@testset "1.1.1.7 P(x) (a+b x)^m (c+d x)^n (e+f x)^p (g+h x)^q" begin
    (A, B, C, a, b, c, d, e, f, g, h, x, ) = @variables A B C a b c d e f g h x

    #= ::Package:: =#

    #= ::Title:: =#
    #=Integrands*of*the*form*P2(x)*(a+b*x)^m*(c+d*x)^n*(e+f*x)^p*(g+h*x)^q=#


    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^m*(c+d*x)^(n/2)*(A+B*x) / (Sqrte+f*x)*sqrt(g+h*x))=#


    #= ::Subsubsection:: =#
    #=n>0=#


    #= ::Subsubsection::Closed:: =#
    #=n<0=#


    #= [(a + b*x)^3*(A + B*x)/(sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 10, (1/(105*d^3*f^3*h^3))*(2*b*(5*d*f*h*(7*a*(2*A*b + a*B)*d*f*h - b*B*(5*b*(d*e*g + c*f*g + c*e*h) + 2*a*(d*f*g + d*e*h + c*f*h))) + 2*(a*d*f*h - 2*b*(d*f*g + d*e*h + c*f*h))*(11*a*B*d*f*h + b*(7*A*d*f*h - 6*B*(d*f*g + d*e*h + c*f*h))))*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)) + (2*b*(11*a*B*d*f*h + b*(7*A*d*f*h - 6*B*(d*f*g + d*e*h + c*f*h)))*(a + b*x)*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/(35*d^2*f^2*h^2) + (2*b*B*(a + b*x)^2*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/(7*d*f*h) - (1/(105*d^4*f^(7/2)*h^4*sqrt(e + f*x)*sqrt((d*(g + h*x))/(d*g - c*h))))*(2*sqrt((-d)*e + c*f)*(2*b*(d*f*g + d*e*h + c*f*h)*(5*d*f*h*(7*a*(2*A*b + a*B)*d*f*h - b*B*(5*b*(d*e*g + c*f*g + c*e*h) + 2*a*(d*f*g + d*e*h + c*f*h))) + 2*(a*d*f*h - 2*b*(d*f*g + d*e*h + c*f*h))*(11*a*B*d*f*h + b*(7*A*d*f*h - 6*B*(d*f*g + d*e*h + c*f*h)))) + 3*d*f*h*(b*(3*b*(d*e*g + c*f*g + c*e*h) + 2*a*(d*f*g + d*e*h + c*f*h))*(11*a*B*d*f*h + b*(7*A*d*f*h - 6*B*(d*f*g + d*e*h + c*f*h))) + 5*d*f*h*(4*b^3*B*c*e*g - 7*a^3*B*d*f*h + 6*a*b^2*B*(d*e*g + c*f*g + c*e*h) - a^2*b*(21*A*d*f*h - 2*B*(d*f*g + d*e*h + c*f*h)))))*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt(g + h*x)*Elliptic.E(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h)))) - (1/(105*d^4*f^(7/2)*h^4*sqrt(e + f*x)*sqrt(g + h*x)))*(2*sqrt((-d)*e + c*f)*(105*a^3*d^3*f^3*h^3*(B*g - A*h) + 105*a^2*b*d^2*f^2*h^2*(3*A*d*f*g*h - B*(c*h*(f*g - e*h) + d*g*(2*f*g + e*h))) - 21*a*b^2*d*f*h*(5*A*d*f*h*(c*h*(f*g - e*h) + d*g*(2*f*g + e*h)) - B*(4*c^2*f*h^2*(f*g - e*h) + c*d*h*(3*f^2*g^2 + e*f*g*h - 4*e^2*h^2) + d^2*g*(8*f^2*g^2 + 3*e*f*g*h + 4*e^2*h^2))) + b^3*(7*A*d*f*h*(4*c^2*f*h^2*(f*g - e*h) + c*d*h*(3*f^2*g^2 + e*f*g*h - 4*e^2*h^2) + d^2*g*(8*f^2*g^2 + 3*e*f*g*h + 4*e^2*h^2)) - B*(24*c^3*f^2*h^3*(f*g - e*h) + c^2*d*f*h^2*(17*f^2*g^2 + 6*e*f*g*h - 23*e^2*h^2) + 2*c*d^2*h*(8*f^3*g^3 + e*f^2*g^2*h + 3*e^2*f*g*h^2 - 12*e^3*h^3) + d^3*g*(48*f^3*g^3 + 16*e*f^2*g^2*h + 17*e^2*f*g*h^2 + 24*e^3*h^3))))*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt((d*(g + h*x))/(d*g - c*h))*Elliptic.F(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))] =#
    @test_int [(a + b*x)^2*(A + B*x)/(sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 9, (2*b*(7*a*B*d*f*h + b*(5*A*d*f*h - 4*B*(d*f*g + d*e*h + c*f*h)))*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/(15*d^2*f^2*h^2) + (2*b*B*(a + b*x)*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/(5*d*f*h) + (1/(15*d^3*f^(5/2)*h^3*sqrt(e + f*x)*sqrt((d*(g + h*x))/(d*g - c*h))))*(2*sqrt((-d)*e + c*f)*(15*a^2*B*d^2*f^2*h^2 + 10*a*b*d*f*h*(3*A*d*f*h - 2*B*(d*f*g + d*e*h + c*f*h)) - b^2*(10*A*d*f*h*(d*f*g + d*e*h + c*f*h) - B*(8*c^2*f^2*h^2 + 7*c*d*f*h*(f*g + e*h) + d^2*(8*f^2*g^2 + 7*e*f*g*h + 8*e^2*h^2))))*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt(g + h*x)*Elliptic.E(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h)))) - (1/(15*d^3*f^(5/2)*h^3*sqrt(e + f*x)*sqrt(g + h*x)))*(2*sqrt((-d)*e + c*f)*(15*a^2*d^2*f^2*h^2*(B*g - A*h) + 10*a*b*d*f*h*(3*A*d*f*g*h - B*(c*h*(f*g - e*h) + d*g*(2*f*g + e*h))) - b^2*(5*A*d*f*h*(c*h*(f*g - e*h) + d*g*(2*f*g + e*h)) - B*(4*c^2*f*h^2*(f*g - e*h) + c*d*h*(3*f^2*g^2 + e*f*g*h - 4*e^2*h^2) + d^2*g*(8*f^2*g^2 + 3*e*f*g*h + 4*e^2*h^2))))*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt((d*(g + h*x))/(d*g - c*h))*Elliptic.F(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))]
    @test_int [(a + b*x)^1*(A + B*x)/(sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 8, (2*b*B*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/(3*d*f*h) + (2*sqrt((-d)*e + c*f)*(3*a*B*d*f*h + b*(3*A*d*f*h - 2*B*(d*f*g + d*e*h + c*f*h)))*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt(g + h*x)*Elliptic.E(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))/(3*d^2*f^(3/2)*h^2*sqrt(e + f*x)*sqrt((d*(g + h*x))/(d*g - c*h))) - (2*sqrt((-d)*e + c*f)*(3*a*d*f*h*(B*g - A*h) + b*(3*A*d*f*g*h - B*(c*h*(f*g - e*h) + d*g*(2*f*g + e*h))))*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt((d*(g + h*x))/(d*g - c*h))*Elliptic.F(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))/(3*d^2*f^(3/2)*h^2*sqrt(e + f*x)*sqrt(g + h*x))]
    @test_int [(a + b*x)^0*(A + B*x)/(sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 6, (2*B*sqrt((-d)*e + c*f)*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt(g + h*x)*Elliptic.E(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))/(d*sqrt(f)*h*sqrt(e + f*x)*sqrt((d*(g + h*x))/(d*g - c*h))) - (2*sqrt((-d)*e + c*f)*(B*g - A*h)*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt((d*(g + h*x))/(d*g - c*h))*Elliptic.F(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))/(d*sqrt(f)*h*sqrt(e + f*x)*sqrt(g + h*x))]
    @test_int [(A + B*x)/((a + b*x)^1*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 9, (2*B*sqrt((-d)*e + c*f)*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt((d*(g + h*x))/(d*g - c*h))*Elliptic.F(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))/(b*d*sqrt(f)*sqrt(e + f*x)*sqrt(g + h*x)) - (2*(A - (a*B)/b)*sqrt((-d)*e + c*f)*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt((d*(g + h*x))/(d*g - c*h))*Elliptic.Pi(-((b*(d*e - c*f))/((b*c - a*d)*f)), asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))/((b*c - a*d)*sqrt(f)*sqrt(e + f*x)*sqrt(g + h*x))]
    @test_int [(A + B*x)/((a + b*x)^2*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 12, -((b*(A*b - a*B)*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*(a + b*x))) + ((A*b - a*B)*sqrt(f)*sqrt((-d)*e + c*f)*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt(g + h*x)*Elliptic.E(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*sqrt(e + f*x)*sqrt((d*(g + h*x))/(d*g - c*h))) - ((A*b - a*B)*sqrt(f)*sqrt((-d)*e + c*f)*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt((d*(g + h*x))/(d*g - c*h))*Elliptic.F(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))/(b*(b*c - a*d)*(b*e - a*f)*sqrt(e + f*x)*sqrt(g + h*x)) + (sqrt((-d)*e + c*f)*(3*a^2*A*b*d*f*h - a^3*B*d*f*h - b^3*(2*B*c*e*g - A*(d*e*g + c*f*g + c*e*h)) + a*b^2*(B*(d*e*g + c*f*g + c*e*h) - 2*A*(d*f*g + d*e*h + c*f*h)))*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt((d*(g + h*x))/(d*g - c*h))*Elliptic.Pi(-((b*(d*e - c*f))/((b*c - a*d)*f)), asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))/(b*(b*c - a*d)^2*sqrt(f)*(b*e - a*f)*(b*g - a*h)*sqrt(e + f*x)*sqrt(g + h*x))]
    #= [(A + B*x)/((a + b*x)^3*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 13, -((b*(A*b - a*B)*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/(2*(b*c - a*d)*(b*e - a*f)*(b*g - a*h)*(a + b*x)^2)) - (b*(5*a^3*B*d*f*h + b^3*(4*B*c*e*g - 3*A*(d*e*g + c*f*g + c*e*h)) - a*b^2*(B*(d*e*g + c*f*g + c*e*h) - 6*A*(d*f*g + d*e*h + c*f*h)) - a^2*b*(9*A*d*f*h + 2*B*(d*f*g + d*e*h + c*f*h)))*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/(4*(b*c - a*d)^2*(b*e - a*f)^2*(b*g - a*h)^2*(a + b*x)) + (sqrt(f)*sqrt((-d)*e + c*f)*(5*a^3*B*d*f*h + b^3*(4*B*c*e*g - 3*A*(d*e*g + c*f*g + c*e*h)) - a*b^2*(B*(d*e*g + c*f*g + c*e*h) - 6*A*(d*f*g + d*e*h + c*f*h)) - a^2*b*(9*A*d*f*h + 2*B*(d*f*g + d*e*h + c*f*h)))*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt(g + h*x)*Elliptic.E(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))/(4*(b*c - a*d)^2*(b*e - a*f)^2*(b*g - a*h)^2*sqrt(e + f*x)*sqrt((d*(g + h*x))/(d*g - c*h))) - (sqrt(f)*sqrt((-d)*e + c*f)*(3*a^3*B*d*f*h - a^2*b*d*f*(2*B*g + 7*A*h) + b^3*(4*B*c*e*g - A*(3*d*e*g + 3*c*f*g + c*e*h)) - a*b^2*(B*(d*e*g + c*f*g + 3*c*e*h) - 2*A*(3*d*f*g + 2*d*e*h + 2*c*f*h)))*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt((d*(g + h*x))/(d*g - c*h))*Elliptic.F(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))/(4*b*(b*c - a*d)^2*(b*e - a*f)^2*(b*g - a*h)*sqrt(e + f*x)*sqrt(g + h*x)) - (sqrt((-d)*e + c*f)*(15*a^4*A*b*d^2*f^2*h^2 - 3*a^5*B*d^2*f^2*h^2 + 10*a^3*b^2*d*f*h*(B*(d*e*g + c*f*g + c*e*h) - 2*A*(d*f*g + d*e*h + c*f*h)) + a*b^4*(B*(d^2*e^2*g^2 + 14*c*d*e*g*(f*g + e*h) + c^2*(f^2*g^2 + 14*e*f*g*h + e^2*h^2)) - 4*A*(2*d^2*e*g*(f*g + e*h) + 2*c^2*f*h*(f*g + e*h) + c*d*(2*f^2*g^2 + 3*e*f*g*h + 2*e^2*h^2))) - b^5*(4*B*c*e*g*(d*e*g + c*f*g + c*e*h) - A*(3*d^2*e^2*g^2 + 2*c*d*e*g*(f*g + e*h) + c^2*(3*f^2*g^2 + 2*e*f*g*h + 3*e^2*h^2))) - 2*a^2*b^3*(2*B*(d^2*e*g*(f*g + e*h) + c^2*f*h*(f*g + e*h) + c*d*(f^2*g^2 + 9*e*f*g*h + e^2*h^2)) - A*(4*c^2*f^2*h^2 + 11*c*d*f*h*(f*g + e*h) + d^2*(4*f^2*g^2 + 11*e*f*g*h + 4*e^2*h^2))))*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt((d*(g + h*x))/(d*g - c*h))*Elliptic.Pi(-((b*(d*e - c*f))/((b*c - a*d)*f)), asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))/(4*b*(b*c - a*d)^3*sqrt(f)*(b*e - a*f)^2*(b*g - a*h)^2*sqrt(e + f*x)*sqrt(g + h*x))] =#


    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^(m/2)*(c+d*x)^(n/2)*(A+B*x) / (Sqrte+f*x)*sqrt(g+h*x))=#


    #= ::Subsubsection:: =#
    #=n>0=#


    #= ::Subsubsection::Closed:: =#
    #=n<0=#


    @test_int [(a + b*x)^(3/2)*(A + B*x)/(sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 10, ((5*a*B*d*f*h + b*(4*A*d*f*h - 3*B*(d*f*g + d*e*h + c*f*h)))*sqrt(a + b*x)*sqrt(e + f*x)*sqrt(g + h*x))/(4*d*f^2*h^2*sqrt(c + d*x)) + (b*B*sqrt(a + b*x)*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/(2*d*f*h) - (sqrt(d*g - c*h)*sqrt(f*g - e*h)*(5*a*B*d*f*h + b*(4*A*d*f*h - 3*B*(d*f*g + d*e*h + c*f*h)))*sqrt(a + b*x)*sqrt(-(((d*e - c*f)*(g + h*x))/((f*g - e*h)*(c + d*x))))*Elliptic.E(asin((sqrt(d*g - c*h)*sqrt(e + f*x))/(sqrt(f*g - e*h)*sqrt(c + d*x))), ((b*c - a*d)*(f*g - e*h))/((b*e - a*f)*(d*g - c*h))))/(4*d^2*f^2*h^2*sqrt(((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x)))*sqrt(g + h*x)) - ((b*e - a*f)*sqrt(b*g - a*h)*(3*a*B*d*f*h + b*(4*A*d*f*h - B*(c*f*h + 3*d*(f*g + e*h))))*sqrt(((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x)))*sqrt(g + h*x)*Elliptic.F(asin((sqrt(b*g - a*h)*sqrt(e + f*x))/(sqrt(f*g - e*h)*sqrt(a + b*x))), -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))))/(4*b*d*f^2*h^2*sqrt(f*g - e*h)*sqrt(c + d*x)*sqrt(-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x))))) + (sqrt((-d)*g + c*h)*(4*d*f*h*(2*a*(2*A*b + a*B)*d*f*h - b*B*(b*(d*e*g + c*f*g + c*e*h) + a*(d*f*g + d*e*h + c*f*h))) - (a*d*f*h + b*(d*f*g + d*e*h + c*f*h))*(5*a*B*d*f*h + b*(4*A*d*f*h - 3*B*(d*f*g + d*e*h + c*f*h))))*(a + b*x)*sqrt(((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x)))*sqrt(((b*g - a*h)*(e + f*x))/((f*g - e*h)*(a + b*x)))*Elliptic.Pi(-((b*(d*g - c*h))/((b*c - a*d)*h)), asin((sqrt(b*c - a*d)*sqrt(g + h*x))/(sqrt((-d)*g + c*h)*sqrt(a + b*x))), ((b*e - a*f)*(d*g - c*h))/((b*c - a*d)*(f*g - e*h))))/(4*b*d^2*sqrt(b*c - a*d)*f^2*h^3*sqrt(c + d*x)*sqrt(e + f*x))]
    @test_int [(a + b*x)^(1/2)*(A + B*x)/(sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 7, (B*sqrt(a + b*x)*sqrt(e + f*x)*sqrt(g + h*x))/(f*h*sqrt(c + d*x)) - (B*sqrt(d*g - c*h)*sqrt(f*g - e*h)*sqrt(a + b*x)*sqrt(-(((d*e - c*f)*(g + h*x))/((f*g - e*h)*(c + d*x))))*Elliptic.E(asin((sqrt(d*g - c*h)*sqrt(e + f*x))/(sqrt(f*g - e*h)*sqrt(c + d*x))), ((b*c - a*d)*(f*g - e*h))/((b*e - a*f)*(d*g - c*h))))/(d*f*h*sqrt(((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x)))*sqrt(g + h*x)) - (B*(b*e - a*f)*sqrt(b*g - a*h)*sqrt(((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x)))*sqrt(g + h*x)*Elliptic.F(asin((sqrt(b*g - a*h)*sqrt(e + f*x))/(sqrt(f*g - e*h)*sqrt(a + b*x))), -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))))/(b*f*h*sqrt(f*g - e*h)*sqrt(c + d*x)*sqrt(-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x))))) + (sqrt((-d)*g + c*h)*(2*A*b*d*f*h + B*(a*d*f*h - b*(d*f*g + d*e*h + c*f*h)))*(a + b*x)*sqrt(((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x)))*sqrt(((b*g - a*h)*(e + f*x))/((f*g - e*h)*(a + b*x)))*Elliptic.Pi(-((b*(d*g - c*h))/((b*c - a*d)*h)), asin((sqrt(b*c - a*d)*sqrt(g + h*x))/(sqrt((-d)*g + c*h)*sqrt(a + b*x))), ((b*e - a*f)*(d*g - c*h))/((b*c - a*d)*(f*g - e*h))))/(b*d*sqrt(b*c - a*d)*f*h^2*sqrt(c + d*x)*sqrt(e + f*x))]
    @test_int [(A + B*x)/((a + b*x)^(1/2)*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 5, (2*(A*b - a*B)*sqrt(((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x)))*sqrt(g + h*x)*Elliptic.F(asin((sqrt(b*g - a*h)*sqrt(e + f*x))/(sqrt(f*g - e*h)*sqrt(a + b*x))), -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))))/(b*sqrt(b*g - a*h)*sqrt(f*g - e*h)*sqrt(c + d*x)*sqrt(-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x))))) + (2*B*sqrt((-d)*g + c*h)*(a + b*x)*sqrt(((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x)))*sqrt(((b*g - a*h)*(e + f*x))/((f*g - e*h)*(a + b*x)))*Elliptic.Pi(-((b*(d*g - c*h))/((b*c - a*d)*h)), asin((sqrt(b*c - a*d)*sqrt(g + h*x))/(sqrt((-d)*g + c*h)*sqrt(a + b*x))), ((b*e - a*f)*(d*g - c*h))/((b*c - a*d)*(f*g - e*h))))/(b*sqrt(b*c - a*d)*h*sqrt(c + d*x)*sqrt(e + f*x))]
    @test_int [(A + B*x)/((a + b*x)^(3/2)*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 7, (2*(A*b - a*B)*d*sqrt(a + b*x)*sqrt(e + f*x)*sqrt(g + h*x))/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*sqrt(c + d*x)) - (2*b*(A*b - a*B)*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*sqrt(a + b*x)) - (2*(A*b - a*B)*sqrt(d*g - c*h)*sqrt(f*g - e*h)*sqrt(a + b*x)*sqrt(-(((d*e - c*f)*(g + h*x))/((f*g - e*h)*(c + d*x))))*Elliptic.E(asin((sqrt(d*g - c*h)*sqrt(e + f*x))/(sqrt(f*g - e*h)*sqrt(c + d*x))), ((b*c - a*d)*(f*g - e*h))/((b*e - a*f)*(d*g - c*h))))/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*sqrt(((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x)))*sqrt(g + h*x)) + (2*(B*c - A*d)*sqrt(((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x)))*sqrt(g + h*x)*Elliptic.F(asin((sqrt(b*g - a*h)*sqrt(e + f*x))/(sqrt(f*g - e*h)*sqrt(a + b*x))), -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))))/((b*c - a*d)*sqrt(b*g - a*h)*sqrt(f*g - e*h)*sqrt(c + d*x)*sqrt(-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))))]
    @test_int [(A + B*x)/((a + b*x)^(5/2)*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 8, (2*d*(3*a^3*B*d*f*h + b^3*(3*B*c*e*g - 2*A*(d*e*g + c*f*g + c*e*h)) - a*b^2*(B*(d*e*g + c*f*g + c*e*h) - 4*A*(d*f*g + d*e*h + c*f*h)) - a^2*b*(6*A*d*f*h + B*(d*f*g + d*e*h + c*f*h)))*sqrt(a + b*x)*sqrt(e + f*x)*sqrt(g + h*x))/(3*(b*c - a*d)^2*(b*e - a*f)^2*(b*g - a*h)^2*sqrt(c + d*x)) - (2*b*(A*b - a*B)*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/(3*(b*c - a*d)*(b*e - a*f)*(b*g - a*h)*(a + b*x)^(3/2)) - (2*b*(3*a^3*B*d*f*h + b^3*(3*B*c*e*g - 2*A*(d*e*g + c*f*g + c*e*h)) - a*b^2*(B*(d*e*g + c*f*g + c*e*h) - 4*A*(d*f*g + d*e*h + c*f*h)) - a^2*b*(6*A*d*f*h + B*(d*f*g + d*e*h + c*f*h)))*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/(3*(b*c - a*d)^2*(b*e - a*f)^2*(b*g - a*h)^2*sqrt(a + b*x)) - (2*sqrt(d*g - c*h)*sqrt(f*g - e*h)*(3*a^3*B*d*f*h + b^3*(3*B*c*e*g - 2*A*(d*e*g + c*f*g + c*e*h)) - a*b^2*(B*(d*e*g + c*f*g + c*e*h) - 4*A*(d*f*g + d*e*h + c*f*h)) - a^2*b*(6*A*d*f*h + B*(d*f*g + d*e*h + c*f*h)))*sqrt(a + b*x)*sqrt(-(((d*e - c*f)*(g + h*x))/((f*g - e*h)*(c + d*x))))*Elliptic.E(asin((sqrt(d*g - c*h)*sqrt(e + f*x))/(sqrt(f*g - e*h)*sqrt(c + d*x))), ((b*c - a*d)*(f*g - e*h))/((b*e - a*f)*(d*g - c*h))))/(3*(b*c - a*d)^2*(b*e - a*f)^2*(b*g - a*h)^2*sqrt(((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x)))*sqrt(g + h*x)) - (2*(3*a^2*d*(B*c - A*d)*f*h + b^2*(3*B*c*d*e*g - A*(2*d^2*e*g - c^2*f*h + c*d*(f*g + e*h))) + a*b*(3*A*d^2*(f*g + e*h) - B*(d^2*e*g + c^2*f*h + 2*c*d*(f*g + e*h))))*sqrt(((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x)))*sqrt(g + h*x)*Elliptic.F(asin((sqrt(b*g - a*h)*sqrt(e + f*x))/(sqrt(f*g - e*h)*sqrt(a + b*x))), -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))))/(3*(b*c - a*d)^2*(b*e - a*f)*(b*g - a*h)^(3/2)*sqrt(f*g - e*h)*sqrt(c + d*x)*sqrt(-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))))]


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


    #= ::Title:: =#
    #=Integrands*of*the*form*P3(x)*(a+b*x)^m*(c+d*x)^n*(e+f*x)^p*(g+h*x)^q=#


    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^m*(c+d*x)^(n/2)*(e+f*x)^(p/2)*(g+h*x)^(q/2)*(A+B*x+C*x^2)*with*A*b^2-a*b*B+a^2*C=0=#


    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^m*(c+d*x)^(n/2)*(A+B*x+C*x^2) / (Sqrte+f*x)*sqrt(g+h*x))=#


    #= ::Subsubsection:: =#
    #=n>0=#


    #= ::Subsubsection::Closed:: =#
    #=n<0=#


    @test_int [(a + b*x)^1*(a*b*B - a^2*C + b^2*B*x + b^2*C*x^2)/(sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 8, (2*b^2*(5*b*B*d*f*h + 2*C*(a*d*f*h - 2*b*(d*f*g + d*e*h + c*f*h)))*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/(15*d^2*f^2*h^2) + (2*b^2*C*(a + b*x)*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/(5*d*f*h) - (1/(15*d^3*f^(5/2)*h^3*sqrt(e + f*x)*sqrt((d*(g + h*x))/(d*g - c*h))))*(2*b*sqrt((-d)*e + c*f)*(15*a^2*C*d^2*f^2*h^2 - 10*a*b*d*f*h*(3*B*d*f*h - C*(d*f*g + d*e*h + c*f*h)) + b^2*(10*B*d*f*h*(d*f*g + d*e*h + c*f*h) - C*(8*c^2*f^2*h^2 + 7*c*d*f*h*(f*g + e*h) + d^2*(8*f^2*g^2 + 7*e*f*g*h + 8*e^2*h^2))))*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt(g + h*x)*Elliptic.E(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h)))) - (1/(15*d^3*f^(5/2)*h^3*sqrt(e + f*x)*sqrt(g + h*x)))*(2*sqrt((-d)*e + c*f)*(15*a^3*C*d^2*f^2*h^3 - 15*a^2*b*d^2*f^2*h^2*(C*g + B*h) + 5*a*b^2*d*f*h*(6*B*d*f*g*h - C*(c*h*(f*g - e*h) + d*g*(2*f*g + e*h))) - b^3*(5*B*d*f*h*(c*h*(f*g - e*h) + d*g*(2*f*g + e*h)) - C*(4*c^2*f*h^2*(f*g - e*h) + c*d*h*(3*f^2*g^2 + e*f*g*h - 4*e^2*h^2) + d^2*g*(8*f^2*g^2 + 3*e*f*g*h + 4*e^2*h^2))))*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt((d*(g + h*x))/(d*g - c*h))*Elliptic.F(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))]
    @test_int [(a + b*x)^0*(a*b*B - a^2*C + b^2*B*x + b^2*C*x^2)/(sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 7, (2*b^2*C*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/(3*d*f*h) + (2*b^2*sqrt((-d)*e + c*f)*(3*B*d*f*h - 2*C*(d*f*g + d*e*h + c*f*h))*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt(g + h*x)*Elliptic.E(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))/(3*d^2*f^(3/2)*h^2*sqrt(e + f*x)*sqrt((d*(g + h*x))/(d*g - c*h))) + (2*sqrt((-d)*e + c*f)*(3*a*b*B*d*f*h^2 - 3*a^2*C*d*f*h^2 - b^2*(3*B*d*f*g*h - C*(c*h*(f*g - e*h) + d*g*(2*f*g + e*h))))*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt((d*(g + h*x))/(d*g - c*h))*Elliptic.F(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))/(3*d^2*f^(3/2)*h^2*sqrt(e + f*x)*sqrt(g + h*x))]
    @test_int [(a*b*B - a^2*C + b^2*B*x + b^2*C*x^2)/((a + b*x)^1*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 7, (2*b*C*sqrt((-d)*e + c*f)*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt(g + h*x)*Elliptic.E(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))/(d*sqrt(f)*h*sqrt(e + f*x)*sqrt((d*(g + h*x))/(d*g - c*h))) - (2*sqrt((-d)*e + c*f)*(b*C*g - b*B*h + a*C*h)*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt((d*(g + h*x))/(d*g - c*h))*Elliptic.F(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))/(d*sqrt(f)*h*sqrt(e + f*x)*sqrt(g + h*x))]
    @test_int [(a*b*B - a^2*C + b^2*B*x + b^2*C*x^2)/((a + b*x)^2*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 10, (2*C*sqrt((-d)*e + c*f)*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt((d*(g + h*x))/(d*g - c*h))*Elliptic.F(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))/(d*sqrt(f)*sqrt(e + f*x)*sqrt(g + h*x)) - (2*(b*B - 2*a*C)*sqrt((-d)*e + c*f)*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt((d*(g + h*x))/(d*g - c*h))*Elliptic.Pi(-((b*(d*e - c*f))/((b*c - a*d)*f)), asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))/((b*c - a*d)*sqrt(f)*sqrt(e + f*x)*sqrt(g + h*x))]
    @test_int [(a*b*B - a^2*C + b^2*B*x + b^2*C*x^2)/((a + b*x)^3*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 13, -((b^2*(b*B - 2*a*C)*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*(a + b*x))) + (b*(b*B - 2*a*C)*sqrt(f)*sqrt((-d)*e + c*f)*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt(g + h*x)*Elliptic.E(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*sqrt(e + f*x)*sqrt((d*(g + h*x))/(d*g - c*h))) - ((b*B - 2*a*C)*sqrt(f)*sqrt((-d)*e + c*f)*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt((d*(g + h*x))/(d*g - c*h))*Elliptic.F(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))/((b*c - a*d)*(b*e - a*f)*sqrt(e + f*x)*sqrt(g + h*x)) - (sqrt((-d)*e + c*f)*(4*a^3*C*d*f*h + 2*a*b^2*B*(d*f*g + d*e*h + c*f*h) - b^3*(B*d*e*g - c*(2*C*e*g - B*f*g - B*e*h)) - a^2*b*(3*B*d*f*h + 2*C*(d*f*g + d*e*h + c*f*h)))*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt((d*(g + h*x))/(d*g - c*h))*Elliptic.Pi(-((b*(d*e - c*f))/((b*c - a*d)*f)), asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))/((b*c - a*d)^2*sqrt(f)*(b*e - a*f)*(b*g - a*h)*sqrt(e + f*x)*sqrt(g + h*x))]


    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^(m/2)*(c+d*x)^(n/2)*(A+B*x+C*x^2) / (Sqrte+f*x)*sqrt(g+h*x))=#


    #= ::Subsubsection:: =#
    #=n>0=#


    #= ::Subsubsection::Closed:: =#
    #=n<0=#


    @test_int [(a + b*x)^(1/2)*(a*b*B - a^2*C + b^2*B*x + b^2*C*x^2)/(sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 9, (b*(4*b*B*d*f*h + C*(a*d*f*h - 3*b*(d*f*g + d*e*h + c*f*h)))*sqrt(a + b*x)*sqrt(e + f*x)*sqrt(g + h*x))/(4*d*f^2*h^2*sqrt(c + d*x)) + (b^2*C*sqrt(a + b*x)*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/(2*d*f*h) - (b*sqrt(d*g - c*h)*sqrt(f*g - e*h)*(4*b*B*d*f*h + C*(a*d*f*h - 3*b*(d*f*g + d*e*h + c*f*h)))*sqrt(a + b*x)*sqrt(-(((d*e - c*f)*(g + h*x))/((f*g - e*h)*(c + d*x))))*Elliptic.E(asin((sqrt(d*g - c*h)*sqrt(e + f*x))/(sqrt(f*g - e*h)*sqrt(c + d*x))), ((b*c - a*d)*(f*g - e*h))/((b*e - a*f)*(d*g - c*h))))/(4*d^2*f^2*h^2*sqrt(((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x)))*sqrt(g + h*x)) + ((b*e - a*f)*sqrt(b*g - a*h)*(a*C*d*f*h - b*(4*B*d*f*h - C*(3*d*f*g + 3*d*e*h + c*f*h)))*sqrt(((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x)))*sqrt(g + h*x)*Elliptic.F(asin((sqrt(b*g - a*h)*sqrt(e + f*x))/(sqrt(f*g - e*h)*sqrt(a + b*x))), -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))))/(4*d*f^2*h^2*sqrt(f*g - e*h)*sqrt(c + d*x)*sqrt(-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x))))) - (1/(4*d^2*sqrt(b*c - a*d)*f^2*h^3*sqrt(c + d*x)*sqrt(e + f*x)))*(sqrt((-d)*g + c*h)*((a*d*f*h + b*(d*f*g + d*e*h + c*f*h))*(4*b*B*d*f*h + C*(a*d*f*h - 3*b*(d*f*g + d*e*h + c*f*h))) + 4*d*f*h*(2*a^2*C*d*f*h + b^2*C*(d*e*g + c*f*g + c*e*h) - a*b*(4*B*d*f*h - C*(d*f*g + d*e*h + c*f*h))))*(a + b*x)*sqrt(((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x)))*sqrt(((b*g - a*h)*(e + f*x))/((f*g - e*h)*(a + b*x)))*Elliptic.Pi(-((b*(d*g - c*h))/((b*c - a*d)*h)), asin((sqrt(b*c - a*d)*sqrt(g + h*x))/(sqrt((-d)*g + c*h)*sqrt(a + b*x))), ((b*e - a*f)*(d*g - c*h))/((b*c - a*d)*(f*g - e*h))))]
    @test_int [(a*b*B - a^2*C + b^2*B*x + b^2*C*x^2)/((a + b*x)^(1/2)*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 8, (b*C*sqrt(a + b*x)*sqrt(e + f*x)*sqrt(g + h*x))/(f*h*sqrt(c + d*x)) - (b*C*sqrt(d*g - c*h)*sqrt(f*g - e*h)*sqrt(a + b*x)*sqrt(-(((d*e - c*f)*(g + h*x))/((f*g - e*h)*(c + d*x))))*Elliptic.E(asin((sqrt(d*g - c*h)*sqrt(e + f*x))/(sqrt(f*g - e*h)*sqrt(c + d*x))), ((b*c - a*d)*(f*g - e*h))/((b*e - a*f)*(d*g - c*h))))/(d*f*h*sqrt(((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x)))*sqrt(g + h*x)) - (C*(b*e - a*f)*sqrt(b*g - a*h)*sqrt(((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x)))*sqrt(g + h*x)*Elliptic.F(asin((sqrt(b*g - a*h)*sqrt(e + f*x))/(sqrt(f*g - e*h)*sqrt(a + b*x))), -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))))/(f*h*sqrt(f*g - e*h)*sqrt(c + d*x)*sqrt(-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x))))) - (sqrt((-d)*g + c*h)*(a*C*d*f*h - b*(2*B*d*f*h - C*(d*f*g + d*e*h + c*f*h)))*(a + b*x)*sqrt(((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x)))*sqrt(((b*g - a*h)*(e + f*x))/((f*g - e*h)*(a + b*x)))*Elliptic.Pi(-((b*(d*g - c*h))/((b*c - a*d)*h)), asin((sqrt(b*c - a*d)*sqrt(g + h*x))/(sqrt((-d)*g + c*h)*sqrt(a + b*x))), ((b*e - a*f)*(d*g - c*h))/((b*c - a*d)*(f*g - e*h))))/(d*sqrt(b*c - a*d)*f*h^2*sqrt(c + d*x)*sqrt(e + f*x))]
    @test_int [(a*b*B - a^2*C + b^2*B*x + b^2*C*x^2)/((a + b*x)^(3/2)*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 6, (2*(b*B - 2*a*C)*sqrt(((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x)))*sqrt(g + h*x)*Elliptic.F(asin((sqrt(b*g - a*h)*sqrt(e + f*x))/(sqrt(f*g - e*h)*sqrt(a + b*x))), -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))))/(sqrt(b*g - a*h)*sqrt(f*g - e*h)*sqrt(c + d*x)*sqrt(-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x))))) + (2*C*sqrt((-d)*g + c*h)*(a + b*x)*sqrt(((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x)))*sqrt(((b*g - a*h)*(e + f*x))/((f*g - e*h)*(a + b*x)))*Elliptic.Pi(-((b*(d*g - c*h))/((b*c - a*d)*h)), asin((sqrt(b*c - a*d)*sqrt(g + h*x))/(sqrt((-d)*g + c*h)*sqrt(a + b*x))), ((b*e - a*f)*(d*g - c*h))/((b*c - a*d)*(f*g - e*h))))/(sqrt(b*c - a*d)*h*sqrt(c + d*x)*sqrt(e + f*x))]
    @test_int [(a*b*B - a^2*C + b^2*B*x + b^2*C*x^2)/((a + b*x)^(5/2)*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 8, (2*b*(b*B - 2*a*C)*d*sqrt(a + b*x)*sqrt(e + f*x)*sqrt(g + h*x))/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*sqrt(c + d*x)) - (2*b^2*(b*B - 2*a*C)*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*sqrt(a + b*x)) - (2*b*(b*B - 2*a*C)*sqrt(d*g - c*h)*sqrt(f*g - e*h)*sqrt(a + b*x)*sqrt(-(((d*e - c*f)*(g + h*x))/((f*g - e*h)*(c + d*x))))*Elliptic.E(asin((sqrt(d*g - c*h)*sqrt(e + f*x))/(sqrt(f*g - e*h)*sqrt(c + d*x))), ((b*c - a*d)*(f*g - e*h))/((b*e - a*f)*(d*g - c*h))))/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*sqrt(((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x)))*sqrt(g + h*x)) + (2*(b*c*C - b*B*d + a*C*d)*sqrt(((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x)))*sqrt(g + h*x)*Elliptic.F(asin((sqrt(b*g - a*h)*sqrt(e + f*x))/(sqrt(f*g - e*h)*sqrt(a + b*x))), -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))))/((b*c - a*d)*sqrt(b*g - a*h)*sqrt(f*g - e*h)*sqrt(c + d*x)*sqrt(-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))))]
    @test_int [(a*b*B - a^2*C + b^2*B*x + b^2*C*x^2)/((a + b*x)^(7/2)*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 9, (2*b*d*(9*a^3*C*d*f*h - b^3*(2*B*d*e*g - c*(3*C*e*g - 2*B*f*g - 2*B*e*h)) + a*b^2*(C*(d*e*g + c*f*g + c*e*h) + 4*B*(d*f*g + d*e*h + c*f*h)) - a^2*b*(6*B*d*f*h + 5*C*(d*f*g + d*e*h + c*f*h)))*sqrt(a + b*x)*sqrt(e + f*x)*sqrt(g + h*x))/(3*(b*c - a*d)^2*(b*e - a*f)^2*(b*g - a*h)^2*sqrt(c + d*x)) - (2*b^2*(b*B - 2*a*C)*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/(3*(b*c - a*d)*(b*e - a*f)*(b*g - a*h)*(a + b*x)^(3/2)) - (2*b^2*(9*a^3*C*d*f*h - b^3*(2*B*d*e*g - c*(3*C*e*g - 2*B*f*g - 2*B*e*h)) + a*b^2*(C*(d*e*g + c*f*g + c*e*h) + 4*B*(d*f*g + d*e*h + c*f*h)) - a^2*b*(6*B*d*f*h + 5*C*(d*f*g + d*e*h + c*f*h)))*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/(3*(b*c - a*d)^2*(b*e - a*f)^2*(b*g - a*h)^2*sqrt(a + b*x)) - (2*b*sqrt(d*g - c*h)*sqrt(f*g - e*h)*(9*a^3*C*d*f*h - b^3*(2*B*d*e*g - c*(3*C*e*g - 2*B*f*g - 2*B*e*h)) + a*b^2*(C*(d*e*g + c*f*g + c*e*h) + 4*B*(d*f*g + d*e*h + c*f*h)) - a^2*b*(6*B*d*f*h + 5*C*(d*f*g + d*e*h + c*f*h)))*sqrt(a + b*x)*sqrt(-(((d*e - c*f)*(g + h*x))/((f*g - e*h)*(c + d*x))))*Elliptic.E(asin((sqrt(d*g - c*h)*sqrt(e + f*x))/(sqrt(f*g - e*h)*sqrt(c + d*x))), ((b*c - a*d)*(f*g - e*h))/((b*e - a*f)*(d*g - c*h))))/(3*(b*c - a*d)^2*(b*e - a*f)^2*(b*g - a*h)^2*sqrt(((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x)))*sqrt(g + h*x)) - (2*(3*a^3*C*d^2*f*h - b^3*(2*B*d^2*e*g - B*c^2*f*h - c*d*(3*C*e*g - B*f*g - B*e*h)) - 3*a^2*b*d*(B*d*f*h + C*(d*f*g + d*e*h - c*f*h)) + a*b^2*(3*B*d^2*(f*g + e*h) + C*(d^2*e*g - c*d*f*g - c*d*e*h - 2*c^2*f*h)))*sqrt(((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x)))*sqrt(g + h*x)*Elliptic.F(asin((sqrt(b*g - a*h)*sqrt(e + f*x))/(sqrt(f*g - e*h)*sqrt(a + b*x))), -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))))/(3*(b*c - a*d)^2*(b*e - a*f)*(b*g - a*h)^(3/2)*sqrt(f*g - e*h)*sqrt(c + d*x)*sqrt(-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))))]


    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^m*(c+d*x)^(n/2)*(e+f*x)^(p/2)*(g+h*x)^(q/2)*(A+B*x+C*x^2)*with*B=0=#


    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^m*(c+d*x)^(n/2)*(A+B*x+C*x^2) / (Sqrte+f*x)*sqrt(g+h*x))=#


    #= ::Subsubsection:: =#
    #=n>0=#


    #= ::Subsubsection::Closed:: =#
    #=n<0=#


    @test_int [(a + b*x)^2*(A + C*x^2)/(sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 9, (2*(4*C*(2*a*d*f*h - 3*b*(d*f*g + d*e*h + c*f*h))*(a*d*f*h - 2*b*(d*f*g + d*e*h + c*f*h)) + 5*b*d*f*h*(7*A*b*d*f*h - C*(5*b*(d*e*g + c*f*g + c*e*h) + 2*a*(d*f*g + d*e*h + c*f*h))))*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/(105*d^3*f^3*h^3) + (4*C*(2*a*d*f*h - 3*b*(d*f*g + d*e*h + c*f*h))*(a + b*x)*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/(35*d^2*f^2*h^2) + (2*C*(a + b*x)^2*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/(7*d*f*h) - (1/(105*d^4*f^(7/2)*h^4*sqrt(e + f*x)*sqrt((d*(g + h*x))/(d*g - c*h))))*(4*sqrt((-d)*e + c*f)*(35*a^2*C*d^2*f^2*h^2*(d*f*g + d*e*h + c*f*h) - 7*a*b*d*f*h*(15*A*d^2*f^2*h^2 + C*(8*c^2*f^2*h^2 + 7*c*d*f*h*(f*g + e*h) + d^2*(8*f^2*g^2 + 7*e*f*g*h + 8*e^2*h^2))) + b^2*(35*A*d^2*f^2*h^2*(d*f*g + d*e*h + c*f*h) + 2*C*(12*c^3*f^3*h^3 + 10*c^2*d*f^2*h^2*(f*g + e*h) + c*d^2*f*h*(10*f^2*g^2 + 9*e*f*g*h + 10*e^2*h^2) + 2*d^3*(6*f^3*g^3 + 5*e*f^2*g^2*h + 5*e^2*f*g*h^2 + 6*e^3*h^3))))*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt(g + h*x)*Elliptic.E(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h)))) + (1/(105*d^4*f^(7/2)*h^4*sqrt(e + f*x)*sqrt(g + h*x)))*(2*sqrt((-d)*e + c*f)*(35*a^2*d^2*f^2*h^2*(3*A*d*f*h^2 + C*(c*h*(f*g - e*h) + d*g*(2*f*g + e*h))) - 14*a*b*d*f*h*(15*A*d^2*f^2*g*h^2 + C*(4*c^2*f*h^2*(f*g - e*h) + c*d*h*(3*f^2*g^2 + e*f*g*h - 4*e^2*h^2) + d^2*g*(8*f^2*g^2 + 3*e*f*g*h + 4*e^2*h^2))) + b^2*(35*A*d^2*f^2*h^2*(c*h*(f*g - e*h) + d*g*(2*f*g + e*h)) + C*(24*c^3*f^2*h^3*(f*g - e*h) + c^2*d*f*h^2*(17*f^2*g^2 + 6*e*f*g*h - 23*e^2*h^2) + 2*c*d^2*h*(8*f^3*g^3 + e*f^2*g^2*h + 3*e^2*f*g*h^2 - 12*e^3*h^3) + d^3*g*(48*f^3*g^3 + 16*e*f^2*g^2*h + 17*e^2*f*g*h^2 + 24*e^3*h^3))))*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt((d*(g + h*x))/(d*g - c*h))*Elliptic.F(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))]
    @test_int [(a + b*x)^1*(A + C*x^2)/(sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 8, (4*C*(a*d*f*h - 2*b*(d*f*g + d*e*h + c*f*h))*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/(15*d^2*f^2*h^2) + (2*C*(a + b*x)*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/(5*d*f*h) - (2*sqrt((-d)*e + c*f)*(10*a*C*d*f*h*(d*f*g + d*e*h + c*f*h) - b*(15*A*d^2*f^2*h^2 + C*(8*c^2*f^2*h^2 + 7*c*d*f*h*(f*g + e*h) + d^2*(8*f^2*g^2 + 7*e*f*g*h + 8*e^2*h^2))))*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt(g + h*x)*Elliptic.E(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))/(15*d^3*f^(5/2)*h^3*sqrt(e + f*x)*sqrt((d*(g + h*x))/(d*g - c*h))) + (1/(15*d^3*f^(5/2)*h^3*sqrt(e + f*x)*sqrt(g + h*x)))*(2*sqrt((-d)*e + c*f)*(5*a*d*f*h*(3*A*d*f*h^2 + C*(c*h*(f*g - e*h) + d*g*(2*f*g + e*h))) - b*(15*A*d^2*f^2*g*h^2 + C*(4*c^2*f*h^2*(f*g - e*h) + c*d*h*(3*f^2*g^2 + e*f*g*h - 4*e^2*h^2) + d^2*g*(8*f^2*g^2 + 3*e*f*g*h + 4*e^2*h^2))))*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt((d*(g + h*x))/(d*g - c*h))*Elliptic.F(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))]
    @test_int [(a + b*x)^0*(A + C*x^2)/(sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 7, (2*C*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/(3*d*f*h) - (4*C*sqrt((-d)*e + c*f)*(d*f*g + d*e*h + c*f*h)*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt(g + h*x)*Elliptic.E(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))/(3*d^2*f^(3/2)*h^2*sqrt(e + f*x)*sqrt((d*(g + h*x))/(d*g - c*h))) + (2*sqrt((-d)*e + c*f)*(3*A*d*f*h^2 + C*(c*h*(f*g - e*h) + d*g*(2*f*g + e*h)))*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt((d*(g + h*x))/(d*g - c*h))*Elliptic.F(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))/(3*d^2*f^(3/2)*h^2*sqrt(e + f*x)*sqrt(g + h*x))]
    @test_int [(A + C*x^2)/((a + b*x)^1*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 11, (2*C*sqrt((-d)*e + c*f)*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt(g + h*x)*Elliptic.E(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))/(b*d*sqrt(f)*h*sqrt(e + f*x)*sqrt((d*(g + h*x))/(d*g - c*h))) - (2*C*sqrt((-d)*e + c*f)*(b*g + a*h)*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt((d*(g + h*x))/(d*g - c*h))*Elliptic.F(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))/(b^2*d*sqrt(f)*h*sqrt(e + f*x)*sqrt(g + h*x)) - (2*(A + (a^2*C)/b^2)*sqrt((-d)*e + c*f)*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt((d*(g + h*x))/(d*g - c*h))*Elliptic.Pi(-((b*(d*e - c*f))/((b*c - a*d)*f)), asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))/((b*c - a*d)*sqrt(f)*sqrt(e + f*x)*sqrt(g + h*x))]
    @test_int [(A + C*x^2)/((a + b*x)^2*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 12, -(((A*b^2 + a^2*C)*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*(a + b*x))) + ((A*b + (a^2*C)/b)*sqrt(f)*sqrt((-d)*e + c*f)*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt(g + h*x)*Elliptic.E(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*sqrt(e + f*x)*sqrt((d*(g + h*x))/(d*g - c*h))) + (sqrt((-d)*e + c*f)*(a^2*C*d*f - 2*a*b*C*(d*e + c*f) + b^2*(2*c*C*e - A*d*f))*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt((d*(g + h*x))/(d*g - c*h))*Elliptic.F(asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))/(b^2*d*(b*c - a*d)*sqrt(f)*(b*e - a*f)*sqrt(e + f*x)*sqrt(g + h*x)) - (1/(b^2*(b*c - a*d)^2*sqrt(f)*(b*e - a*f)*(b*g - a*h)*sqrt(e + f*x)*sqrt(g + h*x)))*(sqrt((-d)*e + c*f)*(a^4*C*d*f*h - A*b^4*(d*e*g + c*f*g + c*e*h) - 2*a^3*b*C*(d*f*g + d*e*h + c*f*h) - 2*a*b^3*(2*c*C*e*g - A*d*f*g - A*d*e*h - A*c*f*h) - 3*a^2*b^2*(A*d*f*h - C*(d*e*g + c*f*g + c*e*h)))*sqrt((d*(e + f*x))/(d*e - c*f))*sqrt((d*(g + h*x))/(d*g - c*h))*Elliptic.Pi(-((b*(d*e - c*f))/((b*c - a*d)*f)), asin((sqrt(f)*sqrt(c + d*x))/sqrt((-d)*e + c*f)), ((d*e - c*f)*h)/(f*(d*g - c*h))))]


    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(a+b*x)^(m/2)*(c+d*x)^(n/2)*(A+B*x+C*x^2) / (Sqrte+f*x)*sqrt(g+h*x))=#


    #= ::Subsubsection:: =#
    #=n>0=#


    #= ::Subsubsection::Closed:: =#
    #=n<0=#


    @test_int [(a + b*x)^(3/2)*(A + C*x^2)/(sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 10, ((C*(3*a*d*f*h - 5*b*(d*f*g + d*e*h + c*f*h))*(a*d*f*h - 3*b*(d*f*g + d*e*h + c*f*h)) + 8*b*d*f*h*(3*A*b*d*f*h - C*(2*b*(d*e*g + c*f*g + c*e*h) + a*(d*f*g + d*e*h + c*f*h))))*sqrt(a + b*x)*sqrt(e + f*x)*sqrt(g + h*x))/(24*b*d^2*f^3*h^3*sqrt(c + d*x)) + (C*(3*a*d*f*h - 5*b*(d*f*g + d*e*h + c*f*h))*sqrt(a + b*x)*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/(12*d^2*f^2*h^2) + (C*(a + b*x)^(3/2)*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/(3*d*f*h) - (sqrt(d*g - c*h)*sqrt(f*g - e*h)*(C*(3*a*d*f*h - 5*b*(d*f*g + d*e*h + c*f*h))*(a*d*f*h - 3*b*(d*f*g + d*e*h + c*f*h)) + 8*b*d*f*h*(3*A*b*d*f*h - C*(2*b*(d*e*g + c*f*g + c*e*h) + a*(d*f*g + d*e*h + c*f*h))))*sqrt(a + b*x)*sqrt(-(((d*e - c*f)*(g + h*x))/((f*g - e*h)*(c + d*x))))*Elliptic.E(asin((sqrt(d*g - c*h)*sqrt(e + f*x))/(sqrt(f*g - e*h)*sqrt(c + d*x))), ((b*c - a*d)*(f*g - e*h))/((b*e - a*f)*(d*g - c*h))))/(24*b*d^3*f^3*h^3*sqrt(((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x)))*sqrt(g + h*x)) + ((b*e - a*f)*sqrt(b*g - a*h)*(3*a^2*C*d^2*f^2*h^2 + 6*a*b*C*d*f*h*(c*f*h + 2*d*(f*g + e*h)) - b^2*(24*A*d^2*f^2*h^2 + C*(5*c^2*f^2*h^2 + 4*c*d*f*h*(f*g + e*h) + d^2*(15*f^2*g^2 + 14*e*f*g*h + 15*e^2*h^2))))*sqrt(((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x)))*sqrt(g + h*x)*Elliptic.F(asin((sqrt(b*g - a*h)*sqrt(e + f*x))/(sqrt(f*g - e*h)*sqrt(a + b*x))), -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))))/(24*b^2*d^2*f^3*h^3*sqrt(f*g - e*h)*sqrt(c + d*x)*sqrt(-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x))))) - (1/(24*b^2*d^3*sqrt(b*c - a*d)*f^3*h^4*sqrt(c + d*x)*sqrt(e + f*x)))*(sqrt((-d)*g + c*h)*(4*b*d*f*h*(C*(b*(d*e*g + c*f*g + c*e*h) + a*(d*f*g + d*e*h + c*f*h))*(3*a*d*f*h - 5*b*(d*f*g + d*e*h + c*f*h)) + 2*d*f*h*(3*b^2*c*C*e*g + 2*a^2*C*(d*f*g + d*e*h + c*f*h) - a*b*(12*A*d*f*h - 5*C*(d*e*g + c*f*g + c*e*h)))) + (a*d*f*h + b*(d*f*g + d*e*h + c*f*h))*(C*(3*a*d*f*h - 5*b*(d*f*g + d*e*h + c*f*h))*(a*d*f*h - 3*b*(d*f*g + d*e*h + c*f*h)) + 8*b*d*f*h*(3*A*b*d*f*h - C*(2*b*(d*e*g + c*f*g + c*e*h) + a*(d*f*g + d*e*h + c*f*h)))))*(a + b*x)*sqrt(((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x)))*sqrt(((b*g - a*h)*(e + f*x))/((f*g - e*h)*(a + b*x)))*Elliptic.Pi(-((b*(d*g - c*h))/((b*c - a*d)*h)), asin((sqrt(b*c - a*d)*sqrt(g + h*x))/(sqrt((-d)*g + c*h)*sqrt(a + b*x))), ((b*e - a*f)*(d*g - c*h))/((b*c - a*d)*(f*g - e*h))))]
    @test_int [(a + b*x)^(1/2)*(A + C*x^2)/(sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 9, (C*(a*d*f*h - 3*b*(d*f*g + d*e*h + c*f*h))*sqrt(a + b*x)*sqrt(e + f*x)*sqrt(g + h*x))/(4*b*d*f^2*h^2*sqrt(c + d*x)) + (C*sqrt(a + b*x)*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/(2*d*f*h) - (C*sqrt(d*g - c*h)*sqrt(f*g - e*h)*(a*d*f*h - 3*b*(d*f*g + d*e*h + c*f*h))*sqrt(a + b*x)*sqrt(-(((d*e - c*f)*(g + h*x))/((f*g - e*h)*(c + d*x))))*Elliptic.E(asin((sqrt(d*g - c*h)*sqrt(e + f*x))/(sqrt(f*g - e*h)*sqrt(c + d*x))), ((b*c - a*d)*(f*g - e*h))/((b*e - a*f)*(d*g - c*h))))/(4*b*d^2*f^2*h^2*sqrt(((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x)))*sqrt(g + h*x)) + (C*(b*e - a*f)*sqrt(b*g - a*h)*(a*d*f*h + b*(c*f*h + 3*d*(f*g + e*h)))*sqrt(((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x)))*sqrt(g + h*x)*Elliptic.F(asin((sqrt(b*g - a*h)*sqrt(e + f*x))/(sqrt(f*g - e*h)*sqrt(a + b*x))), -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))))/(4*b^2*d*f^2*h^2*sqrt(f*g - e*h)*sqrt(c + d*x)*sqrt(-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x))))) - (sqrt((-d)*g + c*h)*(C*(a*d*f*h - 3*b*(d*f*g + d*e*h + c*f*h))*(a*d*f*h + b*(d*f*g + d*e*h + c*f*h)) - 4*b*d*f*h*(2*A*b*d*f*h - C*(b*(d*e*g + c*f*g + c*e*h) + a*(d*f*g + d*e*h + c*f*h))))*(a + b*x)*sqrt(((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x)))*sqrt(((b*g - a*h)*(e + f*x))/((f*g - e*h)*(a + b*x)))*Elliptic.Pi(-((b*(d*g - c*h))/((b*c - a*d)*h)), asin((sqrt(b*c - a*d)*sqrt(g + h*x))/(sqrt((-d)*g + c*h)*sqrt(a + b*x))), ((b*e - a*f)*(d*g - c*h))/((b*c - a*d)*(f*g - e*h))))/(4*b^2*d^2*sqrt(b*c - a*d)*f^2*h^3*sqrt(c + d*x)*sqrt(e + f*x))]
    @test_int [(A + C*x^2)/((a + b*x)^(1/2)*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 8, (C*sqrt(a + b*x)*sqrt(e + f*x)*sqrt(g + h*x))/(b*f*h*sqrt(c + d*x)) - (C*sqrt(d*g - c*h)*sqrt(f*g - e*h)*sqrt(a + b*x)*sqrt(-(((d*e - c*f)*(g + h*x))/((f*g - e*h)*(c + d*x))))*Elliptic.E(asin((sqrt(d*g - c*h)*sqrt(e + f*x))/(sqrt(f*g - e*h)*sqrt(c + d*x))), ((b*c - a*d)*(f*g - e*h))/((b*e - a*f)*(d*g - c*h))))/(b*d*f*h*sqrt(((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x)))*sqrt(g + h*x)) + ((a^2*C*f*h + a*b*C*(f*g + e*h) - b^2*(C*e*g - 2*A*f*h))*sqrt(((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x)))*sqrt(g + h*x)*Elliptic.F(asin((sqrt(b*g - a*h)*sqrt(e + f*x))/(sqrt(f*g - e*h)*sqrt(a + b*x))), -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))))/(b^2*f*h*sqrt(b*g - a*h)*sqrt(f*g - e*h)*sqrt(c + d*x)*sqrt(-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x))))) - (C*sqrt((-d)*g + c*h)*(a*d*f*h + b*(d*f*g + d*e*h + c*f*h))*(a + b*x)*sqrt(((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x)))*sqrt(((b*g - a*h)*(e + f*x))/((f*g - e*h)*(a + b*x)))*Elliptic.Pi(-((b*(d*g - c*h))/((b*c - a*d)*h)), asin((sqrt(b*c - a*d)*sqrt(g + h*x))/(sqrt((-d)*g + c*h)*sqrt(a + b*x))), ((b*e - a*f)*(d*g - c*h))/((b*c - a*d)*(f*g - e*h))))/(b^2*d*sqrt(b*c - a*d)*f*h^2*sqrt(c + d*x)*sqrt(e + f*x))]
    @test_int [(A + C*x^2)/((a + b*x)^(3/2)*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 9, (2*(A*b^2 + a^2*C)*d*sqrt(a + b*x)*sqrt(e + f*x)*sqrt(g + h*x))/(b*(b*c - a*d)*(b*e - a*f)*(b*g - a*h)*sqrt(c + d*x)) - (2*(A*b^2 + a^2*C)*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/((b*c - a*d)*(b*e - a*f)*(b*g - a*h)*sqrt(a + b*x)) - (2*(A*b^2 + a^2*C)*sqrt(d*g - c*h)*sqrt(f*g - e*h)*sqrt(a + b*x)*sqrt(-(((d*e - c*f)*(g + h*x))/((f*g - e*h)*(c + d*x))))*Elliptic.E(asin((sqrt(d*g - c*h)*sqrt(e + f*x))/(sqrt(f*g - e*h)*sqrt(c + d*x))), ((b*c - a*d)*(f*g - e*h))/((b*e - a*f)*(d*g - c*h))))/(b*(b*c - a*d)*(b*e - a*f)*(b*g - a*h)*sqrt(((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x)))*sqrt(g + h*x)) - (2*(2*a*b*c*C + A*b^2*d - a^2*C*d)*sqrt(((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x)))*sqrt(g + h*x)*Elliptic.F(asin((sqrt(b*g - a*h)*sqrt(e + f*x))/(sqrt(f*g - e*h)*sqrt(a + b*x))), -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))))/(b^2*(b*c - a*d)*sqrt(b*g - a*h)*sqrt(f*g - e*h)*sqrt(c + d*x)*sqrt(-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x))))) + (2*C*sqrt((-d)*g + c*h)*(a + b*x)*sqrt(((b*g - a*h)*(c + d*x))/((d*g - c*h)*(a + b*x)))*sqrt(((b*g - a*h)*(e + f*x))/((f*g - e*h)*(a + b*x)))*Elliptic.Pi(-((b*(d*g - c*h))/((b*c - a*d)*h)), asin((sqrt(b*c - a*d)*sqrt(g + h*x))/(sqrt((-d)*g + c*h)*sqrt(a + b*x))), ((b*e - a*f)*(d*g - c*h))/((b*c - a*d)*(f*g - e*h))))/(b^2*sqrt(b*c - a*d)*h*sqrt(c + d*x)*sqrt(e + f*x))]
    @test_int [(A + C*x^2)/((a + b*x)^(5/2)*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x)), x, 8, -((4*d*(A*b^3*(d*e*g + c*f*g + c*e*h) + a^3*C*(d*f*g + d*e*h + c*f*h) + a^2*b*(3*A*d*f*h - 2*C*(d*e*g + c*f*g + c*e*h)) - a*b^2*(2*A*d*(f*g + e*h) - c*(3*C*e*g - 2*A*f*h)))*sqrt(a + b*x)*sqrt(e + f*x)*sqrt(g + h*x))/(3*(b*c - a*d)^2*(b*e - a*f)^2*(b*g - a*h)^2*sqrt(c + d*x))) - (2*(A*b^2 + a^2*C)*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/(3*(b*c - a*d)*(b*e - a*f)*(b*g - a*h)*(a + b*x)^(3/2)) + (4*b*(A*b^3*(d*e*g + c*f*g + c*e*h) + a^3*C*(d*f*g + d*e*h + c*f*h) + a^2*b*(3*A*d*f*h - 2*C*(d*e*g + c*f*g + c*e*h)) - a*b^2*(2*A*d*(f*g + e*h) - c*(3*C*e*g - 2*A*f*h)))*sqrt(c + d*x)*sqrt(e + f*x)*sqrt(g + h*x))/(3*(b*c - a*d)^2*(b*e - a*f)^2*(b*g - a*h)^2*sqrt(a + b*x)) + (4*sqrt(d*g - c*h)*sqrt(f*g - e*h)*(A*b^3*(d*e*g + c*f*g + c*e*h) + a^3*C*(d*f*g + d*e*h + c*f*h) + a^2*b*(3*A*d*f*h - 2*C*(d*e*g + c*f*g + c*e*h)) - a*b^2*(2*A*d*(f*g + e*h) - c*(3*C*e*g - 2*A*f*h)))*sqrt(a + b*x)*sqrt(-(((d*e - c*f)*(g + h*x))/((f*g - e*h)*(c + d*x))))*Elliptic.E(asin((sqrt(d*g - c*h)*sqrt(e + f*x))/(sqrt(f*g - e*h)*sqrt(c + d*x))), ((b*c - a*d)*(f*g - e*h))/((b*e - a*f)*(d*g - c*h))))/(3*(b*c - a*d)^2*(b*e - a*f)^2*(b*g - a*h)^2*sqrt(((d*e - c*f)*(a + b*x))/((b*e - a*f)*(c + d*x)))*sqrt(g + h*x)) - (2*(3*a*b*(c^2*C + A*d^2)*(f*g + e*h) - b^2*(2*A*d^2*e*g + A*c*d*(f*g + e*h) + c^2*(3*C*e*g - A*f*h)) - a^2*(3*A*d^2*f*h - C*(d^2*e*g - c*d*f*g - c*d*e*h - 2*c^2*f*h)))*sqrt(((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x)))*sqrt(g + h*x)*Elliptic.F(asin((sqrt(b*g - a*h)*sqrt(e + f*x))/(sqrt(f*g - e*h)*sqrt(a + b*x))), -(((b*c - a*d)*(f*g - e*h))/((d*e - c*f)*(b*g - a*h)))))/(3*(b*c - a*d)^2*(b*e - a*f)*(b*g - a*h)^(3/2)*sqrt(f*g - e*h)*sqrt(c + d*x)*sqrt(-(((b*e - a*f)*(g + h*x))/((f*g - e*h)*(a + b*x)))))]
    end
