^2))*(a + b*x)^(13/2))/(13*b^10) - (2*f*(8*a*b*e*f - 12*a^2*f^2 - b^2*(e^2 + d*f))*(a + b*x)^(15/2))/(5*b^10) + (6*f^2*(b*e - 3*a*f)*(a + b*x)^(17/2))/(17*b^10) + (2*f^3*(a + b*x)^(19/2))/(19*b^10)]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*Pq(x)*(a+b*x^3)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*P1(x)*(a+b*x^3)^p=#

    @test_int [(c + d*x)/(a + b*x^3), x, 6, -(((b^(1/3)*c + a^(1/3)*d)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(2/3)*b^(2/3))) + ((b^(1/3)*c - a^(1/3)*d)*log(a^(1/3) + b^(1/3)*x))/(3*a^(2/3)*b^(2/3)) - ((c - (a^(1/3)*d)/b^(1/3))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(2/3)*b^(1/3))]

    @test_int [(c + d*x)/(a + b*x^3)^2, x, 7, (x*(c + d*x))/(3*a*(a + b*x^3)) - ((2*b^(1/3)*c + a^(1/3)*d)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(5/3)*b^(2/3)) + ((2*b^(1/3)*c - a^(1/3)*d)*log(a^(1/3) + b^(1/3)*x))/(9*a^(5/3)*b^(2/3)) - ((2*b^(1/3)*c - a^(1/3)*d)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(5/3)*b^(2/3))]

    @test_int [(c + d*x)/(a + b*x^3)^3, x, 8, (x*(c + d*x))/(6*a*(a + b*x^3)^2) + (x*(5*c + 4*d*x))/(18*a^2*(a + b*x^3)) - ((5*b^(1/3)*c + 2*a^(1/3)*d)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(8/3)*b^(2/3)) + ((5*b^(1/3)*c - 2*a^(1/3)*d)*log(a^(1/3) + b^(1/3)*x))/(27*a^(8/3)*b^(2/3)) - ((5*b^(1/3)*c - 2*a^(1/3)*d)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(8/3)*b^(2/3))]

    @test_int [(c + d*x)/(a + b*x^3)^4, x, 9, (x*(c + d*x))/(9*a*(a + b*x^3)^3) + (x*(8*c + 7*d*x))/(54*a^2*(a + b*x^3)^2) + (2*x*(10*c + 7*d*x))/(81*a^3*(a + b*x^3)) - (2*(20*b^(1/3)*c + 7*a^(1/3)*d)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(81*sqrt(3)*a^(11/3)*b^(2/3)) + (2*(20*b^(1/3)*c - 7*a^(1/3)*d)*log(a^(1/3) + b^(1/3)*x))/(243*a^(11/3)*b^(2/3)) - ((20*b^(1/3)*c - 7*a^(1/3)*d)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(243*a^(11/3)*b^(2/3))]

    @test_int [(a + b*x)/(d + e*x^3), x, 6, -(((b*d^(1/3) + a*e^(1/3))*atan((d^(1/3) - 2*e^(1/3)*x)/(sqrt(3)*d^(1/3))))/(sqrt(3)*d^(2/3)*e^(2/3))) - ((b*d^(1/3) - a*e^(1/3))*log(d^(1/3) + e^(1/3)*x))/(3*d^(2/3)*e^(2/3)) - ((a - (b*d^(1/3))/e^(1/3))*log(d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2))/(6*d^(2/3)*e^(1/3))]
    @test_int [(a + b*x)/(d - e*x^3), x, 6, -(((b*d^(1/3) - a*e^(1/3))*atan((d^(1/3) + 2*e^(1/3)*x)/(sqrt(3)*d^(1/3))))/(sqrt(3)*d^(2/3)*e^(2/3))) - ((b*d^(1/3) + a*e^(1/3))*log(d^(1/3) - e^(1/3)*x))/(3*d^(2/3)*e^(2/3)) + ((b*d^(1/3) + a*e^(1/3))*log(d^(2/3) + d^(1/3)*e^(1/3)*x + e^(2/3)*x^2))/(6*d^(2/3)*e^(2/3))]

    @test_int [(1 + x)/(1 + x^3), x, 3, -((2*atan((1 - 2*x)/sqrt(3)))/sqrt(3))]
    @test_int [(1 - x)/(1 - x^3), x, 3, (2*atan((1 + 2*x)/sqrt(3)))/sqrt(3)]
    @test_int [(1 + x)/(1 - x^3), x, 3, -(2/3)*log(1 - x) + (1/3)*log(1 + x + x^2)]
    @test_int [(1 - x)/(1 + x^3), x, 3, (2/3)*log(1 + x) - (1/3)*log(1 - x + x^2)]

    @test_int [(3 - x)/(1 - x^3), x, 6, (4*atan((1 + 2*x)/sqrt(3)))/sqrt(3) - (2/3)*log(1 - x) + (1/3)*log(1 + x + x^2)]

    @test_int [(c + d*x)/(c^3 + d^3*x^3), x, 3, -((2*atan((c - 2*d*x)/(sqrt(3)*c)))/(sqrt(3)*c*d))]
    @test_int [(c - d*x)/(c^3 - d^3*x^3), x, 3, (2*atan((c + 2*d*x)/(sqrt(3)*c)))/(sqrt(3)*c*d)]

    @test_int [(a^(1/3)*b^(1/3)*B + b^(2/3)*B*x)/(a + b*x^3), x, 3, -((2*B*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(1/3)))]
    @test_int [(a^(1/3)*(-b)^(1/3)*B - (-b)^(2/3)*B*x)/(a + b*x^3), x, 3, (2*B*atan((a^(1/3) + 2*(-b)^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(1/3))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*P2(x)*(a+b*x^3)^p=#

    @test_int [(0 + B*x + C*x^2)/(a + b*x^3) - (C*x^2)/(a + b*x^3), x, 12, -((B*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(1/3)*b^(2/3))) - (B*log(a^(1/3) + b^(1/3)*x))/(3*a^(1/3)*b^(2/3)) + (B*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(1/3)*b^(2/3))]
    @test_int [(A + 0*x + C*x^2)/(a + b*x^3) - (C*x^2)/(a + b*x^3), x, 11, -((A*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(2/3)*b^(1/3))) + (A*log(a^(1/3) + b^(1/3)*x))/(3*a^(2/3)*b^(1/3)) - (A*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(2/3)*b^(1/3))]
    @test_int [(A + B*x + C*x^2)/(a + b*x^3) - (C*x^2)/(a + b*x^3), x, 10, -(((A*b^(1/3) + a^(1/3)*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(2/3)*b^(2/3))) + ((A*b^(1/3) - a^(1/3)*B)*log(a^(1/3) + b^(1/3)*x))/(3*a^(2/3)*b^(2/3)) - ((A - (a^(1/3)*B)/b^(1/3))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(2/3)*b^(1/3))]

    @test_int [(b*x + c*x^2)/(d + e*x^3), x, 10, -((b*atan((d^(1/3) - 2*e^(1/3)*x)/(sqrt(3)*d^(1/3))))/(sqrt(3)*d^(1/3)*e^(2/3))) - (b*log(d^(1/3) + e^(1/3)*x))/(3*d^(1/3)*e^(2/3)) + (b*log(d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2))/(6*d^(1/3)*e^(2/3)) + (c*log(d + e*x^3))/(3*e)]
    @test_int [(a + c*x^2)/(d - e*x^3), x, 9, (a*atan((d^(1/3) + 2*e^(1/3)*x)/(sqrt(3)*d^(1/3))))/(sqrt(3)*d^(2/3)*e^(1/3)) - (a*log(d^(1/3) - e^(1/3)*x))/(3*d^(2/3)*e^(1/3)) + (a*log(d^(2/3) + d^(1/3)*e^(1/3)*x + e^(2/3)*x^2))/(6*d^(2/3)*e^(1/3)) - (c*log(d - e*x^3))/(3*e)]

    @test_int [(2*a^2 + b^2*x^2)/(a^3 + b^3*x^3), x, 4, -((2*atan((a - 2*b*x)/(sqrt(3)*a)))/(sqrt(3)*b)) + log(a + b*x)/b]
    @test_int [(2*a^2 + b^2*x^2)/(a^3 - b^3*x^3), x, 4, (2*atan((a + 2*b*x)/(sqrt(3)*a)))/(sqrt(3)*b) - log(a - b*x)/b]

    @test_int [(8*C + b^(2/3)*C*x^2)/(8 + b*x^3), x, 4, -((2*C*atan((1 - b^(1/3)*x)/sqrt(3)))/(sqrt(3)*b^(1/3))) + (C*log(2 + b^(1/3)*x))/b^(1/3)]
    @test_int [(a^(2/3)*C + 2*C*x^2)/(a + 8*x^3), x, 4, -((C*atan((a^(1/3) - 4*x)/(sqrt(3)*a^(1/3))))/(2*sqrt(3))) + (1/4)*C*log(a^(1/3) + 2*x)]

    @test_int [(8*C + (-b)^(2/3)*C*x^2)/(-8 + b*x^3), x, 4, (2*C*atan((1 - (-b)^(1/3)*x)/sqrt(3)))/(sqrt(3)*(-b)^(1/3)) - (C*log(2 + (-b)^(1/3)*x))/(-b)^(1/3)]
    @test_int [((-a)^(2/3)*C + 2*C*x^2)/(a - 8*x^3), x, 4, (C*atan((1 - (4*x)/(-a)^(1/3))/sqrt(3)))/(2*sqrt(3)) - (1/4)*C*log((-a)^(1/3) + 2*x)]

    @test_int [(2*C*(a/b)^(2/3) + C*x^2)/(a + b*x^3), x, 4, -((2*C*atan((1 - (2*x)/(a/b)^(1/3))/sqrt(3)))/(sqrt(3)*b)) + (C*log((a/b)^(1/3) + x))/b]
    @test_int [(2*C*(-a/b)^(2/3) + C*x^2)/(a - b*x^3), x, 4, (2*C*atan((1 - (2*x)/(-(a/b))^(1/3))/sqrt(3)))/(sqrt(3)*b) - (C*log((-(a/b))^(1/3) + x))/b]

    @test_int [(2*C*(-a/b)^(2/3) + C*x^2)/(a + b*x^3), x, 4, -((2*C*atan((1 + (2*x)/(-(a/b))^(1/3))/sqrt(3)))/(sqrt(3)*b)) + (C*log((-(a/b))^(1/3) - x))/b]
    @test_int [(2*C*(a/b)^(2/3) + C*x^2)/(a - b*x^3), x, 4, (2*C*atan((1 + (2*x)/(a/b)^(1/3))/sqrt(3)))/(sqrt(3)*b) - (C*log((a/b)^(1/3) - x))/b]

    @test_int [(2*a^(2/3)*C + b^(2/3)*C*x^2)/(a + b*x^3), x, 4, -((2*C*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^(1/3))) + (C*log(a^(1/3) + b^(1/3)*x))/b^(1/3)]
    @test_int [(-2*a^(2/3)*C - (-b)^(2/3)*C*x^2)/(a + b*x^3), x, 4, -((2*C*atan((a^(1/3) + 2*(-b)^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*(-b)^(1/3))) + (C*log(a^(1/3) - (-b)^(1/3)*x))/(-b)^(1/3)]

    @test_int [(-3 + x^2)/(-1 + x^3), x, 6, sqrt(3)*atan((1 + 2*x)/sqrt(3)) - (2*log(1 - x))/3 + (5*log(1 + x + x^2))/6]

    @test_int [(a^(1/3)*b^(1/3)*B + 2*a^(2/3)*C + b^(2/3)*B*x + b^(2/3)*C*x^2)/(a + b*x^3), x, 4, -((2*(B/a^(1/3) + C/b^(1/3))*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/sqrt(3)) + (C*log(a^(1/3) + b^(1/3)*x))/b^(1/3)]
    @test_int [(a^(1/3)*(-b)^(1/3)*B - 2*a^(2/3)*C - (-b)^(2/3)*B*x - (-b)^(2/3)*C*x^2)/(a + b*x^3), x, 4, (2*(b*B + a^(1/3)*(-b)^(2/3)*C)*atan((a^(1/3) + 2*(-b)^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(1/3)*b) + (C*log(a^(1/3) - (-b)^(1/3)*x))/(-b)^(1/3)]

    @test_int [(B^2 + B*C*x + C^2*x^2)/(-B^3 + C^3*x^3), x, 2, log(B - C*x)/C]
    @test_int [(a^(2/3)*C - a^(1/3)*b^(1/3)*C*x + b^(2/3)*C*x^2)/(a + b*x^3), x, 2, (C*log(a^(1/3) + b^(1/3)*x))/b^(1/3)]

    @test_int [((a/b)^(1/3)*B + 2*(a/b)^(2/3)*C + B*x + C*x^2)/(a + b*x^3), x, 4, -((2*(a/b)^(2/3)*(B + (a/b)^(1/3)*C)*atan((1 - (2*x)/(a/b)^(1/3))/sqrt(3)))/(sqrt(3)*a)) + (C*log((a/b)^(1/3) + x))/b]
    @test_int [((-(a/b))^(1/3)*B + 2*(-(a/b))^(2/3)*C + B*x + C*x^2)/(a - b*x^3), x, 4, (2*(B + (-(a/b))^(1/3)*C)*atan((1 - (2*x)/(-(a/b))^(1/3))/sqrt(3)))/(sqrt(3)*(-(a/b))^(1/3)*b) - (C*log((-(a/b))^(1/3) + x))/b]

    @test_int [((-(-(a/b))^(1/3))*B + 2*(-(a/b))^(2/3)*C + B*x + C*x^2)/(a + b*x^3), x, 4, (2*(B - (-(a/b))^(1/3)*C)*atan((1 + (2*x)/(-(a/b))^(1/3))/sqrt(3)))/(sqrt(3)*(-(a/b))^(1/3)*b) + (C*log((-(a/b))^(1/3) - x))/b]
    @test_int [((-(a/b)^(1/3))*B + 2*(a/b)^(2/3)*C + B*x + C*x^2)/(a - b*x^3), x, 4, -((2*(a/b)^(2/3)*(B - (a/b)^(1/3)*C)*atan((1 + (2*x)/(a/b)^(1/3))/sqrt(3)))/(sqrt(3)*a)) - (C*log((a/b)^(1/3) - x))/b]

    @test_int [(a + a*x + c*x^2)/(1 - x^3), x, 3, (-(1/3))*(2*a + c)*log(1 - x) + (1/3)*(a - c)*log(1 + x + x^2)]
    @test_int [(a + b*x + c*x^2)/(1 - x^3), x, 6, ((a - b)*atan((1 + 2*x)/sqrt(3)))/sqrt(3) - (1/3)*(a + b + c)*log(1 - x) + (1/6)*(a + b - 2*c)*log(1 + x + x^2)]

    @test_int [(1 + x + x^2)/(1 - x^3), x, 2, -log(1-x)]
    @test_int [(1 - x + 3*x^2)/(1 - x^3), x, 5, ((2*atan((1 + 2*x)/sqrt(3)))/sqrt(3)) - log(1 - x^3)]
    @test_int [(1 + x + 4*x^2)/(1 - x^3), x, 3, -2*log(1 - x) - log(1 + x + x^2)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*P4(x)*(a+b*x^3)^p=#

    @test_int [(a*c + a*d*x + b*c*x^3 + b*d*x^4)*(a + b*x^3)^3, x, 2, a^4*c*x + (1/2)*a^4*d*x^2 + a^3*b*c*x^4 + (4/5)*a^3*b*d*x^5 + (6/7)*a^2*b^2*c*x^7 + (3/4)*a^2*b^2*d*x^8 + (2/5)*a*b^3*c*x^10 + (4/11)*a*b^3*d*x^11 + (1/13)*b^4*c*x^13 + (1/14)*b^4*d*x^14]
    @test_int [(a*c + a*d*x + b*c*x^3 + b*d*x^4)*(a + b*x^3)^2, x, 2, a^3*c*x + (1/2)*a^3*d*x^2 + (3/4)*a^2*b*c*x^4 + (3/5)*a^2*b*d*x^5 + (3/7)*a*b^2*c*x^7 + (3/8)*a*b^2*d*x^8 + (1/10)*b^3*c*x^10 + (1/11)*b^3*d*x^11]
    @test_int [(a*c + a*d*x + b*c*x^3 + b*d*x^4)*(a + b*x^3)^1, x, 2, a^2*c*x + (1/2)*a^2*d*x^2 + (1/2)*a*b*c*x^4 + (2/5)*a*b*d*x^5 + (1/7)*b^2*c*x^7 + (1/8)*b^2*d*x^8]
    @test_int [(a*c + a*d*x + b*c*x^3 + b*d*x^4)/(a + b*x^3)^1, x, 2, c*x + (d*x^2)/2]
    @test_int [(a*c + a*d*x + b*c*x^3 + b*d*x^4)/(a + b*x^3)^2, x, 7, -(((b^(1/3)*c + a^(1/3)*d)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(2/3)*b^(2/3))) + ((b^(1/3)*c - a^(1/3)*d)*log(a^(1/3) + b^(1/3)*x))/(3*a^(2/3)*b^(2/3)) - ((c - (a^(1/3)*d)/b^(1/3))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(2/3)*b^(1/3))]
    @test_int [(a*c + a*d*x + b*c*x^3 + b*d*x^4)/(a + b*x^3)^3, x, 8, (x*(c + d*x))/(3*a*(a + b*x^3)) - ((2*b^(1/3)*c + a^(1/3)*d)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(5/3)*b^(2/3)) + ((2*b^(1/3)*c - a^(1/3)*d)*log(a^(1/3) + b^(1/3)*x))/(9*a^(5/3)*b^(2/3)) - ((2*b^(1/3)*c - a^(1/3)*d)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(5/3)*b^(2/3))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*P4(x)*(a+b*x^3)^(p/2)=#

    @test_int [(a*c + a*d*x + b*c*x^3 + b*d*x^4)*(a + b*x^3)^(3/2), x, 7, (810*a^3*d*sqrt(a + b*x^3))/(1729*b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (54*a^2*(1729*c*x + 935*d*x^2)*sqrt(a + b*x^3))/323323 + (30*a*(247*c*x + 187*d*x^2)*(a + b*x^3)^(3/2))/46189 + (2/323)*(19*c*x + 17*d*x^2)*(a + b*x^3)^(5/2) - (405*3^(1/4)*sqrt(2 - sqrt(3))*a^(10/3)*d*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(1729*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (54*3^(3/4)*sqrt(2 + sqrt(3))*a^3*(1729*b^(1/3)*c - 935*(1 - sqrt(3))*a^(1/3)*d)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(323323*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(a*c + a*d*x + b*c*x^3 + b*d*x^4)*(a + b*x^3)^(1/2), x, 6, (54*a^2*d*sqrt(a + b*x^3))/(91*b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (18*a*(91*c*x + 55*d*x^2)*sqrt(a + b*x^3))/5005 + (2/143)*(13*c*x + 11*d*x^2)*(a + b*x^3)^(3/2) - (27*3^(1/4)*sqrt(2 - sqrt(3))*a^(7/3)*d*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(91*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (18*3^(3/4)*sqrt(2 + sqrt(3))*a^2*(91*b^(1/3)*c - 55*(1 - sqrt(3))*a^(1/3)*d)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(5005*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(a*c + a*d*x + b*c*x^3 + b*d*x^4)/(a + b*x^3)^(1/2), x, 5, (6*a*d*sqrt(a + b*x^3))/(7*b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (2/35)*(7*c*x + 5*d*x^2)*sqrt(a + b*x^3) - (3*3^(1/4)*sqrt(2 - sqrt(3))*a^(4/3)*d*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(7*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (2*3^(3/4)*sqrt(2 + sqrt(3))*a*(7*b^(1/3)*c - 5*(1 - sqrt(3))*a^(1/3)*d)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(35*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(a*c + a*d*x + b*c*x^3 + b*d*x^4)/(a + b*x^3)^(3/2), x, 4, (2*d*sqrt(a + b*x^3))/(b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*d*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (2*sqrt(2 + sqrt(3))*(b^(1/3)*c - (1 - sqrt(3))*a^(1/3)*d)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3^(1/4)*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(a*c + a*d*x + b*c*x^3 + b*d*x^4)/(a + b*x^3)^(5/2), x, 5, (2*x*(c + d*x))/(3*a*sqrt(a + b*x^3)) - (2*d*sqrt(a + b*x^3))/(3*a*b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (sqrt(2 - sqrt(3))*d*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3^(3/4)*a^(2/3)*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (2*sqrt(2 + sqrt(3))*(b^(1/3)*c + (1 - sqrt(3))*a^(1/3)*d)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3*3^(1/4)*a*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(a*c + a*d*x + b*c*x^3 + b*d*x^4)/(a + b*x^3)^(7/2), x, 6, (2*x*(c + d*x))/(9*a*(a + b*x^3)^(3/2)) + (2*x*(7*c + 5*d*x))/(27*a^2*sqrt(a + b*x^3)) - (10*d*sqrt(a + b*x^3))/(27*a^2*b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (5*sqrt(2 - sqrt(3))*d*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(9*3^(3/4)*a^(5/3)*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (2*sqrt(2 + sqrt(3))*(7*b^(1/3)*c + 5*(1 - sqrt(3))*a^(1/3)*d)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(27*3^(1/4)*a^2*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(a*c + a*d*x + b*c*x^3 + b*d*x^4)/(a + b*x^3)^(9/2), x, 7, (2*x*(c + d*x))/(15*a*(a + b*x^3)^(5/2)) + (2*x*(13*c + 11*d*x))/(135*a^2*(a + b*x^3)^(3/2)) + (2*x*(91*c + 55*d*x))/(405*a^3*sqrt(a + b*x^3)) - (22*d*sqrt(a + b*x^3))/(81*a^3*b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (11*sqrt(2 - sqrt(3))*d*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(27*3^(3/4)*a^(8/3)*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (2*sqrt(2 + sqrt(3))*(91*b^(1/3)*c + 55*(1 - sqrt(3))*a^(1/3)*d)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(405*3^(1/4)*a^3*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]

    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)/(a + b*x^3)^(1/2), x, 7, (2*e*sqrt(a + b*x^3))/(3*b) + (2*f*x*sqrt(a + b*x^3))/(5*b) + (2*g*x^2*sqrt(a + b*x^3))/(7*b) + (2*(7*b*d - 4*a*g)*sqrt(a + b*x^3))/(7*b^(5/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*(7*b*d - 4*a*g)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(7*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (2*sqrt(2 + sqrt(3))*(7*b^(1/3)*(5*b*c - 2*a*f) - 5*(1 - sqrt(3))*a^(1/3)*(7*b*d - 4*a*g))*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(35*3^(1/4)*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)/(a + b*x^3)^(3/2), x, 6, (2*x*(b*c - a*f + (b*d - a*g)*x + b*e*x^2))/(3*a*b*sqrt(a + b*x^3)) - (2*e*sqrt(a + b*x^3))/(3*a*b) - (2*(b*d - 4*a*g)*sqrt(a + b*x^3))/(3*a*b^(5/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (sqrt(2 - sqrt(3))*(b*d - 4*a*g)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3^(3/4)*a^(2/3)*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (2*sqrt(2 + sqrt(3))*(b^(1/3)*(b*c + 2*a*f) + (1 - sqrt(3))*a^(1/3)*(b*d - 4*a*g))*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3*3^(1/4)*a*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)/(a + b*x^3)^(5/2), x, 5, (2*x*(b*c - a*f + (b*d - a*g)*x + b*e*x^2))/(9*a*b*(a + b*x^3)^(3/2)) - (2*(5*b*d + 4*a*g)*sqrt(a + b*x^3))/(27*a^2*b^(5/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (2*(3*a*e - x*(7*b*c + 2*a*f + (5*b*d + 4*a*g)*x)))/(27*a^2*b*sqrt(a + b*x^3)) + (sqrt(2 - sqrt(3))*(5*b*d + 4*a*g)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(9*3^(3/4)*a^(5/3)*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (2*sqrt(2 + sqrt(3))*(b^(1/3)*(7*b*c + 2*a*f) + (1 - sqrt(3))*a^(1/3)*(5*b*d + 4*a*g))*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(27*3^(1/4)*a^2*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)/(a + b*x^3)^(7/2), x, 6, (2*x*(b*c - a*f + (b*d - a*g)*x + b*e*x^2))/(15*a*b*(a + b*x^3)^(5/2)) + (2*x*(7*(13*b*c + 2*a*f) + 5*(11*b*d + 4*a*g)*x))/(405*a^3*b*sqrt(a + b*x^3)) - (2*(11*b*d + 4*a*g)*sqrt(a + b*x^3))/(81*a^3*b^(5/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (2*(9*a*e - x*(13*b*c + 2*a*f + (11*b*d + 4*a*g)*x)))/(135*a^2*b*(a + b*x^3)^(3/2)) + (sqrt(2 - sqrt(3))*(11*b*d + 4*a*g)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(27*3^(3/4)*a^(8/3)*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (2*sqrt(2 + sqrt(3))*(7*b^(1/3)*(13*b*c + 2*a*f) + 5*(1 - sqrt(3))*a^(1/3)*(11*b*d + 4*a*g))*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(405*3^(1/4)*a^3*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*Pq(x)*(a+b*x^3)^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [(a + b*x)^2/(c + d*x^3), x, 8, -((a*(2*b*c^(1/3) + a*d^(1/3))*atan((c^(1/3) - 2*d^(1/3)*x)/(sqrt(3)*c^(1/3))))/(sqrt(3)*c^(2/3)*d^(2/3))) - (a*(2*b*c^(1/3) - a*d^(1/3))*log(c^(1/3) + d^(1/3)*x))/(3*c^(2/3)*d^(2/3)) + (a*(2*b*c^(1/3) - a*d^(1/3))*log(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2))/(6*c^(2/3)*d^(2/3)) + (b^2*log(c + d*x^3))/(3*d)]
    @test_int [(a + b*x)^3/(c + d*x^3), x, 10, (b^3*x)/d + ((b^3*c - 3*a^2*b*c^(1/3)*d^(2/3) - a^3*d)*atan((c^(1/3) - 2*d^(1/3)*x)/(sqrt(3)*c^(1/3))))/(sqrt(3)*c^(2/3)*d^(4/3)) - ((b^3*c + 3*a^2*b*c^(1/3)*d^(2/3) - a^3*d)*log(c^(1/3) + d^(1/3)*x))/(3*c^(2/3)*d^(4/3)) + ((b^3*c + 3*a^2*b*c^(1/3)*d^(2/3) - a^3*d)*log(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2))/(6*c^(2/3)*d^(4/3)) + (a*b^2*log(c + d*x^3))/d]
    @test_int [(a + b*x)^4/(c + d*x^3), x, 10, (4*a*b^3*x)/d + (b^4*x^2)/(2*d) + ((b^4*c^(4/3) + 4*a*b^3*c*d^(1/3) - 4*a^3*b*c^(1/3)*d - a^4*d^(4/3))*atan((c^(1/3) - 2*d^(1/3)*x)/(sqrt(3)*c^(1/3))))/(sqrt(3)*c^(2/3)*d^(5/3)) + ((b*c^(1/3)*(b^3*c - 4*a^3*d) - d^(1/3)*(4*a*b^3*c - a^4*d))*log(c^(1/3) + d^(1/3)*x))/(3*c^(2/3)*d^(5/3)) - ((b*c^(1/3)*(b^3*c - 4*a^3*d) - d^(1/3)*(4*a*b^3*c - a^4*d))*log(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2))/(6*c^(2/3)*d^(5/3)) + (2*a^2*b^2*log(c + d*x^3))/d]

    @test_int [(a + b*x + c*x^2)^2/(d + e*x^3), x, 10, (2*b*c*x)/e + (c^2*x^2)/(2*e) + ((c^2*d^(4/3) + 2*b*c*d*e^(1/3) - a*(2*b*d^(1/3) + a*e^(1/3))*e)*atan((d^(1/3) - 2*e^(1/3)*x)/(sqrt(3)*d^(1/3))))/(sqrt(3)*d^(2/3)*e^(5/3)) - ((e^(1/3)*(2*b*c*d - a^2*e) - d^(1/3)*(c^2*d - 2*a*b*e))*log(d^(1/3) + e^(1/3)*x))/(3*d^(2/3)*e^(5/3)) + ((e^(1/3)*(2*b*c*d - a^2*e) - d^(1/3)*(c^2*d - 2*a*b*e))*log(d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2))/(6*d^(2/3)*e^(5/3)) + ((b^2 + 2*a*c)*log(d + e*x^3))/(3*e)]
    @test_int [(a + b*x + c*x^2)^3/(d + e*x^3), x, 10, -(((c^3*d - b^3*e - 6*a*b*c*e)*x)/e^2) + (3*c*(b^2 + a*c)*x^2)/(2*e) + (b*c^2*x^3)/e + (c^3*x^4)/(4*e) - ((c^3*d^2 - 3*b^2*c*d^(4/3)*e^(2/3) - 3*a*c^2*d^(4/3)*e^(2/3) - b^3*d*e - 6*a*b*c*d*e + 3*a^2*b*d^(1/3)*e^(5/3) + a^3*e^2)*atan((d^(1/3) - 2*e^(1/3)*x)/(sqrt(3)*d^(1/3))))/(sqrt(3)*d^(2/3)*e^(7/3)) + ((c^3*d^2 - 6*a*b*c*d*e - e*(b^3*d - a^3*e) + 3*d^(1/3)*e^(2/3)*(b^2*c*d + a*c^2*d - a^2*b*e))*log(d^(1/3) + e^(1/3)*x))/(3*d^(2/3)*e^(7/3)) - ((c^3*d^2 - 6*a*b*c*d*e - e*(b^3*d - a^3*e) + 3*d^(1/3)*e^(2/3)*(b^2*c*d + a*c^2*d - a^2*b*e))*log(d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2))/(6*d^(2/3)*e^(7/3)) - ((b*c^2*d - a*b^2*e - a^2*c*e)*log(d + e*x^3))/e^2]
    @test_int [(a + b*x + c*x^2)^4/(d + e*x^3), x, 10, -((2*(3*b^2*c^2*d + 2*a*c^3*d - 2*a*b^3*e - 6*a^2*b*c*e)*x)/e^2) - ((4*b*c^3*d - b^4*e - 12*a*b^2*c*e - 6*a^2*c^2*e)*x^2)/(2*e^2) - (c*(c^3*d - 4*b^3*e - 12*a*b*c*e)*x^3)/(3*e^2) + (c^2*(3*b^2 + 2*a*c)*x^4)/(2*e) + (4*b*c^3*x^5)/(5*e) + (c^4*x^6)/(6*e) - (1/(sqrt(3)*d^(2/3)*e^(8/3)))*((b*d^(1/3) + a*e^(1/3))*(4*c^3*d^2 + 6*c^2*(b*d^(5/3)*e^(1/3) - a*d^(4/3)*e^(2/3)) - 12*a*b*c*d*e - e*(b^3*d + 3*a*b^2*d^(2/3)*e^(1/3) - 3*a^2*b*d^(1/3)*e^(2/3) - a^3*e))*atan((d^(1/3) - 2*e^(1/3)*x)/(sqrt(3)*d^(1/3)))) + (1/(3*d^(2/3)*e^(8/3)))*((e^(1/3)*(6*b^2*c^2*d^2 + 4*a*c^3*d^2 - 4*a*b^3*d*e - 12*a^2*b*c*d*e + a^4*e^2) + d^(1/3)*(b^4*d*e + 12*a*b^2*c*d*e + 6*a^2*c^2*d*e - 4*b*(c^3*d^2 + a^3*e^2)))*log(d^(1/3) + e^(1/3)*x)) - (1/(6*d^(2/3)*e^(8/3)))*((e^(1/3)*(6*b^2*c^2*d^2 + 4*a*c^3*d^2 - 4*a*b^3*d*e - 12*a^2*b*c*d*e + a^4*e^2) + d^(1/3)*(b^4*d*e + 12*a*b^2*c*d*e + 6*a^2*c^2*d*e - 4*b*(c^3*d^2 + a^3*e^2)))*log(d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2)) + ((c^4*d^2 - 12*a*b*c^2*d*e + 6*a^2*b^2*e^2 - 4*c*e*(b^3*d - a^3*e))*log(d + e*x^3))/(3*e^3)]

    @test_int [(2*x^2 + x^4)/(1 + x^3), x, 9, x^2/2 + atan((1 - 2*x)/sqrt(3))/sqrt(3) + log(1 + x) + (1/2)*log(1 - x + x^2)]
    @test_int [(2*x^2 + x^4)/(1 - x^3), x, 9, -x^2/2 - atan((1 + 2*x)/sqrt(3))/sqrt(3) - log(1 - x) - (1/2)*log(1 + x + x^2)]

    @test_int [(1 - x + 4*x^3)/(1 + x^3), x, 8, 4*x + (4*atan((1 - 2*x)/sqrt(3)))/sqrt(3) - (2/3)*log(1 + x) + (1/3)*log(1 - x + x^2)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(c+d*x) / (a+b*x^3)^(p/2)*with*b*c^3 - 2*(5+3*sqrt(3))*a*d^3=0=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [(1 + sqrt(3) + x)/sqrt(1 + x^3), x, 3, (2*sqrt(1 + x^3))/(1 + sqrt(3) + x) - (3^(1/4)*sqrt(2 - sqrt(3))*(1 + x)*sqrt((1 - x + x^2)/(1 + sqrt(3) + x)^2)*Elliptic.E(asin((1 - sqrt(3) + x)/(1 + sqrt(3) + x)), -7 - 4*sqrt(3)))/(sqrt((1 + x)/(1 + sqrt(3) + x)^2)*sqrt(1 + x^3)) + (4*3^(1/4)*sqrt(2 + sqrt(3))*(1 + x)*sqrt((1 - x + x^2)/(1 + sqrt(3) + x)^2)*Elliptic.F(asin((1 - sqrt(3) + x)/(1 + sqrt(3) + x)), -7 - 4*sqrt(3)))/(sqrt((1 + x)/(1 + sqrt(3) + x)^2)*sqrt(1 + x^3))]
    @test_int [(1 + sqrt(3) - x)/sqrt(1 - x^3), x, 3, -((2*sqrt(1 - x^3))/(1 + sqrt(3) - x)) + (3^(1/4)*sqrt(2 - sqrt(3))*(1 - x)*sqrt((1 + x + x^2)/(1 + sqrt(3) - x)^2)*Elliptic.E(asin((1 - sqrt(3) - x)/(1 + sqrt(3) - x)), -7 - 4*sqrt(3)))/(sqrt((1 - x)/(1 + sqrt(3) - x)^2)*sqrt(1 - x^3)) - (4*3^(1/4)*sqrt(2 + sqrt(3))*(1 - x)*sqrt((1 + x + x^2)/(1 + sqrt(3) - x)^2)*Elliptic.F(asin((1 - sqrt(3) - x)/(1 + sqrt(3) - x)), -7 - 4*sqrt(3)))/(sqrt((1 - x)/(1 + sqrt(3) - x)^2)*sqrt(1 - x^3))]
    @test_int [(1 + sqrt(3) - x)/sqrt(-1 + x^3), x, 1, (2*sqrt(-1 + x^3))/(1 - sqrt(3) - x) - (3^(1/4)*sqrt(2 + sqrt(3))*(1 - x)*sqrt((1 + x + x^2)/(1 - sqrt(3) - x)^2)*Elliptic.E(asin((1 + sqrt(3) - x)/(1 - sqrt(3) - x)), -7 + 4*sqrt(3)))/(sqrt(-((1 - x)/(1 - sqrt(3) - x)^2))*sqrt(-1 + x^3))]
    @test_int [(1 + sqrt(3) + x)/sqrt(-1 - x^3), x, 1, -((2*sqrt(-1 - x^3))/(1 - sqrt(3) + x)) + (3^(1/4)*sqrt(2 + sqrt(3))*(1 + x)*sqrt((1 - x + x^2)/(1 - sqrt(3) + x)^2)*Elliptic.E(asin((1 + sqrt(3) + x)/(1 - sqrt(3) + x)), -7 + 4*sqrt(3)))/(sqrt(-((1 + x)/(1 - sqrt(3) + x)^2))*sqrt(-1 - x^3))]

    @test_int [((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)/sqrt(a + b*x^3), x, 3, (2*sqrt(a + b*x^3))/(b^(1/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(b^(1/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (4*3^(1/4)*sqrt(2 + sqrt(3))*a^(1/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(b^(1/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)/sqrt(a - b*x^3), x, 3, -((2*sqrt(a - b*x^3))/(b^(1/3)*((1 + sqrt(3))*a^(1/3) - b^(1/3)*x))) + (3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*(a^(1/3) - b^(1/3)*x)*sqrt((a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)), -7 - 4*sqrt(3)))/(b^(1/3)*sqrt((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*sqrt(a - b*x^3)) - (4*3^(1/4)*sqrt(2 + sqrt(3))*a^(1/3)*(a^(1/3) - b^(1/3)*x)*sqrt((a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)), -7 - 4*sqrt(3)))/(b^(1/3)*sqrt((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*sqrt(a - b*x^3))]
    @test_int [((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)/sqrt(-a + b*x^3), x, 1, (2*sqrt(-a + b*x^3))/(b^(1/3)*((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)) - (3^(1/4)*sqrt(2 + sqrt(3))*a^(1/3)*(a^(1/3) - b^(1/3)*x)*sqrt((a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*Elliptic.E(asin(((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)), -7 + 4*sqrt(3)))/(b^(1/3)*sqrt(-((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)^2))*sqrt(-a + b*x^3))]
    @test_int [((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)/sqrt(-a - b*x^3), x, 1, -((2*sqrt(-a - b*x^3))/(b^(1/3)*((1 - sqrt(3))*a^(1/3) + b^(1/3)*x))) + (3^(1/4)*sqrt(2 + sqrt(3))*a^(1/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 + 4*sqrt(3)))/(b^(1/3)*sqrt(-((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)^2))*sqrt(-a - b*x^3))]

    @test_int [(1 + sqrt(3) + (b/a)^(1/3)*x)/sqrt(a + b*x^3), x, 3, (2*(b/a)^(1/3)*sqrt(a + b*x^3))/(b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*(b/a)^(1/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (2*sqrt(2 + sqrt(3))*((1 + sqrt(3))*b^(1/3) - (1 - sqrt(3))*a^(1/3)*(b/a)^(1/3))*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3^(1/4)*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(1 + sqrt(3) - (b/a)^(1/3)*x)/sqrt(a - b*x^3), x, 3, -((2*(b/a)^(1/3)*sqrt(a - b*x^3))/(b^(2/3)*((1 + sqrt(3))*a^(1/3) - b^(1/3)*x))) + (3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*(b/a)^(1/3)*(a^(1/3) - b^(1/3)*x)*sqrt((a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)), -7 - 4*sqrt(3)))/(b^(2/3)*sqrt((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*sqrt(a - b*x^3)) - (2*sqrt(2 + sqrt(3))*((1 + sqrt(3))*b^(1/3) - (1 - sqrt(3))*a^(1/3)*(b/a)^(1/3))*(a^(1/3) - b^(1/3)*x)*sqrt((a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)), -7 - 4*sqrt(3)))/(3^(1/4)*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*sqrt(a - b*x^3))]
    @test_int [(1 + sqrt(3) - (b/a)^(1/3)*x)/sqrt(-a + b*x^3), x, 1, (2*(b/a)^(2/3)*sqrt(-a + b*x^3))/(b*(1 - sqrt(3) - (b/a)^(1/3)*x)) - (3^(1/4)*sqrt(2 + sqrt(3))*(1 - (b/a)^(1/3)*x)*sqrt((1 + (b/a)^(1/3)*x + (b/a)^(2/3)*x^2)/(1 - sqrt(3) - (b/a)^(1/3)*x)^2)*Elliptic.E(asin((1 + sqrt(3) - (b/a)^(1/3)*x)/(1 - sqrt(3) - (b/a)^(1/3)*x)), -7 + 4*sqrt(3)))/((b/a)^(1/3)*sqrt(-((1 - (b/a)^(1/3)*x)/(1 - sqrt(3) - (b/a)^(1/3)*x)^2))*sqrt(-a + b*x^3))]
    @test_int [(1 + sqrt(3) + (b/a)^(1/3)*x)/sqrt(-a - b*x^3), x, 1, -((2*(b/a)^(2/3)*sqrt(-a - b*x^3))/(b*(1 - sqrt(3) + (b/a)^(1/3)*x))) + (3^(1/4)*sqrt(2 + sqrt(3))*(1 + (b/a)^(1/3)*x)*sqrt((1 - (b/a)^(1/3)*x + (b/a)^(2/3)*x^2)/(1 - sqrt(3) + (b/a)^(1/3)*x)^2)*Elliptic.E(asin((1 + sqrt(3) + (b/a)^(1/3)*x)/(1 - sqrt(3) + (b/a)^(1/3)*x)), -7 + 4*sqrt(3)))/((b/a)^(1/3)*sqrt(-((1 + (b/a)^(1/3)*x)/(1 - sqrt(3) + (b/a)^(1/3)*x)^2))*sqrt(-a - b*x^3))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(c+d*x) / (a+b*x^3)^(p/2)*with*b*c^3 - 2*(5-3*sqrt(3))*a*d^3=0=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [(1 - sqrt(3) + x)/sqrt(1 + x^3), x, 1, (2*sqrt(1 + x^3))/(1 + sqrt(3) + x) - (3^(1/4)*sqrt(2 - sqrt(3))*(1 + x)*sqrt((1 - x + x^2)/(1 + sqrt(3) + x)^2)*Elliptic.E(asin((1 - sqrt(3) + x)/(1 + sqrt(3) + x)), -7 - 4*sqrt(3)))/(sqrt((1 + x)/(1 + sqrt(3) + x)^2)*sqrt(1 + x^3))]
    @test_int [(1 - sqrt(3) - x)/sqrt(1 - x^3), x, 1, -((2*sqrt(1 - x^3))/(1 + sqrt(3) - x)) + (3^(1/4)*sqrt(2 - sqrt(3))*(1 - x)*sqrt((1 + x + x^2)/(1 + sqrt(3) - x)^2)*Elliptic.E(asin((1 - sqrt(3) - x)/(1 + sqrt(3) - x)), -7 - 4*sqrt(3)))/(sqrt((1 - x)/(1 + sqrt(3) - x)^2)*sqrt(1 - x^3))]
    @test_int [(1 - sqrt(3) - x)/sqrt(-1 + x^3), x, 3, (2*sqrt(-1 + x^3))/(1 - sqrt(3) - x) - (3^(1/4)*sqrt(2 + sqrt(3))*(1 - x)*sqrt((1 + x + x^2)/(1 - sqrt(3) - x)^2)*Elliptic.E(asin((1 + sqrt(3) - x)/(1 - sqrt(3) - x)), -7 + 4*sqrt(3)))/(sqrt(-((1 - x)/(1 - sqrt(3) - x)^2))*sqrt(-1 + x^3)) + (4*3^(1/4)*sqrt(2 - sqrt(3))*(1 - x)*sqrt((1 + x + x^2)/(1 - sqrt(3) - x)^2)*Elliptic.F(asin((1 + sqrt(3) - x)/(1 - sqrt(3) - x)), -7 + 4*sqrt(3)))/(sqrt(-((1 - x)/(1 - sqrt(3) - x)^2))*sqrt(-1 + x^3))]
    @test_int [(1 - sqrt(3) + x)/sqrt(-1 - x^3), x, 3, -((2*sqrt(-1 - x^3))/(1 - sqrt(3) + x)) + (3^(1/4)*sqrt(2 + sqrt(3))*(1 + x)*sqrt((1 - x + x^2)/(1 - sqrt(3) + x)^2)*Elliptic.E(asin((1 + sqrt(3) + x)/(1 - sqrt(3) + x)), -7 + 4*sqrt(3)))/(sqrt(-((1 + x)/(1 - sqrt(3) + x)^2))*sqrt(-1 - x^3)) - (4*3^(1/4)*sqrt(2 - sqrt(3))*(1 + x)*sqrt((1 - x + x^2)/(1 - sqrt(3) + x)^2)*Elliptic.F(asin((1 + sqrt(3) + x)/(1 - sqrt(3) + x)), -7 + 4*sqrt(3)))/(sqrt(-((1 + x)/(1 - sqrt(3) + x)^2))*sqrt(-1 - x^3))]

    @test_int [(-1 + sqrt(3) - x)/sqrt(1 + x^3), x, 1, -((2*sqrt(1 + x^3))/(1 + sqrt(3) + x)) + (3^(1/4)*sqrt(2 - sqrt(3))*(1 + x)*sqrt((1 - x + x^2)/(1 + sqrt(3) + x)^2)*Elliptic.E(asin((1 - sqrt(3) + x)/(1 + sqrt(3) + x)), -7 - 4*sqrt(3)))/(sqrt((1 + x)/(1 + sqrt(3) + x)^2)*sqrt(1 + x^3))]
    @test_int [(-1 + sqrt(3) + x)/sqrt(1 - x^3), x, 1, (2*sqrt(1 - x^3))/(1 + sqrt(3) - x) - (3^(1/4)*sqrt(2 - sqrt(3))*(1 - x)*sqrt((1 + x + x^2)/(1 + sqrt(3) - x)^2)*Elliptic.E(asin((1 - sqrt(3) - x)/(1 + sqrt(3) - x)), -7 - 4*sqrt(3)))/(sqrt((1 - x)/(1 + sqrt(3) - x)^2)*sqrt(1 - x^3))]
    @test_int [(-1 + sqrt(3) + x)/sqrt(-1 + x^3), x, 3, -((2*sqrt(-1 + x^3))/(1 - sqrt(3) - x)) + (3^(1/4)*sqrt(2 + sqrt(3))*(1 - x)*sqrt((1 + x + x^2)/(1 - sqrt(3) - x)^2)*Elliptic.E(asin((1 + sqrt(3) - x)/(1 - sqrt(3) - x)), -7 + 4*sqrt(3)))/(sqrt(-((1 - x)/(1 - sqrt(3) - x)^2))*sqrt(-1 + x^3)) - (4*3^(1/4)*sqrt(2 - sqrt(3))*(1 - x)*sqrt((1 + x + x^2)/(1 - sqrt(3) - x)^2)*Elliptic.F(asin((1 + sqrt(3) - x)/(1 - sqrt(3) - x)), -7 + 4*sqrt(3)))/(sqrt(-((1 - x)/(1 - sqrt(3) - x)^2))*sqrt(-1 + x^3))]
    @test_int [(-1 + sqrt(3) - x)/sqrt(-1 - x^3), x, 3, (2*sqrt(-1 - x^3))/(1 - sqrt(3) + x) - (3^(1/4)*sqrt(2 + sqrt(3))*(1 + x)*sqrt((1 - x + x^2)/(1 - sqrt(3) + x)^2)*Elliptic.E(asin((1 + sqrt(3) + x)/(1 - sqrt(3) + x)), -7 + 4*sqrt(3)))/(sqrt(-((1 + x)/(1 - sqrt(3) + x)^2))*sqrt(-1 - x^3)) + (4*3^(1/4)*sqrt(2 - sqrt(3))*(1 + x)*sqrt((1 - x + x^2)/(1 - sqrt(3) + x)^2)*Elliptic.F(asin((1 + sqrt(3) + x)/(1 - sqrt(3) + x)), -7 + 4*sqrt(3)))/(sqrt(-((1 + x)/(1 - sqrt(3) + x)^2))*sqrt(-1 - x^3))]

    @test_int [((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/sqrt(a + b*x^3), x, 1, (2*sqrt(a + b*x^3))/(b^(1/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(b^(1/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)/sqrt(a - b*x^3), x, 1, -((2*sqrt(a - b*x^3))/(b^(1/3)*((1 + sqrt(3))*a^(1/3) - b^(1/3)*x))) + (3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*(a^(1/3) - b^(1/3)*x)*sqrt((a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)), -7 - 4*sqrt(3)))/(b^(1/3)*sqrt((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*sqrt(a - b*x^3))]
    @test_int [((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)/sqrt(-a + b*x^3), x, 3, (2*sqrt(-a + b*x^3))/(b^(1/3)*((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)) - (3^(1/4)*sqrt(2 + sqrt(3))*a^(1/3)*(a^(1/3) - b^(1/3)*x)*sqrt((a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*Elliptic.E(asin(((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)), -7 + 4*sqrt(3)))/(b^(1/3)*sqrt(-((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)^2))*sqrt(-a + b*x^3)) + (4*3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*(a^(1/3) - b^(1/3)*x)*sqrt((a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*Elliptic.F(asin(((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)), -7 + 4*sqrt(3)))/(b^(1/3)*sqrt(-((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)^2))*sqrt(-a + b*x^3))]
    @test_int [((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/sqrt(-a - b*x^3), x, 3, -((2*sqrt(-a - b*x^3))/(b^(1/3)*((1 - sqrt(3))*a^(1/3) + b^(1/3)*x))) + (3^(1/4)*sqrt(2 + sqrt(3))*a^(1/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 + 4*sqrt(3)))/(b^(1/3)*sqrt(-((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)^2))*sqrt(-a - b*x^3)) - (4*3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 + 4*sqrt(3)))/(b^(1/3)*sqrt(-((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)^2))*sqrt(-a - b*x^3))]

    @test_int [(1 - sqrt(3) + (b/a)^(1/3)*x)/sqrt(a + b*x^3), x, 1, (2*(b/a)^(2/3)*sqrt(a + b*x^3))/(b*(1 + sqrt(3) + (b/a)^(1/3)*x)) - (3^(1/4)*sqrt(2 - sqrt(3))*(1 + (b/a)^(1/3)*x)*sqrt((1 - (b/a)^(1/3)*x + (b/a)^(2/3)*x^2)/(1 + sqrt(3) + (b/a)^(1/3)*x)^2)*Elliptic.E(asin((1 - sqrt(3) + (b/a)^(1/3)*x)/(1 + sqrt(3) + (b/a)^(1/3)*x)), -7 - 4*sqrt(3)))/((b/a)^(1/3)*sqrt((1 + (b/a)^(1/3)*x)/(1 + sqrt(3) + (b/a)^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(1 - sqrt(3) - (b/a)^(1/3)*x)/sqrt(a - b*x^3), x, 1, -((2*(b/a)^(2/3)*sqrt(a - b*x^3))/(b*(1 + sqrt(3) - (b/a)^(1/3)*x))) + (3^(1/4)*sqrt(2 - sqrt(3))*(1 - (b/a)^(1/3)*x)*sqrt((1 + (b/a)^(1/3)*x + (b/a)^(2/3)*x^2)/(1 + sqrt(3) - (b/a)^(1/3)*x)^2)*Elliptic.E(asin((1 - sqrt(3) - (b/a)^(1/3)*x)/(1 + sqrt(3) - (b/a)^(1/3)*x)), -7 - 4*sqrt(3)))/((b/a)^(1/3)*sqrt((1 - (b/a)^(1/3)*x)/(1 + sqrt(3) - (b/a)^(1/3)*x)^2)*sqrt(a - b*x^3))]
    @test_int [(1 - sqrt(3) - (b/a)^(1/3)*x)/sqrt(-a + b*x^3), x, 3, (2*(b/a)^(1/3)*sqrt(-a + b*x^3))/(b^(2/3)*((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)) - (3^(1/4)*sqrt(2 + sqrt(3))*a^(1/3)*(b/a)^(1/3)*(a^(1/3) - b^(1/3)*x)*sqrt((a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*Elliptic.E(asin(((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)), -7 + 4*sqrt(3)))/(b^(2/3)*sqrt(-((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)^2))*sqrt(-a + b*x^3)) - (2*sqrt(2 - sqrt(3))*((1 - sqrt(3))*b^(1/3) - (1 + sqrt(3))*a^(1/3)*(b/a)^(1/3))*(a^(1/3) - b^(1/3)*x)*sqrt((a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*Elliptic.F(asin(((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)), -7 + 4*sqrt(3)))/(3^(1/4)*b^(2/3)*sqrt(-((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)^2))*sqrt(-a + b*x^3))]
    @test_int [(1 - sqrt(3) + (b/a)^(1/3)*x)/sqrt(-a - b*x^3), x, 3, -((2*(b/a)^(1/3)*sqrt(-a - b*x^3))/(b^(2/3)*((1 - sqrt(3))*a^(1/3) + b^(1/3)*x))) + (3^(1/4)*sqrt(2 + sqrt(3))*a^(1/3)*(b/a)^(1/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 + 4*sqrt(3)))/(b^(2/3)*sqrt(-((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)^2))*sqrt(-a - b*x^3)) + (2*sqrt(2 - sqrt(3))*((1 - sqrt(3))*b^(1/3) - (1 + sqrt(3))*a^(1/3)*(b/a)^(1/3))*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 + 4*sqrt(3)))/(3^(1/4)*b^(2/3)*sqrt(-((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)^2))*sqrt(-a - b*x^3))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(c+d*x) / (a+b*x^3)^(p/2)=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [(c + d*x)/sqrt(a + b*x^3), x, 3, (2*d*sqrt(a + b*x^3))/(b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*d*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (2*sqrt(2 + sqrt(3))/3^(1/4)*(b^(1/3)*c - (1 - sqrt(3))*a^(1/3)*d)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x)/sqrt(a - b*x^3), x, 3, (2*d*sqrt(a - b*x^3))/(b^(2/3)*((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)) - (3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*d*(a^(1/3) - b^(1/3)*x)*sqrt((a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)), -7 - 4*sqrt(3)))/(b^(2/3)*sqrt((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*sqrt(a - b*x^3)) - (2*sqrt(2 + sqrt(3))*(b^(1/3)*c + (1 - sqrt(3))*a^(1/3)*d)*(a^(1/3) - b^(1/3)*x)*sqrt((a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)), -7 - 4*sqrt(3)))/(3^(1/4)*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*sqrt(a - b*x^3))]
    @test_int [(c + d*x)/sqrt(-a + b*x^3), x, 3, -((2*d*sqrt(-a + b*x^3))/(b^(2/3)*((1 - sqrt(3))*a^(1/3) - b^(1/3)*x))) + (3^(1/4)*sqrt(2 + sqrt(3))*a^(1/3)*d*(a^(1/3) - b^(1/3)*x)*sqrt((a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*Elliptic.E(asin(((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)), -7 + 4*sqrt(3)))/(b^(2/3)*sqrt(-((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)^2))*sqrt(-a + b*x^3)) - (2*sqrt(2 - sqrt(3))*(b^(1/3)*c + (1 + sqrt(3))*a^(1/3)*d)*(a^(1/3) - b^(1/3)*x)*sqrt((a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*Elliptic.F(asin(((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)), -7 + 4*sqrt(3)))/(3^(1/4)*b^(2/3)*sqrt(-((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)^2))*sqrt(-a + b*x^3))]
    @test_int [(c + d*x)/sqrt(-a - b*x^3), x, 3, -((2*d*sqrt(-a - b*x^3))/(b^(2/3)*((1 - sqrt(3))*a^(1/3) + b^(1/3)*x))) + (3^(1/4)*sqrt(2 + sqrt(3))*a^(1/3)*d*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 + 4*sqrt(3)))/(b^(2/3)*sqrt(-((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)^2))*sqrt(-a - b*x^3)) + (2*sqrt(2 - sqrt(3))*(b^(1/3)*c - (1 + sqrt(3))*a^(1/3)*d)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 + 4*sqrt(3)))/(3^(1/4)*b^(2/3)*sqrt(-((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)^2))*sqrt(-a - b*x^3))]

    @test_int [(c + d*x)/sqrt(1 + x^3), x, 3, (2*d*sqrt(1 + x^3))/(1 + sqrt(3) + x) - (3^(1/4)*sqrt(2 - sqrt(3))*d*(1 + x)*sqrt((1 - x + x^2)/(1 + sqrt(3) + x)^2)*Elliptic.E(asin((1 - sqrt(3) + x)/(1 + sqrt(3) + x)), -7 - 4*sqrt(3)))/(sqrt((1 + x)/(1 + sqrt(3) + x)^2)*sqrt(1 + x^3)) + (2*sqrt(2 + sqrt(3))/3^(1/4)*(c - (1 - sqrt(3))*d)*(1 + x)*sqrt((1 - x + x^2)/(1 + sqrt(3) + x)^2)*Elliptic.F(asin((1 - sqrt(3) + x)/(1 + sqrt(3) + x)), -7 - 4*sqrt(3)))/(sqrt((1 + x)/(1 + sqrt(3) + x)^2)*sqrt(1 + x^3))]
    @test_int [(c + d*x)/sqrt(1 - x^3), x, 3, (2*d*sqrt(1 - x^3))/(1 + sqrt(3) - x) - (3^(1/4)*sqrt(2 - sqrt(3))*d*(1 - x)*sqrt((1 + x + x^2)/(1 + sqrt(3) - x)^2)*Elliptic.E(asin((1 - sqrt(3) - x)/(1 + sqrt(3) - x)), -7 - 4*sqrt(3)))/(sqrt((1 - x)/(1 + sqrt(3) - x)^2)*sqrt(1 - x^3)) - (2*sqrt(2 + sqrt(3))/3^(1/4)*(c + d - sqrt(3)*d)*(1 - x)*sqrt((1 + x + x^2)/(1 + sqrt(3) - x)^2)*Elliptic.F(asin((1 - sqrt(3) - x)/(1 + sqrt(3) - x)), -7 - 4*sqrt(3)))/(sqrt((1 - x)/(1 + sqrt(3) - x)^2)*sqrt(1 - x^3))]
    @test_int [(c + d*x)/sqrt(-1 + x^3), x, 3, -((2*d*sqrt(-1 + x^3))/(1 - sqrt(3) - x)) + (3^(1/4)*sqrt(2 + sqrt(3))*d*(1 - x)*sqrt((1 + x + x^2)/(1 - sqrt(3) - x)^2)*Elliptic.E(asin((1 + sqrt(3) - x)/(1 - sqrt(3) - x)), -7 + 4*sqrt(3)))/(sqrt(-((1 - x)/(1 - sqrt(3) - x)^2))*sqrt(-1 + x^3)) - (2*sqrt(2 - sqrt(3))/3^(1/4)*(c + d + sqrt(3)*d)*(1 - x)*sqrt((1 + x + x^2)/(1 - sqrt(3) - x)^2)*Elliptic.F(asin((1 + sqrt(3) - x)/(1 - sqrt(3) - x)), -7 + 4*sqrt(3)))/(sqrt(-((1 - x)/(1 - sqrt(3) - x)^2))*sqrt(-1 + x^3))]
    @test_int [(c + d*x)/sqrt(-1 - x^3), x, 3, (-((2*d*sqrt(-1 - x^3))/(1 - sqrt(3) + x)) + (3^(1/4)*sqrt(2 + sqrt(3))*d*(1 + x)*sqrt((1 - x + x^2)/(1 - sqrt(3) + x)^2)*Elliptic.E(asin((1 + sqrt(3) + x)/(1 - sqrt(3) + x)), -7 + 4*sqrt(3)))/(sqrt(-((1 + x)/(1 - sqrt(3) + x)^2))*sqrt(-1 - x^3)) + (2*sqrt(2 - sqrt(3))/3^(1/4)*(c - (1 + sqrt(3))*d)*(1 + x)*sqrt((1 - x + x^2)/(1 - sqrt(3) + x)^2)*Elliptic.F(asin((1 + sqrt(3) + x)/(1 - sqrt(3) + x)), -7 + 4*sqrt(3)))/(sqrt(-((1 + x)/(1 - sqrt(3) + x)^2))*sqrt(-1 - x^3)))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*Pq(x)*(a+b*x^4)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*P1(x)*(a+b*x^4)^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [(c + d*x)/(a - b*x^4), x, 7, (c*atan((b^(1/4)*x)/a^(1/4)))/(2*a^(3/4)*b^(1/4)) + (c*atanh((b^(1/4)*x)/a^(1/4)))/(2*a^(3/4)*b^(1/4)) + (d*atanh((sqrt(b)*x^2)/sqrt(a)))/(2*sqrt(a)*sqrt(b))]

    @test_int [(c + d*x)/(a + b*x^4), x, 13, (d*atan((sqrt(b)*x^2)/sqrt(a)))/(2*sqrt(a)*sqrt(b)) - (c*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*a^(3/4)*b^(1/4)) + (c*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*a^(3/4)*b^(1/4)) - (c*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*a^(3/4)*b^(1/4)) + (c*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*a^(3/4)*b^(1/4))]

    @test_int [(c + d*x)/(a - b*x^4)^2, x, 8, (x*(c + d*x))/(4*a*(a - b*x^4)) + (3*c*atan((b^(1/4)*x)/a^(1/4)))/(8*a^(7/4)*b^(1/4)) + (3*c*atanh((b^(1/4)*x)/a^(1/4)))/(8*a^(7/4)*b^(1/4)) + (d*atanh((sqrt(b)*x^2)/sqrt(a)))/(4*a^(3/2)*sqrt(b))]

    @test_int [(c + d*x)/(a + b*x^4)^2, x, 14, (x*(c + d*x))/(4*a*(a + b*x^4)) + (d*atan((sqrt(b)*x^2)/sqrt(a)))/(4*a^(3/2)*sqrt(b)) - (3*c*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(8*sqrt(2)*a^(7/4)*b^(1/4)) + (3*c*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(8*sqrt(2)*a^(7/4)*b^(1/4)) - (3*c*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(16*sqrt(2)*a^(7/4)*b^(1/4)) + (3*c*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(16*sqrt(2)*a^(7/4)*b^(1/4))]

    @test_int [(c + d*x)/(a - b*x^4)^3, x, 9, (x*(c + d*x))/(8*a*(a - b*x^4)^2) + (x*(7*c + 6*d*x))/(32*a^2*(a - b*x^4)) + (21*c*atan((b^(1/4)*x)/a^(1/4)))/(64*a^(11/4)*b^(1/4)) + (21*c*atanh((b^(1/4)*x)/a^(1/4)))/(64*a^(11/4)*b^(1/4)) + (3*d*atanh((sqrt(b)*x^2)/sqrt(a)))/(16*a^(5/2)*sqrt(b))]

    @test_int [(c + d*x)/(a + b*x^4)^3, x, 15, (x*(c + d*x))/(8*a*(a + b*x^4)^2) + (x*(7*c + 6*d*x))/(32*a^2*(a + b*x^4)) + (3*d*atan((sqrt(b)*x^2)/sqrt(a)))/(16*a^(5/2)*sqrt(b)) - (21*c*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(64*sqrt(2)*a^(11/4)*b^(1/4)) + (21*c*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(64*sqrt(2)*a^(11/4)*b^(1/4)) - (21*c*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(128*sqrt(2)*a^(11/4)*b^(1/4)) + (21*c*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(128*sqrt(2)*a^(11/4)*b^(1/4))]

    @test_int [(c + d*x)/(a - b*x^4)^4, x, 10, (x*(c + d*x))/(12*a*(a - b*x^4)^3) + (x*(11*c + 10*d*x))/(96*a^2*(a - b*x^4)^2) + (x*(77*c + 60*d*x))/(384*a^3*(a - b*x^4)) + (77*c*atan((b^(1/4)*x)/a^(1/4)))/(256*a^(15/4)*b^(1/4)) + (77*c*atanh((b^(1/4)*x)/a^(1/4)))/(256*a^(15/4)*b^(1/4)) + (5*d*atanh((sqrt(b)*x^2)/sqrt(a)))/(32*a^(7/2)*sqrt(b))]

    @test_int [(c + d*x)/(a + b*x^4)^4, x, 16, (x*(c + d*x))/(12*a*(a + b*x^4)^3) + (x*(11*c + 10*d*x))/(96*a^2*(a + b*x^4)^2) + (x*(77*c + 60*d*x))/(384*a^3*(a + b*x^4)) + (5*d*atan((sqrt(b)*x^2)/sqrt(a)))/(32*a^(7/2)*sqrt(b)) - (77*c*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(256*sqrt(2)*a^(15/4)*b^(1/4)) + (77*c*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(256*sqrt(2)*a^(15/4)*b^(1/4)) - (77*c*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(512*sqrt(2)*a^(15/4)*b^(1/4)) + (77*c*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(512*sqrt(2)*a^(15/4)*b^(1/4))]

    @test_int [(c + d*x)/(1 - x^4), x, 7, (1/2)*c*atan(x) + (1/2)*c*atanh(x) + (1/2)*d*atanh(x^2)]

    @test_int [(c + d*x)/(1 + x^4), x, 13, (1/2)*d*atan(x^2) - (c*atan(1 - sqrt(2)*x))/(2*sqrt(2)) + (c*atan(1 + sqrt(2)*x))/(2*sqrt(2)) - (c*log(1 - sqrt(2)*x + x^2))/(4*sqrt(2)) + (c*log(1 + sqrt(2)*x + x^2))/(4*sqrt(2))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*P2(x)*(a+b*x^4)^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [(c + d*x + e*x^2)/(a - b*x^4), x, 7, ((sqrt(b)*c - sqrt(a)*e)*atan((b^(1/4)*x)/a^(1/4)))/(2*a^(3/4)*b^(3/4)) + ((sqrt(b)*c + sqrt(a)*e)*atanh((b^(1/4)*x)/a^(1/4)))/(2*a^(3/4)*b^(3/4)) + (d*atanh((sqrt(b)*x^2)/sqrt(a)))/(2*sqrt(a)*sqrt(b))]

    @test_int [(c + d*x + e*x^2)/(a + b*x^4), x, 13, (d*atan((sqrt(b)*x^2)/sqrt(a)))/(2*sqrt(a)*sqrt(b)) - ((sqrt(b)*c + sqrt(a)*e)*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*a^(3/4)*b^(3/4)) + ((sqrt(b)*c + sqrt(a)*e)*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*a^(3/4)*b^(3/4)) - ((sqrt(b)*c - sqrt(a)*e)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*a^(3/4)*b^(3/4)) + ((sqrt(b)*c - sqrt(a)*e)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*a^(3/4)*b^(3/4))]

    @test_int [(c + d*x + e*x^2)/(a - b*x^4)^2, x, 8, (x*(c + d*x + e*x^2))/(4*a*(a - b*x^4)) + ((3*sqrt(b)*c - sqrt(a)*e)*atan((b^(1/4)*x)/a^(1/4)))/(8*a^(7/4)*b^(3/4)) + ((3*sqrt(b)*c + sqrt(a)*e)*atanh((b^(1/4)*x)/a^(1/4)))/(8*a^(7/4)*b^(3/4)) + (d*atanh((sqrt(b)*x^2)/sqrt(a)))/(4*a^(3/2)*sqrt(b))]

    @test_int [(c + d*x + e*x^2)/(a + b*x^4)^2, x, 14, (x*(c + d*x + e*x^2))/(4*a*(a + b*x^4)) + (d*atan((sqrt(b)*x^2)/sqrt(a)))/(4*a^(3/2)*sqrt(b)) - ((3*sqrt(b)*c + sqrt(a)*e)*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(8*sqrt(2)*a^(7/4)*b^(3/4)) + ((3*sqrt(b)*c + sqrt(a)*e)*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(8*sqrt(2)*a^(7/4)*b^(3/4)) - ((3*sqrt(b)*c - sqrt(a)*e)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(16*sqrt(2)*a^(7/4)*b^(3/4)) + ((3*sqrt(b)*c - sqrt(a)*e)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(16*sqrt(2)*a^(7/4)*b^(3/4))]

    @test_int [(c + d*x + e*x^2)/(a - b*x^4)^3, x, 9, (x*(c + d*x + e*x^2))/(8*a*(a - b*x^4)^2) + (x*(7*c + 6*d*x + 5*e*x^2))/(32*a^2*(a - b*x^4)) + ((21*sqrt(b)*c - 5*sqrt(a)*e)*atan((b^(1/4)*x)/a^(1/4)))/(64*a^(11/4)*b^(3/4)) + ((21*sqrt(b)*c + 5*sqrt(a)*e)*atanh((b^(1/4)*x)/a^(1/4)))/(64*a^(11/4)*b^(3/4)) + (3*d*atanh((sqrt(b)*x^2)/sqrt(a)))/(16*a^(5/2)*sqrt(b))]

    @test_int [(c + d*x + e*x^2)/(a + b*x^4)^3, x, 15, (x*(c + d*x + e*x^2))/(8*a*(a + b*x^4)^2) + (x*(7*c + 6*d*x + 5*e*x^2))/(32*a^2*(a + b*x^4)) + (3*d*atan((sqrt(b)*x^2)/sqrt(a)))/(16*a^(5/2)*sqrt(b)) - ((21*sqrt(b)*c + 5*sqrt(a)*e)*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(64*sqrt(2)*a^(11/4)*b^(3/4)) + ((21*sqrt(b)*c + 5*sqrt(a)*e)*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(64*sqrt(2)*a^(11/4)*b^(3/4)) - ((21*sqrt(b)*c - 5*sqrt(a)*e)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(128*sqrt(2)*a^(11/4)*b^(3/4)) + ((21*sqrt(b)*c - 5*sqrt(a)*e)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(128*sqrt(2)*a^(11/4)*b^(3/4))]

    @test_int [(c + d*x + e*x^2)/(a - b*x^4)^4, x, 10, (x*(c + d*x + e*x^2))/(12*a*(a - b*x^4)^3) + (x*(11*c + 10*d*x + 9*e*x^2))/(96*a^2*(a - b*x^4)^2) + (x*(77*c + 60*d*x + 45*e*x^2))/(384*a^3*(a - b*x^4)) + ((77*sqrt(b)*c - 15*sqrt(a)*e)*atan((b^(1/4)*x)/a^(1/4)))/(256*a^(15/4)*b^(3/4)) + ((77*sqrt(b)*c + 15*sqrt(a)*e)*atanh((b^(1/4)*x)/a^(1/4)))/(256*a^(15/4)*b^(3/4)) + (5*d*atanh((sqrt(b)*x^2)/sqrt(a)))/(32*a^(7/2)*sqrt(b))]

    @test_int [(c + d*x + e*x^2)/(a + b*x^4)^4, x, 16, (x*(c + d*x + e*x^2))/(12*a*(a + b*x^4)^3) + (x*(11*c + 10*d*x + 9*e*x^2))/(96*a^2*(a + b*x^4)^2) + (x*(77*c + 60*d*x + 45*e*x^2))/(384*a^3*(a + b*x^4)) + (5*d*atan((sqrt(b)*x^2)/sqrt(a)))/(32*a^(7/2)*sqrt(b)) - ((77*sqrt(b)*c + 15*sqrt(a)*e)*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(256*sqrt(2)*a^(15/4)*b^(3/4)) + ((77*sqrt(b)*c + 15*sqrt(a)*e)*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(256*sqrt(2)*a^(15/4)*b^(3/4)) - ((77*sqrt(b)*c - 15*sqrt(a)*e)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(512*sqrt(2)*a^(15/4)*b^(3/4)) + ((77*sqrt(b)*c - 15*sqrt(a)*e)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(512*sqrt(2)*a^(15/4)*b^(3/4))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*P3(x)*(a+b*x^4)^p=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [(a + 0*x + 0*x^2 + 0*x^3)*(e + f*x^4)^2, x, 3, a*e^2*x + (2/5)*a*e*f*x^5 + (1/9)*a*f^2*x^9]
    @test_int [(0 + b*x + 0*x^2 + 0*x^3)*(e + f*x^4)^2, x, 3, (1/2)*b*e^2*x^2 + (1/3)*b*e*f*x^6 + (1/10)*b*f^2*x^10]
    @test_int [(a + b*x + 0*x^2 + 0*x^3)*(e + f*x^4)^2, x, 2, a*e^2*x + (1/2)*b*e^2*x^2 + (2/5)*a*e*f*x^5 + (1/3)*b*e*f*x^6 + (1/9)*a*f^2*x^9 + (1/10)*b*f^2*x^10]
    @test_int [(0 + 0*x + c*x^2 + 0*x^3)*(e + f*x^4)^2, x, 3, (1/3)*c*e^2*x^3 + (2/7)*c*e*f*x^7 + (1/11)*c*f^2*x^11]
    @test_int [(a + 0*x + c*x^2 + 0*x^3)*(e + f*x^4)^2, x, 2, a*e^2*x + (1/3)*c*e^2*x^3 + (2/5)*a*e*f*x^5 + (2/7)*c*e*f*x^7 + (1/9)*a*f^2*x^9 + (1/11)*c*f^2*x^11]
    @test_int [(0 + b*x + c*x^2 + 0*x^3)*(e + f*x^4)^2, x, 3, (1/2)*b*e^2*x^2 + (1/3)*c*e^2*x^3 + (1/3)*b*e*f*x^6 + (2/7)*c*e*f*x^7 + (1/10)*b*f^2*x^10 + (1/11)*c*f^2*x^11]
    @test_int [(a + b*x + c*x^2 + 0*x^3)*(e + f*x^4)^2, x, 2, a*e^2*x + (1/2)*b*e^2*x^2 + (1/3)*c*e^2*x^3 + (2/5)*a*e*f*x^5 + (1/3)*b*e*f*x^6 + (2/7)*c*e*f*x^7 + (1/9)*a*f^2*x^9 + (1/10)*b*f^2*x^10 + (1/11)*c*f^2*x^11]

    @test_int [(0 + 0*x + 0*x^2 + d*x^3)*(e + f*x^4)^2, x, 2, (d*(e + f*x^4)^3)/(12*f)]
    @test_int [(a + 0*x + 0*x^2 + d*x^3)*(e + f*x^4)^2, x, 4, a*e^2*x + (2/5)*a*e*f*x^5 + (1/9)*a*f^2*x^9 + (d*(e + f*x^4)^3)/(12*f)]
    @test_int [(0 + b*x + 0*x^2 + d*x^3)*(e + f*x^4)^2, x, 4, (1/2)*b*e^2*x^2 + (1/3)*b*e*f*x^6 + (1/10)*b*f^2*x^10 + (d*(e + f*x^4)^3)/(12*f)]
    @test_int [(a + b*x + 0*x^2 + d*x^3)*(e + f*x^4)^2, x, 3, a*e^2*x + (1/2)*b*e^2*x^2 + (2/5)*a*e*f*x^5 + (1/3)*b*e*f*x^6 + (1/9)*a*f^2*x^9 + (1/10)*b*f^2*x^10 + (d*(e + f*x^4)^3)/(12*f)]
    @test_int [(0 + 0*x + c*x^2 + d*x^3)*(e + f*x^4)^2, x, 4, (1/3)*c*e^2*x^3 + (2/7)*c*e*f*x^7 + (1/11)*c*f^2*x^11 + (d*(e + f*x^4)^3)/(12*f)]
    @test_int [(a + 0*x + c*x^2 + d*x^3)*(e + f*x^4)^2, x, 3, a*e^2*x + (1/3)*c*e^2*x^3 + (2/5)*a*e*f*x^5 + (2/7)*c*e*f*x^7 + (1/9)*a*f^2*x^9 + (1/11)*c*f^2*x^11 + (d*(e + f*x^4)^3)/(12*f)]
    @test_int [(0 + b*x + c*x^2 + d*x^3)*(e + f*x^4)^2, x, 4, (1/2)*b*e^2*x^2 + (1/3)*c*e^2*x^3 + (1/3)*b*e*f*x^6 + (2/7)*c*e*f*x^7 + (1/10)*b*f^2*x^10 + (1/11)*c*f^2*x^11 + (d*(e + f*x^4)^3)/(12*f)]
    @test_int [(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^2, x, 3, a^2*c*x + (1/2)*a^2*d*x^2 + (1/3)*a^2*e*x^3 + (2/5)*a*b*c*x^5 + (1/3)*a*b*d*x^6 + (2/7)*a*b*e*x^7 + (1/9)*b^2*c*x^9 + (1/10)*b^2*d*x^10 + (1/11)*b^2*e*x^11 + (f*(a + b*x^4)^3)/(12*b)]

    @test_int [(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^3, x, 3, a^3*c*x + (1/2)*a^3*d*x^2 + (1/3)*a^3*e*x^3 + (3/5)*a^2*b*c*x^5 + (1/2)*a^2*b*d*x^6 + (3/7)*a^2*b*e*x^7 + (1/3)*a*b^2*c*x^9 + (3/10)*a*b^2*d*x^10 + (3/11)*a*b^2*e*x^11 + (1/13)*b^3*c*x^13 + (1/14)*b^3*d*x^14 + (1/15)*b^3*e*x^15 + (f*(a + b*x^4)^4)/(16*b)]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [(c + d*x + e*x^2 + f*x^3)/(a - b*x^4)^2, x, 8, (a*f + b*x*(c + d*x + e*x^2))/(4*a*b*(a - b*x^4)) + ((3*sqrt(b)*c - sqrt(a)*e)*atan((b^(1/4)*x)/a^(1/4)))/(8*a^(7/4)*b^(3/4)) + ((3*sqrt(b)*c + sqrt(a)*e)*atanh((b^(1/4)*x)/a^(1/4)))/(8*a^(7/4)*b^(3/4)) + (d*atanh((sqrt(b)*x^2)/sqrt(a)))/(4*a^(3/2)*sqrt(b))]

    @test_int [(c + d*x + e*x^2 + f*x^3)/(a - b*x^4)^3, x, 9, (x*(7*c + 6*d*x + 5*e*x^2))/(32*a^2*(a - b*x^4)) + (a*f + b*x*(c + d*x + e*x^2))/(8*a*b*(a - b*x^4)^2) + ((21*sqrt(b)*c - 5*sqrt(a)*e)*atan((b^(1/4)*x)/a^(1/4)))/(64*a^(11/4)*b^(3/4)) + ((21*sqrt(b)*c + 5*sqrt(a)*e)*atanh((b^(1/4)*x)/a^(1/4)))/(64*a^(11/4)*b^(3/4)) + (3*d*atanh((sqrt(b)*x^2)/sqrt(a)))/(16*a^(5/2)*sqrt(b))]

    @test_int [(c + d*x + e*x^2 + f*x^3)/(a - b*x^4)^4, x, 10, (x*(11*c + 10*d*x + 9*e*x^2))/(96*a^2*(a - b*x^4)^2) + (x*(77*c + 60*d*x + 45*e*x^2))/(384*a^3*(a - b*x^4)) + (a*f + b*x*(c + d*x + e*x^2))/(12*a*b*(a - b*x^4)^3) + ((77*sqrt(b)*c - 15*sqrt(a)*e)*atan((b^(1/4)*x)/a^(1/4)))/(256*a^(15/4)*b^(3/4)) + ((77*sqrt(b)*c + 15*sqrt(a)*e)*atanh((b^(1/4)*x)/a^(1/4)))/(256*a^(15/4)*b^(3/4)) + (5*d*atanh((sqrt(b)*x^2)/sqrt(a)))/(32*a^(7/2)*sqrt(b))]

    @test_int [(a + 0*x + 0*x^2 + 0*x^3)/(2 + 3*x^4), x, 10, -((a*atan(1 - 6^(1/4)*x))/(4*6^(1/4))) + (a*atan(1 + 6^(1/4)*x))/(4*6^(1/4)) - (a*log(sqrt(6) - 6^(3/4)*x + 3*x^2))/(8*6^(1/4)) + (a*log(sqrt(6) + 6^(3/4)*x + 3*x^2))/(8*6^(1/4))]
    @test_int [(0 + b*x + 0*x^2 + 0*x^3)/(2 + 3*x^4), x, 3, (b*atan(sqrt(3/2)*x^2))/(2*sqrt(6))]
    @test_int [(a + b*x + 0*x^2 + 0*x^3)/(2 + 3*x^4), x, 13, (b*atan(sqrt(3/2)*x^2))/(2*sqrt(6)) - (a*atan(1 - 6^(1/4)*x))/(4*6^(1/4)) + (a*atan(1 + 6^(1/4)*x))/(4*6^(1/4)) - (a*log(sqrt(6) - 6^(3/4)*x + 3*x^2))/(8*6^(1/4)) + (a*log(sqrt(6) + 6^(3/4)*x + 3*x^2))/(8*6^(1/4))]
    @test_int [(0 + 0*x + c*x^2 + 0*x^3)/(2 + 3*x^4), x, 10, -((c*atan(1 - 6^(1/4)*x))/(2*6^(3/4))) + (c*atan(1 + 6^(1/4)*x))/(2*6^(3/4)) + (c*log(sqrt(6) - 6^(3/4)*x + 3*x^2))/(4*6^(3/4)) - (c*log(sqrt(6) + 6^(3/4)*x + 3*x^2))/(4*6^(3/4))]
    @test_int [(a + 0*x + c*x^2 + 0*x^3)/(2 + 3*x^4), x, 9, -(((sqrt(6)*a + 2*c)*atan(1 - 6^(1/4)*x))/(4*6^(3/4))) + ((sqrt(6)*a + 2*c)*atan(1 + 6^(1/4)*x))/(4*6^(3/4)) - ((sqrt(6)*a - 2*c)*log(sqrt(6) - 6^(3/4)*x + 3*x^2))/(8*6^(3/4)) + ((sqrt(6)*a - 2*c)*log(sqrt(6) + 6^(3/4)*x + 3*x^2))/(8*6^(3/4))]
    @test_int [(0 + b*x + c*x^2 + 0*x^3)/(2 + 3*x^4), x, 14, (b*atan(sqrt(3/2)*x^2))/(2*sqrt(6)) - (c*atan(1 - 6^(1/4)*x))/(2*6^(3/4)) + (c*atan(1 + 6^(1/4)*x))/(2*6^(3/4)) + (c*log(sqrt(6) - 6^(3/4)*x + 3*x^2))/(4*6^(3/4)) - (c*log(sqrt(6) + 6^(3/4)*x + 3*x^2))/(4*6^(3/4))]
    @test_int [(a + b*x + c*x^2 + 0*x^3)/(2 + 3*x^4), x, 13, (b*atan(sqrt(3/2)*x^2))/(2*sqrt(6)) - ((sqrt(6)*a + 2*c)*atan(1 - 6^(1/4)*x))/(4*6^(3/4)) + ((sqrt(6)*a + 2*c)*atan(1 + 6^(1/4)*x))/(4*6^(3/4)) - ((sqrt(6)*a - 2*c)*log(sqrt(6) - 6^(3/4)*x + 3*x^2))/(8*6^(3/4)) + ((sqrt(6)*a - 2*c)*log(sqrt(6) + 6^(3/4)*x + 3*x^2))/(8*6^(3/4))]

    @test_int [(0 + 0*x + 0*x^2 + d*x^3)/(2 + 3*x^4), x, 2, (1/12)*d*log(2 + 3*x^4)]
    @test_int [(a + 0*x + 0*x^2 + d*x^3)/(2 + 3*x^4), x, 12, -((a*atan(1 - 6^(1/4)*x))/(4*6^(1/4))) + (a*atan(1 + 6^(1/4)*x))/(4*6^(1/4)) - (a*log(sqrt(6) - 6^(3/4)*x + 3*x^2))/(8*6^(1/4)) + (a*log(sqrt(6) + 6^(3/4)*x + 3*x^2))/(8*6^(1/4)) + (1/12)*d*log(2 + 3*x^4)]
    @test_int [(0 + b*x + 0*x^2 + d*x^3)/(2 + 3*x^4), x, 5, (b*atan(sqrt(3/2)*x^2))/(2*sqrt(6)) + (1/12)*d*log(2 + 3*x^4)]
    @test_int [(a + b*x + 0*x^2 + d*x^3)/(2 + 3*x^4), x, 15, (b*atan(sqrt(3/2)*x^2))/(2*sqrt(6)) - (a*atan(1 - 6^(1/4)*x))/(4*6^(1/4)) + (a*atan(1 + 6^(1/4)*x))/(4*6^(1/4)) - (a*log(sqrt(6) - 6^(3/4)*x + 3*x^2))/(8*6^(1/4)) + (a*log(sqrt(6) + 6^(3/4)*x + 3*x^2))/(8*6^(1/4)) + (1/12)*d*log(2 + 3*x^4)]
    @test_int [(0 + 0*x + c*x^2 + d*x^3)/(2 + 3*x^4), x, 13, -((c*atan(1 - 6^(1/4)*x))/(2*6^(3/4))) + (c*atan(1 + 6^(1/4)*x))/(2*6^(3/4)) + (c*log(sqrt(6) - 6^(3/4)*x + 3*x^2))/(4*6^(3/4)) - (c*log(sqrt(6) + 6^(3/4)*x + 3*x^2))/(4*6^(3/4)) + (1/12)*d*log(2 + 3*x^4)]
    @test_int [(a + 0*x + c*x^2 + d*x^3)/(2 + 3*x^4), x, 12, -(((sqrt(6)*a + 2*c)*atan(1 - 6^(1/4)*x))/(4*6^(3/4))) + ((sqrt(6)*a + 2*c)*atan(1 + 6^(1/4)*x))/(4*6^(3/4)) - ((sqrt(6)*a - 2*c)*log(sqrt(6) - 6^(3/4)*x + 3*x^2))/(8*6^(3/4)) + ((sqrt(6)*a - 2*c)*log(sqrt(6) + 6^(3/4)*x + 3*x^2))/(8*6^(3/4)) + (1/12)*d*log(2 + 3*x^4)]
    @test_int [(0 + b*x + c*x^2 + d*x^3)/(2 + 3*x^4), x, 16, (b*atan(sqrt(3/2)*x^2))/(2*sqrt(6)) - (c*atan(1 - 6^(1/4)*x))/(2*6^(3/4)) + (c*atan(1 + 6^(1/4)*x))/(2*6^(3/4)) + (c*log(sqrt(6) - 6^(3/4)*x + 3*x^2))/(4*6^(3/4)) - (c*log(sqrt(6) + 6^(3/4)*x + 3*x^2))/(4*6^(3/4)) + (1/12)*d*log(2 + 3*x^4)]
    @test_int [(a + b*x + c*x^2 + d*x^3)/(2 + 3*x^4), x, 15, (b*atan(sqrt(3/2)*x^2))/(2*sqrt(6)) - ((sqrt(6)*a + 2*c)*atan(1 - 6^(1/4)*x))/(4*6^(3/4)) + ((sqrt(6)*a + 2*c)*atan(1 + 6^(1/4)*x))/(4*6^(3/4)) - ((sqrt(6)*a - 2*c)*log(sqrt(6) - 6^(3/4)*x + 3*x^2))/(8*6^(3/4)) + ((sqrt(6)*a - 2*c)*log(sqrt(6) + 6^(3/4)*x + 3*x^2))/(8*6^(3/4)) + (1/12)*d*log(2 + 3*x^4)]

    @test_int [(1 + x + x^2 + x^3)/(1 - x^4), x, 2, -log(1 - x)]

    @test_int [(1 + x + x^2 + x^3)/(1 + x^4), x, 11, atan(x^2)/2 - atan(1 - sqrt(2)*x)/sqrt(2) + atan(1 + sqrt(2)*x)/sqrt(2) + (1/4)*log(1 + x^4)]

    @test_int [(1 + x + x^2 + x^3)/(a - b*x^4), x, 9, -(((sqrt(a) - sqrt(b))*atan((b^(1/4)*x)/a^(1/4)))/(2*a^(3/4)*b^(3/4))) + ((sqrt(a) + sqrt(b))*atanh((b^(1/4)*x)/a^(1/4)))/(2*a^(3/4)*b^(3/4)) + atanh((sqrt(b)*x^2)/sqrt(a))/(2*sqrt(a)*sqrt(b)) - log(a - b*x^4)/(4*b)]

    @test_int [(1 + x + x^2 + x^3)/(a + b*x^4), x, 15, atan((sqrt(b)*x^2)/sqrt(a))/(2*sqrt(a)*sqrt(b)) - ((sqrt(a) + sqrt(b))*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*a^(3/4)*b^(3/4)) + ((sqrt(a) + sqrt(b))*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*a^(3/4)*b^(3/4)) + ((sqrt(a) - sqrt(b))*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*a^(3/4)*b^(3/4)) - ((sqrt(a) - sqrt(b))*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*a^(3/4)*b^(3/4)) + log(a + b*x^4)/(4*b)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*P4(x)*(a+b*x^4)^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)/(a - b*x^4)^1, x, 11, -((g*x)/b) + ((b*c - sqrt(a)*sqrt(b)*e + a*g)*atan((b^(1/4)*x)/a^(1/4)))/(2*a^(3/4)*b^(5/4)) + ((b*c + sqrt(a)*sqrt(b)*e + a*g)*atanh((b^(1/4)*x)/a^(1/4)))/(2*a^(3/4)*b^(5/4)) + (d*atanh((sqrt(b)*x^2)/sqrt(a)))/(2*sqrt(a)*sqrt(b)) - (f*log(a - b*x^4))/(4*b)]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)/(a - b*x^4)^2, x, 8, (x*(b*c + a*g + b*d*x + b*e*x^2 + b*f*x^3))/(4*a*b*(a - b*x^4)) + ((3*b*c - sqrt(a)*sqrt(b)*e - a*g)*atan((b^(1/4)*x)/a^(1/4)))/(8*a^(7/4)*b^(5/4)) + ((3*b*c + sqrt(a)*sqrt(b)*e - a*g)*atanh((b^(1/4)*x)/a^(1/4)))/(8*a^(7/4)*b^(5/4)) + (d*atanh((sqrt(b)*x^2)/sqrt(a)))/(4*a^(3/2)*sqrt(b))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)/(a - b*x^4)^3, x, 9, (x*(b*c + a*g + b*d*x + b*e*x^2 + b*f*x^3))/(8*a*b*(a - b*x^4)^2) + (4*a*f + x*(7*b*c - a*g + 6*b*d*x + 5*b*e*x^2))/(32*a^2*b*(a - b*x^4)) + ((21*b*c - 5*sqrt(a)*sqrt(b)*e - 3*a*g)*atan((b^(1/4)*x)/a^(1/4)))/(64*a^(11/4)*b^(5/4)) + ((21*b*c + 5*sqrt(a)*sqrt(b)*e - 3*a*g)*atanh((b^(1/4)*x)/a^(1/4)))/(64*a^(11/4)*b^(5/4)) + (3*d*atanh((sqrt(b)*x^2)/sqrt(a)))/(16*a^(5/2)*sqrt(b))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)/(a - b*x^4)^4, x, 10, (x*(b*c + a*g + b*d*x + b*e*x^2 + b*f*x^3))/(12*a*b*(a - b*x^4)^3) + (x*(7*(11*b*c - a*g) + 60*b*d*x + 45*b*e*x^2))/(384*a^3*b*(a - b*x^4)) + (8*a*f + x*(11*b*c - a*g + 10*b*d*x + 9*b*e*x^2))/(96*a^2*b*(a - b*x^4)^2) + ((77*b*c - 15*sqrt(a)*sqrt(b)*e - 7*a*g)*atan((b^(1/4)*x)/a^(1/4)))/(256*a^(15/4)*b^(5/4)) + ((77*b*c + 15*sqrt(a)*sqrt(b)*e - 7*a*g)*atanh((b^(1/4)*x)/a^(1/4)))/(256*a^(15/4)*b^(5/4)) + (5*d*atanh((sqrt(b)*x^2)/sqrt(a)))/(32*a^(7/2)*sqrt(b))]

    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)/(a + b*x^4)^1, x, 17, (g*x)/b + (d*atan((sqrt(b)*x^2)/sqrt(a)))/(2*sqrt(a)*sqrt(b)) - ((b*c + sqrt(a)*sqrt(b)*e - a*g)*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*a^(3/4)*b^(5/4)) + ((b*c + sqrt(a)*sqrt(b)*e - a*g)*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*a^(3/4)*b^(5/4)) - ((b*c - sqrt(a)*sqrt(b)*e - a*g)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*a^(3/4)*b^(5/4)) + ((b*c - sqrt(a)*sqrt(b)*e - a*g)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*a^(3/4)*b^(5/4)) + (f*log(a + b*x^4))/(4*b)]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)/(a + b*x^4)^2, x, 14, (x*(b*c - a*g + b*d*x + b*e*x^2 + b*f*x^3))/(4*a*b*(a + b*x^4)) + (d*atan((sqrt(b)*x^2)/sqrt(a)))/(4*a^(3/2)*sqrt(b)) - ((3*b*c + sqrt(a)*sqrt(b)*e + a*g)*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(8*sqrt(2)*a^(7/4)*b^(5/4)) + ((3*b*c + sqrt(a)*sqrt(b)*e + a*g)*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(8*sqrt(2)*a^(7/4)*b^(5/4)) - ((3*b*c - sqrt(a)*sqrt(b)*e + a*g)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(16*sqrt(2)*a^(7/4)*b^(5/4)) + ((3*b*c - sqrt(a)*sqrt(b)*e + a*g)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(16*sqrt(2)*a^(7/4)*b^(5/4))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)/(a + b*x^4)^3, x, 15, (x*(b*c - a*g + b*d*x + b*e*x^2 + b*f*x^3))/(8*a*b*(a + b*x^4)^2) - (4*a*f - x*(7*b*c + a*g + 6*b*d*x + 5*b*e*x^2))/(32*a^2*b*(a + b*x^4)) + (3*d*atan((sqrt(b)*x^2)/sqrt(a)))/(16*a^(5/2)*sqrt(b)) - ((21*b*c + 5*sqrt(a)*sqrt(b)*e + 3*a*g)*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(64*sqrt(2)*a^(11/4)*b^(5/4)) + ((21*b*c + 5*sqrt(a)*sqrt(b)*e + 3*a*g)*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(64*sqrt(2)*a^(11/4)*b^(5/4)) - ((21*b*c - 5*sqrt(a)*sqrt(b)*e + 3*a*g)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(128*sqrt(2)*a^(11/4)*b^(5/4)) + ((21*b*c - 5*sqrt(a)*sqrt(b)*e + 3*a*g)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(128*sqrt(2)*a^(11/4)*b^(5/4))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)/(a + b*x^4)^4, x, 16, (x*(b*c - a*g + b*d*x + b*e*x^2 + b*f*x^3))/(12*a*b*(a + b*x^4)^3) + (x*(7*(11*b*c + a*g) + 60*b*d*x + 45*b*e*x^2))/(384*a^3*b*(a + b*x^4)) - (8*a*f - x*(11*b*c + a*g + 10*b*d*x + 9*b*e*x^2))/(96*a^2*b*(a + b*x^4)^2) + (5*d*atan((sqrt(b)*x^2)/sqrt(a)))/(32*a^(7/2)*sqrt(b)) - ((77*b*c + 15*sqrt(a)*sqrt(b)*e + 7*a*g)*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(256*sqrt(2)*a^(15/4)*b^(5/4)) + ((77*b*c + 15*sqrt(a)*sqrt(b)*e + 7*a*g)*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(256*sqrt(2)*a^(15/4)*b^(5/4)) - ((77*b*c - 15*sqrt(a)*sqrt(b)*e + 7*a*g)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(512*sqrt(2)*a^(15/4)*b^(5/4)) + ((77*b*c - 15*sqrt(a)*sqrt(b)*e + 7*a*g)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(512*sqrt(2)*a^(15/4)*b^(5/4))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*Pq(x)*(a+b*x^4)^p*with*q>4=#
    #==#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [(1 - x^4)^3/(1 + x + x^2 + x^3)^3, x, 2, (-(1/4))*(1 - x)^4]
    @test_int [(1 - x^4)^2/(1 + x + x^2 + x^3)^2, x, 2, (-(1/3))*(1 - x)^3]
    @test_int [(1 - x^4)^1/(1 + x + x^2 + x^3)^1, x, 2, x - x^2/2]
    @test_int [(1 + x + x^2 + x^3)^1/(1 - x^4)^1, x, 2, -log(1 - x)]
    @test_int [(1 + x + x^2 + x^3)^2/(1 - x^4)^2, x, 2, 1/(1 - x)]
    @test_int [(1 + x + x^2 + x^3)^3/(1 - x^4)^3, x, 2, 1/(2*(1 - x)^2)]
    @test_int [(1 + x + x^2 + x^3)^4/(1 - x^4)^4, x, 2, 1/(3*(1 - x)^3)]

    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a - b*x^4), x, 13, -((g*x)/b) - (h*x^2)/(2*b) + ((b*c - sqrt(a)*sqrt(b)*e + a*g)*atan((b^(1/4)*x)/a^(1/4)))/(2*a^(3/4)*b^(5/4)) + ((b*c + sqrt(a)*sqrt(b)*e + a*g)*atanh((b^(1/4)*x)/a^(1/4)))/(2*a^(3/4)*b^(5/4)) + ((b*d + a*h)*atanh((sqrt(b)*x^2)/sqrt(a)))/(2*sqrt(a)*b^(3/2)) - (f*log(a - b*x^4))/(4*b)]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6)/(a - b*x^4), x, 13, -((g*x)/b) - (h*x^2)/(2*b) - (i*x^3)/(3*b) - ((b*e - (sqrt(b)*(b*c + a*g))/sqrt(a) + a*i)*atan((b^(1/4)*x)/a^(1/4)))/(2*a^(1/4)*b^(7/4)) + ((b*e + (sqrt(b)*(b*c + a*g))/sqrt(a) + a*i)*atanh((b^(1/4)*x)/a^(1/4)))/(2*a^(1/4)*b^(7/4)) + ((b*d + a*h)*atanh((sqrt(b)*x^2)/sqrt(a)))/(2*sqrt(a)*b^(3/2)) - (f*log(a - b*x^4))/(4*b)]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6 + j*x^7)/(a - b*x^4), x, 13, -((g*x)/b) - (h*x^2)/(2*b) - (i*x^3)/(3*b) - (j*x^4)/(4*b) - ((b*e - (sqrt(b)*(b*c + a*g))/sqrt(a) + a*i)*atan((b^(1/4)*x)/a^(1/4)))/(2*a^(1/4)*b^(7/4)) + ((b*e + (sqrt(b)*(b*c + a*g))/sqrt(a) + a*i)*atanh((b^(1/4)*x)/a^(1/4)))/(2*a^(1/4)*b^(7/4)) + ((b*d + a*h)*atanh((sqrt(b)*x^2)/sqrt(a)))/(2*sqrt(a)*b^(3/2)) - ((b*f + a*j)*log(a - b*x^4))/(4*b^2)]

    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^4), x, 19, (g*x)/b + (h*x^2)/(2*b) + ((b*d - a*h)*atan((sqrt(b)*x^2)/sqrt(a)))/(2*sqrt(a)*b^(3/2)) - ((b*c + sqrt(a)*sqrt(b)*e - a*g)*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*a^(3/4)*b^(5/4)) + ((b*c + sqrt(a)*sqrt(b)*e - a*g)*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*a^(3/4)*b^(5/4)) - ((b*c - sqrt(a)*sqrt(b)*e - a*g)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*a^(3/4)*b^(5/4)) + ((b*c - sqrt(a)*sqrt(b)*e - a*g)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*a^(3/4)*b^(5/4)) + (f*log(a + b*x^4))/(4*b)]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6)/(a + b*x^4), x, 19, (g*x)/b + (h*x^2)/(2*b) + (i*x^3)/(3*b) + ((b*d - a*h)*atan((sqrt(b)*x^2)/sqrt(a)))/(2*sqrt(a)*b^(3/2)) - ((sqrt(b)*(b*c - a*g) + sqrt(a)*(b*e - a*i))*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*a^(3/4)*b^(7/4)) + ((sqrt(b)*(b*c - a*g) + sqrt(a)*(b*e - a*i))*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*a^(3/4)*b^(7/4)) - ((sqrt(b)*(b*c - a*g) - sqrt(a)*(b*e - a*i))*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*a^(3/4)*b^(7/4)) + ((sqrt(b)*(b*c - a*g) - sqrt(a)*(b*e - a*i))*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*a^(3/4)*b^(7/4)) + (f*log(a + b*x^4))/(4*b)]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6 + j*x^7)/(a + b*x^4), x, 19, (g*x)/b + (h*x^2)/(2*b) + (i*x^3)/(3*b) + (j*x^4)/(4*b) + ((b*d - a*h)*atan((sqrt(b)*x^2)/sqrt(a)))/(2*sqrt(a)*b^(3/2)) - ((sqrt(b)*(b*c - a*g) + sqrt(a)*(b*e - a*i))*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*a^(3/4)*b^(7/4)) + ((sqrt(b)*(b*c - a*g) + sqrt(a)*(b*e - a*i))*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*a^(3/4)*b^(7/4)) - ((sqrt(b)*(b*c - a*g) - sqrt(a)*(b*e - a*i))*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*a^(3/4)*b^(7/4)) + ((sqrt(b)*(b*c - a*g) - sqrt(a)*(b*e - a*i))*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*a^(3/4)*b^(7/4)) + ((b*f - a*j)*log(a + b*x^4))/(4*b^2)]

    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a - b*x^4)^2, x, 8, (x*(b*c + a*g + (b*d + a*h)*x + b*e*x^2 + b*f*x^3))/(4*a*b*(a - b*x^4)) + ((3*b*c - sqrt(a)*sqrt(b)*e - a*g)*atan((b^(1/4)*x)/a^(1/4)))/(8*a^(7/4)*b^(5/4)) + ((3*b*c + sqrt(a)*sqrt(b)*e - a*g)*atanh((b^(1/4)*x)/a^(1/4)))/(8*a^(7/4)*b^(5/4)) + ((b*d - a*h)*atanh((sqrt(b)*x^2)/sqrt(a)))/(4*a^(3/2)*b^(3/2))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6)/(a - b*x^4)^2, x, 8, (x*(b*c + a*g + (b*d + a*h)*x + (b*e + a*i)*x^2 + b*f*x^3))/(4*a*b*(a - b*x^4)) - ((b*e - (sqrt(b)*(3*b*c - a*g))/sqrt(a) - 3*a*i)*atan((b^(1/4)*x)/a^(1/4)))/(8*a^(5/4)*b^(7/4)) + ((b*e + (sqrt(b)*(3*b*c - a*g))/sqrt(a) - 3*a*i)*atanh((b^(1/4)*x)/a^(1/4)))/(8*a^(5/4)*b^(7/4)) + ((b*d - a*h)*atanh((sqrt(b)*x^2)/sqrt(a)))/(4*a^(3/2)*b^(3/2))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6 + j*x^7)/(a - b*x^4)^2, x, 10, (x*(b*c + a*g + (b*d + a*h)*x + (b*e + a*i)*x^2 + (b*f + a*j)*x^3))/(4*a*b*(a - b*x^4)) - ((b*e - (sqrt(b)*(3*b*c - a*g))/sqrt(a) - 3*a*i)*atan((b^(1/4)*x)/a^(1/4)))/(8*a^(5/4)*b^(7/4)) + ((b*e + (sqrt(b)*(3*b*c - a*g))/sqrt(a) - 3*a*i)*atanh((b^(1/4)*x)/a^(1/4)))/(8*a^(5/4)*b^(7/4)) + ((b*d - a*h)*atanh((sqrt(b)*x^2)/sqrt(a)))/(4*a^(3/2)*b^(3/2)) + (j*log(a - b*x^4))/(4*b^2)]

    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^4)^2, x, 14, (x*(b*c - a*g + (b*d - a*h)*x + b*e*x^2 + b*f*x^3))/(4*a*b*(a + b*x^4)) + ((b*d + a*h)*atan((sqrt(b)*x^2)/sqrt(a)))/(4*a^(3/2)*b^(3/2)) - ((3*b*c + sqrt(a)*sqrt(b)*e + a*g)*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(8*sqrt(2)*a^(7/4)*b^(5/4)) + ((3*b*c + sqrt(a)*sqrt(b)*e + a*g)*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(8*sqrt(2)*a^(7/4)*b^(5/4)) - ((3*b*c - sqrt(a)*sqrt(b)*e + a*g)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(16*sqrt(2)*a^(7/4)*b^(5/4)) + ((3*b*c - sqrt(a)*sqrt(b)*e + a*g)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(16*sqrt(2)*a^(7/4)*b^(5/4))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6)/(a + b*x^4)^2, x, 14, (x*(b*c - a*g + (b*d - a*h)*x + (b*e - a*i)*x^2 + b*f*x^3))/(4*a*b*(a + b*x^4)) + ((b*d + a*h)*atan((sqrt(b)*x^2)/sqrt(a)))/(4*a^(3/2)*b^(3/2)) - ((sqrt(b)*(3*b*c + a*g) + sqrt(a)*(b*e + 3*a*i))*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(8*sqrt(2)*a^(7/4)*b^(7/4)) + ((sqrt(b)*(3*b*c + a*g) + sqrt(a)*(b*e + 3*a*i))*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(8*sqrt(2)*a^(7/4)*b^(7/4)) - ((sqrt(b)*(3*b*c + a*g) - sqrt(a)*(b*e + 3*a*i))*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(16*sqrt(2)*a^(7/4)*b^(7/4)) + ((sqrt(b)*(3*b*c + a*g) - sqrt(a)*(b*e + 3*a*i))*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(16*sqrt(2)*a^(7/4)*b^(7/4))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6 + j*x^7)/(a + b*x^4)^2, x, 16, (x*(b*c - a*g + (b*d - a*h)*x + (b*e - a*i)*x^2 + (b*f - a*j)*x^3))/(4*a*b*(a + b*x^4)) + ((b*d + a*h)*atan((sqrt(b)*x^2)/sqrt(a)))/(4*a^(3/2)*b^(3/2)) - ((sqrt(b)*(3*b*c + a*g) + sqrt(a)*(b*e + 3*a*i))*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(8*sqrt(2)*a^(7/4)*b^(7/4)) + ((sqrt(b)*(3*b*c + a*g) + sqrt(a)*(b*e + 3*a*i))*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(8*sqrt(2)*a^(7/4)*b^(7/4)) - ((sqrt(b)*(3*b*c + a*g) - sqrt(a)*(b*e + 3*a*i))*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(16*sqrt(2)*a^(7/4)*b^(7/4)) + ((sqrt(b)*(3*b*c + a*g) - sqrt(a)*(b*e + 3*a*i))*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(16*sqrt(2)*a^(7/4)*b^(7/4)) + (j*log(a + b*x^4))/(4*b^2)]

    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a - b*x^4)^3, x, 9, (x*(b*c + a*g + (b*d + a*h)*x + b*e*x^2 + b*f*x^3))/(8*a*b*(a - b*x^4)^2) + (4*a*f + x*(7*b*c - a*g + 2*(3*b*d - a*h)*x + 5*b*e*x^2))/(32*a^2*b*(a - b*x^4)) + ((21*b*c - 5*sqrt(a)*sqrt(b)*e - 3*a*g)*atan((b^(1/4)*x)/a^(1/4)))/(64*a^(11/4)*b^(5/4)) + ((21*b*c + 5*sqrt(a)*sqrt(b)*e - 3*a*g)*atanh((b^(1/4)*x)/a^(1/4)))/(64*a^(11/4)*b^(5/4)) + ((3*b*d - a*h)*atanh((sqrt(b)*x^2)/sqrt(a)))/(16*a^(5/2)*b^(3/2))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6)/(a - b*x^4)^3, x, 9, (x*(b*c + a*g + (b*d + a*h)*x + (b*e + a*i)*x^2 + b*f*x^3))/(8*a*b*(a - b*x^4)^2) + (4*a*f + x*(7*b*c - a*g + 2*(3*b*d - a*h)*x + (5*b*e - 3*a*i)*x^2))/(32*a^2*b*(a - b*x^4)) - ((5*b*e - (3*sqrt(b)*(7*b*c - a*g))/sqrt(a) - 3*a*i)*atan((b^(1/4)*x)/a^(1/4)))/(64*a^(9/4)*b^(7/4)) + ((5*b*e + (3*sqrt(b)*(7*b*c - a*g))/sqrt(a) - 3*a*i)*atanh((b^(1/4)*x)/a^(1/4)))/(64*a^(9/4)*b^(7/4)) + ((3*b*d - a*h)*atanh((sqrt(b)*x^2)/sqrt(a)))/(16*a^(5/2)*b^(3/2))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6 + j*x^7)/(a - b*x^4)^3, x, 9, (x*(b*c + a*g + (b*d + a*h)*x + (b*e + a*i)*x^2 + (b*f + a*j)*x^3))/(8*a*b*(a - b*x^4)^2) + (4*a*(b*f - a*j) + x*(b*(7*b*c - a*g) + 2*b*(3*b*d - a*h)*x + b*(5*b*e - 3*a*i)*x^2))/(32*a^2*b^2*(a - b*x^4)) - ((5*b*e - (3*sqrt(b)*(7*b*c - a*g))/sqrt(a) - 3*a*i)*atan((b^(1/4)*x)/a^(1/4)))/(64*a^(9/4)*b^(7/4)) + ((5*b*e + (3*sqrt(b)*(7*b*c - a*g))/sqrt(a) - 3*a*i)*atanh((b^(1/4)*x)/a^(1/4)))/(64*a^(9/4)*b^(7/4)) + ((3*b*d - a*h)*atanh((sqrt(b)*x^2)/sqrt(a)))/(16*a^(5/2)*b^(3/2))]

    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^4)^3, x, 15, (x*(b*c - a*g + (b*d - a*h)*x + b*e*x^2 + b*f*x^3))/(8*a*b*(a + b*x^4)^2) - (4*a*f - x*(7*b*c + a*g + 2*(3*b*d + a*h)*x + 5*b*e*x^2))/(32*a^2*b*(a + b*x^4)) + ((3*b*d + a*h)*atan((sqrt(b)*x^2)/sqrt(a)))/(16*a^(5/2)*b^(3/2)) - ((21*b*c + 5*sqrt(a)*sqrt(b)*e + 3*a*g)*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(64*sqrt(2)*a^(11/4)*b^(5/4)) + ((21*b*c + 5*sqrt(a)*sqrt(b)*e + 3*a*g)*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(64*sqrt(2)*a^(11/4)*b^(5/4)) - ((21*b*c - 5*sqrt(a)*sqrt(b)*e + 3*a*g)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(128*sqrt(2)*a^(11/4)*b^(5/4)) + ((21*b*c - 5*sqrt(a)*sqrt(b)*e + 3*a*g)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(128*sqrt(2)*a^(11/4)*b^(5/4))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6)/(a + b*x^4)^3, x, 15, (x*(b*c - a*g + (b*d - a*h)*x + (b*e - a*i)*x^2 + b*f*x^3))/(8*a*b*(a + b*x^4)^2) - (4*a*f - x*(7*b*c + a*g + 2*(3*b*d + a*h)*x + (5*b*e + 3*a*i)*x^2))/(32*a^2*b*(a + b*x^4)) + ((3*b*d + a*h)*atan((sqrt(b)*x^2)/sqrt(a)))/(16*a^(5/2)*b^(3/2)) - ((3*sqrt(b)*(7*b*c + a*g) + sqrt(a)*(5*b*e + 3*a*i))*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(64*sqrt(2)*a^(11/4)*b^(7/4)) + ((3*sqrt(b)*(7*b*c + a*g) + sqrt(a)*(5*b*e + 3*a*i))*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(64*sqrt(2)*a^(11/4)*b^(7/4)) - ((3*sqrt(b)*(7*b*c + a*g) - sqrt(a)*(5*b*e + 3*a*i))*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(128*sqrt(2)*a^(11/4)*b^(7/4)) + ((3*sqrt(b)*(7*b*c + a*g) - sqrt(a)*(5*b*e + 3*a*i))*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(128*sqrt(2)*a^(11/4)*b^(7/4))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6 + j*x^7)/(a + b*x^4)^3, x, 15, (x*(b*c - a*g + (b*d - a*h)*x + (b*e - a*i)*x^2 + (b*f - a*j)*x^3))/(8*a*b*(a + b*x^4)^2) - (4*a*(b*f + a*j) - x*(b*(7*b*c + a*g) + 2*b*(3*b*d + a*h)*x + b*(5*b*e + 3*a*i)*x^2))/(32*a^2*b^2*(a + b*x^4)) + ((3*b*d + a*h)*atan((sqrt(b)*x^2)/sqrt(a)))/(16*a^(5/2)*b^(3/2)) - ((3*sqrt(b)*(7*b*c + a*g) + sqrt(a)*(5*b*e + 3*a*i))*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(64*sqrt(2)*a^(11/4)*b^(7/4)) + ((3*sqrt(b)*(7*b*c + a*g) + sqrt(a)*(5*b*e + 3*a*i))*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(64*sqrt(2)*a^(11/4)*b^(7/4)) - ((3*sqrt(b)*(7*b*c + a*g) - sqrt(a)*(5*b*e + 3*a*i))*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(128*sqrt(2)*a^(11/4)*b^(7/4)) + ((3*sqrt(b)*(7*b*c + a*g) - sqrt(a)*(5*b*e + 3*a*i))*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(128*sqrt(2)*a^(11/4)*b^(7/4))]

    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a - b*x^4)^4, x, 10, (x*(b*c + a*g + (b*d + a*h)*x + b*e*x^2 + b*f*x^3))/(12*a*b*(a - b*x^4)^3) + (x*(7*(11*b*c - a*g) + 12*(5*b*d - a*h)*x + 45*b*e*x^2))/(384*a^3*b*(a - b*x^4)) + (8*a*f + x*(11*b*c - a*g + 2*(5*b*d - a*h)*x + 9*b*e*x^2))/(96*a^2*b*(a - b*x^4)^2) + ((77*b*c - 15*sqrt(a)*sqrt(b)*e - 7*a*g)*atan((b^(1/4)*x)/a^(1/4)))/(256*a^(15/4)*b^(5/4)) + ((77*b*c + 15*sqrt(a)*sqrt(b)*e - 7*a*g)*atanh((b^(1/4)*x)/a^(1/4)))/(256*a^(15/4)*b^(5/4)) + ((5*b*d - a*h)*atanh((sqrt(b)*x^2)/sqrt(a)))/(32*a^(7/2)*b^(3/2))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6)/(a - b*x^4)^4, x, 10, (x*(b*c + a*g + (b*d + a*h)*x + (b*e + a*i)*x^2 + b*f*x^3))/(12*a*b*(a - b*x^4)^3) + (x*(7*(11*b*c - a*g) + 12*(5*b*d - a*h)*x + 15*(3*b*e - a*i)*x^2))/(384*a^3*b*(a - b*x^4)) + (8*a*f + x*(11*b*c - a*g + 2*(5*b*d - a*h)*x + 3*(3*b*e - a*i)*x^2))/(96*a^2*b*(a - b*x^4)^2) + (((7*sqrt(b)*(11*b*c - a*g))/sqrt(a) - 5*(3*b*e - a*i))*atan((b^(1/4)*x)/a^(1/4)))/(256*a^(13/4)*b^(7/4)) + ((15*b*e + (7*sqrt(b)*(11*b*c - a*g))/sqrt(a) - 5*a*i)*atanh((b^(1/4)*x)/a^(1/4)))/(256*a^(13/4)*b^(7/4)) + ((5*b*d - a*h)*atanh((sqrt(b)*x^2)/sqrt(a)))/(32*a^(7/2)*b^(3/2))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6 + j*x^7)/(a - b*x^4)^4, x, 10, (x*(b*c + a*g + (b*d + a*h)*x + (b*e + a*i)*x^2 + (b*f + a*j)*x^3))/(12*a*b*(a - b*x^4)^3) + (x*(7*(11*b*c - a*g) + 12*(5*b*d - a*h)*x + 15*(3*b*e - a*i)*x^2))/(384*a^3*b*(a - b*x^4)) + (4*a*(2*b*f - a*j) + x*(b*(11*b*c - a*g) + 2*b*(5*b*d - a*h)*x + 3*b*(3*b*e - a*i)*x^2))/(96*a^2*b^2*(a - b*x^4)^2) + (((7*sqrt(b)*(11*b*c - a*g))/sqrt(a) - 5*(3*b*e - a*i))*atan((b^(1/4)*x)/a^(1/4)))/(256*a^(13/4)*b^(7/4)) + ((15*b*e + (7*sqrt(b)*(11*b*c - a*g))/sqrt(a) - 5*a*i)*atanh((b^(1/4)*x)/a^(1/4)))/(256*a^(13/4)*b^(7/4)) + ((5*b*d - a*h)*atanh((sqrt(b)*x^2)/sqrt(a)))/(32*a^(7/2)*b^(3/2))]

    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^4)^4, x, 16, (x*(b*c - a*g + (b*d - a*h)*x + b*e*x^2 + b*f*x^3))/(12*a*b*(a + b*x^4)^3) + (x*(7*(11*b*c + a*g) + 12*(5*b*d + a*h)*x + 45*b*e*x^2))/(384*a^3*b*(a + b*x^4)) - (8*a*f - x*(11*b*c + a*g + 2*(5*b*d + a*h)*x + 9*b*e*x^2))/(96*a^2*b*(a + b*x^4)^2) + ((5*b*d + a*h)*atan((sqrt(b)*x^2)/sqrt(a)))/(32*a^(7/2)*b^(3/2)) - ((77*b*c + 15*sqrt(a)*sqrt(b)*e + 7*a*g)*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(256*sqrt(2)*a^(15/4)*b^(5/4)) + ((77*b*c + 15*sqrt(a)*sqrt(b)*e + 7*a*g)*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(256*sqrt(2)*a^(15/4)*b^(5/4)) - ((77*b*c - 15*sqrt(a)*sqrt(b)*e + 7*a*g)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(512*sqrt(2)*a^(15/4)*b^(5/4)) + ((77*b*c - 15*sqrt(a)*sqrt(b)*e + 7*a*g)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(512*sqrt(2)*a^(15/4)*b^(5/4))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6)/(a + b*x^4)^4, x, 16, (x*(b*c - a*g + (b*d - a*h)*x + (b*e - a*i)*x^2 + b*f*x^3))/(12*a*b*(a + b*x^4)^3) + (x*(7*(11*b*c + a*g) + 12*(5*b*d + a*h)*x + 15*(3*b*e + a*i)*x^2))/(384*a^3*b*(a + b*x^4)) - (8*a*f - x*(11*b*c + a*g + 2*(5*b*d + a*h)*x + 3*(3*b*e + a*i)*x^2))/(96*a^2*b*(a + b*x^4)^2) + ((5*b*d + a*h)*atan((sqrt(b)*x^2)/sqrt(a)))/(32*a^(7/2)*b^(3/2)) - ((7*sqrt(b)*(11*b*c + a*g) + 5*sqrt(a)*(3*b*e + a*i))*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(256*sqrt(2)*a^(15/4)*b^(7/4)) + ((7*sqrt(b)*(11*b*c + a*g) + 5*sqrt(a)*(3*b*e + a*i))*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(256*sqrt(2)*a^(15/4)*b^(7/4)) - ((7*sqrt(b)*(11*b*c + a*g) - 5*sqrt(a)*(3*b*e + a*i))*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(512*sqrt(2)*a^(15/4)*b^(7/4)) + ((7*sqrt(b)*(11*b*c + a*g) - 5*sqrt(a)*(3*b*e + a*i))*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(512*sqrt(2)*a^(15/4)*b^(7/4))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6 + j*x^7)/(a + b*x^4)^4, x, 16, (x*(b*c - a*g + (b*d - a*h)*x + (b*e - a*i)*x^2 + (b*f - a*j)*x^3))/(12*a*b*(a + b*x^4)^3) + (x*(7*(11*b*c + a*g) + 12*(5*b*d + a*h)*x + 15*(3*b*e + a*i)*x^2))/(384*a^3*b*(a + b*x^4)) - (4*a*(2*b*f + a*j) - x*(b*(11*b*c + a*g) + 2*b*(5*b*d + a*h)*x + 3*b*(3*b*e + a*i)*x^2))/(96*a^2*b^2*(a + b*x^4)^2) + ((5*b*d + a*h)*atan((sqrt(b)*x^2)/sqrt(a)))/(32*a^(7/2)*b^(3/2)) - ((7*sqrt(b)*(11*b*c + a*g) + 5*sqrt(a)*(3*b*e + a*i))*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(256*sqrt(2)*a^(15/4)*b^(7/4)) + ((7*sqrt(b)*(11*b*c + a*g) + 5*sqrt(a)*(3*b*e + a*i))*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(256*sqrt(2)*a^(15/4)*b^(7/4)) - ((7*sqrt(b)*(11*b*c + a*g) - 5*sqrt(a)*(3*b*e + a*i))*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(512*sqrt(2)*a^(15/4)*b^(7/4)) + ((7*sqrt(b)*(11*b*c + a*g) - 5*sqrt(a)*(3*b*e + a*i))*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(512*sqrt(2)*a^(15/4)*b^(7/4))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*P1(x)*(a+b*x^4)^(p/2)=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [(c + d*x)/sqrt(a + b*x^4), x, 6, (d*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(2*sqrt(b)) + (c*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(2*a^(1/4)*b^(1/4)*sqrt(a + b*x^4))]
    @test_int [(c + d*x)/sqrt(a - b*x^4), x, 7, (d*atan((sqrt(b)*x^2)/sqrt(a - b*x^4)))/(2*sqrt(b)) + (a^(1/4)*c*sqrt(1 - (b*x^4)/a)*Elliptic.F(asin((b^(1/4)*x)/a^(1/4)), -1))/(b^(1/4)*sqrt(a - b*x^4))]
    @test_int [(c + d*x)/sqrt(-a + b*x^4), x, 7, (d*atanh((sqrt(b)*x^2)/sqrt(-a + b*x^4)))/(2*sqrt(b)) + (a^(1/4)*c*sqrt(1 - (b*x^4)/a)*Elliptic.F(asin((b^(1/4)*x)/a^(1/4)), -1))/(b^(1/4)*sqrt(-a + b*x^4))]
    @test_int [(c + d*x)/sqrt(-a - b*x^4), x, 6, (d*atan((sqrt(b)*x^2)/sqrt(-a - b*x^4)))/(2*sqrt(b)) + (c*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(2*a^(1/4)*b^(1/4)*sqrt(-a - b*x^4))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*P2(x)*(a+b*x^4)^(p/2)=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [(c + d*x + e*x^2)/sqrt(a + b*x^4), x, 8, (e*x*sqrt(a + b*x^4))/(sqrt(b)*(sqrt(a) + sqrt(b)*x^2)) + (d*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(2*sqrt(b)) - (a^(1/4)*e*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(b^(3/4)*sqrt(a + b*x^4)) + (a^(1/4)*((sqrt(b)*c)/sqrt(a) + e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(2*b^(3/4)*sqrt(a + b*x^4))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*P4(x)*(a+b*x^4)^(p/2)=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [(a*g - b*g*x^4)/(a + b*x^4)^(3/2), x, 1, (g*x)/sqrt(a + b*x^4)]
    @test_int [(a*g + e*x - b*g*x^4)/(a + b*x^4)^(3/2), x, 1, (2*a*g*x + e*x^2)/(2*a*sqrt(a + b*x^4))]
    @test_int [(a*g + f*x^3 - b*g*x^4)/(a + b*x^4)^(3/2), x, 1, -((f - 2*b*g*x)/(2*b*sqrt(a + b*x^4)))]
    @test_int [(a*g + e*x + f*x^3 - b*g*x^4)/(a + b*x^4)^(3/2), x, 1, -((a*f - 2*a*b*g*x - b*e*x^2)/(2*a*b*sqrt(a + b*x^4)))]

    @test_int [(-1 + x^4)/(1 + x^4)^(3/2), x, 1, -(x/sqrt(1 + x^4))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*P4(x)*(a+b*x^4)^(p/2)*with*q>4=#

    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5 + i*x^6)/sqrt(a + b*x^4), x, 12, (f*sqrt(a + b*x^4))/(2*b) + (g*x*sqrt(a + b*x^4))/(3*b) + (h*x^2*sqrt(a + b*x^4))/(4*b) + (i*x^3*sqrt(a + b*x^4))/(5*b) + ((5*b*e - 3*a*i)*x*sqrt(a + b*x^4))/(5*b^(3/2)*(sqrt(a) + sqrt(b)*x^2)) + ((2*b*d - a*h)*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(4*b^(3/2)) - (a^(1/4)*(5*b*e - 3*a*i)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(5*b^(7/4)*sqrt(a + b*x^4)) + (a^(1/4)*(15*b*e + (5*sqrt(b)*(3*b*c - a*g))/sqrt(a) - 9*a*i)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(30*b^(7/4)*sqrt(a + b*x^4))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*Pq(x)*(a+b*x^5)^p=#

    @test_int [(1 + x)/(1 + x^5), x, 3, (-(1/5))*(-1)^(1/5)*(1 + (-1)^(1/5))*log((-1)^(1/5) - x) + (1/5)*(-1)^(4/5)*(1 - (-1)^(4/5))*log(-(-1)^(4/5) - x) + (1/5)*(-1)^(2/5)*(1 - (-1)^(2/5))*log((-1)^(2/5) + x) - (1/5)*(-1)^(3/5)*(1 + (-1)^(3/5))*log(-(-1)^(3/5) + x)]
    @test_int [(1 - x)/(1 - x^5), x, 3, (-(1/5))*(-1)^(2/5)*(1 - (-1)^(2/5))*log((-1)^(2/5) - x) + (1/5)*(-1)^(3/5)*(1 + (-1)^(3/5))*log(-(-1)^(3/5) - x) + (1/5)*(-1)^(1/5)*(1 + (-1)^(1/5))*log((-1)^(1/5) + x) - (1/5)*(-1)^(4/5)*(1 - (-1)^(4/5))*log(-(-1)^(4/5) + x)]

    #= ::Title::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*Pq(x)*(a+b*x^n)^p=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*Pq(x)*(a+b*x^3)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*Pq(x^3)*(a+b*x^3)^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^11*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3), x, 3, (a^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^3)/(3*b^6) - (a*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^6)/(6*b^5) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^9)/(9*b^4) + ((b^2*d - a*b*e + a^2*f)*x^12)/(12*b^3) + ((b*e - a*f)*x^15)/(15*b^2) + (f*x^18)/(18*b) - (a^3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a + b*x^3))/(3*b^7)]
    @test_int [x^8*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3), x, 3, -((a*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^3)/(3*b^5)) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^6)/(6*b^4) + ((b^2*d - a*b*e + a^2*f)*x^9)/(9*b^3) + ((b*e - a*f)*x^12)/(12*b^2) + (f*x^15)/(15*b) + (a^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a + b*x^3))/(3*b^6)]
    @test_int [x^5*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3), x, 3, ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^3)/(3*b^4) + ((b^2*d - a*b*e + a^2*f)*x^6)/(6*b^3) + ((b*e - a*f)*x^9)/(9*b^2) + (f*x^12)/(12*b) - (a*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a + b*x^3))/(3*b^5)]
    @test_int [x^2*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3), x, 3, ((b^2*d - a*b*e + a^2*f)*x^3)/(3*b^3) + ((b*e - a*f)*x^6)/(6*b^2) + (f*x^9)/(9*b) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a + b*x^3))/(3*b^4)]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^1*(a + b*x^3)), x, 3, ((b*e - a*f)*x^3)/(3*b^2) + (f*x^6)/(6*b) + (c*log(x))/a - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a + b*x^3))/(3*a*b^3)]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^4*(a + b*x^3)), x, 3, -(c/(3*a*x^3)) + (f*x^3)/(3*b) - ((b*c - a*d)*log(x))/a^2 + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a + b*x^3))/(3*a^2*b^2)]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^7*(a + b*x^3)), x, 3, -(c/(6*a*x^6)) + (b*c - a*d)/(3*a^2*x^3) + ((b^2*c - a*b*d + a^2*e)*log(x))/a^3 - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a + b*x^3))/(3*a^3*b)]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^10*(a + b*x^3)), x, 3, -(c/(9*a*x^9)) + (b*c - a*d)/(6*a^2*x^6) - (b^2*c - a*b*d + a^2*e)/(3*a^3*x^3) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(x))/a^4 + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a + b*x^3))/(3*a^4)]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^13*(a + b*x^3)), x, 3, -(c/(12*a*x^12)) + (b*c - a*d)/(9*a^2*x^9) - (b^2*c - a*b*d + a^2*e)/(6*a^3*x^6) + (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(3*a^4*x^3) + (b*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(x))/a^5 - (b*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a + b*x^3))/(3*a^5)]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^16*(a + b*x^3)), x, 3, -(c/(15*a*x^15)) + (b*c - a*d)/(12*a^2*x^12) - (b^2*c - a*b*d + a^2*e)/(9*a^3*x^9) + (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(6*a^4*x^6) - (b*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(3*a^5*x^3) - (b^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(x))/a^6 + (b^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a + b*x^3))/(3*a^6)]

    @test_int [x^9*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3), x, 9, (a^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/b^6 - (a*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^4)/(4*b^5) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^7)/(7*b^4) + ((b^2*d - a*b*e + a^2*f)*x^10)/(10*b^3) + ((b*e - a*f)*x^13)/(13*b^2) + (f*x^16)/(16*b) + (a^(7/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^(19/3)) - (a^(7/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(1/3) + b^(1/3)*x))/(3*b^(19/3)) + (a^(7/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*b^(19/3))]
    @test_int [x^7*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3), x, 9, -((a*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(2*b^5)) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^5)/(5*b^4) + ((b^2*d - a*b*e + a^2*f)*x^8)/(8*b^3) + ((b*e - a*f)*x^11)/(11*b^2) + (f*x^14)/(14*b) - (a^(5/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^(17/3)) - (a^(5/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(1/3) + b^(1/3)*x))/(3*b^(17/3)) + (a^(5/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*b^(17/3))]
    @test_int [x^6*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3), x, 9, -((a*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/b^5) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^4)/(4*b^4) + ((b^2*d - a*b*e + a^2*f)*x^7)/(7*b^3) + ((b*e - a*f)*x^10)/(10*b^2) + (f*x^13)/(13*b) - (a^(4/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^(16/3)) + (a^(4/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(1/3) + b^(1/3)*x))/(3*b^(16/3)) - (a^(4/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*b^(16/3))]
    @test_int [x^4*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3), x, 9, ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(2*b^4) + ((b^2*d - a*b*e + a^2*f)*x^5)/(5*b^3) + ((b*e - a*f)*x^8)/(8*b^2) + (f*x^11)/(11*b) + (a^(2/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^(14/3)) + (a^(2/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(1/3) + b^(1/3)*x))/(3*b^(14/3)) - (a^(2/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*b^(14/3))]
    @test_int [x^3*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3), x, 9, ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/b^4 + ((b^2*d - a*b*e + a^2*f)*x^4)/(4*b^3) + ((b*e - a*f)*x^7)/(7*b^2) + (f*x^10)/(10*b) + (a^(1/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^(13/3)) - (a^(1/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(1/3) + b^(1/3)*x))/(3*b^(13/3)) + (a^(1/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*b^(13/3))]
    @test_int [x^1*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3), x, 9, ((b^2*d - a*b*e + a^2*f)*x^2)/(2*b^3) + ((b*e - a*f)*x^5)/(5*b^2) + (f*x^8)/(8*b) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(1/3)*b^(11/3)) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(1/3) + b^(1/3)*x))/(3*a^(1/3)*b^(11/3)) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(1/3)*b^(11/3))]
    @test_int [x^0*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3), x, 8, ((b^2*d - a*b*e + a^2*f)*x)/b^3 + ((b*e - a*f)*x^4)/(4*b^2) + (f*x^7)/(7*b) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(2/3)*b^(10/3)) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(1/3) + b^(1/3)*x))/(3*a^(2/3)*b^(10/3)) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(2/3)*b^(10/3))]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^2*(a + b*x^3)), x, 8, -(c/(a*x)) + ((b*e - a*f)*x^2)/(2*b^2) + (f*x^5)/(5*b) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(4/3)*b^(8/3)) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(1/3) + b^(1/3)*x))/(3*a^(4/3)*b^(8/3)) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(4/3)*b^(8/3))]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^3*(a + b*x^3)), x, 8, -c/(2*a*x^2) + ((b*e - a*f)*x)/b^2 + (f*x^4)/(4*b) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(5/3)*b^(7/3)) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(1/3) + b^(1/3)*x))/(3*a^(5/3)*b^(7/3)) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(5/3)*b^(7/3))]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^5*(a + b*x^3)), x, 8, -(c/(4*a*x^4)) + (b*c - a*d)/(a^2*x) + (f*x^2)/(2*b) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(7/3)*b^(5/3)) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(1/3) + b^(1/3)*x))/(3*a^(7/3)*b^(5/3)) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(7/3)*b^(5/3))]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^6*(a + b*x^3)), x, 8, -(c/(5*a*x^5)) + (b*c - a*d)/(2*a^2*x^2) + (f*x)/b - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(8/3)*b^(4/3)) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(1/3) + b^(1/3)*x))/(3*a^(8/3)*b^(4/3)) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(8/3)*b^(4/3))]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^8*(a + b*x^3)), x, 8, -(c/(7*a*x^7)) + (b*c - a*d)/(4*a^2*x^4) - (b^2*c - a*b*d + a^2*e)/(a^3*x) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(10/3)*b^(2/3)) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(1/3) + b^(1/3)*x))/(3*a^(10/3)*b^(2/3)) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(10/3)*b^(2/3))]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^9*(a + b*x^3)), x, 8, -c/(8*a*x^8) + (b*c - a*d)/(5*a^2*x^5) - (b^2*c - a*b*d + a^2*e)/(2*a^3*x^2) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(11/3)*b^(1/3)) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(1/3) + b^(1/3)*x))/(3*a^(11/3)*b^(1/3)) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(11/3)*b^(1/3))]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^11*(a + b*x^3)), x, 8, -(c/(10*a*x^10)) + (b*c - a*d)/(7*a^2*x^7) - (b^2*c - a*b*d + a^2*e)/(4*a^3*x^4) + (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(a^4*x) - (b^(1/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(13/3)) - (b^(1/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(1/3) + b^(1/3)*x))/(3*a^(13/3)) + (b^(1/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(13/3))]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^12*(a + b*x^3)), x, 8, -c/(11*a*x^11) + (b*c - a*d)/(8*a^2*x^8) - (b^2*c - a*b*d + a^2*e)/(5*a^3*x^5) + (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(2*a^4*x^2) - (b^(2/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(14/3)) + (b^(2/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(1/3) + b^(1/3)*x))/(3*a^(14/3)) - (b^(2/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(14/3))]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^14*(a + b*x^3)), x, 8, -(c/(13*a*x^13)) + (b*c - a*d)/(10*a^2*x^10) - (b^2*c - a*b*d + a^2*e)/(7*a^3*x^7) + (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(4*a^4*x^4) - (b*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(a^5*x) + (b^(4/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(16/3)) + (b^(4/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(1/3) + b^(1/3)*x))/(3*a^(16/3)) - (b^(4/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(16/3))]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^15*(a + b*x^3)), x, 8, -c/(14*a*x^14) + (b*c - a*d)/(11*a^2*x^11) - (b^2*c - a*b*d + a^2*e)/(8*a^3*x^8) + (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(5*a^4*x^5) - (b*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(2*a^5*x^2) + (b^(5/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(17/3)) - (b^(5/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(1/3) + b^(1/3)*x))/(3*a^(17/3)) + (b^(5/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(17/3))]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^17*(a + b*x^3)), x, 8, -(c/(16*a*x^16)) + (b*c - a*d)/(13*a^2*x^13) - (b^2*c - a*b*d + a^2*e)/(10*a^3*x^10) + (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(7*a^4*x^7) - (b*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(4*a^5*x^4) + (b^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(a^6*x) - (b^(7/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(19/3)) - (b^(7/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(1/3) + b^(1/3)*x))/(3*a^(19/3)) + (b^(7/3)*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(19/3))]

    @test_int [x^11*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3)^2, x, 3, -((a*(2*b^3*c - 3*a*b^2*d + 4*a^2*b*e - 5*a^3*f)*x^3)/(3*b^6)) + ((b^3*c - 2*a*b^2*d + 3*a^2*b*e - 4*a^3*f)*x^6)/(6*b^5) + ((b^2*d - 2*a*b*e + 3*a^2*f)*x^9)/(9*b^4) + ((b*e - 2*a*f)*x^12)/(12*b^3) + (f*x^15)/(15*b^2) + (a^3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(3*b^7*(a + b*x^3)) + (a^2*(3*b^3*c - 4*a*b^2*d + 5*a^2*b*e - 6*a^3*f)*log(a + b*x^3))/(3*b^7)]
    @test_int [x^8*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3)^2, x, 3, ((b^3*c - 2*a*b^2*d + 3*a^2*b*e - 4*a^3*f)*x^3)/(3*b^5) + ((b^2*d - 2*a*b*e + 3*a^2*f)*x^6)/(6*b^4) + ((b*e - 2*a*f)*x^9)/(9*b^3) + (f*x^12)/(12*b^2) - (a^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(3*b^6*(a + b*x^3)) - (a*(2*b^3*c - 3*a*b^2*d + 4*a^2*b*e - 5*a^3*f)*log(a + b*x^3))/(3*b^6)]
    @test_int [x^5*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3)^2, x, 3, ((b^2*d - 2*a*b*e + 3*a^2*f)*x^3)/(3*b^4) + ((b*e - 2*a*f)*x^6)/(6*b^3) + (f*x^9)/(9*b^2) + (a*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(3*b^5*(a + b*x^3)) + ((b^3*c - 2*a*b^2*d + 3*a^2*b*e - 4*a^3*f)*log(a + b*x^3))/(3*b^5)]
    @test_int [x^2*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3)^2, x, 3, ((b*e - 2*a*f)*x^3)/(3*b^3) + (f*x^6)/(6*b^2) - (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(3*b^4*(a + b*x^3)) + ((b^2*d - 2*a*b*e + 3*a^2*f)*log(a + b*x^3))/(3*b^4)]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^1*(a + b*x^3)^2), x, 3, (f*x^3)/(3*b^2) + (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(3*a*b^3*(a + b*x^3)) + (c*log(x))/a^2 - ((b^3*c - a^2*b*e + 2*a^3*f)*log(a + b*x^3))/(3*a^2*b^3)]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^4*(a + b*x^3)^2), x, 3, -(c/(3*a^2*x^3)) - (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(3*a^2*b^2*(a + b*x^3)) - ((2*b*c - a*d)*log(x))/a^3 + ((2*b^3*c - a*b^2*d + a^3*f)*log(a + b*x^3))/(3*a^3*b^2)]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^7*(a + b*x^3)^2), x, 3, -(c/(6*a^2*x^6)) + (2*b*c - a*d)/(3*a^3*x^3) + (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(3*a^3*b*(a + b*x^3)) + ((3*b^2*c - 2*a*b*d + a^2*e)*log(x))/a^4 - ((3*b^2*c - 2*a*b*d + a^2*e)*log(a + b*x^3))/(3*a^4)]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^10*(a + b*x^3)^2), x, 3, -(c/(9*a^2*x^9)) + (2*b*c - a*d)/(6*a^3*x^6) - (3*b^2*c - 2*a*b*d + a^2*e)/(3*a^4*x^3) - (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(3*a^4*(a + b*x^3)) - ((4*b^3*c - 3*a*b^2*d + 2*a^2*b*e - a^3*f)*log(x))/a^5 + ((4*b^3*c - 3*a*b^2*d + 2*a^2*b*e - a^3*f)*log(a + b*x^3))/(3*a^5)]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^13*(a + b*x^3)^2), x, 3, -(c/(12*a^2*x^12)) + (2*b*c - a*d)/(9*a^3*x^9) - (3*b^2*c - 2*a*b*d + a^2*e)/(6*a^4*x^6) + (4*b^3*c - 3*a*b^2*d + 2*a^2*b*e - a^3*f)/(3*a^5*x^3) + (b*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(3*a^5*(a + b*x^3)) + (b*(5*b^3*c - 4*a*b^2*d + 3*a^2*b*e - 2*a^3*f)*log(x))/a^6 - (b*(5*b^3*c - 4*a*b^2*d + 3*a^2*b*e - 2*a^3*f)*log(a + b*x^3))/(3*a^6)]

    @test_int [x^9*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3)^2, x, 9, -((a*(2*b^3*c - 3*a*b^2*d + 4*a^2*b*e - 5*a^3*f)*x)/b^6) + ((b^3*c - 2*a*b^2*d + 3*a^2*b*e - 4*a^3*f)*x^4)/(4*b^5) + ((b^2*d - 2*a*b*e + 3*a^2*f)*x^7)/(7*b^4) + ((b*e - 2*a*f)*x^10)/(10*b^3) + (f*x^13)/(13*b^2) - (a^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(3*b^6*(a + b*x^3)) - (a^(4/3)*(7*b^3*c - 10*a*b^2*d + 13*a^2*b*e - 16*a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*b^(19/3)) + (a^(4/3)*(7*b^3*c - 10*a*b^2*d + 13*a^2*b*e - 16*a^3*f)*log(a^(1/3) + b^(1/3)*x))/(9*b^(19/3)) - (a^(4/3)*(7*b^3*c - 10*a*b^2*d + 13*a^2*b*e - 16*a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*b^(19/3))]
    @test_int [x^7*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3)^2, x, 12, ((b^3*c - 2*a*b^2*d + 3*a^2*b*e - 4*a^3*f)*x^2)/(2*b^5) + ((b^2*d - 2*a*b*e + 3*a^2*f)*x^5)/(5*b^4) + ((b*e - 2*a*f)*x^8)/(8*b^3) + (f*x^11)/(11*b^2) + (a*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(3*b^5*(a + b*x^3)) + (a^(2/3)*(5*b^3*c - 8*a*b^2*d + 11*a^2*b*e - 14*a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*b^(17/3)) + (a^(2/3)*(5*b^3*c - 8*a*b^2*d + 11*a^2*b*e - 14*a^3*f)*log(a^(1/3) + b^(1/3)*x))/(9*b^(17/3)) - (a^(2/3)*(5*b^3*c - 8*a*b^2*d + 11*a^2*b*e - 14*a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*b^(17/3))]
    @test_int [x^6*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3)^2, x, 9, ((b^3*c - 2*a*b^2*d + 3*a^2*b*e - 4*a^3*f)*x)/b^5 + ((b^2*d - 2*a*b*e + 3*a^2*f)*x^4)/(4*b^4) + ((b*e - 2*a*f)*x^7)/(7*b^3) + (f*x^10)/(10*b^2) + (a*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(3*b^5*(a + b*x^3)) + (a^(1/3)*(4*b^3*c - 7*a*b^2*d + 10*a^2*b*e - 13*a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*b^(16/3)) - (a^(1/3)*(4*b^3*c - 7*a*b^2*d + 10*a^2*b*e - 13*a^3*f)*log(a^(1/3) + b^(1/3)*x))/(9*b^(16/3)) + (a^(1/3)*(4*b^3*c - 7*a*b^2*d + 10*a^2*b*e - 13*a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*b^(16/3))]
    @test_int [x^4*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3)^2, x, 11, ((b^2*d - 2*a*b*e + 3*a^2*f)*x^2)/(2*b^4) + ((b*e - 2*a*f)*x^5)/(5*b^3) + (f*x^8)/(8*b^2) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(3*b^4*(a + b*x^3)) - ((2*b^3*c - 5*a*b^2*d + 8*a^2*b*e - 11*a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(1/3)*b^(14/3)) - ((2*b^3*c - 5*a*b^2*d + 8*a^2*b*e - 11*a^3*f)*log(a^(1/3) + b^(1/3)*x))/(9*a^(1/3)*b^(14/3)) + ((2*b^3*c - 5*a*b^2*d + 8*a^2*b*e - 11*a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(1/3)*b^(14/3))]
    @test_int [x^3*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3)^2, x, 9, ((b^2*d - 2*a*b*e + 3*a^2*f)*x)/b^4 + ((b*e - 2*a*f)*x^4)/(4*b^3) + (f*x^7)/(7*b^2) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(3*b^4*(a + b*x^3)) - ((b^3*c - 4*a*b^2*d + 7*a^2*b*e - 10*a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(2/3)*b^(13/3)) + ((b^3*c - 4*a*b^2*d + 7*a^2*b*e - 10*a^3*f)*log(a^(1/3) + b^(1/3)*x))/(9*a^(2/3)*b^(13/3)) - ((b^3*c - 4*a*b^2*d + 7*a^2*b*e - 10*a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(2/3)*b^(13/3))]
    @test_int [x^1*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3)^2, x, 10, ((b*e - 2*a*f)*x^2)/(2*b^3) + (f*x^5)/(5*b^2) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(3*a*b^3*(a + b*x^3)) - ((b^3*c + 2*a*b^2*d - 5*a^2*b*e + 8*a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(4/3)*b^(11/3)) - ((b^3*c + 2*a*b^2*d - 5*a^2*b*e + 8*a^3*f)*log(a^(1/3) + b^(1/3)*x))/(9*a^(4/3)*b^(11/3)) + ((b^3*c + 2*a*b^2*d - 5*a^2*b*e + 8*a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(4/3)*b^(11/3))]
    @test_int [x^0*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3)^2, x, 9, ((b*e - 2*a*f)*x)/b^3 + (f*x^4)/(4*b^2) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(3*a*b^3*(a + b*x^3)) - ((2*b^3*c + a*b^2*d - 4*a^2*b*e + 7*a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(5/3)*b^(10/3)) + ((2*b^3*c + a*b^2*d - 4*a^2*b*e + 7*a^3*f)*log(a^(1/3) + b^(1/3)*x))/(9*a^(5/3)*b^(10/3)) - ((2*b^3*c + a*b^2*d - 4*a^2*b*e + 7*a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(5/3)*b^(10/3))]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^2*(a + b*x^3)^2), x, 9, -(c/(a^2*x)) + (f*x^2)/(2*b^2) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(3*a^2*b^2*(a + b*x^3)) + ((4*b^3*c - a*b^2*d - 2*a^2*b*e + 5*a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(7/3)*b^(8/3)) + ((4*b^3*c - a*b^2*d - 2*a^2*b*e + 5*a^3*f)*log(a^(1/3) + b^(1/3)*x))/(9*a^(7/3)*b^(8/3)) - ((4*b^3*c - a*b^2*d - 2*a^2*b*e + 5*a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(7/3)*b^(8/3))]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^3*(a + b*x^3)^2), x, 9, -c/(2*a^2*x^2) + (f*x)/b^2 - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(3*a^2*b^2*(a + b*x^3)) + ((5*b^3*c - 2*a*b^2*d - a^2*b*e + 4*a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(8/3)*b^(7/3)) - ((5*b^3*c - 2*a*b^2*d - a^2*b*e + 4*a^3*f)*log(a^(1/3) + b^(1/3)*x))/(9*a^(8/3)*b^(7/3)) + ((5*b^3*c - 2*a*b^2*d - a^2*b*e + 4*a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(8/3)*b^(7/3))]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^5*(a + b*x^3)^2), x, 9, -(c/(4*a^2*x^4)) + (2*b*c - a*d)/(a^3*x) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(3*a^3*b*(a + b*x^3)) - ((7*b^3*c - 4*a*b^2*d + a^2*b*e + 2*a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(10/3)*b^(5/3)) - ((7*b^3*c - 4*a*b^2*d + a^2*b*e + 2*a^3*f)*log(a^(1/3) + b^(1/3)*x))/(9*a^(10/3)*b^(5/3)) + ((7*b^3*c - 4*a*b^2*d + a^2*b*e + 2*a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(10/3)*b^(5/3))]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^6*(a + b*x^3)^2), x, 9, -c/(5*a^2*x^5) + (2*b*c - a*d)/(2*a^3*x^2) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(3*a^3*b*(a + b*x^3)) - ((8*b^3*c - 5*a*b^2*d + 2*a^2*b*e + a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(11/3)*b^(4/3)) + ((8*b^3*c - 5*a*b^2*d + 2*a^2*b*e + a^3*f)*log(a^(1/3) + b^(1/3)*x))/(9*a^(11/3)*b^(4/3)) - ((8*b^3*c - 5*a*b^2*d + 2*a^2*b*e + a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(11/3)*b^(4/3))]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^8*(a + b*x^3)^2), x, 9, -(c/(7*a^2*x^7)) + (2*b*c - a*d)/(4*a^3*x^4) - (3*b^2*c - 2*a*b*d + a^2*e)/(a^4*x) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(3*a^4*(a + b*x^3)) + ((10*b^3*c - 7*a*b^2*d + 4*a^2*b*e - a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(13/3)*b^(2/3)) + ((10*b^3*c - 7*a*b^2*d + 4*a^2*b*e - a^3*f)*log(a^(1/3) + b^(1/3)*x))/(9*a^(13/3)*b^(2/3)) - ((10*b^3*c - 7*a*b^2*d + 4*a^2*b*e - a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(13/3)*b^(2/3))]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^9*(a + b*x^3)^2), x, 9, -c/(8*a^2*x^8) + (2*b*c - a*d)/(5*a^3*x^5) - (3*b^2*c - 2*a*b*d + a^2*e)/(2*a^4*x^2) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(3*a^4*(a + b*x^3)) + ((11*b^3*c - 8*a*b^2*d + 5*a^2*b*e - 2*a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(14/3)*b^(1/3)) - ((11*b^3*c - 8*a*b^2*d + 5*a^2*b*e - 2*a^3*f)*log(a^(1/3) + b^(1/3)*x))/(9*a^(14/3)*b^(1/3)) + ((11*b^3*c - 8*a*b^2*d + 5*a^2*b*e - 2*a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(14/3)*b^(1/3))]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^11*(a + b*x^3)^2), x, 9, -(c/(10*a^2*x^10)) + (2*b*c - a*d)/(7*a^3*x^7) - (3*b^2*c - 2*a*b*d + a^2*e)/(4*a^4*x^4) + (4*b^3*c - 3*a*b^2*d + 2*a^2*b*e - a^3*f)/(a^5*x) + (b*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(3*a^5*(a + b*x^3)) - (b^(1/3)*(13*b^3*c - 10*a*b^2*d + 7*a^2*b*e - 4*a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(16/3)) - (b^(1/3)*(13*b^3*c - 10*a*b^2*d + 7*a^2*b*e - 4*a^3*f)*log(a^(1/3) + b^(1/3)*x))/(9*a^(16/3)) + (b^(1/3)*(13*b^3*c - 10*a*b^2*d + 7*a^2*b*e - 4*a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(16/3))]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^12*(a + b*x^3)^2), x, 9, -c/(11*a^2*x^11) + (2*b*c - a*d)/(8*a^3*x^8) - (3*b^2*c - 2*a*b*d + a^2*e)/(5*a^4*x^5) + (4*b^3*c - 3*a*b^2*d + 2*a^2*b*e - a^3*f)/(2*a^5*x^2) + (b*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(3*a^5*(a + b*x^3)) - (b^(2/3)*(14*b^3*c - 11*a*b^2*d + 8*a^2*b*e - 5*a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(17/3)) + (b^(2/3)*(14*b^3*c - 11*a*b^2*d + 8*a^2*b*e - 5*a^3*f)*log(a^(1/3) + b^(1/3)*x))/(9*a^(17/3)) - (b^(2/3)*(14*b^3*c - 11*a*b^2*d + 8*a^2*b*e - 5*a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(17/3))]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^14*(a + b*x^3)^2), x, 9, -(c/(13*a^2*x^13)) + (2*b*c - a*d)/(10*a^3*x^10) - (3*b^2*c - 2*a*b*d + a^2*e)/(7*a^4*x^7) + (4*b^3*c - 3*a*b^2*d + 2*a^2*b*e - a^3*f)/(4*a^5*x^4) - (b*(5*b^3*c - 4*a*b^2*d + 3*a^2*b*e - 2*a^3*f))/(a^6*x) - (b^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(3*a^6*(a + b*x^3)) + (b^(4/3)*(16*b^3*c - 13*a*b^2*d + 10*a^2*b*e - 7*a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(19/3)) + (b^(4/3)*(16*b^3*c - 13*a*b^2*d + 10*a^2*b*e - 7*a^3*f)*log(a^(1/3) + b^(1/3)*x))/(9*a^(19/3)) - (b^(4/3)*(16*b^3*c - 13*a*b^2*d + 10*a^2*b*e - 7*a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(19/3))]

    @test_int [x^14*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3)^3, x, 3, -((a*(3*b^3*c - 6*a*b^2*d + 10*a^2*b*e - 15*a^3*f)*x^3)/(3*b^7)) + ((b^3*c - 3*a*b^2*d + 6*a^2*b*e - 10*a^3*f)*x^6)/(6*b^6) + ((b^2*d - 3*a*b*e + 6*a^2*f)*x^9)/(9*b^5) + ((b*e - 3*a*f)*x^12)/(12*b^4) + (f*x^15)/(15*b^3) - (a^4*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(6*b^8*(a + b*x^3)^2) + (a^3*(4*b^3*c - 5*a*b^2*d + 6*a^2*b*e - 7*a^3*f))/(3*b^8*(a + b*x^3)) + (a^2*(6*b^3*c - 10*a*b^2*d + 15*a^2*b*e - 21*a^3*f)*log(a + b*x^3))/(3*b^8)]
    @test_int [x^11*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3)^3, x, 3, ((b^3*c - 3*a*b^2*d + 6*a^2*b*e - 10*a^3*f)*x^3)/(3*b^6) + ((b^2*d - 3*a*b*e + 6*a^2*f)*x^6)/(6*b^5) + ((b*e - 3*a*f)*x^9)/(9*b^4) + (f*x^12)/(12*b^3) + (a^3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(6*b^7*(a + b*x^3)^2) - (a^2*(3*b^3*c - 4*a*b^2*d + 5*a^2*b*e - 6*a^3*f))/(3*b^7*(a + b*x^3)) - (a*(3*b^3*c - 6*a*b^2*d + 10*a^2*b*e - 15*a^3*f)*log(a + b*x^3))/(3*b^7)]
    @test_int [x^8*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3)^3, x, 3, ((b^2*d - 3*a*b*e + 6*a^2*f)*x^3)/(3*b^5) + ((b*e - 3*a*f)*x^6)/(6*b^4) + (f*x^9)/(9*b^3) - (a^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(6*b^6*(a + b*x^3)^2) + (a*(2*b^3*c - 3*a*b^2*d + 4*a^2*b*e - 5*a^3*f))/(3*b^6*(a + b*x^3)) + ((b^3*c - 3*a*b^2*d + 6*a^2*b*e - 10*a^3*f)*log(a + b*x^3))/(3*b^6)]
    @test_int [x^5*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3)^3, x, 3, ((b*e - 3*a*f)*x^3)/(3*b^4) + (f*x^6)/(6*b^3) + (a*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(6*b^5*(a + b*x^3)^2) - (b^3*c - 2*a*b^2*d + 3*a^2*b*e - 4*a^3*f)/(3*b^5*(a + b*x^3)) + ((b^2*d - 3*a*b*e + 6*a^2*f)*log(a + b*x^3))/(3*b^5)]
    @test_int [x^2*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3)^3, x, 3, (f*x^3)/(3*b^3) - (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(6*b^4*(a + b*x^3)^2) - (b^2*d - 2*a*b*e + 3*a^2*f)/(3*b^4*(a + b*x^3)) + ((b*e - 3*a*f)*log(a + b*x^3))/(3*b^4)]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^1*(a + b*x^3)^3), x, 3, (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(6*a*b^3*(a + b*x^3)^2) + (b^3*c - a^2*b*e + 2*a^3*f)/(3*a^2*b^3*(a + b*x^3)) + (c*log(x))/a^3 - (1/3)*(c/a^3 - f/b^3)*log(a + b*x^3)]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^4*(a + b*x^3)^3), x, 3, -(c/(3*a^3*x^3)) - (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(6*a^2*b^2*(a + b*x^3)^2) - (2*b^3*c - a*b^2*d + a^3*f)/(3*a^3*b^2*(a + b*x^3)) - ((3*b*c - a*d)*log(x))/a^4 + ((3*b*c - a*d)*log(a + b*x^3))/(3*a^4)]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^7*(a + b*x^3)^3), x, 3, -(c/(6*a^3*x^6)) + (3*b*c - a*d)/(3*a^4*x^3) + (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(6*a^3*b*(a + b*x^3)^2) + (3*b^2*c - 2*a*b*d + a^2*e)/(3*a^4*(a + b*x^3)) + ((6*b^2*c - 3*a*b*d + a^2*e)*log(x))/a^5 - ((6*b^2*c - 3*a*b*d + a^2*e)*log(a + b*x^3))/(3*a^5)]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^10*(a + b*x^3)^3), x, 3, -(c/(9*a^3*x^9)) + (3*b*c - a*d)/(6*a^4*x^6) - (6*b^2*c - 3*a*b*d + a^2*e)/(3*a^5*x^3) - (b^3*c - a*b^2*d + a^2*b*e - a^3*f)/(6*a^4*(a + b*x^3)^2) - (4*b^3*c - 3*a*b^2*d + 2*a^2*b*e - a^3*f)/(3*a^5*(a + b*x^3)) - ((10*b^3*c - 6*a*b^2*d + 3*a^2*b*e - a^3*f)*log(x))/a^6 + ((10*b^3*c - 6*a*b^2*d + 3*a^2*b*e - a^3*f)*log(a + b*x^3))/(3*a^6)]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^13*(a + b*x^3)^3), x, 3, -(c/(12*a^3*x^12)) + (3*b*c - a*d)/(9*a^4*x^9) - (6*b^2*c - 3*a*b*d + a^2*e)/(6*a^5*x^6) + (10*b^3*c - 6*a*b^2*d + 3*a^2*b*e - a^3*f)/(3*a^6*x^3) + (b*(b^3*c - a*b^2*d + a^2*b*e - a^3*f))/(6*a^5*(a + b*x^3)^2) + (b*(5*b^3*c - 4*a*b^2*d + 3*a^2*b*e - 2*a^3*f))/(3*a^6*(a + b*x^3)) + (b*(15*b^3*c - 10*a*b^2*d + 6*a^2*b*e - 3*a^3*f)*log(x))/a^7 - (b*(15*b^3*c - 10*a*b^2*d + 6*a^2*b*e - 3*a^3*f)*log(a + b*x^3))/(3*a^7)]

    @test_int [x^12*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3)^3, x, 10, -((a*(3*b^3*c - 6*a*b^2*d + 10*a^2*b*e - 15*a^3*f)*x)/b^7) + ((b^3*c - 3*a*b^2*d + 6*a^2*b*e - 10*a^3*f)*x^4)/(4*b^6) + ((b^2*d - 3*a*b*e + 6*a^2*f)*x^7)/(7*b^5) + ((b*e - 3*a*f)*x^10)/(10*b^4) + (f*x^13)/(13*b^3) + (a^3*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(6*b^7*(a + b*x^3)^2) - (a^2*(19*b^3*c - 25*a*b^2*d + 31*a^2*b*e - 37*a^3*f)*x)/(18*b^7*(a + b*x^3)) - (a^(4/3)*(35*b^3*c - 65*a*b^2*d + 104*a^2*b*e - 152*a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*b^(22/3)) + (a^(4/3)*(35*b^3*c - 65*a*b^2*d + 104*a^2*b*e - 152*a^3*f)*log(a^(1/3) + b^(1/3)*x))/(27*b^(22/3)) - (a^(4/3)*(35*b^3*c - 65*a*b^2*d + 104*a^2*b*e - 152*a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*b^(22/3))]
    @test_int [x^10*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3)^3, x, 14, ((b^3*c - 3*a*b^2*d + 6*a^2*b*e - 10*a^3*f)*x^2)/(2*b^6) + ((b^2*d - 3*a*b*e + 6*a^2*f)*x^5)/(5*b^5) + ((b*e - 3*a*f)*x^8)/(8*b^4) + (f*x^11)/(11*b^3) - (a^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(6*b^6*(a + b*x^3)^2) + (a*(7*b^3*c - 10*a*b^2*d + 13*a^2*b*e - 16*a^3*f)*x^2)/(9*b^6*(a + b*x^3)) + (a^(2/3)*(20*b^3*c - 44*a*b^2*d + 77*a^2*b*e - 119*a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*b^(20/3)) + (a^(2/3)*(20*b^3*c - 44*a*b^2*d + 77*a^2*b*e - 119*a^3*f)*log(a^(1/3) + b^(1/3)*x))/(27*b^(20/3)) - (a^(2/3)*(20*b^3*c - 44*a*b^2*d + 77*a^2*b*e - 119*a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*b^(20/3))]
    @test_int [x^9*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3)^3, x, 10, ((b^3*c - 3*a*b^2*d + 6*a^2*b*e - 10*a^3*f)*x)/b^6 + ((b^2*d - 3*a*b*e + 6*a^2*f)*x^4)/(4*b^5) + ((b*e - 3*a*f)*x^7)/(7*b^4) + (f*x^10)/(10*b^3) - (a^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(6*b^6*(a + b*x^3)^2) + (a*(13*b^3*c - 19*a*b^2*d + 25*a^2*b*e - 31*a^3*f)*x)/(18*b^6*(a + b*x^3)) + (a^(1/3)*(14*b^3*c - 35*a*b^2*d + 65*a^2*b*e - 104*a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*b^(19/3)) - (a^(1/3)*(14*b^3*c - 35*a*b^2*d + 65*a^2*b*e - 104*a^3*f)*log(a^(1/3) + b^(1/3)*x))/(27*b^(19/3)) + (a^(1/3)*(14*b^3*c - 35*a*b^2*d + 65*a^2*b*e - 104*a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*b^(19/3))]
    @test_int [x^7*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3)^3, x, 13, ((b^2*d - 3*a*b*e + 6*a^2*f)*x^2)/(2*b^5) + ((b*e - 3*a*f)*x^5)/(5*b^4) + (f*x^8)/(8*b^3) + (a*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(6*b^5*(a + b*x^3)^2) - ((4*b^3*c - 7*a*b^2*d + 10*a^2*b*e - 13*a^3*f)*x^2)/(9*b^5*(a + b*x^3)) - ((5*b^3*c - 20*a*b^2*d + 44*a^2*b*e - 77*a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(1/3)*b^(17/3)) - ((5*b^3*c - 20*a*b^2*d + 44*a^2*b*e - 77*a^3*f)*log(a^(1/3) + b^(1/3)*x))/(27*a^(1/3)*b^(17/3)) + ((5*b^3*c - 20*a*b^2*d + 44*a^2*b*e - 77*a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(1/3)*b^(17/3))]
    @test_int [x^6*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3)^3, x, 10, ((b^2*d - 3*a*b*e + 6*a^2*f)*x)/b^5 + ((b*e - 3*a*f)*x^4)/(4*b^4) + (f*x^7)/(7*b^3) + (a*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(6*b^5*(a + b*x^3)^2) - ((7*b^3*c - 13*a*b^2*d + 19*a^2*b*e - 25*a^3*f)*x)/(18*b^5*(a + b*x^3)) - ((2*b^3*c - 14*a*b^2*d + 35*a^2*b*e - 65*a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(2/3)*b^(16/3)) + ((2*b^3*c - 14*a*b^2*d + 35*a^2*b*e - 65*a^3*f)*log(a^(1/3) + b^(1/3)*x))/(27*a^(2/3)*b^(16/3)) - ((2*b^3*c - 14*a*b^2*d + 35*a^2*b*e - 65*a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(2/3)*b^(16/3))]
    @test_int [x^4*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3)^3, x, 12, ((b*e - 3*a*f)*x^2)/(2*b^4) + (f*x^5)/(5*b^3) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(6*b^4*(a + b*x^3)^2) + ((b^3*c - 4*a*b^2*d + 7*a^2*b*e - 10*a^3*f)*x^2)/(9*a*b^4*(a + b*x^3)) - ((b^3*c + 5*a*b^2*d - 20*a^2*b*e + 44*a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(4/3)*b^(14/3)) - ((b^3*c + 5*a*b^2*d - 20*a^2*b*e + 44*a^3*f)*log(a^(1/3) + b^(1/3)*x))/(27*a^(4/3)*b^(14/3)) + ((b^3*c + 5*a*b^2*d - 20*a^2*b*e + 44*a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(4/3)*b^(14/3))]
    @test_int [x^3*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3)^3, x, 10, ((b*e - 3*a*f)*x)/b^4 + (f*x^4)/(4*b^3) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(6*b^4*(a + b*x^3)^2) + ((b^3*c - 7*a*b^2*d + 13*a^2*b*e - 19*a^3*f)*x)/(18*a*b^4*(a + b*x^3)) - ((b^3*c + 2*a*b^2*d - 14*a^2*b*e + 35*a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(5/3)*b^(13/3)) + ((b^3*c + 2*a*b^2*d - 14*a^2*b*e + 35*a^3*f)*log(a^(1/3) + b^(1/3)*x))/(27*a^(5/3)*b^(13/3)) - ((b^3*c + 2*a*b^2*d - 14*a^2*b*e + 35*a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(5/3)*b^(13/3))]
    @test_int [x^1*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3)^3, x, 10, (f*x^2)/(2*b^3) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(6*a*b^3*(a + b*x^3)^2) + ((2*b^3*c + a*b^2*d - 4*a^2*b*e + 7*a^3*f)*x^2)/(9*a^2*b^3*(a + b*x^3)) - ((2*b^3*c + a*b^2*d + 5*a^2*b*e - 20*a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(7/3)*b^(11/3)) - ((2*b^3*c + a*b^2*d + 5*a^2*b*e - 20*a^3*f)*log(a^(1/3) + b^(1/3)*x))/(27*a^(7/3)*b^(11/3)) + ((2*b^3*c + a*b^2*d + 5*a^2*b*e - 20*a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(7/3)*b^(11/3))]
    @test_int [x^0*(c + d*x^3 + e*x^6 + f*x^9)/(a + b*x^3)^3, x, 9, (f*x)/b^3 + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(6*a*b^3*(a + b*x^3)^2) + ((5*b^3*c + a*b^2*d - 7*a^2*b*e + 13*a^3*f)*x)/(18*a^2*b^3*(a + b*x^3)) - ((5*b^3*c + a*b^2*d + 2*a^2*b*e - 14*a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(8/3)*b^(10/3)) + ((5*b^3*c + a*b^2*d + 2*a^2*b*e - 14*a^3*f)*log(a^(1/3) + b^(1/3)*x))/(27*a^(8/3)*b^(10/3)) - ((5*b^3*c + a*b^2*d + 2*a^2*b*e - 14*a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(8/3)*b^(10/3))]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^2*(a + b*x^3)^3), x, 9, -(c/(a^3*x)) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(6*a^2*b^2*(a + b*x^3)^2) - ((5*b^3*c - 2*a*b^2*d - a^2*b*e + 4*a^3*f)*x^2)/(9*a^3*b^2*(a + b*x^3)) + ((14*b^3*c - 2*a*b^2*d - a^2*b*e - 5*a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(10/3)*b^(8/3)) + ((14*b^3*c - 2*a*b^2*d - a^2*b*e - 5*a^3*f)*log(a^(1/3) + b^(1/3)*x))/(27*a^(10/3)*b^(8/3)) - ((14*b^3*c - 2*a*b^2*d - a^2*b*e - 5*a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(10/3)*b^(8/3))]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^3*(a + b*x^3)^3), x, 9, -(c/(2*a^3*x^2)) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(6*a^2*b^2*(a + b*x^3)^2) - ((11*b^3*c - 5*a*b^2*d - a^2*b*e + 7*a^3*f)*x)/(18*a^3*b^2*(a + b*x^3)) + ((20*b^3*c - 5*a*b^2*d - a^2*b*e - 2*a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(11/3)*b^(7/3)) - ((20*b^3*c - 5*a*b^2*d - a^2*b*e - 2*a^3*f)*log(a^(1/3) + b^(1/3)*x))/(27*a^(11/3)*b^(7/3)) + ((20*b^3*c - 5*a*b^2*d - a^2*b*e - 2*a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(11/3)*b^(7/3))]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^5*(a + b*x^3)^3), x, 10, -(c/(4*a^3*x^4)) + (3*b*c - a*d)/(a^4*x) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(6*a^3*b*(a + b*x^3)^2) + ((8*b^3*c - 5*a*b^2*d + 2*a^2*b*e + a^3*f)*x^2)/(9*a^4*b*(a + b*x^3)) - ((35*b^3*c - 14*a*b^2*d + 2*a^2*b*e + a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(13/3)*b^(5/3)) - ((35*b^3*c - 14*a*b^2*d + 2*a^2*b*e + a^3*f)*log(a^(1/3) + b^(1/3)*x))/(27*a^(13/3)*b^(5/3)) + ((35*b^3*c - 14*a*b^2*d + 2*a^2*b*e + a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(13/3)*b^(5/3))]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^6*(a + b*x^3)^3), x, 10, -(c/(5*a^3*x^5)) + (3*b*c - a*d)/(2*a^4*x^2) + ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(6*a^3*b*(a + b*x^3)^2) + ((17*b^3*c - 11*a*b^2*d + 5*a^2*b*e + a^3*f)*x)/(18*a^4*b*(a + b*x^3)) - ((44*b^3*c - 20*a*b^2*d + 5*a^2*b*e + a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(14/3)*b^(4/3)) + ((44*b^3*c - 20*a*b^2*d + 5*a^2*b*e + a^3*f)*log(a^(1/3) + b^(1/3)*x))/(27*a^(14/3)*b^(4/3)) - ((44*b^3*c - 20*a*b^2*d + 5*a^2*b*e + a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(14/3)*b^(4/3))]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^8*(a + b*x^3)^3), x, 10, -(c/(7*a^3*x^7)) + (3*b*c - a*d)/(4*a^4*x^4) - (6*b^2*c - 3*a*b*d + a^2*e)/(a^5*x) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(6*a^4*(a + b*x^3)^2) - ((11*b^3*c - 8*a*b^2*d + 5*a^2*b*e - 2*a^3*f)*x^2)/(9*a^5*(a + b*x^3)) + ((65*b^3*c - 35*a*b^2*d + 14*a^2*b*e - 2*a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(16/3)*b^(2/3)) + ((65*b^3*c - 35*a*b^2*d + 14*a^2*b*e - 2*a^3*f)*log(a^(1/3) + b^(1/3)*x))/(27*a^(16/3)*b^(2/3)) - ((65*b^3*c - 35*a*b^2*d + 14*a^2*b*e - 2*a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(16/3)*b^(2/3))]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^9*(a + b*x^3)^3), x, 10, -c/(8*a^3*x^8) + (3*b*c - a*d)/(5*a^4*x^5) - (6*b^2*c - 3*a*b*d + a^2*e)/(2*a^5*x^2) - ((b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(6*a^4*(a + b*x^3)^2) - ((23*b^3*c - 17*a*b^2*d + 11*a^2*b*e - 5*a^3*f)*x)/(18*a^5*(a + b*x^3)) + ((77*b^3*c - 44*a*b^2*d + 20*a^2*b*e - 5*a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(17/3)*b^(1/3)) - ((77*b^3*c - 44*a*b^2*d + 20*a^2*b*e - 5*a^3*f)*log(a^(1/3) + b^(1/3)*x))/(27*a^(17/3)*b^(1/3)) + ((77*b^3*c - 44*a*b^2*d + 20*a^2*b*e - 5*a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(17/3)*b^(1/3))]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^11*(a + b*x^3)^3), x, 10, -(c/(10*a^3*x^10)) + (3*b*c - a*d)/(7*a^4*x^7) - (6*b^2*c - 3*a*b*d + a^2*e)/(4*a^5*x^4) + (10*b^3*c - 6*a*b^2*d + 3*a^2*b*e - a^3*f)/(a^6*x) + (b*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(6*a^5*(a + b*x^3)^2) + (b*(14*b^3*c - 11*a*b^2*d + 8*a^2*b*e - 5*a^3*f)*x^2)/(9*a^6*(a + b*x^3)) - (b^(1/3)*(104*b^3*c - 65*a*b^2*d + 35*a^2*b*e - 14*a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(19/3)) - (b^(1/3)*(104*b^3*c - 65*a*b^2*d + 35*a^2*b*e - 14*a^3*f)*log(a^(1/3) + b^(1/3)*x))/(27*a^(19/3)) + (b^(1/3)*(104*b^3*c - 65*a*b^2*d + 35*a^2*b*e - 14*a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(19/3))]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^12*(a + b*x^3)^3), x, 10, -c/(11*a^3*x^11) + (3*b*c - a*d)/(8*a^4*x^8) - (6*b^2*c - 3*a*b*d + a^2*e)/(5*a^5*x^5) + (10*b^3*c - 6*a*b^2*d + 3*a^2*b*e - a^3*f)/(2*a^6*x^2) + (b*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x)/(6*a^5*(a + b*x^3)^2) + (b*(29*b^3*c - 23*a*b^2*d + 17*a^2*b*e - 11*a^3*f)*x)/(18*a^6*(a + b*x^3)) - (b^(2/3)*(119*b^3*c - 77*a*b^2*d + 44*a^2*b*e - 20*a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(20/3)) + (b^(2/3)*(119*b^3*c - 77*a*b^2*d + 44*a^2*b*e - 20*a^3*f)*log(a^(1/3) + b^(1/3)*x))/(27*a^(20/3)) - (b^(2/3)*(119*b^3*c - 77*a*b^2*d + 44*a^2*b*e - 20*a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(20/3))]
    @test_int [(c + d*x^3 + e*x^6 + f*x^9)/(x^14*(a + b*x^3)^3), x, 10, -(c/(13*a^3*x^13)) + (3*b*c - a*d)/(10*a^4*x^10) - (6*b^2*c - 3*a*b*d + a^2*e)/(7*a^5*x^7) + (10*b^3*c - 6*a*b^2*d + 3*a^2*b*e - a^3*f)/(4*a^6*x^4) - (b*(15*b^3*c - 10*a*b^2*d + 6*a^2*b*e - 3*a^3*f))/(a^7*x) - (b^2*(b^3*c - a*b^2*d + a^2*b*e - a^3*f)*x^2)/(6*a^6*(a + b*x^3)^2) - (b^2*(17*b^3*c - 14*a*b^2*d + 11*a^2*b*e - 8*a^3*f)*x^2)/(9*a^7*(a + b*x^3)) + (b^(4/3)*(152*b^3*c - 104*a*b^2*d + 65*a^2*b*e - 35*a^3*f)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(22/3)) + (b^(4/3)*(152*b^3*c - 104*a*b^2*d + 65*a^2*b*e - 35*a^3*f)*log(a^(1/3) + b^(1/3)*x))/(27*a^(22/3)) - (b^(4/3)*(152*b^3*c - 104*a*b^2*d + 65*a^2*b*e - 35*a^3*f)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(22/3))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*P1(x)*(a+b*x^3)^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^4*(1 - x)/(1 + x^3), x, 8, x^2/2 - x^3/3 + atan((1 - 2*x)/sqrt(3))/sqrt(3) + (2/3)*log(1 + x) + (1/6)*log(1 - x + x^2)]
    @test_int [x^3*(1 - x)/(1 + x^3), x, 5, x - x^2/2 - (2/3)*log(1 + x) + (1/3)*log(1 - x + x^2)]
    @test_int [x^2*(1 - x)/(1 + x^3), x, 8, -x - atan((1 - 2*x)/sqrt(3))/sqrt(3) + (2/3)*log(1 + x) + (1/6)*log(1 - x + x^2)]
    @test_int [x^1*(1 - x)/(1 + x^3), x, 6, -(atan((1 - 2*x)/sqrt(3))/sqrt(3)) - (2/3)*log(1 + x) - (1/6)*log(1 - x + x^2)]
    @test_int [(1 - x)/(x^1*(1 + x^3)), x, 6, atan((1 - 2*x)/sqrt(3))/sqrt(3) + log(x) - (2/3)*log(1 + x) - (1/6)*log(1 - x + x^2)]
    @test_int [(1 - x)/(x^2*(1 + x^3)), x, 6, -(1/x) + atan((1 - 2*x)/sqrt(3))/sqrt(3) - log(x) + (2/3)*log(1 + x) + (1/6)*log(1 - x + x^2)]
    @test_int [(1 - x)/(x^3*(1 + x^3)), x, 3, -(1/(2*x^2)) + 1/x - (2/3)*log(1 + x) + (1/3)*log(1 - x + x^2)]

    @test_int [x*(1 + 2*x)/(1 + x^3), x, 6, -(atan((1 - 2*x)/sqrt(3))/sqrt(3)) + (1/3)*log(1 + x) + (5/6)*log(1 - x + x^2)]
    @test_int [x*(1 + 2*x)/(1 - x^3), x, 6, -atan((1 + 2*x)/sqrt(3))/sqrt(3) - log(1 - x) - (1/2)*log(1 + x + x^2)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*P2(x)*(a+b*x^3)^p=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^2*(c + d*x + e*x^2)*(a + b*x^3), x, 2, (1/3)*a*c*x^3 + (1/4)*a*d*x^4 + (1/5)*a*e*x^5 + (1/6)*b*c*x^6 + (1/7)*b*d*x^7 + (1/8)*b*e*x^8]
    @test_int [x^1*(c + d*x + e*x^2)*(a + b*x^3), x, 2, (1/2)*a*c*x^2 + (1/3)*a*d*x^3 + (1/4)*a*e*x^4 + (1/5)*b*c*x^5 + (1/6)*b*d*x^6 + (1/7)*b*e*x^7]
    @test_int [x^0*(c + d*x + e*x^2)*(a + b*x^3), x, 2, a*c*x + (1/2)*a*d*x^2 + (1/3)*a*e*x^3 + (1/4)*b*c*x^4 + (1/5)*b*d*x^5 + (1/6)*b*e*x^6]
    @test_int [(c + d*x + e*x^2)*(a + b*x^3)/x^1, x, 2, a*d*x + (1/2)*a*e*x^2 + (1/3)*b*c*x^3 + (1/4)*b*d*x^4 + (1/5)*b*e*x^5 + a*c*log(x)]
    @test_int [(c + d*x + e*x^2)*(a + b*x^3)/x^2, x, 2, -((a*c)/x) + a*e*x + (1/2)*b*c*x^2 + (1/3)*b*d*x^3 + (1/4)*b*e*x^4 + a*d*log(x)]
    @test_int [(c + d*x + e*x^2)*(a + b*x^3)/x^3, x, 2, -((a*c)/(2*x^2)) - (a*d)/x + b*c*x + (1/2)*b*d*x^2 + (1/3)*b*e*x^3 + a*e*log(x)]

    @test_int [x^2*(c + d*x + e*x^2)*(a + b*x^3)^2, x, 3, (1/4)*a^2*d*x^4 + (1/5)*a^2*e*x^5 + (2/7)*a*b*d*x^7 + (1/4)*a*b*e*x^8 + (1/10)*b^2*d*x^10 + (1/11)*b^2*e*x^11 + (c*(a + b*x^3)^3)/(9*b)]
    @test_int [x^1*(c + d*x + e*x^2)*(a + b*x^3)^2, x, 3, (1/2)*a^2*c*x^2 + (1/4)*a^2*e*x^4 + (2/5)*a*b*c*x^5 + (2/7)*a*b*e*x^7 + (1/8)*b^2*c*x^8 + (1/10)*b^2*e*x^10 + (d*(a + b*x^3)^3)/(9*b)]
    @test_int [x^0*(c + d*x + e*x^2)*(a + b*x^3)^2, x, 3, a^2*c*x + (1/2)*a^2*d*x^2 + (1/2)*a*b*c*x^4 + (2/5)*a*b*d*x^5 + (1/7)*b^2*c*x^7 + (1/8)*b^2*d*x^8 + (e*(a + b*x^3)^3)/(9*b)]
    @test_int [(c + d*x + e*x^2)*(a + b*x^3)^2/x^1, x, 2, a^2*d*x + (1/2)*a^2*e*x^2 + (2/3)*a*b*c*x^3 + (1/2)*a*b*d*x^4 + (2/5)*a*b*e*x^5 + (1/6)*b^2*c*x^6 + (1/7)*b^2*d*x^7 + (1/8)*b^2*e*x^8 + a^2*c*log(x)]
    @test_int [(c + d*x + e*x^2)*(a + b*x^3)^2/x^2, x, 2, -((a^2*c)/x) + a^2*e*x + a*b*c*x^2 + (2/3)*a*b*d*x^3 + (1/2)*a*b*e*x^4 + (1/5)*b^2*c*x^5 + (1/6)*b^2*d*x^6 + (1/7)*b^2*e*x^7 + a^2*d*log(x)]
    @test_int [(c + d*x + e*x^2)*(a + b*x^3)^2/x^3, x, 2, -((a^2*c)/(2*x^2)) - (a^2*d)/x + 2*a*b*c*x + a*b*d*x^2 + (2/3)*a*b*e*x^3 + (1/4)*b^2*c*x^4 + (1/5)*b^2*d*x^5 + (1/6)*b^2*e*x^6 + a^2*e*log(x)]

    @test_int [x^2*(c + d*x + e*x^2)*(a + b*x^3)^3, x, 3, (1/4)*a^3*d*x^4 + (1/5)*a^3*e*x^5 + (3/7)*a^2*b*d*x^7 + (3/8)*a^2*b*e*x^8 + (3/10)*a*b^2*d*x^10 + (3/11)*a*b^2*e*x^11 + (1/13)*b^3*d*x^13 + (1/14)*b^3*e*x^14 + (c*(a + b*x^3)^4)/(12*b)]
    @test_int [x^1*(c + d*x + e*x^2)*(a + b*x^3)^3, x, 3, (1/2)*a^3*c*x^2 + (1/4)*a^3*e*x^4 + (3/5)*a^2*b*c*x^5 + (3/7)*a^2*b*e*x^7 + (3/8)*a*b^2*c*x^8 + (3/10)*a*b^2*e*x^10 + (1/11)*b^3*c*x^11 + (1/13)*b^3*e*x^13 + (d*(a + b*x^3)^4)/(12*b)]
    @test_int [x^0*(c + d*x + e*x^2)*(a + b*x^3)^3, x, 3, a^3*c*x + (1/2)*a^3*d*x^2 + (3/4)*a^2*b*c*x^4 + (3/5)*a^2*b*d*x^5 + (3/7)*a*b^2*c*x^7 + (3/8)*a*b^2*d*x^8 + (1/10)*b^3*c*x^10 + (1/11)*b^3*d*x^11 + (e*(a + b*x^3)^4)/(12*b)]
    @test_int [(c + d*x + e*x^2)*(a + b*x^3)^3/x^1, x, 2, a^3*d*x + (1/2)*a^3*e*x^2 + a^2*b*c*x^3 + (3/4)*a^2*b*d*x^4 + (3/5)*a^2*b*e*x^5 + (1/2)*a*b^2*c*x^6 + (3/7)*a*b^2*d*x^7 + (3/8)*a*b^2*e*x^8 + (1/9)*b^3*c*x^9 + (1/10)*b^3*d*x^10 + (1/11)*b^3*e*x^11 + a^3*c*log(x)]
    @test_int [(c + d*x + e*x^2)*(a + b*x^3)^3/x^2, x, 2, -((a^3*c)/x) + a^3*e*x + (3/2)*a^2*b*c*x^2 + a^2*b*d*x^3 + (3/4)*a^2*b*e*x^4 + (3/5)*a*b^2*c*x^5 + (1/2)*a*b^2*d*x^6 + (3/7)*a*b^2*e*x^7 + (1/8)*b^3*c*x^8 + (1/9)*b^3*d*x^9 + (1/10)*b^3*e*x^10 + a^3*d*log(x)]
    @test_int [(c + d*x + e*x^2)*(a + b*x^3)^3/x^3, x, 2, -((a^3*c)/(2*x^2)) - (a^3*d)/x + 3*a^2*b*c*x + (3/2)*a^2*b*d*x^2 + a^2*b*e*x^3 + (3/4)*a*b^2*c*x^4 + (3/5)*a*b^2*d*x^5 + (1/2)*a*b^2*e*x^6 + (1/7)*b^3*c*x^7 + (1/8)*b^3*d*x^8 + (1/9)*b^3*e*x^9 + a^3*e*log(x)]

    @test_int [x^2*(c + d*x + e*x^2)*(a + b*x^3)^4, x, 3, (1/4)*a^4*d*x^4 + (1/5)*a^4*e*x^5 + (4/7)*a^3*b*d*x^7 + (1/2)*a^3*b*e*x^8 + (3/5)*a^2*b^2*d*x^10 + (6/11)*a^2*b^2*e*x^11 + (4/13)*a*b^3*d*x^13 + (2/7)*a*b^3*e*x^14 + (1/16)*b^4*d*x^16 + (1/17)*b^4*e*x^17 + (c*(a + b*x^3)^5)/(15*b)]
    @test_int [x^1*(c + d*x + e*x^2)*(a + b*x^3)^4, x, 3, (1/2)*a^4*c*x^2 + (1/4)*a^4*e*x^4 + (4/5)*a^3*b*c*x^5 + (4/7)*a^3*b*e*x^7 + (3/4)*a^2*b^2*c*x^8 + (3/5)*a^2*b^2*e*x^10 + (4/11)*a*b^3*c*x^11 + (4/13)*a*b^3*e*x^13 + (1/14)*b^4*c*x^14 + (1/16)*b^4*e*x^16 + (d*(a + b*x^3)^5)/(15*b)]
    @test_int [x^0*(c + d*x + e*x^2)*(a + b*x^3)^4, x, 3, a^4*c*x + (1/2)*a^4*d*x^2 + a^3*b*c*x^4 + (4/5)*a^3*b*d*x^5 + (6/7)*a^2*b^2*c*x^7 + (3/4)*a^2*b^2*d*x^8 + (2/5)*a*b^3*c*x^10 + (4/11)*a*b^3*d*x^11 + (1/13)*b^4*c*x^13 + (1/14)*b^4*d*x^14 + (e*(a + b*x^3)^5)/(15*b)]
    @test_int [(c + d*x + e*x^2)*(a + b*x^3)^4/x^1, x, 2, a^4*d*x + (1/2)*a^4*e*x^2 + (4/3)*a^3*b*c*x^3 + a^3*b*d*x^4 + (4/5)*a^3*b*e*x^5 + a^2*b^2*c*x^6 + (6/7)*a^2*b^2*d*x^7 + (3/4)*a^2*b^2*e*x^8 + (4/9)*a*b^3*c*x^9 + (2/5)*a*b^3*d*x^10 + (4/11)*a*b^3*e*x^11 + (1/12)*b^4*c*x^12 + (1/13)*b^4*d*x^13 + (1/14)*b^4*e*x^14 + a^4*c*log(x)]
    @test_int [(c + d*x + e*x^2)*(a + b*x^3)^4/x^2, x, 2, -((a^4*c)/x) + a^4*e*x + 2*a^3*b*c*x^2 + (4/3)*a^3*b*d*x^3 + a^3*b*e*x^4 + (6/5)*a^2*b^2*c*x^5 + a^2*b^2*d*x^6 + (6/7)*a^2*b^2*e*x^7 + (1/2)*a*b^3*c*x^8 + (4/9)*a*b^3*d*x^9 + (2/5)*a*b^3*e*x^10 + (1/11)*b^4*c*x^11 + (1/12)*b^4*d*x^12 + (1/13)*b^4*e*x^13 + a^4*d*log(x)]
    @test_int [(c + d*x + e*x^2)*(a + b*x^3)^4/x^3, x, 2, -((a^4*c)/(2*x^2)) - (a^4*d)/x + 4*a^3*b*c*x + 2*a^3*b*d*x^2 + (4/3)*a^3*b*e*x^3 + (3/2)*a^2*b^2*c*x^4 + (6/5)*a^2*b^2*d*x^5 + a^2*b^2*e*x^6 + (4/7)*a*b^3*c*x^7 + (1/2)*a*b^3*d*x^8 + (4/9)*a*b^3*e*x^9 + (1/10)*b^4*c*x^10 + (1/11)*b^4*d*x^11 + (1/12)*b^4*e*x^12 + a^4*e*log(x)]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^3*(c + d*x + e*x^2)/(a + b*x^3), x, 10, (c*x)/b + (d*x^2)/(2*b) + (e*x^3)/(3*b) + (a^(1/3)*(b^(1/3)*c + a^(1/3)*d)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^(5/3)) - (a^(1/3)*(b^(1/3)*c - a^(1/3)*d)*log(a^(1/3) + b^(1/3)*x))/(3*b^(5/3)) + (a^(1/3)*(c - (a^(1/3)*d)/b^(1/3))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*b^(4/3)) - (a*e*log(a + b*x^3))/(3*b^2)]
    @test_int [x^2*(c + d*x + e*x^2)/(a + b*x^3), x, 10, (d*x)/b + (e*x^2)/(2*b) + (a^(1/3)*(b^(1/3)*d + a^(1/3)*e)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^(5/3)) - (a^(1/3)*(b^(1/3)*d - a^(1/3)*e)*log(a^(1/3) + b^(1/3)*x))/(3*b^(5/3)) + (a^(1/3)*(d - (a^(1/3)*e)/b^(1/3))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*b^(4/3)) + (c*log(a + b*x^3))/(3*b)]
    @test_int [x^1*(c + d*x + e*x^2)/(a + b*x^3), x, 10, (e*x)/b - ((b^(2/3)*c - a^(2/3)*e)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(1/3)*b^(4/3)) - ((b^(2/3)*c + a^(2/3)*e)*log(a^(1/3) + b^(1/3)*x))/(3*a^(1/3)*b^(4/3)) + ((b^(2/3)*c + a^(2/3)*e)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(1/3)*b^(4/3)) + (d*log(a + b*x^3))/(3*b)]
    @test_int [x^0*(c + d*x + e*x^2)/(a + b*x^3), x, 8, -(((b^(1/3)*c + a^(1/3)*d)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(2/3)*b^(2/3))) + ((b^(1/3)*c - a^(1/3)*d)*log(a^(1/3) + b^(1/3)*x))/(3*a^(2/3)*b^(2/3)) - ((c - (a^(1/3)*d)/b^(1/3))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(2/3)*b^(1/3)) + (e*log(a + b*x^3))/(3*b)]
    @test_int [(c + d*x + e*x^2)/(x^1*(a + b*x^3)), x, 10, -(((b^(1/3)*d + a^(1/3)*e)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(2/3)*b^(2/3))) + (c*log(x))/a + ((b^(1/3)*d - a^(1/3)*e)*log(a^(1/3) + b^(1/3)*x))/(3*a^(2/3)*b^(2/3)) - ((d - (a^(1/3)*e)/b^(1/3))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(2/3)*b^(1/3)) - (c*log(a + b*x^3))/(3*a)]
    @test_int [(c + d*x + e*x^2)/(x^2*(a + b*x^3)), x, 10, -(c/(a*x)) + ((b^(2/3)*c - a^(2/3)*e)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(4/3)*b^(1/3)) + (d*log(x))/a + ((b^(2/3)*c + a^(2/3)*e)*log(a^(1/3) + b^(1/3)*x))/(3*a^(4/3)*b^(1/3)) - ((b^(2/3)*c + a^(2/3)*e)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(4/3)*b^(1/3)) - (d*log(a + b*x^3))/(3*a)]
    @test_int [(c + d*x + e*x^2)/(x^3*(a + b*x^3)), x, 10, -(c/(2*a*x^2)) - d/(a*x) + (b^(1/3)*(b^(1/3)*c + a^(1/3)*d)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(5/3)) + (e*log(x))/a - (b^(1/3)*(b^(1/3)*c - a^(1/3)*d)*log(a^(1/3) + b^(1/3)*x))/(3*a^(5/3)) + (b^(2/3)*(c - (a^(1/3)*d)/b^(1/3))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(5/3)) - (e*log(a + b*x^3))/(3*a)]

    @test_int [x^2*(c + d*x + e*x^2)/(a + b*x^3)^2, x, 7, -((c + d*x + e*x^2)/(3*b*(a + b*x^3))) - ((b^(1/3)*d + 2*a^(1/3)*e)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(2/3)*b^(5/3)) + ((b^(1/3)*d - 2*a^(1/3)*e)*log(a^(1/3) + b^(1/3)*x))/(9*a^(2/3)*b^(5/3)) - ((d - (2*a^(1/3)*e)/b^(1/3))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(2/3)*b^(4/3))]
    @test_int [x^1*(c + d*x + e*x^2)/(a + b*x^3)^2, x, 7, -((x*(a*e - b*c*x - b*d*x^2))/(3*a*b*(a + b*x^3))) - ((b^(2/3)*c + a^(2/3)*e)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(4/3)*b^(4/3)) - ((b^(2/3)*c - a^(2/3)*e)*log(a^(1/3) + b^(1/3)*x))/(9*a^(4/3)*b^(4/3)) + ((b^(2/3)*c - a^(2/3)*e)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(4/3)*b^(4/3))]
    @test_int [x^0*(c + d*x + e*x^2)/(a + b*x^3)^2, x, 7, -((a*e - b*x*(c + d*x))/(3*a*b*(a + b*x^3))) - ((2*b^(1/3)*c + a^(1/3)*d)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(5/3)*b^(2/3)) + ((2*b^(1/3)*c - a^(1/3)*d)*log(a^(1/3) + b^(1/3)*x))/(9*a^(5/3)*b^(2/3)) - ((2*b^(1/3)*c - a^(1/3)*d)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(5/3)*b^(2/3))]
    @test_int [(c + d*x + e*x^2)/(x^1*(a + b*x^3)^2), x, 11, (x*(a*d + a*e*x - b*c*x^2))/(3*a^2*(a + b*x^3)) - ((2*b^(1/3)*d + a^(1/3)*e)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(5/3)*b^(2/3)) + (c*log(x))/a^2 + ((2*b^(1/3)*d - a^(1/3)*e)*log(a^(1/3) + b^(1/3)*x))/(9*a^(5/3)*b^(2/3)) - ((2*b^(1/3)*d - a^(1/3)*e)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(5/3)*b^(2/3)) - (c*log(a + b*x^3))/(3*a^2)]
    @test_int [(c + d*x + e*x^2)/(x^2*(a + b*x^3)^2), x, 11, -(c/(a^2*x)) + (x*(a*e - b*c*x - b*d*x^2))/(3*a^2*(a + b*x^3)) + (2*(2*b^(2/3)*c - a^(2/3)*e)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(7/3)*b^(1/3)) + (d*log(x))/a^2 + (2*(2*b^(2/3)*c + a^(2/3)*e)*log(a^(1/3) + b^(1/3)*x))/(9*a^(7/3)*b^(1/3)) - ((2*b^(2/3)*c + a^(2/3)*e)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(9*a^(7/3)*b^(1/3)) - (d*log(a + b*x^3))/(3*a^2)]
    @test_int [(c + d*x + e*x^2)/(x^3*(a + b*x^3)^2), x, 11, -(c/(2*a^2*x^2)) - d/(a^2*x) - (x*(b*c + b*d*x + b*e*x^2))/(3*a^2*(a + b*x^3)) + (b^(1/3)*(5*b^(1/3)*c + 4*a^(1/3)*d)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(8/3)) + (e*log(x))/a^2 - (b^(1/3)*(5*b^(1/3)*c - 4*a^(1/3)*d)*log(a^(1/3) + b^(1/3)*x))/(9*a^(8/3)) + (b^(1/3)*(5*b^(1/3)*c - 4*a^(1/3)*d)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(8/3)) - (e*log(a + b*x^3))/(3*a^2)]
    @test_int [(c + d*x + e*x^2)/(x^4*(a + b*x^3)^2), x, 11, -(c/(3*a^2*x^3)) - d/(2*a^2*x^2) - e/(a^2*x) - (x*(b*d + b*e*x - (b^2*c*x^2)/a))/(3*a^2*(a + b*x^3)) + (b^(1/3)*(5*b^(1/3)*d + 4*a^(1/3)*e)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(8/3)) - (2*b*c*log(x))/a^3 - (b^(1/3)*(5*b^(1/3)*d - 4*a^(1/3)*e)*log(a^(1/3) + b^(1/3)*x))/(9*a^(8/3)) + (b^(1/3)*(5*b^(1/3)*d - 4*a^(1/3)*e)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(8/3)) + (2*b*c*log(a + b*x^3))/(3*a^3)]

    @test_int [x^2*(c + d*x + e*x^2)/(a + b*x^3)^3, x, 8, -((c + d*x + e*x^2)/(6*b*(a + b*x^3)^2)) + (x*(d + 2*e*x))/(18*a*b*(a + b*x^3)) - ((b^(1/3)*d + a^(1/3)*e)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(5/3)*b^(5/3)) + ((b^(1/3)*d - a^(1/3)*e)*log(a^(1/3) + b^(1/3)*x))/(27*a^(5/3)*b^(5/3)) - ((d - (a^(1/3)*e)/b^(1/3))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(5/3)*b^(4/3))]
    @test_int [x^1*(c + d*x + e*x^2)/(a + b*x^3)^3, x, 8, -((x*(a*e - b*c*x - b*d*x^2))/(6*a*b*(a + b*x^3)^2)) - (3*a*d - x*(a*e + 4*b*c*x))/(18*a^2*b*(a + b*x^3)) - ((2*b^(2/3)*c + a^(2/3)*e)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(7/3)*b^(4/3)) - ((2*b^(2/3)*c - a^(2/3)*e)*log(a^(1/3) + b^(1/3)*x))/(27*a^(7/3)*b^(4/3)) + ((2*b^(2/3)*c - a^(2/3)*e)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(7/3)*b^(4/3))]
    @test_int [x^0*(c + d*x + e*x^2)/(a + b*x^3)^3, x, 8, (x*(5*c + 4*d*x))/(18*a^2*(a + b*x^3)) - (a*e - b*x*(c + d*x))/(6*a*b*(a + b*x^3)^2) - ((5*b^(1/3)*c + 2*a^(1/3)*d)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(8/3)*b^(2/3)) + ((5*b^(1/3)*c - 2*a^(1/3)*d)*log(a^(1/3) + b^(1/3)*x))/(27*a^(8/3)*b^(2/3)) - ((5*b^(1/3)*c - 2*a^(1/3)*d)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(8/3)*b^(2/3))]
    @test_int [(c + d*x + e*x^2)/(x^1*(a + b*x^3)^3), x, 12, (x*(a*d + a*e*x - b*c*x^2))/(6*a^2*(a + b*x^3)^2) + (x*(5*a*d + 4*a*e*x - 9*b*c*x^2))/(18*a^3*(a + b*x^3)) - ((5*b^(1/3)*d + 2*a^(1/3)*e)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(8/3)*b^(2/3)) + (c*log(x))/a^3 + ((5*b^(1/3)*d - 2*a^(1/3)*e)*log(a^(1/3) + b^(1/3)*x))/(27*a^(8/3)*b^(2/3)) - ((5*b^(1/3)*d - 2*a^(1/3)*e)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(8/3)*b^(2/3)) - (c*log(a + b*x^3))/(3*a^3)]
    @test_int [(c + d*x + e*x^2)/(x^2*(a + b*x^3)^3), x, 12, -(c/(a^3*x)) + (x*(a*e - b*c*x - b*d*x^2))/(6*a^2*(a + b*x^3)^2) + (x*(5*a*e - 10*b*c*x - 9*b*d*x^2))/(18*a^3*(a + b*x^3)) + ((14*b^(2/3)*c - 5*a^(2/3)*e)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(10/3)*b^(1/3)) + (d*log(x))/a^3 + ((14*b^(2/3)*c + 5*a^(2/3)*e)*log(a^(1/3) + b^(1/3)*x))/(27*a^(10/3)*b^(1/3)) - ((14*b^(2/3)*c + 5*a^(2/3)*e)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(10/3)*b^(1/3)) - (d*log(a + b*x^3))/(3*a^3)]
    @test_int [(c + d*x + e*x^2)/(x^3*(a + b*x^3)^3), x, 12, -(c/(2*a^3*x^2)) - d/(a^3*x) - (x*(b*c + b*d*x + b*e*x^2))/(6*a^2*(a + b*x^3)^2) - (x*(11*b*c + 10*b*d*x + 9*b*e*x^2))/(18*a^3*(a + b*x^3)) + (2*b^(1/3)*(10*b^(1/3)*c + 7*a^(1/3)*d)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(11/3)) + (e*log(x))/a^3 - (2*b^(1/3)*(10*b^(1/3)*c - 7*a^(1/3)*d)*log(a^(1/3) + b^(1/3)*x))/(27*a^(11/3)) + (b^(1/3)*(10*b^(1/3)*c - 7*a^(1/3)*d)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(27*a^(11/3)) - (e*log(a + b*x^3))/(3*a^3)]
    @test_int [(c + d*x + e*x^2)/(x^4*(a + b*x^3)^3), x, 12, -(c/(3*a^3*x^3)) - d/(2*a^3*x^2) - e/(a^3*x) - (x*(b*d + b*e*x - (b^2*c*x^2)/a))/(6*a^2*(a + b*x^3)^2) - (x*(11*b*d + 10*b*e*x - (15*b^2*c*x^2)/a))/(18*a^3*(a + b*x^3)) + (2*b^(1/3)*(10*b^(1/3)*d + 7*a^(1/3)*e)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(11/3)) - (3*b*c*log(x))/a^4 - (2*b^(1/3)*(10*b^(1/3)*d - 7*a^(1/3)*e)*log(a^(1/3) + b^(1/3)*x))/(27*a^(11/3)) + (b^(1/3)*(10*b^(1/3)*d - 7*a^(1/3)*e)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(27*a^(11/3)) + (b*c*log(a + b*x^3))/a^4]

    @test_int [x^2*(c + d*x + e*x^2)/(a + b*x^3)^4, x, 9, -((c + d*x + e*x^2)/(9*b*(a + b*x^3)^3)) + (x*(d + 2*e*x))/(54*a*b*(a + b*x^3)^2) + (x*(5*d + 8*e*x))/(162*a^2*b*(a + b*x^3)) - ((5*b^(1/3)*d + 4*a^(1/3)*e)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(81*sqrt(3)*a^(8/3)*b^(5/3)) + ((5*b^(1/3)*d - 4*a^(1/3)*e)*log(a^(1/3) + b^(1/3)*x))/(243*a^(8/3)*b^(5/3)) - ((5*b^(1/3)*d - 4*a^(1/3)*e)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(486*a^(8/3)*b^(5/3))]
    @test_int [x^1*(c + d*x + e*x^2)/(a + b*x^3)^4, x, 9, -((x*(a*e - b*c*x - b*d*x^2))/(9*a*b*(a + b*x^3)^3)) + (x*(5*a*e + 28*b*c*x))/(162*a^3*b*(a + b*x^3)) - (6*a*d - x*(a*e + 7*b*c*x))/(54*a^2*b*(a + b*x^3)^2) - ((14*b^(2/3)*c + 5*a^(2/3)*e)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(81*sqrt(3)*a^(10/3)*b^(4/3)) - ((14*b^(2/3)*c - 5*a^(2/3)*e)*log(a^(1/3) + b^(1/3)*x))/(243*a^(10/3)*b^(4/3)) + ((14*b^(2/3)*c - 5*a^(2/3)*e)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(486*a^(10/3)*b^(4/3))]
    @test_int [x^0*(c + d*x + e*x^2)/(a + b*x^3)^4, x, 9, (x*(8*c + 7*d*x))/(54*a^2*(a + b*x^3)^2) + (2*x*(10*c + 7*d*x))/(81*a^3*(a + b*x^3)) - (a*e - b*x*(c + d*x))/(9*a*b*(a + b*x^3)^3) - (2*(20*b^(1/3)*c + 7*a^(1/3)*d)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(81*sqrt(3)*a^(11/3)*b^(2/3)) + (2*(20*b^(1/3)*c - 7*a^(1/3)*d)*log(a^(1/3) + b^(1/3)*x))/(243*a^(11/3)*b^(2/3)) - ((20*b^(1/3)*c - 7*a^(1/3)*d)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(243*a^(11/3)*b^(2/3))]
    @test_int [(c + d*x + e*x^2)/(x^1*(a + b*x^3)^4), x, 13, (x*(a*d + a*e*x - b*c*x^2))/(9*a^2*(a + b*x^3)^3) + (x*(8*a*d + 7*a*e*x - 15*b*c*x^2))/(54*a^3*(a + b*x^3)^2) + (x*(40*a*d + 28*a*e*x - 99*b*c*x^2))/(162*a^4*(a + b*x^3)) - (2*(20*b^(1/3)*d + 7*a^(1/3)*e)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(81*sqrt(3)*a^(11/3)*b^(2/3)) + (c*log(x))/a^4 + (2*(20*b^(1/3)*d - 7*a^(1/3)*e)*log(a^(1/3) + b^(1/3)*x))/(243*a^(11/3)*b^(2/3)) - ((20*b^(1/3)*d - 7*a^(1/3)*e)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(243*a^(11/3)*b^(2/3)) - (c*log(a + b*x^3))/(3*a^4)]
    @test_int [(c + d*x + e*x^2)/(x^2*(a + b*x^3)^4), x, 13, -(c/(a^4*x)) + (x*(a*e - b*c*x - b*d*x^2))/(9*a^2*(a + b*x^3)^3) + (x*(8*a*e - 16*b*c*x - 15*b*d*x^2))/(54*a^3*(a + b*x^3)^2) + (x*(40*a*e - 118*b*c*x - 99*b*d*x^2))/(162*a^4*(a + b*x^3)) + (20*(7*b^(2/3)*c - 2*a^(2/3)*e)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(81*sqrt(3)*a^(13/3)*b^(1/3)) + (d*log(x))/a^4 + (20*(7*b^(2/3)*c + 2*a^(2/3)*e)*log(a^(1/3) + b^(1/3)*x))/(243*a^(13/3)*b^(1/3)) - (10*(7*b^(2/3)*c + 2*a^(2/3)*e)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(243*a^(13/3)*b^(1/3)) - (d*log(a + b*x^3))/(3*a^4)]
    @test_int [(c + d*x + e*x^2)/(x^3*(a + b*x^3)^4), x, 13, -(c/(2*a^4*x^2)) - d/(a^4*x) - (x*(b*c + b*d*x + b*e*x^2))/(9*a^2*(a + b*x^3)^3) - (x*(17*b*c + 16*b*d*x + 15*b*e*x^2))/(54*a^3*(a + b*x^3)^2) - (x*(139*b*c + 118*b*d*x + 99*b*e*x^2))/(162*a^4*(a + b*x^3)) + (20*b^(1/3)*(11*b^(1/3)*c + 7*a^(1/3)*d)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(81*sqrt(3)*a^(14/3)) + (e*log(x))/a^4 - (20*b^(1/3)*(11*b^(1/3)*c - 7*a^(1/3)*d)*log(a^(1/3) + b^(1/3)*x))/(243*a^(14/3)) + (10*b^(1/3)*(11*b^(1/3)*c - 7*a^(1/3)*d)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(243*a^(14/3)) - (e*log(a + b*x^3))/(3*a^4)]
    @test_int [(c + d*x + e*x^2)/(x^4*(a + b*x^3)^4), x, 13, -(c/(3*a^4*x^3)) - d/(2*a^4*x^2) - e/(a^4*x) - (x*(b*d + b*e*x - (b^2*c*x^2)/a))/(9*a^2*(a + b*x^3)^3) - (x*(17*b*d + 16*b*e*x - (24*b^2*c*x^2)/a))/(54*a^3*(a + b*x^3)^2) - (x*(139*b*d + 118*b*e*x - (234*b^2*c*x^2)/a))/(162*a^4*(a + b*x^3)) + (20*b^(1/3)*(11*b^(1/3)*d + 7*a^(1/3)*e)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(81*sqrt(3)*a^(14/3)) - (4*b*c*log(x))/a^5 - (20*b^(1/3)*(11*b^(1/3)*d - 7*a^(1/3)*e)*log(a^(1/3) + b^(1/3)*x))/(243*a^(14/3)) + (10*b^(1/3)*(11*b^(1/3)*d - 7*a^(1/3)*e)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(243*a^(14/3)) + (4*b*c*log(a + b*x^3))/(3*a^5)]

    @test_int [(2*a*x - x^2)/(a^3 + x^3), x, 5, -((2*atan((a - 2*x)/(sqrt(3)*a)))/sqrt(3)) - log(a + x)]
    @test_int [x*(2*a - x)/(a^3 + x^3), x, 4, -((2*atan((a - 2*x)/(sqrt(3)*a)))/sqrt(3)) - log(a + x)]

    @test_int [(2*a*x + x^2)/(a^3 - x^3), x, 5, -((2*atan((a + 2*x)/(sqrt(3)*a)))/sqrt(3)) - log(a - x)]
    @test_int [x*(2*a + x)/(a^3 - x^3), x, 4, -((2*atan((a + 2*x)/(sqrt(3)*a)))/sqrt(3)) - log(a - x)]

    @test_int [x*(-2*(a/b)^(1/3)*C + C*x)/(a + b*x^3), x, 4, (2*C*atan((1 - (2*x)/(a/b)^(1/3))/sqrt(3)))/(sqrt(3)*b) + (C*log((a/b)^(1/3) + x))/b]
    @test_int [x*(-2*(-(a/b))^(1/3)*C + C*x)/(a - b*x^3), x, 4, -((2*C*atan((1 - (2*x)/(-(a/b))^(1/3))/sqrt(3)))/(sqrt(3)*b)) - (C*log((-(a/b))^(1/3) + x))/b]

    @test_int [x*(2*(-(a/b))^(1/3)*C + C*x)/(a + b*x^3), x, 4, (2*C*atan((1 + (2*x)/(-(a/b))^(1/3))/sqrt(3)))/(sqrt(3)*b) + (C*log((-(a/b))^(1/3) - x))/b]
    @test_int [x*(2*(a/b)^(1/3)*C + C*x)/(a - b*x^3), x, 4, -((2*C*atan((1 + (2*x)/(a/b)^(1/3))/sqrt(3)))/(sqrt(3)*b)) - (C*log((a/b)^(1/3) - x))/b]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*P5(x)*(a+b*x^3)^p=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^4*(a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5), x, 2, (a*c*x^5)/5 + (a*d*x^6)/6 + (a*e*x^7)/7 + ((b*c + a*f)*x^8)/8 + ((b*d + a*g)*x^9)/9 + ((b*e + a*h)*x^10)/10 + (b*f*x^11)/11 + (b*g*x^12)/12 + (b*h*x^13)/13]
    @test_int [x^3*(a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5), x, 2, (a*c*x^4)/4 + (a*d*x^5)/5 + (a*e*x^6)/6 + ((b*c + a*f)*x^7)/7 + ((b*d + a*g)*x^8)/8 + ((b*e + a*h)*x^9)/9 + (b*f*x^10)/10 + (b*g*x^11)/11 + (b*h*x^12)/12]
    @test_int [x^2*(a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5), x, 2, (a*c*x^3)/3 + (a*d*x^4)/4 + (a*e*x^5)/5 + ((b*c + a*f)*x^6)/6 + ((b*d + a*g)*x^7)/7 + ((b*e + a*h)*x^8)/8 + (b*f*x^9)/9 + (b*g*x^10)/10 + (b*h*x^11)/11]
    @test_int [x^1*(a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5), x, 2, (a*c*x^2)/2 + (a*d*x^3)/3 + (a*e*x^4)/4 + ((b*c + a*f)*x^5)/5 + ((b*d + a*g)*x^6)/6 + ((b*e + a*h)*x^7)/7 + (b*f*x^8)/8 + (b*g*x^9)/9 + (b*h*x^10)/10]
    @test_int [x^0*(a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5), x, 2, a*c*x + (a*d*x^2)/2 + (a*e*x^3)/3 + ((b*c + a*f)*x^4)/4 + ((b*d + a*g)*x^5)/5 + ((b*e + a*h)*x^6)/6 + (b*f*x^7)/7 + (b*g*x^8)/8 + (b*h*x^9)/9]
    @test_int [((a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^1, x, 2, a*d*x + (a*e*x^2)/2 + ((b*c + a*f)*x^3)/3 + ((b*d + a*g)*x^4)/4 + ((b*e + a*h)*x^5)/5 + (b*f*x^6)/6 + (b*g*x^7)/7 + (b*h*x^8)/8 + a*c*log(x)]
    @test_int [((a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^2, x, 2, -((a*c)/x) + a*e*x + ((b*c + a*f)*x^2)/2 + ((b*d + a*g)*x^3)/3 + ((b*e + a*h)*x^4)/4 + (b*f*x^5)/5 + (b*g*x^6)/6 + (b*h*x^7)/7 + a*d*log(x)]
    @test_int [((a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^3, x, 2, -(a*c)/(2*x^2) - (a*d)/x + (b*c + a*f)*x + ((b*d + a*g)*x^2)/2 + ((b*e + a*h)*x^3)/3 + (b*f*x^4)/4 + (b*g*x^5)/5 + (b*h*x^6)/6 + a*e*log(x)]
    @test_int [((a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^4, x, 2, -(a*c)/(3*x^3) - (a*d)/(2*x^2) - (a*e)/x + (b*d + a*g)*x + ((b*e + a*h)*x^2)/2 + (b*f*x^3)/3 + (b*g*x^4)/4 + (b*h*x^5)/5 + (b*c + a*f)*log(x)]
    @test_int [((a + b*x^3)*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^5, x, 2, -(a*c)/(4*x^4) - (a*d)/(3*x^3) - (a*e)/(2*x^2) - (b*c + a*f)/x + (b*e + a*h)*x + (b*f*x^2)/2 + (b*g*x^3)/3 + (b*h*x^4)/4 + (b*d + a*g)*log(x)]

    @test_int [x^4*(a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5), x, 2, (a^2*c*x^5)/5 + (a^2*d*x^6)/6 + (a^2*e*x^7)/7 + (a*(2*b*c + a*f)*x^8)/8 + (a*(2*b*d + a*g)*x^9)/9 + (a*(2*b*e + a*h)*x^10)/10 + (b*(b*c + 2*a*f)*x^11)/11 + (b*(b*d + 2*a*g)*x^12)/12 + (b*(b*e + 2*a*h)*x^13)/13 + (b^2*f*x^14)/14 + (b^2*g*x^15)/15 + (b^2*h*x^16)/16]
    @test_int [x^3*(a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5), x, 2, (a^2*c*x^4)/4 + (a^2*d*x^5)/5 + (a^2*e*x^6)/6 + (a*(2*b*c + a*f)*x^7)/7 + (a*(2*b*d + a*g)*x^8)/8 + (a*(2*b*e + a*h)*x^9)/9 + (b*(b*c + 2*a*f)*x^10)/10 + (b*(b*d + 2*a*g)*x^11)/11 + (b*(b*e + 2*a*h)*x^12)/12 + (b^2*f*x^13)/13 + (b^2*g*x^14)/14 + (b^2*h*x^15)/15]
    @test_int [x^2*(a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5), x, 3, (a^2*d*x^4)/4 + (a^2*e*x^5)/5 + (a^2*f*x^6)/6 + (a*(2*b*d + a*g)*x^7)/7 + (a*(2*b*e + a*h)*x^8)/8 + (2*a*b*f*x^9)/9 + (b*(b*d + 2*a*g)*x^10)/10 + (b*(b*e + 2*a*h)*x^11)/11 + (b^2*f*x^12)/12 + (b^2*g*x^13)/13 + (b^2*h*x^14)/14 + (c*(a + b*x^3)^3)/(9*b)]
    @test_int [x^1*(a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5), x, 3, (a^2*c*x^2)/2 + (a^2*e*x^4)/4 + (a*(2*b*c + a*f)*x^5)/5 + (a^2*g*x^6)/6 + (a*(2*b*e + a*h)*x^7)/7 + (b*(b*c + 2*a*f)*x^8)/8 + (2*a*b*g*x^9)/9 + (b*(b*e + 2*a*h)*x^10)/10 + (b^2*f*x^11)/11 + (b^2*g*x^12)/12 + (b^2*h*x^13)/13 + (d*(a + b*x^3)^3)/(9*b)]
    @test_int [x^0*(a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5), x, 3, a^2*c*x + (a^2*d*x^2)/2 + (a*(2*b*c + a*f)*x^4)/4 + (a*(2*b*d + a*g)*x^5)/5 + (a^2*h*x^6)/6 + (b*(b*c + 2*a*f)*x^7)/7 + (b*(b*d + 2*a*g)*x^8)/8 + (2*a*b*h*x^9)/9 + (b^2*f*x^10)/10 + (b^2*g*x^11)/11 + (b^2*h*x^12)/12 + (e*(a + b*x^3)^3)/(9*b)]
    @test_int [((a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^1, x, 3, a^2*d*x + (a^2*e*x^2)/2 + (2*a*b*c*x^3)/3 + (a*(2*b*d + a*g)*x^4)/4 + (a*(2*b*e + a*h)*x^5)/5 + (b^2*c*x^6)/6 + (b*(b*d + 2*a*g)*x^7)/7 + (b*(b*e + 2*a*h)*x^8)/8 + (b^2*g*x^10)/10 + (b^2*h*x^11)/11 + (f*(a + b*x^3)^3)/(9*b) + a^2*c*log(x)]
    @test_int [((a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^2, x, 3, -((a^2*c)/x) + a^2*e*x + (a*(2*b*c + a*f)*x^2)/2 + (2*a*b*d*x^3)/3 + (a*(2*b*e + a*h)*x^4)/4 + (b*(b*c + 2*a*f)*x^5)/5 + (b^2*d*x^6)/6 + (b*(b*e + 2*a*h)*x^7)/7 + (b^2*f*x^8)/8 + (b^2*h*x^10)/10 + (g*(a + b*x^3)^3)/(9*b) + a^2*d*log(x)]
    @test_int [((a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^3, x, 3, -(a^2*c)/(2*x^2) - (a^2*d)/x + a*(2*b*c + a*f)*x + (a*(2*b*d + a*g)*x^2)/2 + (2*a*b*e*x^3)/3 + (b*(b*c + 2*a*f)*x^4)/4 + (b*(b*d + 2*a*g)*x^5)/5 + (b^2*e*x^6)/6 + (b^2*f*x^7)/7 + (b^2*g*x^8)/8 + (h*(a + b*x^3)^3)/(9*b) + a^2*e*log(x)]
    @test_int [((a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^4, x, 2, -(a^2*c)/(3*x^3) - (a^2*d)/(2*x^2) - (a^2*e)/x + a*(2*b*d + a*g)*x + (a*(2*b*e + a*h)*x^2)/2 + (b*(b*c + 2*a*f)*x^3)/3 + (b*(b*d + 2*a*g)*x^4)/4 + (b*(b*e + 2*a*h)*x^5)/5 + (b^2*f*x^6)/6 + (b^2*g*x^7)/7 + (b^2*h*x^8)/8 + a*(2*b*c + a*f)*log(x)]
    @test_int [((a + b*x^3)^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^5, x, 2, -(a^2*c)/(4*x^4) - (a^2*d)/(3*x^3) - (a^2*e)/(2*x^2) - (a*(2*b*c + a*f))/x + a*(2*b*e + a*h)*x + (b*(b*c + 2*a*f)*x^2)/2 + (b*(b*d + 2*a*g)*x^3)/3 + (b*(b*e + 2*a*h)*x^4)/4 + (b^2*f*x^5)/5 + (b^2*g*x^6)/6 + (b^2*h*x^7)/7 + a*(2*b*d + a*g)*log(x)]

    @test_int [x^4*(a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5), x, 2, (a^3*c*x^5)/5 + (a^3*d*x^6)/6 + (a^3*e*x^7)/7 + (a^2*(3*b*c + a*f)*x^8)/8 + (a^2*(3*b*d + a*g)*x^9)/9 + (a^2*(3*b*e + a*h)*x^10)/10 + (3*a*b*(b*c + a*f)*x^11)/11 + (a*b*(b*d + a*g)*x^12)/4 + (3*a*b*(b*e + a*h)*x^13)/13 + (b^2*(b*c + 3*a*f)*x^14)/14 + (b^2*(b*d + 3*a*g)*x^15)/15 + (b^2*(b*e + 3*a*h)*x^16)/16 + (b^3*f*x^17)/17 + (b^3*g*x^18)/18 + (b^3*h*x^19)/19]
    @test_int [x^3*(a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5), x, 2, (a^3*c*x^4)/4 + (a^3*d*x^5)/5 + (a^3*e*x^6)/6 + (a^2*(3*b*c + a*f)*x^7)/7 + (a^2*(3*b*d + a*g)*x^8)/8 + (a^2*(3*b*e + a*h)*x^9)/9 + (3*a*b*(b*c + a*f)*x^10)/10 + (3*a*b*(b*d + a*g)*x^11)/11 + (a*b*(b*e + a*h)*x^12)/4 + (b^2*(b*c + 3*a*f)*x^13)/13 + (b^2*(b*d + 3*a*g)*x^14)/14 + (b^2*(b*e + 3*a*h)*x^15)/15 + (b^3*f*x^16)/16 + (b^3*g*x^17)/17 + (b^3*h*x^18)/18]
    @test_int [x^2*(a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5), x, 3, (a^3*d*x^4)/4 + (a^3*e*x^5)/5 + (a^3*f*x^6)/6 + (a^2*(3*b*d + a*g)*x^7)/7 + (a^2*(3*b*e + a*h)*x^8)/8 + (a^2*b*f*x^9)/3 + (3*a*b*(b*d + a*g)*x^10)/10 + (3*a*b*(b*e + a*h)*x^11)/11 + (a*b^2*f*x^12)/4 + (b^2*(b*d + 3*a*g)*x^13)/13 + (b^2*(b*e + 3*a*h)*x^14)/14 + (b^3*f*x^15)/15 + (b^3*g*x^16)/16 + (b^3*h*x^17)/17 + (c*(a + b*x^3)^4)/(12*b)]
    @test_int [x^1*(a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5), x, 3, (a^3*c*x^2)/2 + (a^3*e*x^4)/4 + (a^2*(3*b*c + a*f)*x^5)/5 + (a^3*g*x^6)/6 + (a^2*(3*b*e + a*h)*x^7)/7 + (3*a*b*(b*c + a*f)*x^8)/8 + (a^2*b*g*x^9)/3 + (3*a*b*(b*e + a*h)*x^10)/10 + (b^2*(b*c + 3*a*f)*x^11)/11 + (a*b^2*g*x^12)/4 + (b^2*(b*e + 3*a*h)*x^13)/13 + (b^3*f*x^14)/14 + (b^3*g*x^15)/15 + (b^3*h*x^16)/16 + (d*(a + b*x^3)^4)/(12*b)]
    @test_int [x^0*(a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5), x, 3, a^3*c*x + (a^3*d*x^2)/2 + (a^2*(3*b*c + a*f)*x^4)/4 + (a^2*(3*b*d + a*g)*x^5)/5 + (a^3*h*x^6)/6 + (3*a*b*(b*c + a*f)*x^7)/7 + (3*a*b*(b*d + a*g)*x^8)/8 + (a^2*b*h*x^9)/3 + (b^2*(b*c + 3*a*f)*x^10)/10 + (b^2*(b*d + 3*a*g)*x^11)/11 + (a*b^2*h*x^12)/4 + (b^3*f*x^13)/13 + (b^3*g*x^14)/14 + (b^3*h*x^15)/15 + (e*(a + b*x^3)^4)/(12*b)]
    @test_int [((a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^1, x, 3, a^3*d*x + (a^3*e*x^2)/2 + a^2*b*c*x^3 + (a^2*(3*b*d + a*g)*x^4)/4 + (a^2*(3*b*e + a*h)*x^5)/5 + (a*b^2*c*x^6)/2 + (3*a*b*(b*d + a*g)*x^7)/7 + (3*a*b*(b*e + a*h)*x^8)/8 + (b^3*c*x^9)/9 + (b^2*(b*d + 3*a*g)*x^10)/10 + (b^2*(b*e + 3*a*h)*x^11)/11 + (b^3*g*x^13)/13 + (b^3*h*x^14)/14 + (f*(a + b*x^3)^4)/(12*b) + a^3*c*log(x)]
    @test_int [((a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^2, x, 3, -((a^3*c)/x) + a^3*e*x + (a^2*(3*b*c + a*f)*x^2)/2 + a^2*b*d*x^3 + (a^2*(3*b*e + a*h)*x^4)/4 + (3*a*b*(b*c + a*f)*x^5)/5 + (a*b^2*d*x^6)/2 + (3*a*b*(b*e + a*h)*x^7)/7 + (b^2*(b*c + 3*a*f)*x^8)/8 + (b^3*d*x^9)/9 + (b^2*(b*e + 3*a*h)*x^10)/10 + (b^3*f*x^11)/11 + (b^3*h*x^13)/13 + (g*(a + b*x^3)^4)/(12*b) + a^3*d*log(x)]
    @test_int [((a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^3, x, 3, -(a^3*c)/(2*x^2) - (a^3*d)/x + a^2*(3*b*c + a*f)*x + (a^2*(3*b*d + a*g)*x^2)/2 + a^2*b*e*x^3 + (3*a*b*(b*c + a*f)*x^4)/4 + (3*a*b*(b*d + a*g)*x^5)/5 + (a*b^2*e*x^6)/2 + (b^2*(b*c + 3*a*f)*x^7)/7 + (b^2*(b*d + 3*a*g)*x^8)/8 + (b^3*e*x^9)/9 + (b^3*f*x^10)/10 + (b^3*g*x^11)/11 + (h*(a + b*x^3)^4)/(12*b) + a^3*e*log(x)]
    @test_int [((a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^4, x, 2, -(a^3*c)/(3*x^3) - (a^3*d)/(2*x^2) - (a^3*e)/x + a^2*(3*b*d + a*g)*x + (a^2*(3*b*e + a*h)*x^2)/2 + a*b*(b*c + a*f)*x^3 + (3*a*b*(b*d + a*g)*x^4)/4 + (3*a*b*(b*e + a*h)*x^5)/5 + (b^2*(b*c + 3*a*f)*x^6)/6 + (b^2*(b*d + 3*a*g)*x^7)/7 + (b^2*(b*e + 3*a*h)*x^8)/8 + (b^3*f*x^9)/9 + (b^3*g*x^10)/10 + (b^3*h*x^11)/11 + a^2*(3*b*c + a*f)*log(x)]
    @test_int [((a + b*x^3)^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5))/x^5, x, 2, -(a^3*c)/(4*x^4) - (a^3*d)/(3*x^3) - (a^3*e)/(2*x^2) - (a^2*(3*b*c + a*f))/x + a^2*(3*b*e + a*h)*x + (3*a*b*(b*c + a*f)*x^2)/2 + a*b*(b*d + a*g)*x^3 + (3*a*b*(b*e + a*h)*x^4)/4 + (b^2*(b*c + 3*a*f)*x^5)/5 + (b^2*(b*d + 3*a*g)*x^6)/6 + (b^2*(b*e + 3*a*h)*x^7)/7 + (b^3*f*x^8)/8 + (b^3*g*x^9)/9 + (b^3*h*x^10)/10 + a^2*(3*b*d + a*g)*log(x)]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^4*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^3), x, 13, -((a*(b*e - a*h)*x)/b^3) + ((b*c - a*f)*x^2)/(2*b^2) + ((b*d - a*g)*x^3)/(3*b^2) + ((b*e - a*h)*x^4)/(4*b^2) + (f*x^5)/(5*b) + (g*x^6)/(6*b) + (h*x^7)/(7*b) + (a^(2/3)*(b^(5/3)*c - a^(2/3)*b*e - a*b^(2/3)*f + a^(5/3)*h)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^(10/3)) + (a^(2/3)*(b^(2/3)*(b*c - a*f) + a^(2/3)*(b*e - a*h))*log(a^(1/3) + b^(1/3)*x))/(3*b^(10/3)) - (a^(2/3)*(b^(2/3)*(b*c - a*f) + a^(2/3)*(b*e - a*h))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*b^(10/3)) - (a*(b*d - a*g)*log(a + b*x^3))/(3*b^3)]
    @test_int [x^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^3), x, 13, ((b*c - a*f)*x)/b^2 + ((b*d - a*g)*x^2)/(2*b^2) + ((b*e - a*h)*x^3)/(3*b^2) + (f*x^4)/(4*b) + (g*x^5)/(5*b) + (h*x^6)/(6*b) + (a^(1/3)*(b^(4/3)*c + a^(1/3)*b*d - a*b^(1/3)*f - a^(4/3)*g)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^(8/3)) - (a^(1/3)*(b^(1/3)*(b*c - a*f) - a^(1/3)*(b*d - a*g))*log(a^(1/3) + b^(1/3)*x))/(3*b^(8/3)) + (a^(1/3)*(b^(1/3)*(b*c - a*f) - a^(1/3)*(b*d - a*g))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*b^(8/3)) - (a*(b*e - a*h)*log(a + b*x^3))/(3*b^3)]
    @test_int [x^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^3), x, 13, ((b*d - a*g)*x)/b^2 + ((b*e - a*h)*x^2)/(2*b^2) + (f*x^3)/(3*b) + (g*x^4)/(4*b) + (h*x^5)/(5*b) + (a^(1/3)*(b^(4/3)*d + a^(1/3)*b*e - a*b^(1/3)*g - a^(4/3)*h)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^(8/3)) - (a^(1/3)*(b^(1/3)*(b*d - a*g) - a^(1/3)*(b*e - a*h))*log(a^(1/3) + b^(1/3)*x))/(3*b^(8/3)) + (a^(1/3)*(b^(1/3)*(b*d - a*g) - a^(1/3)*(b*e - a*h))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*b^(8/3)) + ((b*c - a*f)*log(a + b*x^3))/(3*b^2)]
    @test_int [x^1*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^3), x, 13, ((b*e - a*h)*x)/b^2 + (f*x^2)/(2*b) + (g*x^3)/(3*b) + (h*x^4)/(4*b) - ((b^(5/3)*c - a^(2/3)*b*e - a*b^(2/3)*f + a^(5/3)*h)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(1/3)*b^(7/3)) - ((b^(2/3)*(b*c - a*f) + a^(2/3)*(b*e - a*h))*log(a^(1/3) + b^(1/3)*x))/(3*a^(1/3)*b^(7/3)) + ((b^(2/3)*(b*c - a*f) + a^(2/3)*(b*e - a*h))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(1/3)*b^(7/3)) + ((b*d - a*g)*log(a + b*x^3))/(3*b^2)]
    @test_int [x^0*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^3), x, 10, (f*x)/b + (g*x^2)/(2*b) + (h*x^3)/(3*b) - ((b^(4/3)*c + a^(1/3)*b*d - a*b^(1/3)*f - a^(4/3)*g)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(2/3)*b^(5/3)) + ((b^(1/3)*(b*c - a*f) - a^(1/3)*(b*d - a*g))*log(a^(1/3) + b^(1/3)*x))/(3*a^(2/3)*b^(5/3)) - ((b^(1/3)*(b*c - a*f) - a^(1/3)*(b*d - a*g))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(2/3)*b^(5/3)) + ((b*e - a*h)*log(a + b*x^3))/(3*b^2)]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x^1*(a + b*x^3)), x, 10, (g*x)/b + (h*x^2)/(2*b) - ((b^(4/3)*d + a^(1/3)*b*e - a*b^(1/3)*g - a^(4/3)*h)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(2/3)*b^(5/3)) + (c*log(x))/a + ((b^(1/3)*(b*d - a*g) - a^(1/3)*(b*e - a*h))*log(a^(1/3) + b^(1/3)*x))/(3*a^(2/3)*b^(5/3)) - ((b^(1/3)*(b*d - a*g) - a^(1/3)*(b*e - a*h))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(2/3)*b^(5/3)) - ((b*c - a*f)*log(a + b*x^3))/(3*a*b)]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x^2*(a + b*x^3)), x, 10, -(c/(a*x)) + (h*x)/b + ((b^(5/3)*c - a^(2/3)*b*e - a*b^(2/3)*f + a^(5/3)*h)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(4/3)*b^(4/3)) + (d*log(x))/a + ((b^(2/3)*(b*c - a*f) + a^(2/3)*(b*e - a*h))*log(a^(1/3) + b^(1/3)*x))/(3*a^(4/3)*b^(4/3)) - ((b^(2/3)*(b*c - a*f) + a^(2/3)*(b*e - a*h))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(4/3)*b^(4/3)) - ((b*d - a*g)*log(a + b*x^3))/(3*a*b)]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x^3*(a + b*x^3)), x, 10, -c/(2*a*x^2) - d/(a*x) + ((b^(4/3)*c + a^(1/3)*b*d - a*b^(1/3)*f - a^(4/3)*g)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(5/3)*b^(2/3)) + (e*log(x))/a - ((b^(1/3)*(b*c - a*f) - a^(1/3)*(b*d - a*g))*log(a^(1/3) + b^(1/3)*x))/(3*a^(5/3)*b^(2/3)) + ((b^(1/3)*(b*c - a*f) - a^(1/3)*(b*d - a*g))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(5/3)*b^(2/3)) - ((b*e - a*h)*log(a + b*x^3))/(3*a*b)]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x^4*(a + b*x^3)), x, 10, -c/(3*a*x^3) - d/(2*a*x^2) - e/(a*x) + ((b^(4/3)*d + a^(1/3)*b*e - a*b^(1/3)*g - a^(4/3)*h)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(5/3)*b^(2/3)) - ((b*c - a*f)*log(x))/a^2 - ((b^(1/3)*(b*d - a*g) - a^(1/3)*(b*e - a*h))*log(a^(1/3) + b^(1/3)*x))/(3*a^(5/3)*b^(2/3)) + ((b^(1/3)*(b*d - a*g) - a^(1/3)*(b*e - a*h))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(5/3)*b^(2/3)) + ((b*c - a*f)*log(a + b*x^3))/(3*a^2)]

    @test_int [x^4*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^3)^2, x, 11, ((b*e - 2*a*h)*x)/b^3 + (f*x^2)/(2*b^2) + (g*x^3)/(3*b^2) + (h*x^4)/(4*b^2) + (x*(a*(b*e - a*h) - b*(b*c - a*f)*x - b*(b*d - a*g)*x^2))/(3*b^3*(a + b*x^3)) - ((2*b^(5/3)*c - 4*a^(2/3)*b*e - 5*a*b^(2/3)*f + 7*a^(5/3)*h)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(1/3)*b^(10/3)) - ((b^(2/3)*(2*b*c - 5*a*f) + a^(2/3)*(4*b*e - 7*a*h))*log(a^(1/3) + b^(1/3)*x))/(9*a^(1/3)*b^(10/3)) + ((b^(2/3)*(2*b*c - 5*a*f) + a^(2/3)*(4*b*e - 7*a*h))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(1/3)*b^(10/3)) + ((b*d - 2*a*g)*log(a + b*x^3))/(3*b^3)]
    @test_int [x^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^3)^2, x, 11, (f*x)/b^2 + (g*x^2)/(2*b^2) + (h*x^3)/(3*b^2) - (x*(b*c - a*f + (b*d - a*g)*x + (b*e - a*h)*x^2))/(3*b^2*(a + b*x^3)) - ((b^(4/3)*c + 2*a^(1/3)*b*d - 4*a*b^(1/3)*f - 5*a^(4/3)*g)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(2/3)*b^(8/3)) + ((b^(1/3)*(b*c - 4*a*f) - a^(1/3)*(2*b*d - 5*a*g))*log(a^(1/3) + b^(1/3)*x))/(9*a^(2/3)*b^(8/3)) - ((b^(1/3)*(b*c - 4*a*f) - a^(1/3)*(2*b*d - 5*a*g))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(2/3)*b^(8/3)) + ((b*e - 2*a*h)*log(a + b*x^3))/(3*b^3)]
    @test_int [x^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^3)^2, x, 11, (4*g*x)/(3*b^2) + (5*h*x^2)/(6*b^2) - (c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(3*b*(a + b*x^3)) - ((b^(4/3)*d + 2*a^(1/3)*b*e - 4*a*b^(1/3)*g - 5*a^(4/3)*h)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(2/3)*b^(8/3)) + ((b^(1/3)*(b*d - 4*a*g) - a^(1/3)*(2*b*e - 5*a*h))*log(a^(1/3) + b^(1/3)*x))/(9*a^(2/3)*b^(8/3)) - ((b^(1/3)*(b*d - 4*a*g) - a^(1/3)*(2*b*e - 5*a*h))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(2/3)*b^(8/3)) + (f*log(a + b*x^3))/(3*b^2)]
    @test_int [x^1*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^3)^2, x, 11, (h*x)/b^2 - (x*(a*(b*e - a*h) - b*(b*c - a*f)*x - b*(b*d - a*g)*x^2))/(3*a*b^2*(a + b*x^3)) - ((b^(5/3)*c + a^(2/3)*b*e + 2*a*b^(2/3)*f - 4*a^(5/3)*h)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(4/3)*b^(7/3)) - ((b^(2/3)*(b*c + 2*a*f) - a^(2/3)*(b*e - 4*a*h))*log(a^(1/3) + b^(1/3)*x))/(9*a^(4/3)*b^(7/3)) + ((b^(2/3)*(b*c + 2*a*f) - a^(2/3)*(b*e - 4*a*h))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(4/3)*b^(7/3)) + (g*log(a + b*x^3))/(3*b^2)]
    @test_int [x^0*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^3)^2, x, 9, (x*(b*c - a*f + (b*d - a*g)*x + (b*e - a*h)*x^2))/(3*a*b*(a + b*x^3)) - ((2*b^(4/3)*c + a^(1/3)*b*d + a*b^(1/3)*f + 2*a^(4/3)*g)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(5/3)*b^(5/3)) + ((b^(1/3)*(2*b*c + a*f) - a^(1/3)*(b*d + 2*a*g))*log(a^(1/3) + b^(1/3)*x))/(9*a^(5/3)*b^(5/3)) - ((b^(1/3)*(2*b*c + a*f) - a^(1/3)*(b*d + 2*a*g))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(5/3)*b^(5/3)) + (h*log(a + b*x^3))/(3*b^2)]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x^1*(a + b*x^3)^2), x, 11, (x*(a*(b*d - a*g) + a*(b*e - a*h)*x - b*(b*c - a*f)*x^2))/(3*a^2*b*(a + b*x^3)) - ((2*b^(4/3)*d + a^(1/3)*b*e + a*b^(1/3)*g + 2*a^(4/3)*h)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(5/3)*b^(5/3)) + (c*log(x))/a^2 + ((b^(1/3)*(2*b*d + a*g) - a^(1/3)*(b*e + 2*a*h))*log(a^(1/3) + b^(1/3)*x))/(9*a^(5/3)*b^(5/3)) - ((b^(1/3)*(2*b*d + a*g) - a^(1/3)*(b*e + 2*a*h))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(5/3)*b^(5/3)) - (c*log(a + b*x^3))/(3*a^2)]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x^2*(a + b*x^3)^2), x, 11, -(c/(a^2*x)) + (x*(a*(b*e - a*h) - b*(b*c - a*f)*x - b*(b*d - a*g)*x^2))/(3*a^2*b*(a + b*x^3)) + ((4*b^(5/3)*c - 2*a^(2/3)*b*e - a*b^(2/3)*f - a^(5/3)*h)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(7/3)*b^(4/3)) + (d*log(x))/a^2 + ((b^(2/3)*(4*b*c - a*f) + a^(2/3)*(2*b*e + a*h))*log(a^(1/3) + b^(1/3)*x))/(9*a^(7/3)*b^(4/3)) - ((b^(2/3)*(4*b*c - a*f) + a^(2/3)*(2*b*e + a*h))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(7/3)*b^(4/3)) - (d*log(a + b*x^3))/(3*a^2)]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x^3*(a + b*x^3)^2), x, 11, -c/(2*a^2*x^2) - d/(a^2*x) - (x*(b*c - a*f + (b*d - a*g)*x + (b*e - a*h)*x^2))/(3*a^2*(a + b*x^3)) + ((5*b^(4/3)*c + 4*a^(1/3)*b*d - 2*a*b^(1/3)*f - a^(4/3)*g)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(8/3)*b^(2/3)) + (e*log(x))/a^2 - ((b^(1/3)*(5*b*c - 2*a*f) - a^(1/3)*(4*b*d - a*g))*log(a^(1/3) + b^(1/3)*x))/(9*a^(8/3)*b^(2/3)) + ((b^(1/3)*(5*b*c - 2*a*f) - a^(1/3)*(4*b*d - a*g))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(8/3)*b^(2/3)) - (e*log(a + b*x^3))/(3*a^2)]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x^4*(a + b*x^3)^2), x, 11, -c/(3*a^2*x^3) - d/(2*a^2*x^2) - e/(a^2*x) - (x*(b*d - a*g + (b*e - a*h)*x - b*((b*c)/a - f)*x^2))/(3*a^2*(a + b*x^3)) + ((5*b^(4/3)*d + 4*a^(1/3)*b*e - 2*a*b^(1/3)*g - a^(4/3)*h)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(8/3)*b^(2/3)) - ((2*b*c - a*f)*log(x))/a^3 - ((b^(1/3)*(5*b*d - 2*a*g) - a^(1/3)*(4*b*e - a*h))*log(a^(1/3) + b^(1/3)*x))/(9*a^(8/3)*b^(2/3)) + ((b^(1/3)*(5*b*d - 2*a*g) - a^(1/3)*(4*b*e - a*h))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(8/3)*b^(2/3)) + ((2*b*c - a*f)*log(a + b*x^3))/(3*a^3)]

    @test_int [x^4*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^3)^3, x, 12, (h*x)/b^3 + (x*(a*(b*e - a*h) - b*(b*c - a*f)*x - b*(b*d - a*g)*x^2))/(6*b^3*(a + b*x^3)^2) - (x*(a*(7*b*e - 13*a*h) - 2*b*(b*c - 4*a*f)*x - 3*b*(b*d - 3*a*g)*x^2))/(18*a*b^3*(a + b*x^3)) - ((b^(5/3)*c + 2*a^(2/3)*b*e + 5*a*b^(2/3)*f - 14*a^(5/3)*h)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(4/3)*b^(10/3)) - ((b^(2/3)*(b*c + 5*a*f) - 2*a^(2/3)*(b*e - 7*a*h))*log(a^(1/3) + b^(1/3)*x))/(27*a^(4/3)*b^(10/3)) + ((b^(2/3)*(b*c + 5*a*f) - 2*a^(2/3)*(b*e - 7*a*h))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(4/3)*b^(10/3)) + (g*log(a + b*x^3))/(3*b^3)]
    @test_int [x^3*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^3)^3, x, 10, -(x*(b*c - a*f + (b*d - a*g)*x + (b*e - a*h)*x^2))/(6*b^2*(a + b*x^3)^2) + (x*(b*c - 7*a*f + 2*(b*d - 4*a*g)*x + 3*(b*e - 3*a*h)*x^2))/(18*a*b^2*(a + b*x^3)) - ((b^(4/3)*c + a^(1/3)*b*d + 2*a*b^(1/3)*f + 5*a^(4/3)*g)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(5/3)*b^(8/3)) + ((b^(1/3)*(b*c + 2*a*f) - a^(1/3)*(b*d + 5*a*g))*log(a^(1/3) + b^(1/3)*x))/(27*a^(5/3)*b^(8/3)) - ((b^(1/3)*(b*c + 2*a*f) - a^(1/3)*(b*d + 5*a*g))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(5/3)*b^(8/3)) + (h*log(a + b*x^3))/(3*b^3)]
    @test_int [x^2*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^3)^3, x, 8, (x*(b*d - 4*a*g + (2*b*e - 5*a*h)*x + 3*b*f*x^2))/(18*a*b^2*(a + b*x^3)) - (c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(6*b*(a + b*x^3)^2) - ((b^(4/3)*d + a^(1/3)*b*e + 2*a*b^(1/3)*g + 5*a^(4/3)*h)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(5/3)*b^(8/3)) + ((b^(1/3)*(b*d + 2*a*g) - a^(1/3)*(b*e + 5*a*h))*log(a^(1/3) + b^(1/3)*x))/(27*a^(5/3)*b^(8/3)) - ((b^(1/3)*(b*d + 2*a*g) - a^(1/3)*(b*e + 5*a*h))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(5/3)*b^(8/3))]
    @test_int [x^1*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^3)^3, x, 8, -(x*(a*(b*e - a*h) - b*(b*c - a*f)*x - b*(b*d - a*g)*x^2))/(6*a*b^2*(a + b*x^3)^2) + (x*(a*(b*e - 7*a*h) + 2*b*(2*b*c + a*f)*x + 3*b*(b*d + a*g)*x^2))/(18*a^2*b^2*(a + b*x^3)) - ((2*b^(5/3)*c + a^(2/3)*b*e + a*b^(2/3)*f + 2*a^(5/3)*h)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(7/3)*b^(7/3)) - ((b^(2/3)*(2*b*c + a*f) - a^(2/3)*(b*e + 2*a*h))*log(a^(1/3) + b^(1/3)*x))/(27*a^(7/3)*b^(7/3)) + ((b^(2/3)*(2*b*c + a*f) - a^(2/3)*(b*e + 2*a*h))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(7/3)*b^(7/3))]
    @test_int [x^0*(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(a + b*x^3)^3, x, 8, (x*(b*c - a*f + (b*d - a*g)*x + (b*e - a*h)*x^2))/(6*a*b*(a + b*x^3)^2) - (3*a*(b*e + a*h) - b*x*(5*b*c + a*f + 2*(2*b*d + a*g)*x))/(18*a^2*b^2*(a + b*x^3)) - ((5*b^(4/3)*c + 2*a^(1/3)*b*d + a*b^(1/3)*f + a^(4/3)*g)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(8/3)*b^(5/3)) + ((b^(1/3)*(5*b*c + a*f) - a^(1/3)*(2*b*d + a*g))*log(a^(1/3) + b^(1/3)*x))/(27*a^(8/3)*b^(5/3)) - ((b^(1/3)*(5*b*c + a*f) - a^(1/3)*(2*b*d + a*g))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(8/3)*b^(5/3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x^1*(a + b*x^3)^3), x, 12, (x*(a*(b*d - a*g) + a*(b*e - a*h)*x - b*(b*c - a*f)*x^2))/(6*a^2*b*(a + b*x^3)^2) + (x*(a*(5*b*d + a*g) + 2*a*(2*b*e + a*h)*x - 3*b*(3*b*c - a*f)*x^2))/(18*a^3*b*(a + b*x^3)) - ((5*b^(4/3)*d + 2*a^(1/3)*b*e + a*b^(1/3)*g + a^(4/3)*h)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(8/3)*b^(5/3)) + (c*log(x))/a^3 + ((b^(1/3)*(5*b*d + a*g) - a^(1/3)*(2*b*e + a*h))*log(a^(1/3) + b^(1/3)*x))/(27*a^(8/3)*b^(5/3)) - ((b^(1/3)*(5*b*d + a*g) - a^(1/3)*(2*b*e + a*h))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(8/3)*b^(5/3)) - (c*log(a + b*x^3))/(3*a^3)]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x^2*(a + b*x^3)^3), x, 12, -(c/(a^3*x)) + (x*(a*(b*e - a*h) - b*(b*c - a*f)*x - b*(b*d - a*g)*x^2))/(6*a^2*b*(a + b*x^3)^2) + (x*(a*(5*b*e + a*h) - 2*b*(5*b*c - 2*a*f)*x - 3*b*(3*b*d - a*g)*x^2))/(18*a^3*b*(a + b*x^3)) + ((14*b^(5/3)*c - 5*a^(2/3)*b*e - 2*a*b^(2/3)*f - a^(5/3)*h)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(10/3)*b^(4/3)) + (d*log(x))/a^3 + ((2*b^(2/3)*(7*b*c - a*f) + a^(2/3)*(5*b*e + a*h))*log(a^(1/3) + b^(1/3)*x))/(27*a^(10/3)*b^(4/3)) - ((2*b^(2/3)*(7*b*c - a*f) + a^(2/3)*(5*b*e + a*h))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(10/3)*b^(4/3)) - (d*log(a + b*x^3))/(3*a^3)]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x^3*(a + b*x^3)^3), x, 12, -c/(2*a^3*x^2) - d/(a^3*x) - (x*(b*c - a*f + (b*d - a*g)*x + (b*e - a*h)*x^2))/(6*a^2*(a + b*x^3)^2) - (x*(11*b*c - 5*a*f + 2*(5*b*d - 2*a*g)*x + 3*(3*b*e - a*h)*x^2))/(18*a^3*(a + b*x^3)) + ((20*b^(4/3)*c + 14*a^(1/3)*b*d - 5*a*b^(1/3)*f - 2*a^(4/3)*g)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(11/3)*b^(2/3)) + (e*log(x))/a^3 - ((5*b^(1/3)*(4*b*c - a*f) - 2*a^(1/3)*(7*b*d - a*g))*log(a^(1/3) + b^(1/3)*x))/(27*a^(11/3)*b^(2/3)) + ((5*b^(1/3)*(4*b*c - a*f) - 2*a^(1/3)*(7*b*d - a*g))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(11/3)*b^(2/3)) - (e*log(a + b*x^3))/(3*a^3)]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4 + h*x^5)/(x^4*(a + b*x^3)^3), x, 12, -c/(3*a^3*x^3) - d/(2*a^3*x^2) - e/(a^3*x) - (x*(b*d - a*g + (b*e - a*h)*x - b*((b*c)/a - f)*x^2))/(6*a^2*(a + b*x^3)^2) - (x*(11*b*d - 5*a*g + 2*(5*b*e - 2*a*h)*x - 3*b*((5*b*c)/a - 3*f)*x^2))/(18*a^3*(a + b*x^3)) + ((20*b^(4/3)*d + 14*a^(1/3)*b*e - 5*a*b^(1/3)*g - 2*a^(4/3)*h)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(11/3)*b^(2/3)) - ((3*b*c - a*f)*log(x))/a^4 - ((5*b^(1/3)*(4*b*d - a*g) - 2*a^(1/3)*(7*b*e - a*h))*log(a^(1/3) + b^(1/3)*x))/(27*a^(11/3)*b^(2/3)) + ((5*b^(1/3)*(4*b*d - a*g) - 2*a^(1/3)*(7*b*e - a*h))*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(11/3)*b^(2/3)) + ((3*b*c - a*f)*log(a + b*x^3))/(3*a^4)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*P2(x)*(a+b*x^3)^(p/2)=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^3*(c + d*x + e*x^2)/sqrt(a + b*x^3), x, 10, -((4*a*e*sqrt(a + b*x^3))/(9*b^2)) + (2*c*x*sqrt(a + b*x^3))/(5*b) + (2*d*x^2*sqrt(a + b*x^3))/(7*b) + (2*e*x^3*sqrt(a + b*x^3))/(9*b) - (8*a*d*sqrt(a + b*x^3))/(7*b^(5/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (4*3^(1/4)*sqrt(2 - sqrt(3))*a^(4/3)*d*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(7*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (4*sqrt(2 + sqrt(3))/3^(1/4)*a*(7*b^(1/3)*c - 10*(1 - sqrt(3))*a^(1/3)*d)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(35*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x^2*(c + d*x + e*x^2)/sqrt(a + b*x^3), x, 8, (2*c*sqrt(a + b*x^3))/(3*b) + (2*d*x*sqrt(a + b*x^3))/(5*b) + (2*e*x^2*sqrt(a + b*x^3))/(7*b) - (8*a*e*sqrt(a + b*x^3))/(7*b^(5/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (4*3^(1/4)*sqrt(2 - sqrt(3))*a^(4/3)*e*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(7*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (4*sqrt(2 + sqrt(3))/3^(1/4)*a*(7*b^(1/3)*d - 10*(1 - sqrt(3))*a^(1/3)*e)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(35*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x^1*(c + d*x + e*x^2)/sqrt(a + b*x^3), x, 6, (2*d*sqrt(a + b*x^3))/(3*b) + (2*e*x*sqrt(a + b*x^3))/(5*b) + (2*c*sqrt(a + b*x^3))/(b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*c*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (2*3^(1/4)*sqrt(2 + sqrt(3))*a^(1/3)*(5*(1 - sqrt(3))*b^(2/3)*c + 2*a^(2/3)*e)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(5*sqrt(3)*b^(4/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x^0*(c + d*x + e*x^2)/sqrt(a + b*x^3), x, 5, (2*e*sqrt(a + b*x^3))/(3*b) + (2*d*sqrt(a + b*x^3))/(b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*d*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (2*sqrt(2 + sqrt(3))/3^(1/4)*(b^(1/3)*c - (1 - sqrt(3))*a^(1/3)*d)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2)/(x^1*sqrt(a + b*x^3)), x, 7, (2*e*sqrt(a + b*x^3))/(b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (2*c*atanh(sqrt(a + b*x^3)/sqrt(a)))/(3*sqrt(a)) - (3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*e*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (2*sqrt(2 + sqrt(3))/3^(1/4)*(b^(1/3)*d - (1 - sqrt(3))*a^(1/3)*e)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2)/(x^2*sqrt(a + b*x^3)), x, 8, -((c*sqrt(a + b*x^3))/(a*x)) + (b^(1/3)*c*sqrt(a + b*x^3))/(a*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (2*d*atanh(sqrt(a + b*x^3)/sqrt(a)))/(3*sqrt(a)) - (3^(1/4)*sqrt(2 - sqrt(3))*b^(1/3)*c*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(2*a^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (sqrt(2 + sqrt(3))/3^(1/4)*((1 - sqrt(3))*b^(2/3)*c - 2*a^(2/3)*e)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(a^(2/3)*b^(1/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2)/(x^3*sqrt(a + b*x^3)), x, 9, -((c*sqrt(a + b*x^3))/(2*a*x^2)) - (d*sqrt(a + b*x^3))/(a*x) + (b^(1/3)*d*sqrt(a + b*x^3))/(a*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (2*e*atanh(sqrt(a + b*x^3)/sqrt(a)))/(3*sqrt(a)) - (3^(1/4)*sqrt(2 - sqrt(3))*b^(1/3)*d*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(2*a^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (3^(1/4)*sqrt(2 + sqrt(3))*b^(1/3)*(b^(1/3)*c + 2*(1 - sqrt(3))*a^(1/3)*d)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(2*sqrt(3)*a*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]

    @test_int [x^5*(c + d*x + e*x^2)/(a + b*x^3)^(3/2), x, 8, (2*x*(a*d + a*e*x - b*c*x^2))/(3*b^2*sqrt(a + b*x^3)) + (4*c*sqrt(a + b*x^3))/(3*b^2) + (2*d*x*sqrt(a + b*x^3))/(5*b^2) + (2*e*x^2*sqrt(a + b*x^3))/(7*b^2) - (80*a*e*sqrt(a + b*x^3))/(21*b^(8/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (40*3^(1/4)*sqrt(2 - sqrt(3))*a^(4/3)*e*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(21*b^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (16*sqrt(2 + sqrt(3))/3^(1/4)*a*(14*b^(1/3)*d - 25*(1 - sqrt(3))*a^(1/3)*e)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(105*b^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x^4*(c + d*x + e*x^2)/(a + b*x^3)^(3/2), x, 7, (2*x*(a*e - b*c*x - b*d*x^2))/(3*b^2*sqrt(a + b*x^3)) + (4*d*sqrt(a + b*x^3))/(3*b^2) + (2*e*x*sqrt(a + b*x^3))/(5*b^2) + (8*c*sqrt(a + b*x^3))/(3*b^(5/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (4*3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*c*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (8*3^(1/4)*sqrt(2 + sqrt(3))*a^(1/3)*(5*(1 - sqrt(3))*b^(2/3)*c + 4*a^(2/3)*e)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(15*sqrt(3)*b^(7/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x^3*(c + d*x + e*x^2)/(a + b*x^3)^(3/2), x, 6, -((2*x*(c + d*x + e*x^2))/(3*b*sqrt(a + b*x^3))) + (4*e*sqrt(a + b*x^3))/(3*b^2) + (8*d*sqrt(a + b*x^3))/(3*b^(5/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (4*3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*d*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (4*sqrt(2 + sqrt(3))/3^(1/4)*(b^(1/3)*c - 2*(1 - sqrt(3))*a^(1/3)*d)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x^2*(c + d*x + e*x^2)/(a + b*x^3)^(3/2), x, 4, -((2*(c + d*x + e*x^2))/(3*b*sqrt(a + b*x^3))) + (8*e*sqrt(a + b*x^3))/(3*b^(5/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (4*3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*e*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (4*sqrt(2 + sqrt(3))/3^(1/4)*(b^(1/3)*d - 2*(1 - sqrt(3))*a^(1/3)*e)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x^1*(c + d*x + e*x^2)/(a + b*x^3)^(3/2), x, 6, -((2*x*(a*e - b*c*x - b*d*x^2))/(3*a*b*sqrt(a + b*x^3))) - (2*d*sqrt(a + b*x^3))/(3*a*b) - (2*c*sqrt(a + b*x^3))/(3*a*b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (sqrt(2 - sqrt(3))*c*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3^(3/4)*a^(2/3)*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (2*sqrt(2 + sqrt(3))*(b^(2/3)*(c - sqrt(3)*c) + 2*a^(2/3)*e)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3*3^(1/4)*a^(2/3)*b^(4/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x^0*(c + d*x + e*x^2)/(a + b*x^3)^(3/2), x, 4, -((2*d*sqrt(a + b*x^3))/(3*a*b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x))) - (2*(a*e - b*x*(c + d*x)))/(3*a*b*sqrt(a + b*x^3)) + (3^(1/4)*sqrt(2 - sqrt(3))*d*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3*a^(2/3)*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (2*sqrt(2 + sqrt(3))/3^(1/4)*(b^(1/3)*c + (1 - sqrt(3))*a^(1/3)*d)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3*a*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2)/(x^1*(a + b*x^3)^(3/2)), x, 10, (2*x*(a*d + a*e*x - b*c*x^2))/(3*a^2*sqrt(a + b*x^3)) + (2*c*sqrt(a + b*x^3))/(3*a^2) - (2*e*sqrt(a + b*x^3))/(3*a*b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (2*c*atanh(sqrt(a + b*x^3)/sqrt(a)))/(3*a^(3/2)) + (sqrt(2 - sqrt(3))*e*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3^(3/4)*a^(2/3)*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (2*sqrt(2 + sqrt(3))*(b^(1/3)*d + (1 - sqrt(3))*a^(1/3)*e)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3*3^(1/4)*a*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2)/(x^2*(a + b*x^3)^(3/2)), x, 11, (2*x*(a*e - b*c*x - b*d*x^2))/(3*a^2*sqrt(a + b*x^3)) + (2*d*sqrt(a + b*x^3))/(3*a^2) - (c*sqrt(a + b*x^3))/(a^2*x) + (5*b^(1/3)*c*sqrt(a + b*x^3))/(3*a^2*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (2*d*atanh(sqrt(a + b*x^3)/sqrt(a)))/(3*a^(3/2)) - (5*3^(1/4)*sqrt(2 - sqrt(3))*b^(1/3)*c*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(6*a^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (3^(1/4)*sqrt(2 + sqrt(3))*(5*(1 - sqrt(3))*b^(2/3)*c - 2*a^(2/3)*e)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3*sqrt(3)*a^(5/3)*b^(1/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*P4(x)*(a+b*x^3)^(p/2)=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)*sqrt(a + b*x^3)*x^3, x, 13, -((4*a^2*e*sqrt(a + b*x^3))/(45*b^2)) + (6*a*(17*b*c - 8*a*f)*x*sqrt(a + b*x^3))/(935*b^2) + (6*a*(19*b*d - 10*a*g)*x^2*sqrt(a + b*x^3))/(1729*b^2) + (2*a*e*x^3*sqrt(a + b*x^3))/(45*b) + (6*a*f*x^4*sqrt(a + b*x^3))/(187*b) + (6*a*g*x^5*sqrt(a + b*x^3))/(247*b) - (24*a^2*(19*b*d - 10*a*g)*sqrt(a + b*x^3))/(1729*b^(8/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (2*x^3*sqrt(a + b*x^3)*(62985*c*x + 53295*d*x^2 + 46189*e*x^3 + 40755*f*x^4 + 36465*g*x^5))/692835 + (12*3^(1/4)*sqrt(2 - sqrt(3))*a^(7/3)*(19*b*d - 10*a*g)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(1729*b^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (4*3^(3/4)*sqrt(2 + sqrt(3))*a^2*(1729*b^(1/3)*(17*b*c - 8*a*f) - 1870*(1 - sqrt(3))*a^(1/3)*(19*b*d - 10*a*g))*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(1616615*b^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)*sqrt(a + b*x^3)*x^2, x, 11, (2*a*(5*b*c - 2*a*f)*sqrt(a + b*x^3))/(45*b^2) + (6*a*(17*b*d - 8*a*g)*x*sqrt(a + b*x^3))/(935*b^2) + (6*a*e*x^2*sqrt(a + b*x^3))/(91*b) + (2*a*f*x^3*sqrt(a + b*x^3))/(45*b) + (6*a*g*x^4*sqrt(a + b*x^3))/(187*b) - (24*a^2*e*sqrt(a + b*x^3))/(91*b^(5/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (2*x^2*sqrt(a + b*x^3)*(12155*c*x + 9945*d*x^2 + 8415*e*x^3 + 7293*f*x^4 + 6435*g*x^5))/109395 + (12*3^(1/4)*sqrt(2 - sqrt(3))*a^(7/3)*e*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(91*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (4*3^(3/4)*sqrt(2 + sqrt(3))*a^2*(1547*b*d - 1870*(1 - sqrt(3))*a^(1/3)*b^(2/3)*e - 728*a*g)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(85085*b^(7/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)*sqrt(a + b*x^3)*x^1, x, 9, (2*a*(5*b*d - 2*a*g)*sqrt(a + b*x^3))/(45*b^2) + (6*a*e*x*sqrt(a + b*x^3))/(55*b) + (6*a*f*x^2*sqrt(a + b*x^3))/(91*b) + (2*a*g*x^3*sqrt(a + b*x^3))/(45*b) + (6*a*(13*b*c - 4*a*f)*sqrt(a + b*x^3))/(91*b^(5/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (2*x*sqrt(a + b*x^3)*(6435*c*x + 5005*d*x^2 + 4095*e*x^3 + 3465*f*x^4 + 3003*g*x^5))/45045 - (3*3^(1/4)*sqrt(2 - sqrt(3))*a^(4/3)*(13*b*c - 4*a*f)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(91*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (2*3^(3/4)*sqrt(2 + sqrt(3))*a^(4/3)*(182*a^(2/3)*b^(1/3)*e + 55*(1 - sqrt(3))*(13*b*c - 4*a*f))*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(5005*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)*sqrt(a + b*x^3)*x^0, x, 8, (2*a*e*sqrt(a + b*x^3))/(9*b) + (6*a*f*x*sqrt(a + b*x^3))/(55*b) + (6*a*g*x^2*sqrt(a + b*x^3))/(91*b) + (6*a*(13*b*d - 4*a*g)*sqrt(a + b*x^3))/(91*b^(5/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (2*sqrt(a + b*x^3)*(9009*c*x + 6435*d*x^2 + 5005*e*x^3 + 4095*f*x^4 + 3465*g*x^5))/45045 - (3*3^(1/4)*sqrt(2 - sqrt(3))*a^(4/3)*(13*b*d - 4*a*g)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(91*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (2*3^(3/4)*sqrt(2 + sqrt(3))*a*(91*b^(1/3)*(11*b*c - 2*a*f) - 55*(1 - sqrt(3))*a^(1/3)*(13*b*d - 4*a*g))*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(5005*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)*sqrt(a + b*x^3)/x^1, x, 11, (2*a*f*sqrt(a + b*x^3))/(9*b) + (6*a*g*x*sqrt(a + b*x^3))/(55*b) + (6*a*e*sqrt(a + b*x^3))/(7*b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (2*sqrt(a + b*x^3)*(1155*c*x + 693*d*x^2 + 495*e*x^3 + 385*f*x^4 + 315*g*x^5))/(3465*x) - (2/3)*sqrt(a)*c*atanh(sqrt(a + b*x^3)/sqrt(a)) - (3*3^(1/4)*sqrt(2 - sqrt(3))*a^(4/3)*e*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(7*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (2*3^(3/4)*sqrt(2 + sqrt(3))*a*(77*b*d - 55*(1 - sqrt(3))*a^(1/3)*b^(2/3)*e - 14*a*g)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(385*b^(4/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)*sqrt(a + b*x^3)/x^2, x, 11, (2*a*g*sqrt(a + b*x^3))/(9*b) - (3*c*sqrt(a + b*x^3))/x + (3*(7*b*c + 2*a*f)*sqrt(a + b*x^3))/(7*b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (2*sqrt(a + b*x^3)*(315*c*x + 105*d*x^2 + 63*e*x^3 + 45*f*x^4 + 35*g*x^5))/(315*x^2) - (2/3)*sqrt(a)*d*atanh(sqrt(a + b*x^3)/sqrt(a)) - (3*3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*(7*b*c + 2*a*f)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(14*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (3^(3/4)*sqrt(2 + sqrt(3))*a^(1/3)*(14*a^(2/3)*b^(1/3)*e - 5*(1 - sqrt(3))*(7*b*c + 2*a*f))*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(35*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)*sqrt(a + b*x^3)/x^3, x, 10, (3*c*sqrt(a + b*x^3))/(2*x^2) - (3*d*sqrt(a + b*x^3))/x + (3*(7*b*d + 2*a*g)*sqrt(a + b*x^3))/(7*b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (2*sqrt(a + b*x^3)*(105*c*x - 105*d*x^2 - 35*e*x^3 - 21*f*x^4 - 15*g*x^5))/(105*x^3) - (2/3)*sqrt(a)*e*atanh(sqrt(a + b*x^3)/sqrt(a)) - (3*3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*(7*b*d + 2*a*g)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(14*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (3^(3/4)*sqrt(2 + sqrt(3))*(7*b^(1/3)*(5*b*c + 4*a*f) - 10*(1 - sqrt(3))*a^(1/3)*(7*b*d + 2*a*g))*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(70*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)*sqrt(a + b*x^3)/x^4, x, 11, (c*sqrt(a + b*x^3))/(3*x^3) + (3*d*sqrt(a + b*x^3))/(2*x^2) - (3*e*sqrt(a + b*x^3))/x + (3*b^(1/3)*e*sqrt(a + b*x^3))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x) - (2*sqrt(a + b*x^3)*(5*c*x + 15*d*x^2 - 15*e*x^3 - 5*f*x^4 - 3*g*x^5))/(15*x^4) - ((b*c + 2*a*f)*atanh(sqrt(a + b*x^3)/sqrt(a)))/(3*sqrt(a)) - (3*3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*b^(1/3)*e*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(2*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (3^(3/4)*sqrt(2 + sqrt(3))*(5*b*d - 10*(1 - sqrt(3))*a^(1/3)*b^(2/3)*e + 4*a*g)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(10*b^(1/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)*sqrt(a + b*x^3)/x^5, x, 12, (3*c*sqrt(a + b*x^3))/(20*x^4) + (d*sqrt(a + b*x^3))/(3*x^3) + (3*e*sqrt(a + b*x^3))/(2*x^2) - (3*(b*c + 8*a*f)*sqrt(a + b*x^3))/(8*a*x) + (3*b^(1/3)*(b*c + 8*a*f)*sqrt(a + b*x^3))/(8*a*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (2*sqrt(a + b*x^3)*(3*c*x + 5*d*x^2 + 15*e*x^3 - 15*f*x^4 - 5*g*x^5))/(15*x^5) - ((b*d + 2*a*g)*atanh(sqrt(a + b*x^3)/sqrt(a)))/(3*sqrt(a)) - (3*3^(1/4)*sqrt(2 - sqrt(3))*b^(1/3)*(b*c + 8*a*f)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(16*a^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (3^(3/4)*sqrt(2 + sqrt(3))*b^(1/3)*(4*a^(2/3)*b^(1/3)*e - (1 - sqrt(3))*(b*c + 8*a*f))*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(8*a^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)*sqrt(a + b*x^3)/x^6, x, 10, (-(1/60))*((12*c)/x^5 + (15*d)/x^4 + (20*e)/x^3 + (30*f)/x^2 + (60*g)/x)*sqrt(a + b*x^3) - (3*b*c*sqrt(a + b*x^3))/(20*a*x^2) - (3*b*d*sqrt(a + b*x^3))/(8*a*x) + (3*b^(1/3)*(b*d + 8*a*g)*sqrt(a + b*x^3))/(8*a*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (b*e*atanh(sqrt(a + b*x^3)/sqrt(a)))/(3*sqrt(a)) - (3*3^(1/4)*sqrt(2 - sqrt(3))*b^(1/3)*(b*d + 8*a*g)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(16*a^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (3^(3/4)*sqrt(2 + sqrt(3))*b^(1/3)*(2*b^(1/3)*(b*c - 10*a*f) + 5*(1 - sqrt(3))*a^(1/3)*(b*d + 8*a*g))*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(40*a*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)*sqrt(a + b*x^3)/x^7, x, 11, (-(1/60))*((10*c)/x^6 + (12*d)/x^5 + (15*e)/x^4 + (20*f)/x^3 + (30*g)/x^2)*sqrt(a + b*x^3) - (b*c*sqrt(a + b*x^3))/(12*a*x^3) - (3*b*d*sqrt(a + b*x^3))/(20*a*x^2) - (3*b*e*sqrt(a + b*x^3))/(8*a*x) + (3*b^(4/3)*e*sqrt(a + b*x^3))/(8*a*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (b*(b*c - 4*a*f)*atanh(sqrt(a + b*x^3)/sqrt(a)))/(12*a^(3/2)) - (3*3^(1/4)*sqrt(2 - sqrt(3))*b^(4/3)*e*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(16*a^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (3^(3/4)*sqrt(2 + sqrt(3))*b^(2/3)*(2*b*d + 5*(1 - sqrt(3))*a^(1/3)*b^(2/3)*e - 20*a*g)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(40*a*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)*sqrt(a + b*x^3)/x^8, x, 12, (-(1/420))*((60*c)/x^7 + (70*d)/x^6 + (84*e)/x^5 + (105*f)/x^4 + (140*g)/x^3)*sqrt(a + b*x^3) - (3*b*c*sqrt(a + b*x^3))/(56*a*x^4) - (b*d*sqrt(a + b*x^3))/(12*a*x^3) - (3*b*e*sqrt(a + b*x^3))/(20*a*x^2) + (3*b*(5*b*c - 14*a*f)*sqrt(a + b*x^3))/(112*a^2*x) - (3*b^(4/3)*(5*b*c - 14*a*f)*sqrt(a + b*x^3))/(112*a^2*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (b*(b*d - 4*a*g)*atanh(sqrt(a + b*x^3)/sqrt(a)))/(12*a^(3/2)) + (3*3^(1/4)*sqrt(2 - sqrt(3))*b^(4/3)*(5*b*c - 14*a*f)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(224*a^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (3^(3/4)*sqrt(2 + sqrt(3))*b^(4/3)*(28*a^(2/3)*b^(1/3)*e - 5*(1 - sqrt(3))*(5*b*c - 14*a*f))*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(560*a^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)*sqrt(a + b*x^3)/x^9, x, 13, (-(1/840))*((105*c)/x^8 + (120*d)/x^7 + (140*e)/x^6 + (168*f)/x^5 + (210*g)/x^4)*sqrt(a + b*x^3) - (3*b*c*sqrt(a + b*x^3))/(80*a*x^5) - (3*b*d*sqrt(a + b*x^3))/(56*a*x^4) - (b*e*sqrt(a + b*x^3))/(12*a*x^3) + (3*b*(7*b*c - 16*a*f)*sqrt(a + b*x^3))/(320*a^2*x^2) + (3*b*(5*b*d - 14*a*g)*sqrt(a + b*x^3))/(112*a^2*x) - (3*b^(4/3)*(5*b*d - 14*a*g)*sqrt(a + b*x^3))/(112*a^2*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (b^2*e*atanh(sqrt(a + b*x^3)/sqrt(a)))/(12*a^(3/2)) + (3*3^(1/4)*sqrt(2 - sqrt(3))*b^(4/3)*(5*b*d - 14*a*g)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(224*a^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (3^(3/4)*sqrt(2 + sqrt(3))*b^(4/3)*(7*b^(1/3)*(7*b*c - 16*a*f) + 20*(1 - sqrt(3))*a^(1/3)*(5*b*d - 14*a*g))*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(2240*a^2*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]

    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)*(a + b*x^3)^(3/2)*x^3, x, 14, -((4*a^3*e*sqrt(a + b*x^3))/(105*b^2)) + (54*a^2*(23*b*c - 8*a*f)*x*sqrt(a + b*x^3))/(21505*b^2) + (54*a^2*(5*b*d - 2*a*g)*x^2*sqrt(a + b*x^3))/(8645*b^2) + (2*a^2*e*x^3*sqrt(a + b*x^3))/(105*b) + (54*a^2*f*x^4*sqrt(a + b*x^3))/(4301*b) + (54*a^2*g*x^5*sqrt(a + b*x^3))/(6175*b) - (216*a^3*(5*b*d - 2*a*g)*sqrt(a + b*x^3))/(8645*b^(8/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (2*x^3*(a + b*x^3)^(3/2)*(229425*c*x + 205275*d*x^2 + 185725*e*x^3 + 169575*f*x^4 + 156009*g*x^5))/3900225 + (2*a*x^3*sqrt(a + b*x^3)*(8947575*c*x + 6774075*d*x^2 + 5311735*e*x^3 + 4279275*f*x^4 + 3522519*g*x^5))/185910725 + (108*3^(1/4)*sqrt(2 - sqrt(3))*a^(10/3)*(5*b*d - 2*a*g)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(8645*b^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (36*3^(3/4)*sqrt(2 + sqrt(3))*a^3*(1729*b^(1/3)*(23*b*c - 8*a*f) - 8602*(1 - sqrt(3))*a^(1/3)*(5*b*d - 2*a*g))*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(37182145*b^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)*(a + b*x^3)^(3/2)*x^2, x, 12, (2*a^2*(7*b*c - 2*a*f)*sqrt(a + b*x^3))/(105*b^2) + (54*a^2*(23*b*d - 8*a*g)*x*sqrt(a + b*x^3))/(21505*b^2) + (54*a^2*e*x^2*sqrt(a + b*x^3))/(1729*b) + (2*a^2*f*x^3*sqrt(a + b*x^3))/(105*b) + (54*a^2*g*x^4*sqrt(a + b*x^3))/(4301*b) - (216*a^3*e*sqrt(a + b*x^3))/(1729*b^(5/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (2*x^2*(a + b*x^3)^(3/2)*(52003*c*x + 45885*d*x^2 + 41055*e*x^3 + 37145*f*x^4 + 33915*g*x^5))/780045 + (2*a*x^2*sqrt(a + b*x^3)*(7436429*c*x + 5368545*d*x^2 + 4064445*e*x^3 + 3187041*f*x^4 + 2567565*g*x^5))/111546435 + (108*3^(1/4)*sqrt(2 - sqrt(3))*a^(10/3)*e*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(1729*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (36*3^(3/4)*sqrt(2 + sqrt(3))*a^3*(43010*(1 - sqrt(3))*a^(1/3)*b^(2/3)*e - 1729*(23*b*d - 8*a*g))*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(37182145*b^(7/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)*(a + b*x^3)^(3/2)*x^1, x, 10, (2*a^2*(7*b*d - 2*a*g)*sqrt(a + b*x^3))/(105*b^2) + (54*a^2*e*x*sqrt(a + b*x^3))/(935*b) + (54*a^2*f*x^2*sqrt(a + b*x^3))/(1729*b) + (2*a^2*g*x^3*sqrt(a + b*x^3))/(105*b) + (54*a^2*(19*b*c - 4*a*f)*sqrt(a + b*x^3))/(1729*b^(5/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (2*x*(a + b*x^3)^(3/2)*(33915*c*x + 29393*d*x^2 + 25935*e*x^3 + 23205*f*x^4 + 20995*g*x^5))/440895 + (2*a*x*sqrt(a + b*x^3)*(479655*c*x + 323323*d*x^2 + 233415*e*x^3 + 176715*f*x^4 + 138567*g*x^5))/4849845 - (27*3^(1/4)*sqrt(2 - sqrt(3))*a^(7/3)*(19*b*c - 4*a*f)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(1729*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (18*3^(3/4)*sqrt(2 + sqrt(3))*a^(7/3)*(3458*a^(2/3)*b^(1/3)*e + 935*(1 - sqrt(3))*(19*b*c - 4*a*f))*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(1616615*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)*(a + b*x^3)^(3/2)*x^0, x, 9, (2*a^2*e*sqrt(a + b*x^3))/(15*b) + (54*a^2*f*x*sqrt(a + b*x^3))/(935*b) + (54*a^2*g*x^2*sqrt(a + b*x^3))/(1729*b) + (54*a^2*(19*b*d - 4*a*g)*sqrt(a + b*x^3))/(1729*b^(5/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (2*(a + b*x^3)^(3/2)*(62985*c*x + 53295*d*x^2 + 46189*e*x^3 + 40755*f*x^4 + 36465*g*x^5))/692835 + (2*a*sqrt(a + b*x^3)*(793611*c*x + 479655*d*x^2 + 323323*e*x^3 + 233415*f*x^4 + 176715*g*x^5))/4849845 - (27*3^(1/4)*sqrt(2 - sqrt(3))*a^(7/3)*(19*b*d - 4*a*g)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(1729*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (18*3^(3/4)*sqrt(2 + sqrt(3))*a^2*(1729*b^(1/3)*(17*b*c - 2*a*f) - 935*(1 - sqrt(3))*a^(1/3)*(19*b*d - 4*a*g))*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(1616615*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)*(a + b*x^3)^(3/2)/x^1, x, 12, (2*a^2*f*sqrt(a + b*x^3))/(15*b) + (54*a^2*g*x*sqrt(a + b*x^3))/(935*b) + (54*a^2*e*sqrt(a + b*x^3))/(91*b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (2*(a + b*x^3)^(3/2)*(12155*c*x + 9945*d*x^2 + 8415*e*x^3 + 7293*f*x^4 + 6435*g*x^5))/(109395*x) + (2*a*sqrt(a + b*x^3)*(85085*c*x + 41769*d*x^2 + 25245*e*x^3 + 17017*f*x^4 + 12285*g*x^5))/(255255*x) - (2/3)*a^(3/2)*c*atanh(sqrt(a + b*x^3)/sqrt(a)) - (27*3^(1/4)*sqrt(2 - sqrt(3))*a^(7/3)*e*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(91*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (18*3^(3/4)*sqrt(2 + sqrt(3))*a^2*(1547*b*d - 935*(1 - sqrt(3))*a^(1/3)*b^(2/3)*e - 182*a*g)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(85085*b^(4/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)*(a + b*x^3)^(3/2)/x^2, x, 12, (2*a^2*g*sqrt(a + b*x^3))/(15*b) - (27*a*c*sqrt(a + b*x^3))/(7*x) + (27*a*(13*b*c + 2*a*f)*sqrt(a + b*x^3))/(91*b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (2*a*sqrt(a + b*x^3)*(19305*c*x + 5005*d*x^2 + 2457*e*x^3 + 1485*f*x^4 + 1001*g*x^5))/(15015*x^2) + (2*(a + b*x^3)^(3/2)*(6435*c*x + 5005*d*x^2 + 4095*e*x^3 + 3465*f*x^4 + 3003*g*x^5))/(45045*x^2) - (2/3)*a^(3/2)*d*atanh(sqrt(a + b*x^3)/sqrt(a)) - (27*3^(1/4)*sqrt(2 - sqrt(3))*a^(4/3)*(13*b*c + 2*a*f)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(182*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (9*3^(3/4)*sqrt(2 + sqrt(3))*a^(4/3)*(182*a^(2/3)*b^(1/3)*e - 55*(1 - sqrt(3))*(13*b*c + 2*a*f))*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(5005*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)*(a + b*x^3)^(3/2)/x^3, x, 11, (27*a*c*sqrt(a + b*x^3))/(10*x^2) - (27*a*d*sqrt(a + b*x^3))/(7*x) + (27*a*(13*b*d + 2*a*g)*sqrt(a + b*x^3))/(91*b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (2*a*sqrt(a + b*x^3)*(27027*c*x - 19305*d*x^2 - 5005*e*x^3 - 2457*f*x^4 - 1485*g*x^5))/(15015*x^3) + (2*(a + b*x^3)^(3/2)*(9009*c*x + 6435*d*x^2 + 5005*e*x^3 + 4095*f*x^4 + 3465*g*x^5))/(45045*x^3) - (2/3)*a^(3/2)*e*atanh(sqrt(a + b*x^3)/sqrt(a)) - (27*3^(1/4)*sqrt(2 - sqrt(3))*a^(4/3)*(13*b*d + 2*a*g)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(182*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (9*3^(3/4)*sqrt(2 + sqrt(3))*a*(91*b^(1/3)*(11*b*c + 4*a*f) - 110*(1 - sqrt(3))*a^(1/3)*(13*b*d + 2*a*g))*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(10010*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)*(a + b*x^3)^(3/2)/x^4, x, 12, (a*c*sqrt(a + b*x^3))/x^3 + (27*a*d*sqrt(a + b*x^3))/(10*x^2) - (27*a*e*sqrt(a + b*x^3))/(7*x) + (27*a*b^(1/3)*e*sqrt(a + b*x^3))/(7*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (2*a*sqrt(a + b*x^3)*(1155*c*x + 2079*d*x^2 - 1485*e*x^3 - 385*f*x^4 - 189*g*x^5))/(1155*x^4) + (2*(a + b*x^3)^(3/2)*(1155*c*x + 693*d*x^2 + 495*e*x^3 + 385*f*x^4 + 315*g*x^5))/(3465*x^4) - (1/3)*sqrt(a)*(3*b*c + 2*a*f)*atanh(sqrt(a + b*x^3)/sqrt(a)) - (27*3^(1/4)*sqrt(2 - sqrt(3))*a^(4/3)*b^(1/3)*e*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(14*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (9*3^(3/4)*sqrt(2 + sqrt(3))*a*(77*b*d - 110*(1 - sqrt(3))*a^(1/3)*b^(2/3)*e + 28*a*g)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(770*b^(1/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)*(a + b*x^3)^(3/2)/x^5, x, 13, (27*a*c*sqrt(a + b*x^3))/(20*x^4) + (a*d*sqrt(a + b*x^3))/x^3 + (27*a*e*sqrt(a + b*x^3))/(10*x^2) - (27*(7*b*c + 8*a*f)*sqrt(a + b*x^3))/(56*x) + (27*b^(1/3)*(7*b*c + 8*a*f)*sqrt(a + b*x^3))/(56*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (2*a*sqrt(a + b*x^3)*(189*c*x + 105*d*x^2 + 189*e*x^3 - 135*f*x^4 - 35*g*x^5))/(105*x^5) + (2*(a + b*x^3)^(3/2)*(315*c*x + 105*d*x^2 + 63*e*x^3 + 45*f*x^4 + 35*g*x^5))/(315*x^5) - (1/3)*sqrt(a)*(3*b*d + 2*a*g)*atanh(sqrt(a + b*x^3)/sqrt(a)) - (27*3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*b^(1/3)*(7*b*c + 8*a*f)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(112*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (9*3^(3/4)*sqrt(2 + sqrt(3))*a^(1/3)*b^(1/3)*(28*a^(2/3)*b^(1/3)*e - 5*(1 - sqrt(3))*(7*b*c + 8*a*f))*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(280*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)*(a + b*x^3)^(3/2)/x^6, x, 11, (27*b*c*sqrt(a + b*x^3))/(20*x^2) - (27*b*d*sqrt(a + b*x^3))/(8*x) + (27*b^(1/3)*(7*b*d + 8*a*g)*sqrt(a + b*x^3))/(56*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (1/60)*((12*c)/x^5 + (15*d)/x^4 + (20*e)/x^3 + (30*f)/x^2 + (60*g)/x)*(a + b*x^3)^(3/2) - (b*sqrt(a + b*x^3)*(252*c*x - 315*d*x^2 - 140*e*x^3 - 126*f*x^4 - 180*g*x^5))/(140*x^3) - sqrt(a)*b*e*atanh(sqrt(a + b*x^3)/sqrt(a)) - (27*3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*b^(1/3)*(7*b*d + 8*a*g)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(112*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (9*3^(3/4)*sqrt(2 + sqrt(3))*b^(1/3)*(14*b^(1/3)*(b*c + 2*a*f) - 5*(1 - sqrt(3))*a^(1/3)*(7*b*d + 8*a*g))*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(280*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)*(a + b*x^3)^(3/2)/x^7, x, 12, (b*c*sqrt(a + b*x^3))/(4*x^3) + (27*b*d*sqrt(a + b*x^3))/(20*x^2) - (27*b*e*sqrt(a + b*x^3))/(8*x) + (27*b^(4/3)*e*sqrt(a + b*x^3))/(8*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (1/60)*((10*c)/x^6 + (12*d)/x^5 + (15*e)/x^4 + (20*f)/x^3 + (30*g)/x^2)*(a + b*x^3)^(3/2) - (b*sqrt(a + b*x^3)*(10*c*x + 36*d*x^2 - 45*e*x^3 - 20*f*x^4 - 18*g*x^5))/(20*x^4) - (b*(b*c + 4*a*f)*atanh(sqrt(a + b*x^3)/sqrt(a)))/(4*sqrt(a)) - (27*3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*b^(4/3)*e*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(16*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (9*3^(3/4)*sqrt(2 + sqrt(3))*b^(2/3)*(2*b*d - 5*(1 - sqrt(3))*a^(1/3)*b^(2/3)*e + 4*a*g)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(40*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)*(a + b*x^3)^(3/2)/x^8, x, 13, (27*b*c*sqrt(a + b*x^3))/(280*x^4) + (b*d*sqrt(a + b*x^3))/(4*x^3) + (27*b*e*sqrt(a + b*x^3))/(20*x^2) - (27*b*(b*c + 14*a*f)*sqrt(a + b*x^3))/(112*a*x) + (27*b^(4/3)*(b*c + 14*a*f)*sqrt(a + b*x^3))/(112*a*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (1/420)*((60*c)/x^7 + (70*d)/x^6 + (84*e)/x^5 + (105*f)/x^4 + (140*g)/x^3)*(a + b*x^3)^(3/2) - (b*sqrt(a + b*x^3)*(36*c*x + 70*d*x^2 + 252*e*x^3 - 315*f*x^4 - 140*g*x^5))/(140*x^5) - (b*(b*d + 4*a*g)*atanh(sqrt(a + b*x^3)/sqrt(a)))/(4*sqrt(a)) - (27*3^(1/4)*sqrt(2 - sqrt(3))*b^(4/3)*(b*c + 14*a*f)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(224*a^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (9*3^(3/4)*sqrt(2 + sqrt(3))*b^(4/3)*(28*a^(2/3)*b^(1/3)*e - 5*(1 - sqrt(3))*(b*c + 14*a*f))*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(560*a^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)*(a + b*x^3)^(3/2)/x^9, x, 11, (-(1/560))*b*((63*c)/x^5 + (90*d)/x^4 + (140*e)/x^3 + (252*f)/x^2 + (630*g)/x)*sqrt(a + b*x^3) - (27*b^2*c*sqrt(a + b*x^3))/(320*a*x^2) - (27*b^2*d*sqrt(a + b*x^3))/(112*a*x) + (27*b^(4/3)*(b*d + 14*a*g)*sqrt(a + b*x^3))/(112*a*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (1/840)*((105*c)/x^8 + (120*d)/x^7 + (140*e)/x^6 + (168*f)/x^5 + (210*g)/x^4)*(a + b*x^3)^(3/2) - (b^2*e*atanh(sqrt(a + b*x^3)/sqrt(a)))/(4*sqrt(a)) - (27*3^(1/4)*sqrt(2 - sqrt(3))*b^(4/3)*(b*d + 14*a*g)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(224*a^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (9*3^(3/4)*sqrt(2 + sqrt(3))*b^(4/3)*(7*b^(1/3)*(b*c - 16*a*f) + 20*(1 - sqrt(3))*a^(1/3)*(b*d + 14*a*g))*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(2240*a*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)*(a + b*x^3)^(3/2)/x^10, x, 12, -((b*((140*c)/x^6 + (189*d)/x^5 + (270*e)/x^4 + (420*f)/x^3 + (756*g)/x^2)*sqrt(a + b*x^3))/1680) - (b^2*c*sqrt(a + b*x^3))/(24*a*x^3) - (27*b^2*d*sqrt(a + b*x^3))/(320*a*x^2) - (27*b^2*e*sqrt(a + b*x^3))/(112*a*x) + (27*b^(7/3)*e*sqrt(a + b*x^3))/(112*a*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (((280*c)/x^9 + (315*d)/x^8 + (360*e)/x^7 + (420*f)/x^6 + (504*g)/x^5)*(a + b*x^3)^(3/2))/2520 + (b^2*(b*c - 6*a*f)*atanh(sqrt(a + b*x^3)/sqrt(a)))/(24*a^(3/2)) - (27*3^(1/4)*sqrt(2 - sqrt(3))*b^(7/3)*e*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(224*a^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (9*3^(3/4)*sqrt(2 + sqrt(3))*b^(5/3)*(7*b*d + 20*(1 - sqrt(3))*a^(1/3)*b^(2/3)*e - 112*a*g)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(2240*a*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)*(a + b*x^3)^(3/2)/x^11, x, 13, -((b*((108*c)/x^7 + (140*d)/x^6 + (189*e)/x^5 + (270*f)/x^4 + (420*g)/x^3)*sqrt(a + b*x^3))/1680) - (27*b^2*c*sqrt(a + b*x^3))/(1120*a*x^4) - (b^2*d*sqrt(a + b*x^3))/(24*a*x^3) - (27*b^2*e*sqrt(a + b*x^3))/(320*a*x^2) + (27*b^2*(b*c - 4*a*f)*sqrt(a + b*x^3))/(448*a^2*x) - (27*b^(7/3)*(b*c - 4*a*f)*sqrt(a + b*x^3))/(448*a^2*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (((252*c)/x^10 + (280*d)/x^9 + (315*e)/x^8 + (360*f)/x^7 + (420*g)/x^6)*(a + b*x^3)^(3/2))/2520 + (b^2*(b*d - 6*a*g)*atanh(sqrt(a + b*x^3)/sqrt(a)))/(24*a^(3/2)) + (27*3^(1/4)*sqrt(2 - sqrt(3))*b^(7/3)*(b*c - 4*a*f)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(896*a^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (9*3^(3/4)*sqrt(2 + sqrt(3))*b^(7/3)*(7*a^(2/3)*b^(1/3)*e - 5*(1 - sqrt(3))*(b*c - 4*a*f))*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(2240*a^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(c + d*x + e*x^2 + f*x^3 + g*x^4)*(a + b*x^3)^(3/2)/x^12, x, 14, -((b*((945*c)/x^8 + (1188*d)/x^7 + (1540*e)/x^6 + (2079*f)/x^5 + (2970*g)/x^4)*sqrt(a + b*x^3))/18480) - (27*b^2*c*sqrt(a + b*x^3))/(1760*a*x^5) - (27*b^2*d*sqrt(a + b*x^3))/(1120*a*x^4) - (b^2*e*sqrt(a + b*x^3))/(24*a*x^3) + (27*b^2*(7*b*c - 22*a*f)*sqrt(a + b*x^3))/(7040*a^2*x^2) + (27*b^2*(b*d - 4*a*g)*sqrt(a + b*x^3))/(448*a^2*x) - (27*b^(7/3)*(b*d - 4*a*g)*sqrt(a + b*x^3))/(448*a^2*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (((2520*c)/x^11 + (2772*d)/x^10 + (3080*e)/x^9 + (3465*f)/x^8 + (3960*g)/x^7)*(a + b*x^3)^(3/2))/27720 + (b^3*e*atanh(sqrt(a + b*x^3)/sqrt(a)))/(24*a^(3/2)) + (27*3^(1/4)*sqrt(2 - sqrt(3))*b^(7/3)*(b*d - 4*a*g)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(896*a^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (9*3^(3/4)*sqrt(2 + sqrt(3))*b^(7/3)*(7*b^(1/3)*(7*b*c - 22*a*f) + 110*(1 - sqrt(3))*a^(1/3)*(b*d - 4*a*g))*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(49280*a^2*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]

    #= ::Subsubsection:: =#
    #=p<0=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*Pq(x)*(a+b*x^3)^p*with*p*symbolic=#

    @test_int [x^0*(c + d*x + e*x^2)*(a + b*x^3)^p, x, 8, (e*(a + b*x^3)^(1 + p))/(3*b*(1 + p)) + (c*x*(a + b*x^3)^(1 + p)*HypergeometricFunctions._₂F₁(1, 4/3 + p, 4/3, -((b*x^3)/a)))/a + (d*x^2*(a + b*x^3)^(1 + p)*HypergeometricFunctions._₂F₁(1, 5/3 + p, 5/3, -((b*x^3)/a)))/(2*a), (e*(a + b*x^3)^(1 + p))/(3*b*(1 + p)) + (c*x*(a + b*x^3)^p*HypergeometricFunctions._₂F₁(1/3, -p, 4/3, -((b*x^3)/a)))/(1 + b*x^3/a)^p + ((1/2)*d*x^2*(a + b*x^3)^p*HypergeometricFunctions._₂F₁(2/3, -p, 5/3, -((b*x^3)/a)))/(1 + b*x^3/a)^p]
    @test_int [x^1*(c + d*x + e*x^2)*(a + b*x^3)^p, x, 7, (d*(a + b*x^3)^(1 + p))/(3*b*(1 + p)) + (c*x^2*(a + b*x^3)^(1 + p)*HypergeometricFunctions._₂F₁(1, 5/3 + p, 5/3, -((b*x^3)/a)))/(2*a) + (e*x^4*(a + b*x^3)^(1 + p)*HypergeometricFunctions._₂F₁(1, 7/3 + p, 7/3, -((b*x^3)/a)))/(4*a), (d*(a + b*x^3)^(1 + p))/(3*b*(1 + p)) + ((1/2)*c*x^2*(a + b*x^3)^p*HypergeometricFunctions._₂F₁(2/3, -p, 5/3, -((b*x^3)/a)))/(1 + b*x^3/a)^p + ((1/4)*e*x^4*(a + b*x^3)^p*HypergeometricFunctions._₂F₁(4/3, -p, 7/3, -((b*x^3)/a)))/(1 + b*x^3/a)^p]
    @test_int [x^2*(c + d*x + e*x^2)*(a + b*x^3)^p, x, 7, (c*(a + b*x^3)^(1 + p))/(3*b*(1 + p)) + (d*x^4*(a + b*x^3)^(1 + p)*HypergeometricFunctions._₂F₁(1, 7/3 + p, 7/3, -((b*x^3)/a)))/(4*a) + (e*x^5*(a + b*x^3)^(1 + p)*HypergeometricFunctions._₂F₁(1, 8/3 + p, 8/3, -((b*x^3)/a)))/(5*a), (c*(a + b*x^3)^(1 + p))/(3*b*(1 + p)) + ((1/4)*d*x^4*(a + b*x^3)^p*HypergeometricFunctions._₂F₁(4/3, -p, 7/3, -((b*x^3)/a)))/(1 + b*x^3/a)^p + ((1/5)*e*x^5*(a + b*x^3)^p*HypergeometricFunctions._₂F₁(5/3, -p, 8/3, -((b*x^3)/a)))/(1 + b*x^3/a)^p]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*Pq(x)*(a+b*x^4)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*P3(x)*(a+b*x^4)^p=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^0*(c + d*x + e*x^2 + f*x^3)*(a + b*x^4), x, 2, a*c*x + (1/2)*a*d*x^2 + (1/3)*a*e*x^3 + (1/4)*a*f*x^4 + (1/5)*b*c*x^5 + (1/6)*b*d*x^6 + (1/7)*b*e*x^7 + (1/8)*b*f*x^8]
    @test_int [x^3*(c + d*x + e*x^2 + f*x^3)*(a + b*x^4), x, 2, (1/4)*a*c*x^4 + (1/5)*a*d*x^5 + (1/6)*a*e*x^6 + (1/7)*a*f*x^7 + (1/8)*b*c*x^8 + (1/9)*b*d*x^9 + (1/10)*b*e*x^10 + (1/11)*b*f*x^11]

    @test_int [x^0*(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^2, x, 3, a^2*c*x + (1/2)*a^2*d*x^2 + (1/3)*a^2*e*x^3 + (2/5)*a*b*c*x^5 + (1/3)*a*b*d*x^6 + (2/7)*a*b*e*x^7 + (1/9)*b^2*c*x^9 + (1/10)*b^2*d*x^10 + (1/11)*b^2*e*x^11 + (f*(a + b*x^4)^3)/(12*b)]
    @test_int [x^3*(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^2, x, 3, (1/5)*a^2*d*x^5 + (1/6)*a^2*e*x^6 + (1/7)*a^2*f*x^7 + (2/9)*a*b*d*x^9 + (1/5)*a*b*e*x^10 + (2/11)*a*b*f*x^11 + (1/13)*b^2*d*x^13 + (1/14)*b^2*e*x^14 + (1/15)*b^2*f*x^15 + (c*(a + b*x^4)^3)/(12*b)]

    @test_int [x^0*(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^3, x, 3, a^3*c*x + (1/2)*a^3*d*x^2 + (1/3)*a^3*e*x^3 + (3/5)*a^2*b*c*x^5 + (1/2)*a^2*b*d*x^6 + (3/7)*a^2*b*e*x^7 + (1/3)*a*b^2*c*x^9 + (3/10)*a*b^2*d*x^10 + (3/11)*a*b^2*e*x^11 + (1/13)*b^3*c*x^13 + (1/14)*b^3*d*x^14 + (1/15)*b^3*e*x^15 + (f*(a + b*x^4)^4)/(16*b)]
    @test_int [x^3*(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^3, x, 3, (1/5)*a^3*d*x^5 + (1/6)*a^3*e*x^6 + (1/7)*a^3*f*x^7 + (1/3)*a^2*b*d*x^9 + (3/10)*a^2*b*e*x^10 + (3/11)*a^2*b*f*x^11 + (3/13)*a*b^2*d*x^13 + (3/14)*a*b^2*e*x^14 + (1/5)*a*b^2*f*x^15 + (1/17)*b^3*d*x^17 + (1/18)*b^3*e*x^18 + (1/19)*b^3*f*x^19 + (c*(a + b*x^4)^4)/(16*b)]

    @test_int [x^0*(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^4, x, 3, a^4*c*x + (1/2)*a^4*d*x^2 + (1/3)*a^4*e*x^3 + (4/5)*a^3*b*c*x^5 + (2/3)*a^3*b*d*x^6 + (4/7)*a^3*b*e*x^7 + (2/3)*a^2*b^2*c*x^9 + (3/5)*a^2*b^2*d*x^10 + (6/11)*a^2*b^2*e*x^11 + (4/13)*a*b^3*c*x^13 + (2/7)*a*b^3*d*x^14 + (4/15)*a*b^3*e*x^15 + (1/17)*b^4*c*x^17 + (1/18)*b^4*d*x^18 + (1/19)*b^4*e*x^19 + (f*(a + b*x^4)^5)/(20*b)]
    @test_int [x^3*(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^4, x, 3, (1/5)*a^4*d*x^5 + (1/6)*a^4*e*x^6 + (1/7)*a^4*f*x^7 + (4/9)*a^3*b*d*x^9 + (2/5)*a^3*b*e*x^10 + (4/11)*a^3*b*f*x^11 + (6/13)*a^2*b^2*d*x^13 + (3/7)*a^2*b^2*e*x^14 + (2/5)*a^2*b^2*f*x^15 + (4/17)*a*b^3*d*x^17 + (2/9)*a*b^3*e*x^18 + (4/19)*a*b^3*f*x^19 + (1/21)*b^4*d*x^21 + (1/22)*b^4*e*x^22 + (1/23)*b^4*f*x^23 + (c*(a + b*x^4)^5)/(20*b)]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^0*(c + d*x + e*x^2 + f*x^3)/(a - b*x^4), x, 9, ((sqrt(b)*c - sqrt(a)*e)*atan((b^(1/4)*x)/a^(1/4)))/(2*a^(3/4)*b^(3/4)) + ((sqrt(b)*c + sqrt(a)*e)*atanh((b^(1/4)*x)/a^(1/4)))/(2*a^(3/4)*b^(3/4)) + (d*atanh((sqrt(b)*x^2)/sqrt(a)))/(2*sqrt(a)*sqrt(b)) - (f*log(a - b*x^4))/(4*b)]
    @test_int [x^3*(c + d*x + e*x^2 + f*x^3)/(a - b*x^4), x, 12, -((d*x)/b) - (e*x^2)/(2*b) - (f*x^3)/(3*b) + (a^(1/4)*(sqrt(b)*d - sqrt(a)*f)*atan((b^(1/4)*x)/a^(1/4)))/(2*b^(7/4)) + (a^(1/4)*(sqrt(b)*d + sqrt(a)*f)*atanh((b^(1/4)*x)/a^(1/4)))/(2*b^(7/4)) + (sqrt(a)*e*atanh((sqrt(b)*x^2)/sqrt(a)))/(2*b^(3/2)) - (c*log(a - b*x^4))/(4*b)]

    @test_int [x^0*(c + d*x + e*x^2 + f*x^3)/(a + b*x^4), x, 15, (d*atan((sqrt(b)*x^2)/sqrt(a)))/(2*sqrt(a)*sqrt(b)) - ((sqrt(b)*c + sqrt(a)*e)*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*a^(3/4)*b^(3/4)) + ((sqrt(b)*c + sqrt(a)*e)*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*a^(3/4)*b^(3/4)) - ((sqrt(b)*c - sqrt(a)*e)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*a^(3/4)*b^(3/4)) + ((sqrt(b)*c - sqrt(a)*e)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*a^(3/4)*b^(3/4)) + (f*log(a + b*x^4))/(4*b)]
    @test_int [x^3*(c + d*x + e*x^2 + f*x^3)/(a + b*x^4), x, 18, (d*x)/b + (e*x^2)/(2*b) + (f*x^3)/(3*b) - (sqrt(a)*e*atan((sqrt(b)*x^2)/sqrt(a)))/(2*b^(3/2)) + (a^(1/4)*(sqrt(b)*d + sqrt(a)*f)*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*b^(7/4)) - (a^(1/4)*(sqrt(b)*d + sqrt(a)*f)*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*b^(7/4)) + (a^(1/4)*(sqrt(b)*d - sqrt(a)*f)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*b^(7/4)) - (a^(1/4)*(sqrt(b)*d - sqrt(a)*f)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*b^(7/4)) + (c*log(a + b*x^4))/(4*b)]

    @test_int [x^0*(c + d*x + e*x^2 + f*x^3)/(a + b*x^4)^2, x, 14, -((a*f - b*x*(c + d*x + e*x^2))/(4*a*b*(a + b*x^4))) + (d*atan((sqrt(b)*x^2)/sqrt(a)))/(4*a^(3/2)*sqrt(b)) - ((3*sqrt(b)*c + sqrt(a)*e)*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(8*sqrt(2)*a^(7/4)*b^(3/4)) + ((3*sqrt(b)*c + sqrt(a)*e)*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(8*sqrt(2)*a^(7/4)*b^(3/4)) - ((3*sqrt(b)*c - sqrt(a)*e)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(16*sqrt(2)*a^(7/4)*b^(3/4)) + ((3*sqrt(b)*c - sqrt(a)*e)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(16*sqrt(2)*a^(7/4)*b^(3/4))]
    @test_int [x^3*(c + d*x + e*x^2 + f*x^3)/(a + b*x^4)^2, x, 14, -((c + d*x + e*x^2 + f*x^3)/(4*b*(a + b*x^4))) + (e*atan((sqrt(b)*x^2)/sqrt(a)))/(4*sqrt(a)*b^(3/2)) - ((sqrt(b)*d + 3*sqrt(a)*f)*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(8*sqrt(2)*a^(3/4)*b^(7/4)) + ((sqrt(b)*d + 3*sqrt(a)*f)*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(8*sqrt(2)*a^(3/4)*b^(7/4)) - ((sqrt(b)*d - 3*sqrt(a)*f)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(16*sqrt(2)*a^(3/4)*b^(7/4)) + ((sqrt(b)*d - 3*sqrt(a)*f)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(16*sqrt(2)*a^(3/4)*b^(7/4))]

    @test_int [x^0*(c + d*x + e*x^2 + f*x^3)/(a + b*x^4)^3, x, 15, (x*(7*c + 6*d*x + 5*e*x^2))/(32*a^2*(a + b*x^4)) - (a*f - b*x*(c + d*x + e*x^2))/(8*a*b*(a + b*x^4)^2) + (3*d*atan((sqrt(b)*x^2)/sqrt(a)))/(16*a^(5/2)*sqrt(b)) - ((21*sqrt(b)*c + 5*sqrt(a)*e)*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(64*sqrt(2)*a^(11/4)*b^(3/4)) + ((21*sqrt(b)*c + 5*sqrt(a)*e)*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(64*sqrt(2)*a^(11/4)*b^(3/4)) - ((21*sqrt(b)*c - 5*sqrt(a)*e)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(128*sqrt(2)*a^(11/4)*b^(3/4)) + ((21*sqrt(b)*c - 5*sqrt(a)*e)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(128*sqrt(2)*a^(11/4)*b^(3/4))]
    @test_int [x^3*(c + d*x + e*x^2 + f*x^3)/(a + b*x^4)^3, x, 15, -((c + d*x + e*x^2 + f*x^3)/(8*b*(a + b*x^4)^2)) + (x*(d + 2*e*x + 3*f*x^2))/(32*a*b*(a + b*x^4)) + (e*atan((sqrt(b)*x^2)/sqrt(a)))/(16*a^(3/2)*b^(3/2)) - (3*(sqrt(b)*d + sqrt(a)*f)*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(64*sqrt(2)*a^(7/4)*b^(7/4)) + (3*(sqrt(b)*d + sqrt(a)*f)*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(64*sqrt(2)*a^(7/4)*b^(7/4)) - (3*(sqrt(b)*d - sqrt(a)*f)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(128*sqrt(2)*a^(7/4)*b^(7/4)) + (3*(sqrt(b)*d - sqrt(a)*f)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(128*sqrt(2)*a^(7/4)*b^(7/4))]

    @test_int [x^0*(c + d*x + e*x^2 + f*x^3)/(a + b*x^4)^4, x, 16, (x*(11*c + 10*d*x + 9*e*x^2))/(96*a^2*(a + b*x^4)^2) + (x*(77*c + 60*d*x + 45*e*x^2))/(384*a^3*(a + b*x^4)) - (a*f - b*x*(c + d*x + e*x^2))/(12*a*b*(a + b*x^4)^3) + (5*d*atan((sqrt(b)*x^2)/sqrt(a)))/(32*a^(7/2)*sqrt(b)) - ((77*sqrt(b)*c + 15*sqrt(a)*e)*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(256*sqrt(2)*a^(15/4)*b^(3/4)) + ((77*sqrt(b)*c + 15*sqrt(a)*e)*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(256*sqrt(2)*a^(15/4)*b^(3/4)) - ((77*sqrt(b)*c - 15*sqrt(a)*e)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(512*sqrt(2)*a^(15/4)*b^(3/4)) + ((77*sqrt(b)*c - 15*sqrt(a)*e)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(512*sqrt(2)*a^(15/4)*b^(3/4))]
    @test_int [x^3*(c + d*x + e*x^2 + f*x^3)/(a + b*x^4)^4, x, 16, -((c + d*x + e*x^2 + f*x^3)/(12*b*(a + b*x^4)^3)) + (x*(d + 2*e*x + 3*f*x^2))/(96*a*b*(a + b*x^4)^2) + (x*(7*d + 12*e*x + 15*f*x^2))/(384*a^2*b*(a + b*x^4)) + (e*atan((sqrt(b)*x^2)/sqrt(a)))/(32*a^(5/2)*b^(3/2)) - ((7*sqrt(b)*d + 5*sqrt(a)*f)*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(256*sqrt(2)*a^(11/4)*b^(7/4)) + ((7*sqrt(b)*d + 5*sqrt(a)*f)*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(256*sqrt(2)*a^(11/4)*b^(7/4)) - ((7*sqrt(b)*d - 5*sqrt(a)*f)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(512*sqrt(2)*a^(11/4)*b^(7/4)) + ((7*sqrt(b)*d - 5*sqrt(a)*f)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(512*sqrt(2)*a^(11/4)*b^(7/4))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*P3(x)*(a+b*x^4)^(p/2)=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^4*(c + d*x + e*x^2 + f*x^3)*sqrt(a + b*x^4), x, 14, (2*a*c*x*sqrt(a + b*x^4))/(21*b) - (a*d*x^2*sqrt(a + b*x^4))/(16*b) + (2*a*e*x^3*sqrt(a + b*x^4))/(45*b) - (2*a^2*e*x*sqrt(a + b*x^4))/(15*b^(3/2)*(sqrt(a) + sqrt(b)*x^2)) + (x^5*(9*c + 7*e*x^2)*sqrt(a + b*x^4))/63 + (f*x^4*(a + b*x^4)^(3/2))/(10*b) - ((8*a*f - 15*b*d*x^2)*(a + b*x^4)^(3/2))/(120*b^2) - (a^2*d*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(16*b^(3/2)) + (2*a^(9/4)*e*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(15*b^(7/4)*sqrt(a + b*x^4)) - (a^(7/4)*(5*sqrt(b)*c + 7*sqrt(a)*e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(105*b^(7/4)*sqrt(a + b*x^4))]
    @test_int [x^3*(c + d*x + e*x^2 + f*x^3)*sqrt(a + b*x^4), x, 13, (2*a*d*x*sqrt(a + b*x^4))/(21*b) - (a*e*x^2*sqrt(a + b*x^4))/(16*b) + (2*a*f*x^3*sqrt(a + b*x^4))/(45*b) - (2*a^2*f*x*sqrt(a + b*x^4))/(15*b^(3/2)*(sqrt(a) + sqrt(b)*x^2)) + (x^5*(9*d + 7*f*x^2)*sqrt(a + b*x^4))/63 + ((4*c + 3*e*x^2)*(a + b*x^4)^(3/2))/(24*b) - (a^2*e*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(16*b^(3/2)) + (2*a^(9/4)*f*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(15*b^(7/4)*sqrt(a + b*x^4)) - (a^(7/4)*(5*sqrt(b)*d + 7*sqrt(a)*f)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(105*b^(7/4)*sqrt(a + b*x^4))]
    @test_int [x^2*(c + d*x + e*x^2 + f*x^3)*sqrt(a + b*x^4), x, 12, (2*a*e*x*sqrt(a + b*x^4))/(21*b) - (a*f*x^2*sqrt(a + b*x^4))/(16*b) + (2*a*c*x*sqrt(a + b*x^4))/(5*sqrt(b)*(sqrt(a) + sqrt(b)*x^2)) + (x^3*(7*c + 5*e*x^2)*sqrt(a + b*x^4))/35 + ((4*d + 3*f*x^2)*(a + b*x^4)^(3/2))/(24*b) - (a^2*f*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(16*b^(3/2)) - (2*a^(5/4)*c*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(5*b^(3/4)*sqrt(a + b*x^4)) + (a^(5/4)*(21*sqrt(b)*c - 5*sqrt(a)*e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(105*b^(5/4)*sqrt(a + b*x^4))]
    @test_int [x^1*(c + d*x + e*x^2 + f*x^3)*sqrt(a + b*x^4), x, 12, (2*a*f*x*sqrt(a + b*x^4))/(21*b) + (c*x^2*sqrt(a + b*x^4))/4 + (2*a*d*x*sqrt(a + b*x^4))/(5*sqrt(b)*(sqrt(a) + sqrt(b)*x^2)) + (x^3*(7*d + 5*f*x^2)*sqrt(a + b*x^4))/35 + (e*(a + b*x^4)^(3/2))/(6*b) + (a*c*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(4*sqrt(b)) - (2*a^(5/4)*d*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(5*b^(3/4)*sqrt(a + b*x^4)) + (a^(5/4)*(21*sqrt(b)*d - 5*sqrt(a)*f)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(105*b^(5/4)*sqrt(a + b*x^4))]
    @test_int [x^0*(c + d*x + e*x^2 + f*x^3)*sqrt(a + b*x^4), x, 11, (d*x^2*sqrt(a + b*x^4))/4 + (2*a*e*x*sqrt(a + b*x^4))/(5*sqrt(b)*(sqrt(a) + sqrt(b)*x^2)) + (x*(5*c + 3*e*x^2)*sqrt(a + b*x^4))/15 + (f*(a + b*x^4)^(3/2))/(6*b) + (a*d*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(4*sqrt(b)) - (2*a^(5/4)*e*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(5*b^(3/4)*sqrt(a + b*x^4)) + (a^(3/4)*(5*sqrt(b)*c + 3*sqrt(a)*e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(15*b^(3/4)*sqrt(a + b*x^4))]
    @test_int [((c + d*x + e*x^2 + f*x^3)*sqrt(a + b*x^4))/x^1, x, 14, (2*a*f*x*sqrt(a + b*x^4))/(5*sqrt(b)*(sqrt(a) + sqrt(b)*x^2)) + ((2*c + e*x^2)*sqrt(a + b*x^4))/4 + (x*(5*d + 3*f*x^2)*sqrt(a + b*x^4))/15 + (a*e*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(4*sqrt(b)) - (sqrt(a)*c*atanh(sqrt(a + b*x^4)/sqrt(a)))/2 - (2*a^(5/4)*f*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(5*b^(3/4)*sqrt(a + b*x^4)) + (a^(3/4)*(5*sqrt(b)*d + 3*sqrt(a)*f)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(15*b^(3/4)*sqrt(a + b*x^4))]
    @test_int [((c + d*x + e*x^2 + f*x^3)*sqrt(a + b*x^4))/x^2, x, 14, (2*sqrt(b)*c*x*sqrt(a + b*x^4))/(sqrt(a) + sqrt(b)*x^2) - ((3*c - e*x^2)*sqrt(a + b*x^4))/(3*x) + ((2*d + f*x^2)*sqrt(a + b*x^4))/4 + (a*f*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(4*sqrt(b)) - (sqrt(a)*d*atanh(sqrt(a + b*x^4)/sqrt(a)))/2 - (2*a^(1/4)*b^(1/4)*c*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/sqrt(a + b*x^4) + (a^(1/4)*(3*sqrt(b)*c + sqrt(a)*e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(3*b^(1/4)*sqrt(a + b*x^4))]
    @test_int [((c + d*x + e*x^2 + f*x^3)*sqrt(a + b*x^4))/x^3, x, 14, (2*sqrt(b)*d*x*sqrt(a + b*x^4))/(sqrt(a) + sqrt(b)*x^2) - ((c - e*x^2)*sqrt(a + b*x^4))/(2*x^2) - ((3*d - f*x^2)*sqrt(a + b*x^4))/(3*x) + (sqrt(b)*c*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/2 - (sqrt(a)*e*atanh(sqrt(a + b*x^4)/sqrt(a)))/2 - (2*a^(1/4)*b^(1/4)*d*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/sqrt(a + b*x^4) + (a^(1/4)*(3*sqrt(b)*d + sqrt(a)*f)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(3*b^(1/4)*sqrt(a + b*x^4))]
    @test_int [((c + d*x + e*x^2 + f*x^3)*sqrt(a + b*x^4))/x^4, x, 15, (-2*e*sqrt(a + b*x^4))/x + (2*sqrt(b)*e*x*sqrt(a + b*x^4))/(sqrt(a) + sqrt(b)*x^2) - ((c - 3*e*x^2)*sqrt(a + b*x^4))/(3*x^3) - ((d - f*x^2)*sqrt(a + b*x^4))/(2*x^2) + (sqrt(b)*d*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/2 - (sqrt(a)*f*atanh(sqrt(a + b*x^4)/sqrt(a)))/2 - (2*a^(1/4)*b^(1/4)*e*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/sqrt(a + b*x^4) + (b^(1/4)*(sqrt(b)*c + 3*sqrt(a)*e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(3*a^(1/4)*sqrt(a + b*x^4))]
    @test_int [((c + d*x + e*x^2 + f*x^3)*sqrt(a + b*x^4))/x^5, x, 13, -(((3*c)/x^4 + (4*d)/x^3 + (6*e)/x^2 + (12*f)/x)*sqrt(a + b*x^4))/12 + (2*sqrt(b)*f*x*sqrt(a + b*x^4))/(sqrt(a) + sqrt(b)*x^2) + (sqrt(b)*e*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/2 - (b*c*atanh(sqrt(a + b*x^4)/sqrt(a)))/(4*sqrt(a)) - (2*a^(1/4)*b^(1/4)*f*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/sqrt(a + b*x^4) + (b^(1/4)*(sqrt(b)*d + 3*sqrt(a)*f)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(3*a^(1/4)*sqrt(a + b*x^4))]
    @test_int [((c + d*x + e*x^2 + f*x^3)*sqrt(a + b*x^4))/x^6, x, 14, -(((12*c)/x^5 + (15*d)/x^4 + (20*e)/x^3 + (30*f)/x^2)*sqrt(a + b*x^4))/60 - (2*b*c*sqrt(a + b*x^4))/(5*a*x) + (2*b^(3/2)*c*x*sqrt(a + b*x^4))/(5*a*(sqrt(a) + sqrt(b)*x^2)) + (sqrt(b)*f*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/2 - (b*d*atanh(sqrt(a + b*x^4)/sqrt(a)))/(4*sqrt(a)) - (2*b^(5/4)*c*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(5*a^(3/4)*sqrt(a + b*x^4)) + (b^(3/4)*(3*sqrt(b)*c + 5*sqrt(a)*e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(15*a^(3/4)*sqrt(a + b*x^4))]
    @test_int [((c + d*x + e*x^2 + f*x^3)*sqrt(a + b*x^4))/x^7, x, 12, -(((10*c)/x^6 + (12*d)/x^5 + (15*e)/x^4 + (20*f)/x^3)*sqrt(a + b*x^4))/60 - (b*c*sqrt(a + b*x^4))/(6*a*x^2) - (2*b*d*sqrt(a + b*x^4))/(5*a*x) + (2*b^(3/2)*d*x*sqrt(a + b*x^4))/(5*a*(sqrt(a) + sqrt(b)*x^2)) - (b*e*atanh(sqrt(a + b*x^4)/sqrt(a)))/(4*sqrt(a)) - (2*b^(5/4)*d*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(5*a^(3/4)*sqrt(a + b*x^4)) + (b^(3/4)*(3*sqrt(b)*d + 5*sqrt(a)*f)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(15*a^(3/4)*sqrt(a + b*x^4))]
    @test_int [((c + d*x + e*x^2 + f*x^3)*sqrt(a + b*x^4))/x^8, x, 13, -(((60*c)/x^7 + (70*d)/x^6 + (84*e)/x^5 + (105*f)/x^4)*sqrt(a + b*x^4))/420 - (2*b*c*sqrt(a + b*x^4))/(21*a*x^3) - (b*d*sqrt(a + b*x^4))/(6*a*x^2) - (2*b*e*sqrt(a + b*x^4))/(5*a*x) + (2*b^(3/2)*e*x*sqrt(a + b*x^4))/(5*a*(sqrt(a) + sqrt(b)*x^2)) - (b*f*atanh(sqrt(a + b*x^4)/sqrt(a)))/(4*sqrt(a)) - (2*b^(5/4)*e*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(5*a^(3/4)*sqrt(a + b*x^4)) - (b^(5/4)*(5*sqrt(b)*c - 21*sqrt(a)*e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(105*a^(5/4)*sqrt(a + b*x^4))]
    @test_int [((c + d*x + e*x^2 + f*x^3)*sqrt(a + b*x^4))/x^9, x, 14, -(((105*c)/x^8 + (120*d)/x^7 + (140*e)/x^6 + (168*f)/x^5)*sqrt(a + b*x^4))/840 - (b*c*sqrt(a + b*x^4))/(16*a*x^4) - (2*b*d*sqrt(a + b*x^4))/(21*a*x^3) - (b*e*sqrt(a + b*x^4))/(6*a*x^2) - (2*b*f*sqrt(a + b*x^4))/(5*a*x) + (2*b^(3/2)*f*x*sqrt(a + b*x^4))/(5*a*(sqrt(a) + sqrt(b)*x^2)) + (b^2*c*atanh(sqrt(a + b*x^4)/sqrt(a)))/(16*a^(3/2)) - (2*b^(5/4)*f*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(5*a^(3/4)*sqrt(a + b*x^4)) - (b^(5/4)*(5*sqrt(b)*d - 21*sqrt(a)*f)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(105*a^(5/4)*sqrt(a + b*x^4))]
    @test_int [((c + d*x + e*x^2 + f*x^3)*sqrt(a + b*x^4))/x^10, x, 15, -(((56*c)/x^9 + (63*d)/x^8 + (72*e)/x^7 + (84*f)/x^6)*sqrt(a + b*x^4))/504 - (2*b*c*sqrt(a + b*x^4))/(45*a*x^5) - (b*d*sqrt(a + b*x^4))/(16*a*x^4) - (2*b*e*sqrt(a + b*x^4))/(21*a*x^3) - (b*f*sqrt(a + b*x^4))/(6*a*x^2) + (2*b^2*c*sqrt(a + b*x^4))/(15*a^2*x) - (2*b^(5/2)*c*x*sqrt(a + b*x^4))/(15*a^2*(sqrt(a) + sqrt(b)*x^2)) + (b^2*d*atanh(sqrt(a + b*x^4)/sqrt(a)))/(16*a^(3/2)) + (2*b^(9/4)*c*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(15*a^(7/4)*sqrt(a + b*x^4)) - (b^(7/4)*(7*sqrt(b)*c + 5*sqrt(a)*e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(105*a^(7/4)*sqrt(a + b*x^4))]

    @test_int [x^4*(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2), x, 16, (4*a^2*c*x*sqrt(a + b*x^4))/(77*b) - (a^2*d*x^2*sqrt(a + b*x^4))/(32*b) + (4*a^2*e*x^3*sqrt(a + b*x^4))/(195*b) - (4*a^3*e*x*sqrt(a + b*x^4))/(65*b^(3/2)*(sqrt(a) + sqrt(b)*x^2)) + (2*a*x^5*(117*c + 77*e*x^2)*sqrt(a + b*x^4))/3003 - (a*d*x^2*(a + b*x^4)^(3/2))/(48*b) + (x^5*(13*c + 11*e*x^2)*(a + b*x^4)^(3/2))/143 + (f*x^4*(a + b*x^4)^(5/2))/(14*b) - ((12*a*f - 35*b*d*x^2)*(a + b*x^4)^(5/2))/(420*b^2) - (a^3*d*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(32*b^(3/2)) + (4*a^(13/4)*e*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(65*b^(7/4)*sqrt(a + b*x^4)) - (2*a^(11/4)*(65*sqrt(b)*c + 77*sqrt(a)*e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(5005*b^(7/4)*sqrt(a + b*x^4))]
    @test_int [x^3*(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2), x, 15, (4*a^2*d*x*sqrt(a + b*x^4))/(77*b) - (a^2*e*x^2*sqrt(a + b*x^4))/(32*b) + (4*a^2*f*x^3*sqrt(a + b*x^4))/(195*b) - (4*a^3*f*x*sqrt(a + b*x^4))/(65*b^(3/2)*(sqrt(a) + sqrt(b)*x^2)) + (2*a*x^5*(117*d + 77*f*x^2)*sqrt(a + b*x^4))/3003 - (a*e*x^2*(a + b*x^4)^(3/2))/(48*b) + (x^5*(13*d + 11*f*x^2)*(a + b*x^4)^(3/2))/143 + ((6*c + 5*e*x^2)*(a + b*x^4)^(5/2))/(60*b) - (a^3*e*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(32*b^(3/2)) + (4*a^(13/4)*f*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(65*b^(7/4)*sqrt(a + b*x^4)) - (2*a^(11/4)*(65*sqrt(b)*d + 77*sqrt(a)*f)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(5005*b^(7/4)*sqrt(a + b*x^4))]
    @test_int [x^2*(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2), x, 14, (4*a^2*e*x*sqrt(a + b*x^4))/(77*b) - (a^2*f*x^2*sqrt(a + b*x^4))/(32*b) + (4*a^2*c*x*sqrt(a + b*x^4))/(15*sqrt(b)*(sqrt(a) + sqrt(b)*x^2)) + (2*a*x^3*(77*c + 45*e*x^2)*sqrt(a + b*x^4))/1155 - (a*f*x^2*(a + b*x^4)^(3/2))/(48*b) + (x^3*(11*c + 9*e*x^2)*(a + b*x^4)^(3/2))/99 + ((6*d + 5*f*x^2)*(a + b*x^4)^(5/2))/(60*b) - (a^3*f*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(32*b^(3/2)) - (4*a^(9/4)*c*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(15*b^(3/4)*sqrt(a + b*x^4)) + (2*a^(9/4)*(77*sqrt(b)*c - 15*sqrt(a)*e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(1155*b^(5/4)*sqrt(a + b*x^4))]
    @test_int [x^1*(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2), x, 14, (4*a^2*f*x*sqrt(a + b*x^4))/(77*b) + (3*a*c*x^2*sqrt(a + b*x^4))/16 + (4*a^2*d*x*sqrt(a + b*x^4))/(15*sqrt(b)*(sqrt(a) + sqrt(b)*x^2)) + (2*a*x^3*(77*d + 45*f*x^2)*sqrt(a + b*x^4))/1155 + (c*x^2*(a + b*x^4)^(3/2))/8 + (x^3*(11*d + 9*f*x^2)*(a + b*x^4)^(3/2))/99 + (e*(a + b*x^4)^(5/2))/(10*b) + (3*a^2*c*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(16*sqrt(b)) - (4*a^(9/4)*d*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(15*b^(3/4)*sqrt(a + b*x^4)) + (2*a^(9/4)*(77*sqrt(b)*d - 15*sqrt(a)*f)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(1155*b^(5/4)*sqrt(a + b*x^4))]
    @test_int [x^0*(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2), x, 13, (3*a*d*x^2*sqrt(a + b*x^4))/16 + (4*a^2*e*x*sqrt(a + b*x^4))/(15*sqrt(b)*(sqrt(a) + sqrt(b)*x^2)) + (2*a*x*(15*c + 7*e*x^2)*sqrt(a + b*x^4))/105 + (d*x^2*(a + b*x^4)^(3/2))/8 + (x*(9*c + 7*e*x^2)*(a + b*x^4)^(3/2))/63 + (f*(a + b*x^4)^(5/2))/(10*b) + (3*a^2*d*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(16*sqrt(b)) - (4*a^(9/4)*e*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(15*b^(3/4)*sqrt(a + b*x^4)) + (2*a^(7/4)*(15*sqrt(b)*c + 7*sqrt(a)*e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(105*b^(3/4)*sqrt(a + b*x^4))]
    @test_int [((c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2))/x^1, x, 16, (4*a^2*f*x*sqrt(a + b*x^4))/(15*sqrt(b)*(sqrt(a) + sqrt(b)*x^2)) + (a*(8*c + 3*e*x^2)*sqrt(a + b*x^4))/16 + (2*a*x*(15*d + 7*f*x^2)*sqrt(a + b*x^4))/105 + ((4*c + 3*e*x^2)*(a + b*x^4)^(3/2))/24 + (x*(9*d + 7*f*x^2)*(a + b*x^4)^(3/2))/63 + (3*a^2*e*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(16*sqrt(b)) - (a^(3/2)*c*atanh(sqrt(a + b*x^4)/sqrt(a)))/2 - (4*a^(9/4)*f*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(15*b^(3/4)*sqrt(a + b*x^4)) + (2*a^(7/4)*(15*sqrt(b)*d + 7*sqrt(a)*f)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(105*b^(3/4)*sqrt(a + b*x^4))]
    @test_int [((c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2))/x^2, x, 16, (12*a*sqrt(b)*c*x*sqrt(a + b*x^4))/(5*(sqrt(a) + sqrt(b)*x^2)) + (2*x*(5*a*e + 21*b*c*x^2)*sqrt(a + b*x^4))/35 + (a*(8*d + 3*f*x^2)*sqrt(a + b*x^4))/16 - ((7*c - e*x^2)*(a + b*x^4)^(3/2))/(7*x) + ((4*d + 3*f*x^2)*(a + b*x^4)^(3/2))/24 + (3*a^2*f*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(16*sqrt(b)) - (a^(3/2)*d*atanh(sqrt(a + b*x^4)/sqrt(a)))/2 - (12*a^(5/4)*b^(1/4)*c*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(5*sqrt(a + b*x^4)) + (2*a^(5/4)*(21*sqrt(b)*c + 5*sqrt(a)*e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(35*b^(1/4)*sqrt(a + b*x^4))]
    @test_int [((c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2))/x^3, x, 16, (12*a*sqrt(b)*d*x*sqrt(a + b*x^4))/(5*(sqrt(a) + sqrt(b)*x^2)) + ((2*a*e + 3*b*c*x^2)*sqrt(a + b*x^4))/4 + (2*x*(5*a*f + 21*b*d*x^2)*sqrt(a + b*x^4))/35 - ((3*c - e*x^2)*(a + b*x^4)^(3/2))/(6*x^2) - ((7*d - f*x^2)*(a + b*x^4)^(3/2))/(7*x) + (3*a*sqrt(b)*c*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/4 - (a^(3/2)*e*atanh(sqrt(a + b*x^4)/sqrt(a)))/2 - (12*a^(5/4)*b^(1/4)*d*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(5*sqrt(a + b*x^4)) + (2*a^(5/4)*(21*sqrt(b)*d + 5*sqrt(a)*f)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(35*b^(1/4)*sqrt(a + b*x^4))]
    @test_int [((c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2))/x^4, x, 16, (12*a*sqrt(b)*e*x*sqrt(a + b*x^4))/(5*(sqrt(a) + sqrt(b)*x^2)) - (2*(9*a*e - 5*b*c*x^2)*sqrt(a + b*x^4))/(15*x) + ((2*a*f + 3*b*d*x^2)*sqrt(a + b*x^4))/4 - ((5*c - 3*e*x^2)*(a + b*x^4)^(3/2))/(15*x^3) - ((3*d - f*x^2)*(a + b*x^4)^(3/2))/(6*x^2) + (3*a*sqrt(b)*d*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/4 - (a^(3/2)*f*atanh(sqrt(a + b*x^4)/sqrt(a)))/2 - (12*a^(5/4)*b^(1/4)*e*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(5*sqrt(a + b*x^4)) + (2*a^(3/4)*b^(1/4)*(5*sqrt(b)*c + 9*sqrt(a)*e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(15*sqrt(a + b*x^4))]
    @test_int [((c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2))/x^5, x, 15, (12*a*sqrt(b)*f*x*sqrt(a + b*x^4))/(5*(sqrt(a) + sqrt(b)*x^2)) + (3*b*(c + e*x^2)*sqrt(a + b*x^4))/4 + (2*b*x*(5*d + 9*f*x^2)*sqrt(a + b*x^4))/15 - (((3*c)/x^4 + (4*d)/x^3 + (6*e)/x^2 + (12*f)/x)*(a + b*x^4)^(3/2))/12 + (3*a*sqrt(b)*e*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/4 - (3*sqrt(a)*b*c*atanh(sqrt(a + b*x^4)/sqrt(a)))/4 - (12*a^(5/4)*b^(1/4)*f*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(5*sqrt(a + b*x^4)) + (2*a^(3/4)*b^(1/4)*(5*sqrt(b)*d + 9*sqrt(a)*f)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(15*sqrt(a + b*x^4))]
    @test_int [((c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2))/x^6, x, 15, (12*b^(3/2)*c*x*sqrt(a + b*x^4))/(5*(sqrt(a) + sqrt(b)*x^2)) - (2*b*(9*c - 5*e*x^2)*sqrt(a + b*x^4))/(15*x) + (3*b*(d + f*x^2)*sqrt(a + b*x^4))/4 - (((12*c)/x^5 + (15*d)/x^4 + (20*e)/x^3 + (30*f)/x^2)*(a + b*x^4)^(3/2))/60 + (3*a*sqrt(b)*f*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/4 - (3*sqrt(a)*b*d*atanh(sqrt(a + b*x^4)/sqrt(a)))/4 - (12*a^(1/4)*b^(5/4)*c*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(5*sqrt(a + b*x^4)) + (2*a^(1/4)*b^(3/4)*(9*sqrt(b)*c + 5*sqrt(a)*e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(15*sqrt(a + b*x^4))]
    @test_int [((c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2))/x^7, x, 15, (12*b^(3/2)*d*x*sqrt(a + b*x^4))/(5*(sqrt(a) + sqrt(b)*x^2)) - (b*(2*c - 3*e*x^2)*sqrt(a + b*x^4))/(4*x^2) - (2*b*(9*d - 5*f*x^2)*sqrt(a + b*x^4))/(15*x) - (((10*c)/x^6 + (12*d)/x^5 + (15*e)/x^4 + (20*f)/x^3)*(a + b*x^4)^(3/2))/60 + (b^(3/2)*c*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/2 - (3*sqrt(a)*b*e*atanh(sqrt(a + b*x^4)/sqrt(a)))/4 - (12*a^(1/4)*b^(5/4)*d*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(5*sqrt(a + b*x^4)) + (2*a^(1/4)*b^(3/4)*(9*sqrt(b)*d + 5*sqrt(a)*f)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(15*sqrt(a + b*x^4))]
    @test_int [((c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2))/x^8, x, 16, (-12*b*e*sqrt(a + b*x^4))/(5*x) + (12*b^(3/2)*e*x*sqrt(a + b*x^4))/(5*(sqrt(a) + sqrt(b)*x^2)) - (2*b*(5*c - 21*e*x^2)*sqrt(a + b*x^4))/(35*x^3) - (b*(2*d - 3*f*x^2)*sqrt(a + b*x^4))/(4*x^2) - (((60*c)/x^7 + (70*d)/x^6 + (84*e)/x^5 + (105*f)/x^4)*(a + b*x^4)^(3/2))/420 + (b^(3/2)*d*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/2 - (3*sqrt(a)*b*f*atanh(sqrt(a + b*x^4)/sqrt(a)))/4 - (12*a^(1/4)*b^(5/4)*e*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(5*sqrt(a + b*x^4)) + (2*b^(5/4)*(5*sqrt(b)*c + 21*sqrt(a)*e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(35*a^(1/4)*sqrt(a + b*x^4))]
    @test_int [((c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2))/x^9, x, 14, -(b*((105*c)/x^4 + (160*d)/x^3 + (280*e)/x^2 + (672*f)/x)*sqrt(a + b*x^4))/560 + (12*b^(3/2)*f*x*sqrt(a + b*x^4))/(5*(sqrt(a) + sqrt(b)*x^2)) - (((105*c)/x^8 + (120*d)/x^7 + (140*e)/x^6 + (168*f)/x^5)*(a + b*x^4)^(3/2))/840 + (b^(3/2)*e*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/2 - (3*b^2*c*atanh(sqrt(a + b*x^4)/sqrt(a)))/(16*sqrt(a)) - (12*a^(1/4)*b^(5/4)*f*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(5*sqrt(a + b*x^4)) + (2*b^(5/4)*(5*sqrt(b)*d + 21*sqrt(a)*f)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(35*a^(1/4)*sqrt(a + b*x^4))]
    @test_int [((c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2))/x^10, x, 15, -(b*((224*c)/x^5 + (315*d)/x^4 + (480*e)/x^3 + (840*f)/x^2)*sqrt(a + b*x^4))/1680 - (4*b^2*c*sqrt(a + b*x^4))/(15*a*x) + (4*b^(5/2)*c*x*sqrt(a + b*x^4))/(15*a*(sqrt(a) + sqrt(b)*x^2)) - (((56*c)/x^9 + (63*d)/x^8 + (72*e)/x^7 + (84*f)/x^6)*(a + b*x^4)^(3/2))/504 + (b^(3/2)*f*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/2 - (3*b^2*d*atanh(sqrt(a + b*x^4)/sqrt(a)))/(16*sqrt(a)) - (4*b^(9/4)*c*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(15*a^(3/4)*sqrt(a + b*x^4)) + (2*b^(7/4)*(7*sqrt(b)*c + 15*sqrt(a)*e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(105*a^(3/4)*sqrt(a + b*x^4))]
    @test_int [((c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2))/x^11, x, 13, -(b*((168*c)/x^6 + (224*d)/x^5 + (315*e)/x^4 + (480*f)/x^3)*sqrt(a + b*x^4))/1680 - (b^2*c*sqrt(a + b*x^4))/(10*a*x^2) - (4*b^2*d*sqrt(a + b*x^4))/(15*a*x) + (4*b^(5/2)*d*x*sqrt(a + b*x^4))/(15*a*(sqrt(a) + sqrt(b)*x^2)) - (((252*c)/x^10 + (280*d)/x^9 + (315*e)/x^8 + (360*f)/x^7)*(a + b*x^4)^(3/2))/2520 - (3*b^2*e*atanh(sqrt(a + b*x^4)/sqrt(a)))/(16*sqrt(a)) - (4*b^(9/4)*d*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(15*a^(3/4)*sqrt(a + b*x^4)) + (2*b^(7/4)*(7*sqrt(b)*d + 15*sqrt(a)*f)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(105*a^(3/4)*sqrt(a + b*x^4))]
    @test_int [((c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2))/x^12, x, 14, -(b*((1440*c)/x^7 + (1848*d)/x^6 + (2464*e)/x^5 + (3465*f)/x^4)*sqrt(a + b*x^4))/18480 - (4*b^2*c*sqrt(a + b*x^4))/(77*a*x^3) - (b^2*d*sqrt(a + b*x^4))/(10*a*x^2) - (4*b^2*e*sqrt(a + b*x^4))/(15*a*x) + (4*b^(5/2)*e*x*sqrt(a + b*x^4))/(15*a*(sqrt(a) + sqrt(b)*x^2)) - (((360*c)/x^11 + (396*d)/x^10 + (440*e)/x^9 + (495*f)/x^8)*(a + b*x^4)^(3/2))/3960 - (3*b^2*f*atanh(sqrt(a + b*x^4)/sqrt(a)))/(16*sqrt(a)) - (4*b^(9/4)*e*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(15*a^(3/4)*sqrt(a + b*x^4)) - (2*b^(9/4)*(15*sqrt(b)*c - 77*sqrt(a)*e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(1155*a^(5/4)*sqrt(a + b*x^4))]
    @test_int [((c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2))/x^13, x, 15, -(b*((1155*c)/x^8 + (1440*d)/x^7 + (1848*e)/x^6 + (2464*f)/x^5)*sqrt(a + b*x^4))/18480 - (b^2*c*sqrt(a + b*x^4))/(32*a*x^4) - (4*b^2*d*sqrt(a + b*x^4))/(77*a*x^3) - (b^2*e*sqrt(a + b*x^4))/(10*a*x^2) - (4*b^2*f*sqrt(a + b*x^4))/(15*a*x) + (4*b^(5/2)*f*x*sqrt(a + b*x^4))/(15*a*(sqrt(a) + sqrt(b)*x^2)) - (((165*c)/x^12 + (180*d)/x^11 + (198*e)/x^10 + (220*f)/x^9)*(a + b*x^4)^(3/2))/1980 + (b^3*c*atanh(sqrt(a + b*x^4)/sqrt(a)))/(32*a^(3/2)) - (4*b^(9/4)*f*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(15*a^(3/4)*sqrt(a + b*x^4)) - (2*b^(9/4)*(15*sqrt(b)*d - 77*sqrt(a)*f)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(1155*a^(5/4)*sqrt(a + b*x^4))]
    @test_int [((c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^(3/2))/x^14, x, 16, -(b*((12320*c)/x^9 + (15015*d)/x^8 + (18720*e)/x^7 + (24024*f)/x^6)*sqrt(a + b*x^4))/240240 - (4*b^2*c*sqrt(a + b*x^4))/(195*a*x^5) - (b^2*d*sqrt(a + b*x^4))/(32*a*x^4) - (4*b^2*e*sqrt(a + b*x^4))/(77*a*x^3) - (b^2*f*sqrt(a + b*x^4))/(10*a*x^2) + (4*b^3*c*sqrt(a + b*x^4))/(65*a^2*x) - (4*b^(7/2)*c*x*sqrt(a + b*x^4))/(65*a^2*(sqrt(a) + sqrt(b)*x^2)) - (((660*c)/x^13 + (715*d)/x^12 + (780*e)/x^11 + (858*f)/x^10)*(a + b*x^4)^(3/2))/8580 + (b^3*d*atanh(sqrt(a + b*x^4)/sqrt(a)))/(32*a^(3/2)) + (4*b^(13/4)*c*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(65*a^(7/4)*sqrt(a + b*x^4)) - (2*b^(11/4)*(77*sqrt(b)*c + 65*sqrt(a)*e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(5005*a^(7/4)*sqrt(a + b*x^4))]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [(x^4*(c + d*x + e*x^2 + f*x^3))/sqrt(a + b*x^4), x, 12, (c*x*sqrt(a + b*x^4))/(3*b) + (e*x^3*sqrt(a + b*x^4))/(5*b) + (f*x^4*sqrt(a + b*x^4))/(6*b) - (3*a*e*x*sqrt(a + b*x^4))/(5*b^(3/2)*(sqrt(a) + sqrt(b)*x^2)) - ((4*a*f - 3*b*d*x^2)*sqrt(a + b*x^4))/(12*b^2) - (a*d*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(4*b^(3/2)) + (3*a^(5/4)*e*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(5*b^(7/4)*sqrt(a + b*x^4)) - (a^(3/4)*(5*sqrt(b)*c + 9*sqrt(a)*e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(30*b^(7/4)*sqrt(a + b*x^4))]
    @test_int [(x^3*(c + d*x + e*x^2 + f*x^3))/sqrt(a + b*x^4), x, 11, (d*x*sqrt(a + b*x^4))/(3*b) + (f*x^3*sqrt(a + b*x^4))/(5*b) - (3*a*f*x*sqrt(a + b*x^4))/(5*b^(3/2)*(sqrt(a) + sqrt(b)*x^2)) + ((2*c + e*x^2)*sqrt(a + b*x^4))/(4*b) - (a*e*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(4*b^(3/2)) + (3*a^(5/4)*f*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(5*b^(7/4)*sqrt(a + b*x^4)) - (a^(3/4)*(5*sqrt(b)*d + 9*sqrt(a)*f)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(30*b^(7/4)*sqrt(a + b*x^4))]
    @test_int [(x^2*(c + d*x + e*x^2 + f*x^3))/sqrt(a + b*x^4), x, 10, (e*x*sqrt(a + b*x^4))/(3*b) + (c*x*sqrt(a + b*x^4))/(sqrt(b)*(sqrt(a) + sqrt(b)*x^2)) + ((2*d + f*x^2)*sqrt(a + b*x^4))/(4*b) - (a*f*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(4*b^(3/2)) - (a^(1/4)*c*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(b^(3/4)*sqrt(a + b*x^4)) + (a^(1/4)*(3*sqrt(b)*c - sqrt(a)*e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(6*b^(5/4)*sqrt(a + b*x^4))]
    @test_int [(x^1*(c + d*x + e*x^2 + f*x^3))/sqrt(a + b*x^4), x, 10, (e*sqrt(a + b*x^4))/(2*b) + (f*x*sqrt(a + b*x^4))/(3*b) + (d*x*sqrt(a + b*x^4))/(sqrt(b)*(sqrt(a) + sqrt(b)*x^2)) + (c*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(2*sqrt(b)) - (a^(1/4)*d*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(b^(3/4)*sqrt(a + b*x^4)) + (a^(1/4)*(3*sqrt(b)*d - sqrt(a)*f)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(6*b^(5/4)*sqrt(a + b*x^4))]
    @test_int [x^0*(c + d*x + e*x^2 + f*x^3)/sqrt(a + b*x^4), x, 9, (f*sqrt(a + b*x^4))/(2*b) + (e*x*sqrt(a + b*x^4))/(sqrt(b)*(sqrt(a) + sqrt(b)*x^2)) + (d*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(2*sqrt(b)) - (a^(1/4)*e*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(b^(3/4)*sqrt(a + b*x^4)) + (a^(1/4)*((sqrt(b)*c)/sqrt(a) + e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(2*b^(3/4)*sqrt(a + b*x^4))]
    @test_int [(c + d*x + e*x^2 + f*x^3)/(x^1*sqrt(a + b*x^4)), x, 12, (f*x*sqrt(a + b*x^4))/(sqrt(b)*(sqrt(a) + sqrt(b)*x^2)) + (e*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(2*sqrt(b)) - (c*atanh(sqrt(a + b*x^4)/sqrt(a)))/(2*sqrt(a)) - (a^(1/4)*f*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(b^(3/4)*sqrt(a + b*x^4)) + (a^(1/4)*((sqrt(b)*d)/sqrt(a) + f)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(2*b^(3/4)*sqrt(a + b*x^4))]
    @test_int [(c + d*x + e*x^2 + f*x^3)/(x^2*sqrt(a + b*x^4)), x, 13, -((c*sqrt(a + b*x^4))/(a*x)) + (sqrt(b)*c*x*sqrt(a + b*x^4))/(a*(sqrt(a) + sqrt(b)*x^2)) + (f*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(2*sqrt(b)) - (d*atanh(sqrt(a + b*x^4)/sqrt(a)))/(2*sqrt(a)) - (b^(1/4)*c*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(a^(3/4)*sqrt(a + b*x^4)) + ((sqrt(b)*c + sqrt(a)*e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(2*a^(3/4)*b^(1/4)*sqrt(a + b*x^4))]
    @test_int [(c + d*x + e*x^2 + f*x^3)/(x^3*sqrt(a + b*x^4)), x, 11, -(c*sqrt(a + b*x^4))/(2*a*x^2) - (d*sqrt(a + b*x^4))/(a*x) + (sqrt(b)*d*x*sqrt(a + b*x^4))/(a*(sqrt(a) + sqrt(b)*x^2)) - (e*atanh(sqrt(a + b*x^4)/sqrt(a)))/(2*sqrt(a)) - (b^(1/4)*d*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(a^(3/4)*sqrt(a + b*x^4)) + ((sqrt(b)*d + sqrt(a)*f)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(2*a^(3/4)*b^(1/4)*sqrt(a + b*x^4))]
    @test_int [(c + d*x + e*x^2 + f*x^3)/(x^4*sqrt(a + b*x^4)), x, 12, -(c*sqrt(a + b*x^4))/(3*a*x^3) - (d*sqrt(a + b*x^4))/(2*a*x^2) - (e*sqrt(a + b*x^4))/(a*x) + (sqrt(b)*e*x*sqrt(a + b*x^4))/(a*(sqrt(a) + sqrt(b)*x^2)) - (f*atanh(sqrt(a + b*x^4)/sqrt(a)))/(2*sqrt(a)) - (b^(1/4)*e*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(a^(3/4)*sqrt(a + b*x^4)) - (b^(1/4)*(sqrt(b)*c - 3*sqrt(a)*e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(6*a^(5/4)*sqrt(a + b*x^4))]
    @test_int [(c + d*x + e*x^2 + f*x^3)/(x^5*sqrt(a + b*x^4)), x, 13, -(c*sqrt(a + b*x^4))/(4*a*x^4) - (d*sqrt(a + b*x^4))/(3*a*x^3) - (e*sqrt(a + b*x^4))/(2*a*x^2) - (f*sqrt(a + b*x^4))/(a*x) + (sqrt(b)*f*x*sqrt(a + b*x^4))/(a*(sqrt(a) + sqrt(b)*x^2)) + (b*c*atanh(sqrt(a + b*x^4)/sqrt(a)))/(4*a^(3/2)) - (b^(1/4)*f*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(a^(3/4)*sqrt(a + b*x^4)) - (b^(1/4)*(sqrt(b)*d - 3*sqrt(a)*f)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(6*a^(5/4)*sqrt(a + b*x^4))]
    @test_int [(c + d*x + e*x^2 + f*x^3)/(x^6*sqrt(a + b*x^4)), x, 14, -(c*sqrt(a + b*x^4))/(5*a*x^5) - (d*sqrt(a + b*x^4))/(4*a*x^4) - (e*sqrt(a + b*x^4))/(3*a*x^3) - (f*sqrt(a + b*x^4))/(2*a*x^2) + (3*b*c*sqrt(a + b*x^4))/(5*a^2*x) - (3*b^(3/2)*c*x*sqrt(a + b*x^4))/(5*a^2*(sqrt(a) + sqrt(b)*x^2)) + (b*d*atanh(sqrt(a + b*x^4)/sqrt(a)))/(4*a^(3/2)) + (3*b^(5/4)*c*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(5*a^(7/4)*sqrt(a + b*x^4)) - (b^(3/4)*(9*sqrt(b)*c + 5*sqrt(a)*e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(30*a^(7/4)*sqrt(a + b*x^4))]

    @test_int [(x^6*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(3/2), x, 12, (x*(a*e + a*f*x - b*c*x^2 - b*d*x^3))/(2*b^2*sqrt(a + b*x^4)) + (d*sqrt(a + b*x^4))/b^2 + (e*x*sqrt(a + b*x^4))/(3*b^2) + (f*x^2*sqrt(a + b*x^4))/(4*b^2) + (3*c*x*sqrt(a + b*x^4))/(2*b^(3/2)*(sqrt(a) + sqrt(b)*x^2)) - (3*a*f*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(4*b^(5/2)) - (3*a^(1/4)*c*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(2*b^(7/4)*sqrt(a + b*x^4)) + (a^(1/4)*(9*sqrt(b)*c - 5*sqrt(a)*e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(12*b^(9/4)*sqrt(a + b*x^4))]
    @test_int [(x^5*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(3/2), x, 11, (x*(a*f - b*c*x - b*d*x^2 - b*e*x^3))/(2*b^2*sqrt(a + b*x^4)) + (e*sqrt(a + b*x^4))/b^2 + (f*x*sqrt(a + b*x^4))/(3*b^2) + (3*d*x*sqrt(a + b*x^4))/(2*b^(3/2)*(sqrt(a) + sqrt(b)*x^2)) + (c*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(2*b^(3/2)) - (3*a^(1/4)*d*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(2*b^(7/4)*sqrt(a + b*x^4)) + (a^(1/4)*(9*sqrt(b)*d - 5*sqrt(a)*f)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(12*b^(9/4)*sqrt(a + b*x^4))]
    @test_int [(x^4*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(3/2), x, 10, -(x*(c + d*x + e*x^2 + f*x^3))/(2*b*sqrt(a + b*x^4)) + (f*sqrt(a + b*x^4))/b^2 + (3*e*x*sqrt(a + b*x^4))/(2*b^(3/2)*(sqrt(a) + sqrt(b)*x^2)) + (d*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(2*b^(3/2)) - (3*a^(1/4)*e*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(2*b^(7/4)*sqrt(a + b*x^4)) + ((sqrt(b)*c + 3*sqrt(a)*e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(4*a^(1/4)*b^(7/4)*sqrt(a + b*x^4))]
    @test_int [(x^3*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(3/2), x, 9, -(c + d*x + e*x^2 + f*x^3)/(2*b*sqrt(a + b*x^4)) + (3*f*x*sqrt(a + b*x^4))/(2*b^(3/2)*(sqrt(a) + sqrt(b)*x^2)) + (e*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(2*b^(3/2)) - (3*a^(1/4)*f*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(2*b^(7/4)*sqrt(a + b*x^4)) + ((sqrt(b)*d + 3*sqrt(a)*f)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(4*a^(1/4)*b^(7/4)*sqrt(a + b*x^4))]
    @test_int [(x^2*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(3/2), x, 10, -(x*(a*e + a*f*x - b*c*x^2 - b*d*x^3))/(2*a*b*sqrt(a + b*x^4)) - (d*sqrt(a + b*x^4))/(2*a*b) - (c*x*sqrt(a + b*x^4))/(2*a*sqrt(b)*(sqrt(a) + sqrt(b)*x^2)) + (f*atanh((sqrt(b)*x^2)/sqrt(a + b*x^4)))/(2*b^(3/2)) + (c*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(2*a^(3/4)*b^(3/4)*sqrt(a + b*x^4)) - ((sqrt(b)*c - sqrt(a)*e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(4*a^(3/4)*b^(5/4)*sqrt(a + b*x^4))]
    @test_int [(x^1*(c + d*x + e*x^2 + f*x^3))/(a + b*x^4)^(3/2), x, 7, -(x*(a*f - b*c*x - b*d*x^2 - b*e*x^3))/(2*a*b*sqrt(a + b*x^4)) - (e*sqrt(a + b*x^4))/(2*a*b) - (d*x*sqrt(a + b*x^4))/(2*a*sqrt(b)*(sqrt(a) + sqrt(b)*x^2)) + (d*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(2*a^(3/4)*b^(3/4)*sqrt(a + b*x^4)) - ((sqrt(b)*d - sqrt(a)*f)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(4*a^(3/4)*b^(5/4)*sqrt(a + b*x^4))]
    @test_int [x^0*(c + d*x + e*x^2 + f*x^3)/(a + b*x^4)^(3/2), x, 4, -(e*x*sqrt(a + b*x^4))/(2*a*sqrt(b)*(sqrt(a) + sqrt(b)*x^2)) - (a*f - b*x*(c + d*x + e*x^2))/(2*a*b*sqrt(a + b*x^4)) + (e*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(2*a^(3/4)*b^(3/4)*sqrt(a + b*x^4)) + ((sqrt(b)*c - sqrt(a)*e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(4*a^(5/4)*b^(3/4)*sqrt(a + b*x^4))]
    @test_int [(c + d*x + e*x^2 + f*x^3)/(x^1*(a + b*x^4)^(3/2)), x, 11, (x*(a*d + a*e*x + a*f*x^2 - b*c*x^3))/(2*a^2*sqrt(a + b*x^4)) + (c*sqrt(a + b*x^4))/(2*a^2) - (f*x*sqrt(a + b*x^4))/(2*a*sqrt(b)*(sqrt(a) + sqrt(b)*x^2)) - (c*atanh(sqrt(a + b*x^4)/sqrt(a)))/(2*a^(3/2)) + (f*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(2*a^(3/4)*b^(3/4)*sqrt(a + b*x^4)) + ((sqrt(b)*d - sqrt(a)*f)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(4*a^(5/4)*b^(3/4)*sqrt(a + b*x^4))]
    @test_int [(c + d*x + e*x^2 + f*x^3)/(x^2*(a + b*x^4)^(3/2)), x, 13, (x*(a*e + a*f*x - b*c*x^2 - b*d*x^3))/(2*a^2*sqrt(a + b*x^4)) + (d*sqrt(a + b*x^4))/(2*a^2) - (c*sqrt(a + b*x^4))/(a^2*x) + (3*sqrt(b)*c*x*sqrt(a + b*x^4))/(2*a^2*(sqrt(a) + sqrt(b)*x^2)) - (d*atanh(sqrt(a + b*x^4)/sqrt(a)))/(2*a^(3/2)) - (3*b^(1/4)*c*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(2*a^(7/4)*sqrt(a + b*x^4)) + ((3*sqrt(b)*c + sqrt(a)*e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(4*a^(7/4)*b^(1/4)*sqrt(a + b*x^4))]
    @test_int [(c + d*x + e*x^2 + f*x^3)/(x^3*(a + b*x^4)^(3/2)), x, 15, (x*(a*f - b*c*x - b*d*x^2 - b*e*x^3))/(2*a^2*sqrt(a + b*x^4)) + (e*sqrt(a + b*x^4))/(2*a^2) - (c*sqrt(a + b*x^4))/(2*a^2*x^2) - (d*sqrt(a + b*x^4))/(a^2*x) + (3*sqrt(b)*d*x*sqrt(a + b*x^4))/(2*a^2*(sqrt(a) + sqrt(b)*x^2)) - (e*atanh(sqrt(a + b*x^4)/sqrt(a)))/(2*a^(3/2)) - (3*b^(1/4)*d*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(2*a^(7/4)*sqrt(a + b*x^4)) + ((3*sqrt(b)*d + sqrt(a)*f)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(4*a^(7/4)*b^(1/4)*sqrt(a + b*x^4))]
    @test_int [(c + d*x + e*x^2 + f*x^3)/(x^4*(a + b*x^4)^(3/2)), x, 17, -(x*(b*c + b*d*x + b*e*x^2 + b*f*x^3))/(2*a^2*sqrt(a + b*x^4)) + (f*sqrt(a + b*x^4))/(2*a^2) - (c*sqrt(a + b*x^4))/(3*a^2*x^3) - (d*sqrt(a + b*x^4))/(2*a^2*x^2) - (e*sqrt(a + b*x^4))/(a^2*x) + (3*sqrt(b)*e*x*sqrt(a + b*x^4))/(2*a^2*(sqrt(a) + sqrt(b)*x^2)) - (f*atanh(sqrt(a + b*x^4)/sqrt(a)))/(2*a^(3/2)) - (3*b^(1/4)*e*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.E(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(2*a^(7/4)*sqrt(a + b*x^4)) - (b^(1/4)*(5*sqrt(b)*c - 9*sqrt(a)*e)*(sqrt(a) + sqrt(b)*x^2)*sqrt((a + b*x^4)/(sqrt(a) + sqrt(b)*x^2)^2)*Elliptic.F(2*atan((b^(1/4)*x)/a^(1/4)), 1/2))/(12*a^(9/4)*sqrt(a + b*x^4))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*Pq(x)*(a+b*x^4)^p*with*p*symbolic=#

    @test_int [(g*x)^m*(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^p, x, 14, (c*(g*x)^(1 + m)*(a + b*x^4)^p*HypergeometricFunctions._₂F₁((1 + m)/4, -p, (5 + m)/4, -((b*x^4)/a)))/((1 + (b*x^4)/a)^p*(g*(1 + m))) + (d*(g*x)^(2 + m)*(a + b*x^4)^p*HypergeometricFunctions._₂F₁((2 + m)/4, -p, (6 + m)/4, -((b*x^4)/a)))/((1 + (b*x^4)/a)^p*(g^2*(2 + m))) + (e*(g*x)^(3 + m)*(a + b*x^4)^p*HypergeometricFunctions._₂F₁((3 + m)/4, -p, (7 + m)/4, -((b*x^4)/a)))/((1 + (b*x^4)/a)^p*(g^3*(3 + m))) + (f*(g*x)^(4 + m)*(a + b*x^4)^p*HypergeometricFunctions._₂F₁((4 + m)/4, -p, (8 + m)/4, -((b*x^4)/a)))/((1 + (b*x^4)/a)^p*(g^4*(4 + m)))]

    @test_int [x^0*(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^p, x, 12, (f*(a + b*x^4)^(1 + p))/(4*b*(1 + p)) + (c*x*(a + b*x^4)^(1 + p)*HypergeometricFunctions._₂F₁(1, 5/4 + p, 5/4, -((b*x^4)/a)))/a + (d*x^2*(a + b*x^4)^(1 + p)*HypergeometricFunctions._₂F₁(1, 3/2 + p, 3/2, -((b*x^4)/a)))/(2*a) + (e*x^3*(a + b*x^4)^(1 + p)*HypergeometricFunctions._₂F₁(1, 7/4 + p, 7/4, -((b*x^4)/a)))/(3*a), (f*(a + b*x^4)^(1 + p))/(4*b*(1 + p)) + (c*x*(a + b*x^4)^p*HypergeometricFunctions._₂F₁(1/4, -p, 5/4, -((b*x^4)/a)))/(1 + (b*x^4)/a)^p + ((1/2)*d*x^2*(a + b*x^4)^p*HypergeometricFunctions._₂F₁(1/2, -p, 3/2, -((b*x^4)/a)))/(1 + (b*x^4)/a)^p + ((1/3)*e*x^3*(a + b*x^4)^p*HypergeometricFunctions._₂F₁(3/4, -p, 7/4, -((b*x^4)/a)))/(1 + (b*x^4)/a)^p]
    @test_int [x^3*(c + d*x + e*x^2 + f*x^3)*(a + b*x^4)^p, x, 13, (c*(a + b*x^4)^(1 + p))/(4*b*(1 + p)) + ((1/5)*d*x^5*(a + b*x^4)^p*HypergeometricFunctions._₂F₁(5/4, -p, 9/4, -((b*x^4)/a)))/(1 + (b*x^4)/a)^p + ((1/6)*e*x^6*(a + b*x^4)^p*HypergeometricFunctions._₂F₁(3/2, -p, 5/2, -((b*x^4)/a)))/(1 + (b*x^4)/a)^p + ((1/7)*f*x^7*(a + b*x^4)^p*HypergeometricFunctions._₂F₁(7/4, -p, 11/4, -((b*x^4)/a)))/(1 + (b*x^4)/a)^p]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*Pq(x)*(a+b*x^5)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*Pq(x)*(a+b*x^5)^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [(1 + x + x^2 + x^3 + x^4)/(1 - x^5), x, 2, -log(1-x)]

    #= ::Subsection:: =#
    #=Integrands*of*the*form*Pq(x)*(a+b*x^5)^(p/2)=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*Pq(x)*(a+b*x^6)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*Pq(x)*(a+b*x^6)^p=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [(243 - 162*x + 108*x^2 - 72*x^3 + 48*x^4 - 32*x^5)/(729 - 64*x^6), x, 2, (1/2)*log(3 + 2*x)]
    @test_int [(243 + 162*x + 108*x^2 + 72*x^3 + 48*x^4 + 32*x^5)/(729 - 64*x^6), x, 2, (-(1/2))*log(3 - 2*x)]
    @test_int [(81 + 36*x^2 + 16*x^4)/(729 - 64*x^6), x, 2, (1/6)*atanh((2*x)/3)]
    @test_int [(81 + 54*x - 24*x^3 - 16*x^4)/(729 - 64*x^6), x, 3, -(atan((3 - 4*x)/(3*sqrt(3)))/(3*sqrt(3)))]
    @test_int [(3 - 2*x)/(729 - 64*x^6), x, 6, atan((3 + 4*x)/(3*sqrt(3)))/(162*sqrt(3)) + (1/486)*log(3 + 2*x) - (1/972)*log(9 - 6*x + 4*x^2)]
    @test_int [(3 + 2*x)/(729 - 64*x^6), x, 6, -(atan((3 - 4*x)/(3*sqrt(3)))/(162*sqrt(3))) - (1/486)*log(3 - 2*x) + (1/972)*log(9 + 6*x + 4*x^2)]
    @test_int [(9 - 6*x + 4*x^2)/(729 - 64*x^6), x, 7, atan((3 + 4*x)/(3*sqrt(3)))/(54*sqrt(3)) - (1/324)*log(3 - 2*x) + (1/108)*log(3 + 2*x) - (1/324)*log(9 + 6*x + 4*x^2)]
    @test_int [(9 + 6*x + 4*x^2)/(729 - 64*x^6), x, 7, -(atan((3 - 4*x)/(3*sqrt(3)))/(54*sqrt(3))) - (1/108)*log(3 - 2*x) + (1/324)*log(3 + 2*x) + (1/324)*log(9 - 6*x + 4*x^2)]
    @test_int [(27 - 8*x^3)/(729 - 64*x^6), x, 7, -(atan((3 - 4*x)/(3*sqrt(3)))/(18*sqrt(3))) + (1/54)*log(3 + 2*x) - (1/108)*log(9 - 6*x + 4*x^2)]
    @test_int [(27 + 36*x + 24*x^2 + 8*x^3)/(729 - 64*x^6), x, 7, -(atan((3 - 4*x)/(3*sqrt(3)))/(18*sqrt(3))) - (1/18)*log(3 - 2*x) + (1/36)*log(9 - 6*x + 4*x^2)]

    @test_int [(243 - 162*x + 108*x^2 - 72*x^3 + 48*x^4 - 32*x^5)/(729 - 64*x^6)^2, x, 11, -(1/(2916*(3 + 2*x))) - atan((3 - 4*x)/(3*sqrt(3)))/(8748*sqrt(3)) + atan((3 + 4*x)/(3*sqrt(3)))/(2916*sqrt(3)) - log(3 - 2*x)/17496 + (5*log(3 + 2*x))/17496 - log(9 - 6*x + 4*x^2)/17496 - log(9 + 6*x + 4*x^2)/17496]
    @test_int [(243 + 162*x + 108*x^2 + 72*x^3 + 48*x^4 + 32*x^5)/(729 - 64*x^6)^2, x, 11, 1/(2916*(3 - 2*x)) - atan((3 - 4*x)/(3*sqrt(3)))/(2916*sqrt(3)) + atan((3 + 4*x)/(3*sqrt(3)))/(8748*sqrt(3)) - (5*log(3 - 2*x))/17496 + log(3 + 2*x)/17496 + log(9 - 6*x + 4*x^2)/17496 + log(9 + 6*x + 4*x^2)/17496]
    @test_int [(81 + 36*x^2 + 16*x^4)/(729 - 64*x^6)^2, x, 8, 1/(17496*(3 - 2*x)) - 1/(17496*(3 + 2*x)) - atan((3 - 4*x)/(3*sqrt(3)))/(13122*sqrt(3)) + atan((3 + 4*x)/(3*sqrt(3)))/(13122*sqrt(3)) + atanh((2*x)/3)/8748]
    @test_int [(81 + 54*x - 24*x^3 - 16*x^4)/(729 - 64*x^6)^2, x, 11, x/(4374*(9 - 6*x + 4*x^2)) - atan((3 - 4*x)/(3*sqrt(3)))/(4374*sqrt(3)) - log(3 - 2*x)/26244 + log(3 + 2*x)/78732 - log(9 - 6*x + 4*x^2)/157464 + log(9 + 6*x + 4*x^2)/52488]
    @test_int [(3 - 2*x)/(729 - 64*x^6)^2, x, 17, -(1/(708588*(3 + 2*x))) + (3 - x)/(708588*(9 - 6*x + 4*x^2)) + x/(236196*(9 + 6*x + 4*x^2)) - atan((3 - 4*x)/(3*sqrt(3)))/(1417176*sqrt(3)) + atan((3 + 4*x)/(3*sqrt(3)))/(157464*sqrt(3)) - log(3 - 2*x)/4251528 + log(3 + 2*x)/472392 - log(9 - 6*x + 4*x^2)/944784 + log(9 + 6*x + 4*x^2)/8503056]
    @test_int [(3 + 2*x)/(729 - 64*x^6)^2, x, 17, 1/(708588*(3 - 2*x)) + x/(236196*(9 - 6*x + 4*x^2)) - (3 + x)/(708588*(9 + 6*x + 4*x^2)) - atan((3 - 4*x)/(3*sqrt(3)))/(157464*sqrt(3)) + atan((3 + 4*x)/(3*sqrt(3)))/(1417176*sqrt(3)) - log(3 - 2*x)/472392 + log(3 + 2*x)/4251528 - log(9 - 6*x + 4*x^2)/8503056 + log(9 + 6*x + 4*x^2)/944784]
    @test_int [(9 - 6*x + 4*x^2)/(729 - 64*x^6)^2, x, 14, 1/(472392*(3 - 2*x)) - 1/(157464*(3 + 2*x)) + (3 + 4*x)/(236196*(9 + 6*x + 4*x^2)) - atan((3 - 4*x)/(3*sqrt(3)))/(472392*sqrt(3)) + atan((3 + 4*x)/(3*sqrt(3)))/(52488*sqrt(3)) - log(3 - 2*x)/354294 + log(3 + 2*x)/118098 - log(9 - 6*x + 4*x^2)/944784 - (5*log(9 + 6*x + 4*x^2))/2834352]
    @test_int [(9 + 6*x + 4*x^2)/(729 - 64*x^6)^2, x, 14, 1/(157464*(3 - 2*x)) - 1/(472392*(3 + 2*x)) - (3 - 4*x)/(236196*(9 - 6*x + 4*x^2)) - atan((3 - 4*x)/(3*sqrt(3)))/(52488*sqrt(3)) + atan((3 + 4*x)/(3*sqrt(3)))/(472392*sqrt(3)) - log(3 - 2*x)/118098 + log(3 + 2*x)/354294 + (5*log(9 - 6*x + 4*x^2))/2834352 + log(9 + 6*x + 4*x^2)/944784]
    @test_int [(27 - 8*x^3)/(729 - 64*x^6)^2, x, 15, x/(4374*(27 + 8*x^3)) - (7*atan((3 - 4*x)/(3*sqrt(3))))/(157464*sqrt(3)) + atan((3 + 4*x)/(3*sqrt(3)))/(52488*sqrt(3)) - log(3 - 2*x)/157464 + (7*log(3 + 2*x))/472392 - (7*log(9 - 6*x + 4*x^2))/944784 + log(9 + 6*x + 4*x^2)/314928]
    @test_int [(27 + 36*x + 24*x^2 + 8*x^3)/(729 - 64*x^6)^2, x, 14, 1/(26244*(3 - 2*x)) - (3 - 2*x)/(26244*(9 - 6*x + 4*x^2)) - (11*atan((3 - 4*x)/(3*sqrt(3))))/(157464*sqrt(3)) - atan((3 + 4*x)/(3*sqrt(3)))/(157464*sqrt(3)) - (7*log(3 - 2*x))/157464 + log(3 + 2*x)/472392 + (17*log(9 - 6*x + 4*x^2))/944784 + log(9 + 6*x + 4*x^2)/314928]

    @test_int [x*(27 - 2*x^3)/(729 - 64*x^6), x, 13, -((5*atan((3 - 4*x)/(3*sqrt(3))))/(96*sqrt(3))) - atan((3 + 4*x)/(3*sqrt(3)))/(32*sqrt(3)) - (1/96)*log(3 - 2*x) - (5/288)*log(3 + 2*x) + (5/576)*log(9 - 6*x + 4*x^2) + (1/192)*log(9 + 6*x + 4*x^2)]

    #= ::Subsection:: =#
    #=Integrands*of*the*form*Pq(x)*(a+b*x^6)^(p/2)=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*Pq(x)*(a+b*x^n)^p=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*Pq(x)*(a+b*x^n)^p=#

    @test_int [(c*x)^m*(d + e*x^n + f*x^(2*n) + g*x^(3*n))/(a + b*x^n), x, 7, ((b*f - a*g)*x^(1 + n)*(c*x)^m)/(b^2*(1 + m + n)) + (g*x^(1 + 2*n)*(c*x)^m)/(b*(1 + m + 2*n)) + ((b^2*e - a*b*f + a^2*g)*(c*x)^(1 + m))/(b^3*c*(1 + m)) + ((b^3*d - a*b^2*e + a^2*b*f - a^3*g)*(c*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)))/(a*b^3*c*(1 + m))]

    @test_int [(c + d*x^(n - 1))*(a + b*x^n)^3, x, 4, a^3*c*x + (3*a^2*b*c*x^(1 + n))/(1 + n) + (3*a*b^2*c*x^(1 + 2*n))/(1 + 2*n) + (b^3*c*x^(1 + 3*n))/(1 + 3*n) + (d*(a + b*x^n)^4)/(4*b*n)]
    @test_int [(c + d*x^(n - 1))*(a + b*x^n)^2, x, 4, a^2*c*x + (2*a*b*c*x^(1 + n))/(1 + n) + (b^2*c*x^(1 + 2*n))/(1 + 2*n) + (d*(a + b*x^n)^3)/(3*b*n)]
    @test_int [(c + d*x^(n - 1))*(a + b*x^n)^1, x, 4, a*c*x + (a*d*x^n)/n + (b*d*x^(2*n))/(2*n) + (b*c*x^(1 + n))/(1 + n)]
    @test_int [(c + d*x^(n - 1))*(a + b*x^n)^0, x, 1, c*x + (d*x^n)/n]
    @test_int [(c + d*x^(n - 1))/(a + b*x^n)^1, x, 3, (c*x*HypergeometricFunctions._₂F₁(1, 1/n, 1 + 1/n, -((b*x^n)/a)))/a + (d*log(a + b*x^n))/(b*n)]
    @test_int [(c + d*x^(n - 1))/(a + b*x^n)^2, x, 3, -(d/(b*n*(a + b*x^n))) + (c*x*HypergeometricFunctions._₂F₁(2, 1/n, 1 + 1/n, -((b*x^n)/a)))/a^2]
    @test_int [(c + d*x^(n - 1))/(a + b*x^n)^3, x, 3, -(d/(2*b*n*(a + b*x^n)^2)) + (c*x*HypergeometricFunctions._₂F₁(3, 1/n, 1 + 1/n, -((b*x^n)/a)))/a^3]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*Pq(x)*(a+b*x^n)^(p/2)=#

    @test_int [(c*x)^m*(d + e*x^n + f*x^(2*n) + g*x^(3*n))/sqrt(a + b*x^n), x, 13, (d*(c*x)^(1 + m)*sqrt(1 + (b*x^n)/a)*HypergeometricFunctions._₂F₁(1/2, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)))/(c*(1 + m)*sqrt(a + b*x^n)) + (e*x^(1 + n)*(c*x)^m*sqrt(1 + (b*x^n)/a)*HypergeometricFunctions._₂F₁(1/2, (1 + m + n)/n, (1 + m + 2*n)/n, -((b*x^n)/a)))/((1 + m + n)*sqrt(a + b*x^n)) + (f*x^(1 + 2*n)*(c*x)^m*sqrt(1 + (b*x^n)/a)*HypergeometricFunctions._₂F₁(1/2, (1 + m + 2*n)/n, (1 + m + 3*n)/n, -((b*x^n)/a)))/((1 + m + 2*n)*sqrt(a + b*x^n)) + (g*x^(1 + 3*n)*(c*x)^m*sqrt(1 + (b*x^n)/a)*HypergeometricFunctions._₂F₁(1/2, (1 + m + 3*n)/n, (1 + m + 4*n)/n, -((b*x^n)/a)))/((1 + m + 3*n)*sqrt(a + b*x^n))]

    @test_int [(-a*h*x^(n/4 - 1) + b*f*x^(n/2 - 1) + b*g*x^(n - 1) + b*h*x^((5*n)/4 - 1))/(a + b*x^n)^(3/2), x, 2, -((2*(a*g + 2*a*h*x^(n/4) - b*f*x^(n/2)))/(a*n*sqrt(a + b*x^n)))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(c*x)^m*Pq(x)*(a+b*x^n)^p*with*p*symbolic=#

    @test_int [(c*x)^m*(d + e*x + f*x^2 + g*x^3)*(a + b*x^n)^p, x, 10, (d*(c*x)^(1 + m)*(a + b*x^n)^p*HypergeometricFunctions._₂F₁((1 + m)/n, -p, (1 + m + n)/n, -((b*x^n)/a)))/((1 + (b*x^n)/a)^p*(c*(1 + m))) + (e*(c*x)^(2 + m)*(a + b*x^n)^p*HypergeometricFunctions._₂F₁((2 + m)/n, -p, (2 + m + n)/n, -((b*x^n)/a)))/((1 + (b*x^n)/a)^p*(c^2*(2 + m))) + (f*(c*x)^(3 + m)*(a + b*x^n)^p*HypergeometricFunctions._₂F₁((3 + m)/n, -p, (3 + m + n)/n, -((b*x^n)/a)))/((1 + (b*x^n)/a)^p*(c^3*(3 + m))) + (g*(c*x)^(4 + m)*(a + b*x^n)^p*HypergeometricFunctions._₂F₁((4 + m)/n, -p, (4 + m + n)/n, -((b*x^n)/a)))/((1 + (b*x^n)/a)^p*(c^4*(4 + m)))]

    @test_int [(c*x)^m*(d + e*x^n + f*x^(2*n) + g*x^(3*n))*(a + b*x^n)^p, x, 13, (d*(c*x)^(1 + m)*(a + b*x^n)^p*HypergeometricFunctions._₂F₁((1 + m)/n, -p, (1 + m + n)/n, -((b*x^n)/a)))/((1 + (b*x^n)/a)^p*(c*(1 + m))) + (e*x^(1 + n)*(c*x)^m*(a + b*x^n)^p*HypergeometricFunctions._₂F₁((1 + m + n)/n, -p, (1 + m + 2*n)/n, -((b*x^n)/a)))/((1 + (b*x^n)/a)^p*(1 + m + n)) + (f*x^(1 + 2*n)*(c*x)^m*(a + b*x^n)^p*HypergeometricFunctions._₂F₁((1 + m + 2*n)/n, -p, (1 + m + 3*n)/n, -((b*x^n)/a)))/((1 + (b*x^n)/a)^p*(1 + m + 2*n)) + (g*x^(1 + 3*n)*(c*x)^m*(a + b*x^n)^p*HypergeometricFunctions._₂F₁((1 + m + 3*n)/n, -p, (1 + m + 4*n)/n, -((b*x^n)/a)))/((1 + (b*x^n)/a)^p*(1 + m + 3*n))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(c*x^(n/2))^m*Pq(x^(n/2))*(a+b*x^n)^p=#

    @test_int [(c + d*x^(n/2) + e*x^n + f*x^(3*(n/2)))/(a + b*x^n)^2, x, 4, (x*(b*c - a*e + (b*d - a*f)*x^(n/2)))/(a*b*n*(a + b*x^n)) - ((b*d*(2 - n) - a*f*(2 + n))*x^((2 + n)/2)*HypergeometricFunctions._₂F₁(1, (1/2)*(1 + 2/n), (1/2)*(3 + 2/n), -((b*x^n)/a)))/(a^2*b*n*(2 + n)) + ((a*e - b*c*(1 - n))*x*HypergeometricFunctions._₂F₁(1, 1/n, 1 + 1/n, -((b*x^n)/a)))/(a^2*b*n)]

    #= ::Title::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*Pq(x)*(a+b*x^n)^p*(c+d*x^n)^q=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*Pq(x)*(a+b*x^n)^p*(c+d*x^n)^q=#

    @test_int [(a*c + 2*(b*c + a*d)*x^2 + 3*b*d*x^4)/(sqrt(a + b*x^2)*sqrt(c + d*x^2)), x, 1, x*sqrt(a + b*x^2)*sqrt(c + d*x^2)]

    @test_int [(1 + x^3)/((1 - x^4)*(1 + x^4)^(1/4)), x, 10, atan((2^(1/4)*x)/(1 + x^4)^(1/4))/(2*2^(1/4)) - atan((1 + x^4)^(1/4)/2^(1/4))/(2*2^(1/4)) + atanh((2^(1/4)*x)/(1 + x^4)^(1/4))/(2*2^(1/4)) + atanh((1 + x^4)^(1/4)/2^(1/4))/(2*2^(1/4))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(h*x)^m*(e+g*x^(2*n))*(a+b*x^n)^p*(c+d*x^n)^q=#

    @test_int [(a*c - b*d*x^(2*n))*(a + b*x^n)^((-1 - n)/n)*(c + d*x^n)^((-1 - n)/n), x, 1, x/((a + b*x^n)^n^(-1)*(c + d*x^n)^n^(-1))]

    @test_int [(h*x)^(-1 - n - n*p)*(a*c - b*d*x^(2*n))*(a + b*x^n)^p*(c + d*x^n)^p, x, 1, -(((a + b*x^n)^(1 + p)*(c + d*x^n)^(1 + p))/((h*x)^(n*(1 + p))*(h*n*(1 + p))))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(h*x)^m*(e+f*x^n+g*x^(2*n))*(a+b*x^n)^p*(c+d*x^n)^q=#

    @test_int [(e + ((b*c + a*d)*e*(1 + n + n*p))/(a*c)*x^n + (b*d*e*(1 + 2*n + 2*n*p))/(a*c)*x^(2*n))*(a + b*x^n)^p*(c + d*x^n)^p, x, 1, (e*x*(a + b*x^n)^(1 + p)*(c + d*x^n)^(1 + p))/(a*c)]

    @test_int [(h*x)^m*(e + ((b*c + a*d)*e*(1 + m + n + n*p))/(a*c*(1 + m))*x^n + (b*d*e*(1 + m + 2*n + 2*n*p))/(a*c*(1 + m))*x^(2*n))*(a + b*x^n)^p*(c + d*x^n)^p, x, 1, (e*(h*x)^(1 + m)*(a + b*x^n)^(1 + p)*(c + d*x^n)^(1 + p))/(a*c*h*(1 + m))]
    end

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