text:
@testset "5.3.4 u (a+b arctan(c x))^p" begin
    (a, b, c, d, e, f, g, m, n, p, q, x, ) = @variables a b c d e f g m n p q x

    #= ::Package:: =#

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

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*x^m*(d+e*x)^q*(a+b*atan(c*x))^p*with*c^2*d^2+e^2=0=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(d+e*x)^q*(a+b*atan(c*x))^1*with*c^2*d^2+e^2=0=#

    #= ::Subsubsection::Closed:: =#
    #=q>0=#

    @test_int [x^3*(d + im*c*d*x)*(a + b*atan(c*x)), x, 7, (b*d*x)/(4*c^3) + ((im/10)*b*d*x^2)/c^2 - (b*d*x^3)/(12*c) - (im/20)*b*d*x^4 - (b*d*atan(c*x))/(4*c^4) + (d*x^4*(a + b*atan(c*x)))/4 + (im/5)*c*d*x^5*(a + b*atan(c*x)) - ((im/10)*b*d*log(1 + c^2*x^2))/c^4]
    @test_int [x^2*(d + im*c*d*x)*(a + b*atan(c*x)), x, 7, ((im/4)*b*d*x)/c^2 - (b*d*x^2)/(6*c) - (im/12)*b*d*x^3 - ((im/4)*b*d*atan(c*x))/c^3 + (d*x^3*(a + b*atan(c*x)))/3 + (im/4)*c*d*x^4*(a + b*atan(c*x)) + (b*d*log(1 + c^2*x^2))/(6*c^3)]
    @test_int [x*(d + im*c*d*x)*(a + b*atan(c*x)), x, 7, -(b*d*x)/(2*c) - (im/6)*b*d*x^2 + (b*d*atan(c*x))/(2*c^2) + (d*x^2*(a + b*atan(c*x)))/2 + (im/3)*c*d*x^3*(a + b*atan(c*x)) + ((im/6)*b*d*log(1 + c^2*x^2))/c^2]
    @test_int [(d + im*c*d*x)*(a + b*atan(c*x)), x, 4, (-im/2)*b*d*x - ((im/2)*d*(1 + im*c*x)^2*(a + b*atan(c*x)))/c - (b*d*log(im + c*x))/c]
    @test_int [((d + im*c*d*x)*(a + b*atan(c*x)))/x, x, 8, im*a*c*d*x + im*b*c*d*x*atan(c*x) + a*d*log(x) - (im/2)*b*d*log(1 + c^2*x^2) + (im/2)*b*d*PolyLog(2, (-im)*c*x) - (im/2)*b*d*PolyLog(2, im*c*x)]
    @test_int [((d + im*c*d*x)*(a + b*atan(c*x)))/x^2, x, 10, -((d*(a + b*atan(c*x)))/x) + im*a*c*d*log(x) + b*c*d*log(x) - (b*c*d*log(1 + c^2*x^2))/2 - (b*c*d*PolyLog(2, (-im)*c*x))/2 + (b*c*d*PolyLog(2, im*c*x))/2]
    @test_int [((d + im*c*d*x)*(a + b*atan(c*x)))/x^3, x, 4, -(b*c*d)/(2*x) - (d*(1 + im*c*x)^2*(a + b*atan(c*x)))/(2*x^2) + im*b*c^2*d*log(x) - im*b*c^2*d*log(im + c*x)]
    @test_int [((d + im*c*d*x)*(a + b*atan(c*x)))/x^4, x, 4, -(b*c*d)/(6*x^2) - ((im/2)*b*c^2*d)/x - (d*(a + b*atan(c*x)))/(3*x^3) - ((im/2)*c*d*(a + b*atan(c*x)))/x^2 - (b*c^3*d*log(x))/3 - (b*c^3*d*log(im - c*x))/12 + (5*b*c^3*d*log(im + c*x))/12]
    @test_int [((d + im*c*d*x)*(a + b*atan(c*x)))/x^5, x, 4, -(b*c*d)/(12*x^3) - ((im/6)*b*c^2*d)/x^2 + (b*c^3*d)/(4*x) - (d*(a + b*atan(c*x)))/(4*x^4) - ((im/3)*c*d*(a + b*atan(c*x)))/x^3 - (im/3)*b*c^4*d*log(x) + (im/24)*b*c^4*d*log(im - c*x) + ((7*im)/24)*b*c^4*d*log(im + c*x)]

    @test_int [x^3*(d + im*c*d*x)^2*(a + b*atan(c*x)), x, 7, (5*b*d^2*x)/(12*c^3) + ((im/5)*b*d^2*x^2)/c^2 - (5*b*d^2*x^3)/(36*c) - (im/10)*b*d^2*x^4 + (b*c*d^2*x^5)/30 - (5*b*d^2*atan(c*x))/(12*c^4) + (d^2*x^4*(a + b*atan(c*x)))/4 + ((2*im)/5)*c*d^2*x^5*(a + b*atan(c*x)) - (c^2*d^2*x^6*(a + b*atan(c*x)))/6 - ((im/5)*b*d^2*log(1 + c^2*x^2))/c^4]
    @test_int [x^2*(d + im*c*d*x)^2*(a + b*atan(c*x)), x, 7, ((im/2)*b*d^2*x)/c^2 - (4*b*d^2*x^2)/(15*c) - (im/6)*b*d^2*x^3 + (b*c*d^2*x^4)/20 - ((im/2)*b*d^2*atan(c*x))/c^3 + (d^2*x^3*(a + b*atan(c*x)))/3 + (im/2)*c*d^2*x^4*(a + b*atan(c*x)) - (c^2*d^2*x^5*(a + b*atan(c*x)))/5 + (4*b*d^2*log(1 + c^2*x^2))/(15*c^3)]
    @test_int [x*(d + im*c*d*x)^2*(a + b*atan(c*x)), x, 7, (-3*b*d^2*x)/(4*c) - (im/3)*b*d^2*x^2 + (b*c*d^2*x^3)/12 + (3*b*d^2*atan(c*x))/(4*c^2) + (d^2*x^2*(a + b*atan(c*x)))/2 + ((2*im)/3)*c*d^2*x^3*(a + b*atan(c*x)) - (c^2*d^2*x^4*(a + b*atan(c*x)))/4 + ((im/3)*b*d^2*log(1 + c^2*x^2))/c^2]
    @test_int [(d + im*c*d*x)^2*(a + b*atan(c*x)), x, 4, (-(2/3))*im*b*d^2*x - (b*d^2*(1 + im*c*x)^2)/(6*c) - (im*d^2*(1 + im*c*x)^3*(a + b*atan(c*x)))/(3*c) - (4*b*d^2*log(1 - im*c*x))/(3*c)]
    @test_int [((d + im*c*d*x)^2*(a + b*atan(c*x)))/x, x, 11, (2*im)*a*c*d^2*x + (b*c*d^2*x)/2 - (b*d^2*atan(c*x))/2 + (2*im)*b*c*d^2*x*atan(c*x) - (c^2*d^2*x^2*(a + b*atan(c*x)))/2 + a*d^2*log(x) - im*b*d^2*log(1 + c^2*x^2) + (im/2)*b*d^2*PolyLog(2, (-im)*c*x) - (im/2)*b*d^2*PolyLog(2, im*c*x)]
    @test_int [((d + im*c*d*x)^2*(a + b*atan(c*x)))/x^2, x, 13, (-a)*c^2*d^2*x - b*c^2*d^2*x*atan(c*x) - (d^2*(a + b*atan(c*x)))/x + 2*im*a*c*d^2*log(x) + b*c*d^2*log(x) - b*c*d^2*PolyLog(2, (-im)*c*x) + b*c*d^2*PolyLog(2, im*c*x)]
    @test_int [((d + im*c*d*x)^2*(a + b*atan(c*x)))/x^3, x, 13, -(b*c*d^2)/(2*x) - (b*c^2*d^2*atan(c*x))/2 - (d^2*(a + b*atan(c*x)))/(2*x^2) - ((2*im)*c*d^2*(a + b*atan(c*x)))/x - a*c^2*d^2*log(x) + (2*im)*b*c^2*d^2*log(x) - im*b*c^2*d^2*log(1 + c^2*x^2) - (im/2)*b*c^2*d^2*PolyLog(2, (-im)*c*x) + (im/2)*b*c^2*d^2*PolyLog(2, im*c*x)]
    @test_int [((d + im*c*d*x)^2*(a + b*atan(c*x)))/x^4, x, 4, -(b*c*d^2)/(6*x^2) - (im*b*c^2*d^2)/x - (d^2*(1 + im*c*x)^3*(a + b*atan(c*x)))/(3*x^3) - (4*b*c^3*d^2*log(x))/3 + (4*b*c^3*d^2*log(im + c*x))/3]
    @test_int [((d + im*c*d*x)^2*(a + b*atan(c*x)))/x^5, x, 4, -(b*c*d^2)/(12*x^3) - ((im/3)*b*c^2*d^2)/x^2 + (3*b*c^3*d^2)/(4*x) - (d^2*(a + b*atan(c*x)))/(4*x^4) - (((2*im)/3)*c*d^2*(a + b*atan(c*x)))/x^3 + (c^2*d^2*(a + b*atan(c*x)))/(2*x^2) - ((2*im)/3)*b*c^4*d^2*log(x) - (im/24)*b*c^4*d^2*log(im - c*x) + ((17*im)/24)*b*c^4*d^2*log(im + c*x)]
    @test_int [((d + im*c*d*x)^2*(a + b*atan(c*x)))/x^6, x, 4, -(b*c*d^2)/(20*x^4) - ((im/6)*b*c^2*d^2)/x^3 + (4*b*c^3*d^2)/(15*x^2) + ((im/2)*b*c^4*d^2)/x - (d^2*(a + b*atan(c*x)))/(5*x^5) - ((im/2)*c*d^2*(a + b*atan(c*x)))/x^4 + (c^2*d^2*(a + b*atan(c*x)))/(3*x^3) + (8*b*c^5*d^2*log(x))/15 - (b*c^5*d^2*log(im - c*x))/60 - (31*b*c^5*d^2*log(im + c*x))/60]

    @test_int [x^3*(d + im*c*d*x)^3*(a + b*atan(c*x)), x, 7, (3*b*d^3*x)/(4*c^3) + (((13*im)/35)*b*d^3*x^2)/c^2 - (b*d^3*x^3)/(4*c) - ((13*im)/70)*b*d^3*x^4 + (b*c*d^3*x^5)/10 + (im/42)*b*c^2*d^3*x^6 - (3*b*d^3*atan(c*x))/(4*c^4) + (d^3*x^4*(a + b*atan(c*x)))/4 + ((3*im)/5)*c*d^3*x^5*(a + b*atan(c*x)) - (c^2*d^3*x^6*(a + b*atan(c*x)))/2 - (im/7)*c^3*d^3*x^7*(a + b*atan(c*x)) - (((13*im)/35)*b*d^3*log(1 + c^2*x^2))/c^4]
    @test_int [x^2*(d + im*c*d*x)^3*(a + b*atan(c*x)), x, 7, (((11*im)/12)*b*d^3*x)/c^2 - (7*b*d^3*x^2)/(15*c) - ((11*im)/36)*b*d^3*x^3 + (3*b*c*d^3*x^4)/20 + (im/30)*b*c^2*d^3*x^5 - (((11*im)/12)*b*d^3*atan(c*x))/c^3 + (d^3*x^3*(a + b*atan(c*x)))/3 + ((3*im)/4)*c*d^3*x^4*(a + b*atan(c*x)) - (3*c^2*d^3*x^5*(a + b*atan(c*x)))/5 - (im/6)*c^3*d^3*x^6*(a + b*atan(c*x)) + (7*b*d^3*log(1 + c^2*x^2))/(15*c^3)]
    @test_int [x*(d + im*c*d*x)^3*(a + b*atan(c*x)), x, 4, (-3*b*d^3*x)/(5*c) - (((3*im)/20)*b*d^3*(im - c*x)^2)/c^2 - (b*d^3*(im - c*x)^3)/(20*c^2) + ((im/20)*b*d^3*(im - c*x)^4)/c^2 + (d^3*(1 + im*c*x)^4*(a + b*atan(c*x)))/(4*c^2) - (d^3*(1 + im*c*x)^5*(a + b*atan(c*x)))/(5*c^2) + (((6*im)/5)*b*d^3*log(im + c*x))/c^2]
    @test_int [(d + im*c*d*x)^3*(a + b*atan(c*x)), x, 4, (-im)*b*d^3*x - (b*d^3*(1 + im*c*x)^2)/(4*c) - (b*d^3*(1 + im*c*x)^3)/(12*c) - (im*d^3*(1 + im*c*x)^4*(a + b*atan(c*x)))/(4*c) - (2*b*d^3*log(1 - im*c*x))/c]
    @test_int [((d + im*c*d*x)^3*(a + b*atan(c*x)))/x, x, 15, (3*im)*a*c*d^3*x + (3*b*c*d^3*x)/2 + (im/6)*b*c^2*d^3*x^2 - (3*b*d^3*atan(c*x))/2 + (3*im)*b*c*d^3*x*atan(c*x) - (3*c^2*d^3*x^2*(a + b*atan(c*x)))/2 - (im/3)*c^3*d^3*x^3*(a + b*atan(c*x)) + a*d^3*log(x) - ((5*im)/3)*b*d^3*log(1 + c^2*x^2) + (im/2)*b*d^3*PolyLog(2, (-im)*c*x) - (im/2)*b*d^3*PolyLog(2, im*c*x)]
    @test_int [((d + im*c*d*x)^3*(a + b*atan(c*x)))/x^2, x, 16, -3*a*c^2*d^3*x + (im/2)*b*c^2*d^3*x - (im/2)*b*c*d^3*atan(c*x) - 3*b*c^2*d^3*x*atan(c*x) - (d^3*(a + b*atan(c*x)))/x - (im/2)*c^3*d^3*x^2*(a + b*atan(c*x)) + (3*im)*a*c*d^3*log(x) + b*c*d^3*log(x) + b*c*d^3*log(1 + c^2*x^2) - (3*b*c*d^3*PolyLog(2, (-im)*c*x))/2 + (3*b*c*d^3*PolyLog(2, im*c*x))/2]
    @test_int [((d + im*c*d*x)^3*(a + b*atan(c*x)))/x^3, x, 16, -(b*c*d^3)/(2*x) - im*a*c^3*d^3*x - (b*c^2*d^3*atan(c*x))/2 - im*b*c^3*d^3*x*atan(c*x) - (d^3*(a + b*atan(c*x)))/(2*x^2) - ((3*im)*c*d^3*(a + b*atan(c*x)))/x - 3*a*c^2*d^3*log(x) + (3*im)*b*c^2*d^3*log(x) - im*b*c^2*d^3*log(1 + c^2*x^2) - ((3*im)/2)*b*c^2*d^3*PolyLog(2, (-im)*c*x) + ((3*im)/2)*b*c^2*d^3*PolyLog(2, im*c*x)]
    @test_int [((d + im*c*d*x)^3*(a + b*atan(c*x)))/x^4, x, 17, -(b*c*d^3)/(6*x^2) - (((3*im)/2)*b*c^2*d^3)/x - ((3*im)/2)*b*c^3*d^3*atan(c*x) - (d^3*(a + b*atan(c*x)))/(3*x^3) - (((3*im)/2)*c*d^3*(a + b*atan(c*x)))/x^2 + (3*c^2*d^3*(a + b*atan(c*x)))/x - im*a*c^3*d^3*log(x) - (10*b*c^3*d^3*log(x))/3 + (5*b*c^3*d^3*log(1 + c^2*x^2))/3 + (b*c^3*d^3*PolyLog(2, (-im)*c*x))/2 - (b*c^3*d^3*PolyLog(2, im*c*x))/2]
    @test_int [((d + im*c*d*x)^3*(a + b*atan(c*x)))/x^5, x, 4, -(b*c*d^3)/(12*x^3) - ((im/2)*b*c^2*d^3)/x^2 + (7*b*c^3*d^3)/(4*x) - (d^3*(1 + im*c*x)^4*(a + b*atan(c*x)))/(4*x^4) - (2*im)*b*c^4*d^3*log(x) + (2*im)*b*c^4*d^3*log(im + c*x)]
    @test_int [((d + im*c*d*x)^3*(a + b*atan(c*x)))/x^6, x, 4, -(b*c*d^3)/(20*x^4) - ((im/4)*b*c^2*d^3)/x^3 + (3*b*c^3*d^3)/(5*x^2) + (((5*im)/4)*b*c^4*d^3)/x - (d^3*(1 + im*c*x)^4*(a + b*atan(c*x)))/(5*x^5) + ((im/20)*c*d^3*(1 + im*c*x)^4*(a + b*atan(c*x)))/x^4 + (6*b*c^5*d^3*log(x))/5 - (6*b*c^5*d^3*log(im + c*x))/5]
    @test_int [((d + im*c*d*x)^3*(a + b*atan(c*x)))/x^7, x, 4, -(b*c*d^3)/(30*x^5) - (((3*im)/20)*b*c^2*d^3)/x^4 + (11*b*c^3*d^3)/(36*x^3) + (((7*im)/15)*b*c^4*d^3)/x^2 - (11*b*c^5*d^3)/(12*x) - (d^3*(a + b*atan(c*x)))/(6*x^6) - (((3*im)/5)*c*d^3*(a + b*atan(c*x)))/x^5 + (3*c^2*d^3*(a + b*atan(c*x)))/(4*x^4) + ((im/3)*c^3*d^3*(a + b*atan(c*x)))/x^3 + ((14*im)/15)*b*c^6*d^3*log(x) - (im/120)*b*c^6*d^3*log(im - c*x) - ((37*im)/40)*b*c^6*d^3*log(im + c*x)]

    @test_int [x^3*(d + im*c*d*x)^4*(a + b*atan(c*x)), x, 7, (11*b*d^4*x)/(8*c^3) + (((24*im)/35)*b*d^4*x^2)/c^2 - (11*b*d^4*x^3)/(24*c) - ((12*im)/35)*b*d^4*x^4 + (9*b*c*d^4*x^5)/40 + ((2*im)/21)*b*c^2*d^4*x^6 - (b*c^3*d^4*x^7)/56 - (11*b*d^4*atan(c*x))/(8*c^4) + (d^4*x^4*(a + b*atan(c*x)))/4 + ((4*im)/5)*c*d^4*x^5*(a + b*atan(c*x)) - c^2*d^4*x^6*(a + b*atan(c*x)) - ((4*im)/7)*c^3*d^4*x^7*(a + b*atan(c*x)) + (c^4*d^4*x^8*(a + b*atan(c*x)))/8 - (((24*im)/35)*b*d^4*log(1 + c^2*x^2))/c^4]
    @test_int [x^2*(d + im*c*d*x)^4*(a + b*atan(c*x)), x, 4, (((5*im)/3)*b*d^4*x)/c^2 - (88*b*d^4*x^2)/(105*c) - ((5*im)/9)*b*d^4*x^3 + (47*b*c*d^4*x^4)/140 + ((2*im)/15)*b*c^2*d^4*x^5 - (b*c^3*d^4*x^6)/42 + ((im/5)*d^4*(1 + im*c*x)^5*(a + b*atan(c*x)))/c^3 - ((im/3)*d^4*(1 + im*c*x)^6*(a + b*atan(c*x)))/c^3 + ((im/7)*d^4*(1 + im*c*x)^7*(a + b*atan(c*x)))/c^3 + (176*b*d^4*log(im + c*x))/(105*c^3)]
    @test_int [x*(d + im*c*d*x)^4*(a + b*atan(c*x)), x, 4, (-16*b*d^4*x)/(15*c) - (((4*im)/15)*b*d^4*(im - c*x)^2)/c^2 - (4*b*d^4*(im - c*x)^3)/(45*c^2) + ((im/30)*b*d^4*(im - c*x)^4)/c^2 + (b*d^4*(im - c*x)^5)/(30*c^2) + (d^4*(1 + im*c*x)^5*(a + b*atan(c*x)))/(5*c^2) - (d^4*(1 + im*c*x)^6*(a + b*atan(c*x)))/(6*c^2) + (((32*im)/15)*b*d^4*log(im + c*x))/c^2]
    @test_int [(d + im*c*d*x)^4*(a + b*atan(c*x)), x, 4, (-(8/5))*im*b*d^4*x - (2*b*d^4*(1 + im*c*x)^2)/(5*c) - (2*b*d^4*(1 + im*c*x)^3)/(15*c) - (b*d^4*(1 + im*c*x)^4)/(20*c) - (im*d^4*(1 + im*c*x)^5*(a + b*atan(c*x)))/(5*c) - (16*b*d^4*log(1 - im*c*x))/(5*c)]
    @test_int [((d + im*c*d*x)^4*(a + b*atan(c*x)))/x, x, 19, (4*im)*a*c*d^4*x + (13*b*c*d^4*x)/4 + ((2*im)/3)*b*c^2*d^4*x^2 - (b*c^3*d^4*x^3)/12 - (13*b*d^4*atan(c*x))/4 + (4*im)*b*c*d^4*x*atan(c*x) - 3*c^2*d^4*x^2*(a + b*atan(c*x)) - ((4*im)/3)*c^3*d^4*x^3*(a + b*atan(c*x)) + (c^4*d^4*x^4*(a + b*atan(c*x)))/4 + a*d^4*log(x) - ((8*im)/3)*b*d^4*log(1 + c^2*x^2) + (im/2)*b*d^4*PolyLog(2, (-im)*c*x) - (im/2)*b*d^4*PolyLog(2, im*c*x)]
    @test_int [((d + im*c*d*x)^4*(a + b*atan(c*x)))/x^2, x, 20, -6*a*c^2*d^4*x + (2*im)*b*c^2*d^4*x - (b*c^3*d^4*x^2)/6 - (2*im)*b*c*d^4*atan(c*x) - 6*b*c^2*d^4*x*atan(c*x) - (d^4*(a + b*atan(c*x)))/x - (2*im)*c^3*d^4*x^2*(a + b*atan(c*x)) + (c^4*d^4*x^3*(a + b*atan(c*x)))/3 + (4*im)*a*c*d^4*log(x) + b*c*d^4*log(x) + (8*b*c*d^4*log(1 + c^2*x^2))/3 - 2*b*c*d^4*PolyLog(2, (-im)*c*x) + 2*b*c*d^4*PolyLog(2, im*c*x)]
    @test_int [((d + im*c*d*x)^4*(a + b*atan(c*x)))/x^3, x, 19, -(b*c*d^4)/(2*x) - (4*im)*a*c^3*d^4*x - (b*c^3*d^4*x)/2 - (4*im)*b*c^3*d^4*x*atan(c*x) - (d^4*(a + b*atan(c*x)))/(2*x^2) - ((4*im)*c*d^4*(a + b*atan(c*x)))/x + (c^4*d^4*x^2*(a + b*atan(c*x)))/2 - 6*a*c^2*d^4*log(x) + (4*im)*b*c^2*d^4*log(x) - (3*im)*b*c^2*d^4*PolyLog(2, (-im)*c*x) + (3*im)*b*c^2*d^4*PolyLog(2, im*c*x)]
    @test_int [((d + im*c*d*x)^4*(a + b*atan(c*x)))/x^4, x, 20, -(b*c*d^4)/(6*x^2) - ((2*im)*b*c^2*d^4)/x + a*c^4*d^4*x - (2*im)*b*c^3*d^4*atan(c*x) + b*c^4*d^4*x*atan(c*x) - (d^4*(a + b*atan(c*x)))/(3*x^3) - ((2*im)*c*d^4*(a + b*atan(c*x)))/x^2 + (6*c^2*d^4*(a + b*atan(c*x)))/x - (4*im)*a*c^3*d^4*log(x) - (19*b*c^3*d^4*log(x))/3 + (8*b*c^3*d^4*log(1 + c^2*x^2))/3 + 2*b*c^3*d^4*PolyLog(2, (-im)*c*x) - 2*b*c^3*d^4*PolyLog(2, im*c*x)]
    @test_int [((d + im*c*d*x)^4*(a + b*atan(c*x)))/x^5, x, 21, -(b*c*d^4)/(12*x^3) - (((2*im)/3)*b*c^2*d^4)/x^2 + (13*b*c^3*d^4)/(4*x) + (13*b*c^4*d^4*atan(c*x))/4 - (d^4*(a + b*atan(c*x)))/(4*x^4) - (((4*im)/3)*c*d^4*(a + b*atan(c*x)))/x^3 + (3*c^2*d^4*(a + b*atan(c*x)))/x^2 + ((4*im)*c^3*d^4*(a + b*atan(c*x)))/x + a*c^4*d^4*log(x) - ((16*im)/3)*b*c^4*d^4*log(x) + ((8*im)/3)*b*c^4*d^4*log(1 + c^2*x^2) + (im/2)*b*c^4*d^4*PolyLog(2, (-im)*c*x) - (im/2)*b*c^4*d^4*PolyLog(2, im*c*x)]
    @test_int [((d + im*c*d*x)^4*(a + b*atan(c*x)))/x^6, x, 4, -(b*c*d^4)/(20*x^4) - ((im/3)*b*c^2*d^4)/x^3 + (11*b*c^3*d^4)/(10*x^2) + ((3*im)*b*c^4*d^4)/x - (d^4*(1 + im*c*x)^5*(a + b*atan(c*x)))/(5*x^5) + (16*b*c^5*d^4*log(x))/5 - (16*b*c^5*d^4*log(im + c*x))/5]
    @test_int [((d + im*c*d*x)^4*(a + b*atan(c*x)))/x^7, x, 4, -(b*c*d^4)/(30*x^5) - ((im/5)*b*c^2*d^4)/x^4 + (5*b*c^3*d^4)/(9*x^3) + (((16*im)/15)*b*c^4*d^4)/x^2 - (13*b*c^5*d^4)/(6*x) - (d^4*(1 + im*c*x)^5*(a + b*atan(c*x)))/(6*x^6) + ((im/30)*c*d^4*(1 + im*c*x)^5*(a + b*atan(c*x)))/x^5 + ((32*im)/15)*b*c^6*d^4*log(x) - ((32*im)/15)*b*c^6*d^4*log(im + c*x)]
    @test_int [((d + im*c*d*x)^4*(a + b*atan(c*x)))/x^8, x, 4, -(b*c*d^4)/(42*x^6) - (((2*im)/15)*b*c^2*d^4)/x^5 + (47*b*c^3*d^4)/(140*x^4) + (((5*im)/9)*b*c^4*d^4)/x^3 - (88*b*c^5*d^4)/(105*x^2) - (((5*im)/3)*b*c^6*d^4)/x - (d^4*(a + b*atan(c*x)))/(7*x^7) - (((2*im)/3)*c*d^4*(a + b*atan(c*x)))/x^6 + (6*c^2*d^4*(a + b*atan(c*x)))/(5*x^5) + (im*c^3*d^4*(a + b*atan(c*x)))/x^4 - (c^4*d^4*(a + b*atan(c*x)))/(3*x^3) - (176*b*c^7*d^4*log(x))/105 + (b*c^7*d^4*log(im - c*x))/210 + (117*b*c^7*d^4*log(im + c*x))/70]

    #= ::Subsubsection::Closed:: =#
    #=q<0=#

    @test_int [(x^3*(a + b*atan(c*x)))/(d + im*c*d*x), x, 16, (im*a*x)/(c^3*d) - (b*x)/(2*c^3*d) + ((im/6)*b*x^2)/(c^2*d) + (b*atan(c*x))/(2*c^4*d) + (im*b*x*atan(c*x))/(c^3*d) + (x^2*(a + b*atan(c*x)))/(2*c^2*d) - ((im/3)*x^3*(a + b*atan(c*x)))/(c*d) + ((a + b*atan(c*x))*log(2/(1 + im*c*x)))/(c^4*d) - (((2*im)/3)*b*log(1 + c^2*x^2))/(c^4*d) + ((im/2)*b*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c^4*d)]
    @test_int [(x^2*(a + b*atan(c*x)))/(d + im*c*d*x), x, 11, (a*x)/(c^2*d) + ((im/2)*b*x)/(c^2*d) - ((im/2)*b*atan(c*x))/(c^3*d) + (b*x*atan(c*x))/(c^2*d) - ((im/2)*x^2*(a + b*atan(c*x)))/(c*d) - (im*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(c^3*d) - (b*log(1 + c^2*x^2))/(2*c^3*d) + (b*PolyLog(2, 1 - 2/(1 + im*c*x)))/(2*c^3*d)]
    @test_int [(x*(a + b*atan(c*x)))/(d + im*c*d*x), x, 7, ((-im)*a*x)/(c*d) - (im*b*x*atan(c*x))/(c*d) - ((a + b*atan(c*x))*log(2/(1 + im*c*x)))/(c^2*d) + ((im/2)*b*log(1 + c^2*x^2))/(c^2*d) - ((im/2)*b*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c^2*d)]
    @test_int [(a + b*atan(c*x))/(d + im*c*d*x), x, 3, (im*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(c*d) - (b*PolyLog(2, 1 - 2/(1 + im*c*x)))/(2*c*d)]
    @test_int [(a + b*atan(c*x))/(x*(d + im*c*d*x)), x, 2, ((a + b*atan(c*x))*log(2 - 2/(1 + im*c*x)))/d + ((im/2)*b*PolyLog(2, -1 + 2/(1 + im*c*x)))/d]
    @test_int [(a + b*atan(c*x))/(x^2*(d + im*c*d*x)), x, 8, -((a + b*atan(c*x))/(d*x)) + (b*c*log(x))/d - (b*c*log(1 + c^2*x^2))/(2*d) - (im*c*(a + b*atan(c*x))*log(2 - 2/(1 + im*c*x)))/d + (b*c*PolyLog(2, -1 + 2/(1 + im*c*x)))/(2*d)]
    @test_int [(a + b*atan(c*x))/(x^3*(d + im*c*d*x)), x, 12, -(b*c)/(2*d*x) - (b*c^2*atan(c*x))/(2*d) - (a + b*atan(c*x))/(2*d*x^2) + (im*c*(a + b*atan(c*x)))/(d*x) - (im*b*c^2*log(x))/d + ((im/2)*b*c^2*log(1 + c^2*x^2))/d - (c^2*(a + b*atan(c*x))*log(2 - 2/(1 + im*c*x)))/d - ((im/2)*b*c^2*PolyLog(2, -1 + 2/(1 + im*c*x)))/d]
    @test_int [(a + b*atan(c*x))/(x^4*(d + im*c*d*x)), x, 17, -(b*c)/(6*d*x^2) + ((im/2)*b*c^2)/(d*x) + ((im/2)*b*c^3*atan(c*x))/d - (a + b*atan(c*x))/(3*d*x^3) + ((im/2)*c*(a + b*atan(c*x)))/(d*x^2) + (c^2*(a + b*atan(c*x)))/(d*x) - (4*b*c^3*log(x))/(3*d) + (2*b*c^3*log(1 + c^2*x^2))/(3*d) + (im*c^3*(a + b*atan(c*x))*log(2 - 2/(1 + im*c*x)))/d - (b*c^3*PolyLog(2, -1 + 2/(1 + im*c*x)))/(2*d)]

    @test_int [(x^3*(a + b*atan(c*x)))/(d + im*c*d*x)^2, x, 16, ((-2*im)*a*x)/(c^3*d^2) + (b*x)/(2*c^3*d^2) + b/(2*c^4*d^2*(im - c*x)) - (b*atan(c*x))/(c^4*d^2) - ((2*im)*b*x*atan(c*x))/(c^3*d^2) - (x^2*(a + b*atan(c*x)))/(2*c^2*d^2) + (im*(a + b*atan(c*x)))/(c^4*d^2*(im - c*x)) - (3*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(c^4*d^2) + (im*b*log(1 + c^2*x^2))/(c^4*d^2) - (((3*im)/2)*b*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c^4*d^2)]
    @test_int [(x^2*(a + b*atan(c*x)))/(d + im*c*d*x)^2, x, 13, -((a*x)/(c^2*d^2)) - ((im/2)*b)/(c^3*d^2*(im - c*x)) + ((im/2)*b*atan(c*x))/(c^3*d^2) - (b*x*atan(c*x))/(c^2*d^2) + (a + b*atan(c*x))/(c^3*d^2*(im - c*x)) + ((2*im)*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(c^3*d^2) + (b*log(1 + c^2*x^2))/(2*c^3*d^2) - (b*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c^3*d^2)]
    @test_int [(x*(a + b*atan(c*x)))/(d + im*c*d*x)^2, x, 10, -b/(2*c^2*d^2*(im - c*x)) + (b*atan(c*x))/(2*c^2*d^2) - (im*(a + b*atan(c*x)))/(c^2*d^2*(im - c*x)) + ((a + b*atan(c*x))*log(2/(1 + im*c*x)))/(c^2*d^2) + ((im/2)*b*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c^2*d^2)]
    @test_int [(a + b*atan(c*x))/(d + im*c*d*x)^2, x, 5, ((im/2)*b)/(c*d^2*(im - c*x)) - ((im/2)*b*atan(c*x))/(c*d^2) + (im*(a + b*atan(c*x)))/(c*d^2*(1 + im*c*x))]
    @test_int [(a + b*atan(c*x))/(x*(d + im*c*d*x)^2), x, 13, b/(2*d^2*(im - c*x)) - (b*atan(c*x))/(2*d^2) + (im*(a + b*atan(c*x)))/(d^2*(im - c*x)) + (a*log(x))/d^2 + ((a + b*atan(c*x))*log(2/(1 + im*c*x)))/d^2 + ((im/2)*b*PolyLog(2, (-im)*c*x))/d^2 - ((im/2)*b*PolyLog(2, im*c*x))/d^2 + ((im/2)*b*PolyLog(2, 1 - 2/(1 + im*c*x)))/d^2]
    @test_int [(a + b*atan(c*x))/(x^2*(d + im*c*d*x)^2), x, 18, ((-im/2)*b*c)/(d^2*(im - c*x)) + ((im/2)*b*c*atan(c*x))/d^2 - (a + b*atan(c*x))/(d^2*x) + (c*(a + b*atan(c*x)))/(d^2*(im - c*x)) - ((2*im)*a*c*log(x))/d^2 + (b*c*log(x))/d^2 - ((2*im)*c*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/d^2 - (b*c*log(1 + c^2*x^2))/(2*d^2) + (b*c*PolyLog(2, (-im)*c*x))/d^2 - (b*c*PolyLog(2, im*c*x))/d^2 + (b*c*PolyLog(2, 1 - 2/(1 + im*c*x)))/d^2]
    @test_int [(a + b*atan(c*x))/(x^3*(d + im*c*d*x)^2), x, 21, -(b*c)/(2*d^2*x) - (b*c^2)/(2*d^2*(im - c*x)) - (a + b*atan(c*x))/(2*d^2*x^2) + ((2*im)*c*(a + b*atan(c*x)))/(d^2*x) - (im*c^2*(a + b*atan(c*x)))/(d^2*(im - c*x)) - (3*a*c^2*log(x))/d^2 - ((2*im)*b*c^2*log(x))/d^2 - (3*c^2*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/d^2 + (im*b*c^2*log(1 + c^2*x^2))/d^2 - (((3*im)/2)*b*c^2*PolyLog(2, (-im)*c*x))/d^2 + (((3*im)/2)*b*c^2*PolyLog(2, im*c*x))/d^2 - (((3*im)/2)*b*c^2*PolyLog(2, 1 - 2/(1 + im*c*x)))/d^2]

    @test_int [(x^4*(a + b*atan(c*x)))/(d + im*c*d*x)^3, x, 21, (-3*a*x)/(c^4*d^3) - ((im/2)*b*x)/(c^4*d^3) - b/(8*c^5*d^3*(im - c*x)^2) - (((15*im)/8)*b)/(c^5*d^3*(im - c*x)) + (((19*im)/8)*b*atan(c*x))/(c^5*d^3) - (3*b*x*atan(c*x))/(c^4*d^3) + ((im/2)*x^2*(a + b*atan(c*x)))/(c^3*d^3) - ((im/2)*(a + b*atan(c*x)))/(c^5*d^3*(im - c*x)^2) + (4*(a + b*atan(c*x)))/(c^5*d^3*(im - c*x)) + ((6*im)*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(c^5*d^3) + (3*b*log(1 + c^2*x^2))/(2*c^5*d^3) - (3*b*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c^5*d^3)]
    @test_int [(x^3*(a + b*atan(c*x)))/(d + im*c*d*x)^3, x, 18, (im*a*x)/(c^3*d^3) + ((im/8)*b)/(c^4*d^3*(im - c*x)^2) - (11*b)/(8*c^4*d^3*(im - c*x)) + (11*b*atan(c*x))/(8*c^4*d^3) + (im*b*x*atan(c*x))/(c^3*d^3) - (a + b*atan(c*x))/(2*c^4*d^3*(im - c*x)^2) - ((3*im)*(a + b*atan(c*x)))/(c^4*d^3*(im - c*x)) + (3*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(c^4*d^3) - ((im/2)*b*log(1 + c^2*x^2))/(c^4*d^3) + (((3*im)/2)*b*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c^4*d^3)]
    @test_int [(x^2*(a + b*atan(c*x)))/(d + im*c*d*x)^3, x, 15, b/(8*c^3*d^3*(im - c*x)^2) + (((7*im)/8)*b)/(c^3*d^3*(im - c*x)) - (((7*im)/8)*b*atan(c*x))/(c^3*d^3) + ((im/2)*(a + b*atan(c*x)))/(c^3*d^3*(im - c*x)^2) - (2*(a + b*atan(c*x)))/(c^3*d^3*(im - c*x)) - (im*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(c^3*d^3) + (b*PolyLog(2, 1 - 2/(1 + im*c*x)))/(2*c^3*d^3)]
    @test_int [(x*(a + b*atan(c*x)))/(d + im*c*d*x)^3, x, 5, ((-im/8)*b)/(c^2*d^3*(im - c*x)^2) + (3*b)/(8*c^2*d^3*(im - c*x)) + (b*atan(c*x))/(8*c^2*d^3) + (x^2*(a + b*atan(c*x)))/(2*d^3*(1 + im*c*x)^2)]
    @test_int [(a + b*atan(c*x))/(d + im*c*d*x)^3, x, 5, -b/(8*c*d^3*(im - c*x)^2) + ((im/8)*b)/(c*d^3*(im - c*x)) - ((im/8)*b*atan(c*x))/(c*d^3) + ((im/2)*(a + b*atan(c*x)))/(c*d^3*(1 + im*c*x)^2)]
    @test_int [(a + b*atan(c*x))/(x*(d + im*c*d*x)^3), x, 18, ((im/8)*b)/(d^3*(im - c*x)^2) + (5*b)/(8*d^3*(im - c*x)) - (5*b*atan(c*x))/(8*d^3) - (a + b*atan(c*x))/(2*d^3*(im - c*x)^2) + (im*(a + b*atan(c*x)))/(d^3*(im - c*x)) + (a*log(x))/d^3 + ((a + b*atan(c*x))*log(2/(1 + im*c*x)))/d^3 + ((im/2)*b*PolyLog(2, (-im)*c*x))/d^3 - ((im/2)*b*PolyLog(2, im*c*x))/d^3 + ((im/2)*b*PolyLog(2, 1 - 2/(1 + im*c*x)))/d^3]
    @test_int [(a + b*atan(c*x))/(x^2*(d + im*c*d*x)^3), x, 23, (b*c)/(8*d^3*(im - c*x)^2) - (((9*im)/8)*b*c)/(d^3*(im - c*x)) + (((9*im)/8)*b*c*atan(c*x))/d^3 - (a + b*atan(c*x))/(d^3*x) + ((im/2)*c*(a + b*atan(c*x)))/(d^3*(im - c*x)^2) + (2*c*(a + b*atan(c*x)))/(d^3*(im - c*x)) - ((3*im)*a*c*log(x))/d^3 + (b*c*log(x))/d^3 - ((3*im)*c*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/d^3 - (b*c*log(1 + c^2*x^2))/(2*d^3) + (3*b*c*PolyLog(2, (-im)*c*x))/(2*d^3) - (3*b*c*PolyLog(2, im*c*x))/(2*d^3) + (3*b*c*PolyLog(2, 1 - 2/(1 + im*c*x)))/(2*d^3)]
    @test_int [(a + b*atan(c*x))/(x^3*(d + im*c*d*x)^3), x, 26, -(b*c)/(2*d^3*x) - ((im/8)*b*c^2)/(d^3*(im - c*x)^2) - (13*b*c^2)/(8*d^3*(im - c*x)) + (9*b*c^2*atan(c*x))/(8*d^3) - (a + b*atan(c*x))/(2*d^3*x^2) + ((3*im)*c*(a + b*atan(c*x)))/(d^3*x) + (c^2*(a + b*atan(c*x)))/(2*d^3*(im - c*x)^2) - ((3*im)*c^2*(a + b*atan(c*x)))/(d^3*(im - c*x)) - (6*a*c^2*log(x))/d^3 - ((3*im)*b*c^2*log(x))/d^3 - (6*c^2*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/d^3 + (((3*im)/2)*b*c^2*log(1 + c^2*x^2))/d^3 - ((3*im)*b*c^2*PolyLog(2, (-im)*c*x))/d^3 + ((3*im)*b*c^2*PolyLog(2, im*c*x))/d^3 - ((3*im)*b*c^2*PolyLog(2, 1 - 2/(1 + im*c*x)))/d^3]

    @test_int [(a + b*atan(c*x))/(1 + im*c*x)^4, x, 5, ((-im/18)*b)/(c*(im - c*x)^3) - b/(24*c*(im - c*x)^2) + ((im/24)*b)/(c*(im - c*x)) - ((im/24)*b*atan(c*x))/c + ((im/3)*(a + b*atan(c*x)))/(c*(1 + im*c*x)^3)]

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

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(d+e*x)^q*(a+b*atan(c*x))^2*with*c^2*d^2+e^2=0=#

    #= ::Subsubsection::Closed:: =#
    #=q>0=#

    @test_int [x^3*(d + im*c*d*x)*(a + b*atan(c*x))^2, x, 27, (a*b*d*x)/(2*c^3) - (((3*im)/10)*b^2*d*x)/c^3 + (b^2*d*x^2)/(12*c^2) + ((im/30)*b^2*d*x^3)/c + (((3*im)/10)*b^2*d*atan(c*x))/c^4 + (b^2*d*x*atan(c*x))/(2*c^3) + ((im/5)*b*d*x^2*(a + b*atan(c*x)))/c^2 - (b*d*x^3*(a + b*atan(c*x)))/(6*c) - (im/10)*b*d*x^4*(a + b*atan(c*x)) - (9*d*(a + b*atan(c*x))^2)/(20*c^4) + (d*x^4*(a + b*atan(c*x))^2)/4 + (im/5)*c*d*x^5*(a + b*atan(c*x))^2 + (((2*im)/5)*b*d*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/c^4 - (b^2*d*log(1 + c^2*x^2))/(3*c^4) - (b^2*d*PolyLog(2, 1 - 2/(1 + im*c*x)))/(5*c^4)]
    @test_int [x^2*(d + im*c*d*x)*(a + b*atan(c*x))^2, x, 22, ((im/2)*a*b*d*x)/c^2 + (b^2*d*x)/(3*c^2) + ((im/12)*b^2*d*x^2)/c - (b^2*d*atan(c*x))/(3*c^3) + ((im/2)*b^2*d*x*atan(c*x))/c^2 - (b*d*x^2*(a + b*atan(c*x)))/(3*c) - (im/6)*b*d*x^3*(a + b*atan(c*x)) - (((7*im)/12)*d*(a + b*atan(c*x))^2)/c^3 + (d*x^3*(a + b*atan(c*x))^2)/3 + (im/4)*c*d*x^4*(a + b*atan(c*x))^2 - (2*b*d*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(3*c^3) - ((im/3)*b^2*d*log(1 + c^2*x^2))/c^3 - ((im/3)*b^2*d*PolyLog(2, 1 - 2/(1 + im*c*x)))/c^3]
    @test_int [x*(d + im*c*d*x)*(a + b*atan(c*x))^2, x, 17, -((a*b*d*x)/c) + ((im/3)*b^2*d*x)/c - ((im/3)*b^2*d*atan(c*x))/c^2 - (b^2*d*x*atan(c*x))/c - (im/3)*b*d*x^2*(a + b*atan(c*x)) + (5*d*(a + b*atan(c*x))^2)/(6*c^2) + (d*x^2*(a + b*atan(c*x))^2)/2 + (im/3)*c*d*x^3*(a + b*atan(c*x))^2 - (((2*im)/3)*b*d*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/c^2 + (b^2*d*log(1 + c^2*x^2))/(2*c^2) + (b^2*d*PolyLog(2, 1 - 2/(1 + im*c*x)))/(3*c^2)]
    @test_int [(d + im*c*d*x)*(a + b*atan(c*x))^2, x, 9, (-im)*a*b*d*x - im*b^2*d*x*atan(c*x) - ((im/2)*d*(1 + im*c*x)^2*(a + b*atan(c*x))^2)/c + (2*b*d*(a + b*atan(c*x))*log(2/(1 - im*c*x)))/c + ((im/2)*b^2*d*log(1 + c^2*x^2))/c - (im*b^2*d*PolyLog(2, 1 - 2/(1 - im*c*x)))/c]
    @test_int [((d + im*c*d*x)*(a + b*atan(c*x))^2)/x, x, 13, -(d*(a + b*atan(c*x))^2) + im*c*d*x*(a + b*atan(c*x))^2 + 2*d*(a + b*atan(c*x))^2*atanh(1 - 2/(1 + im*c*x)) + (2*im)*b*d*(a + b*atan(c*x))*log(2/(1 + im*c*x)) - b^2*d*PolyLog(2, 1 - 2/(1 + im*c*x)) - im*b*d*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)) + im*b*d*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 + im*c*x)) - (b^2*d*PolyLog(3, 1 - 2/(1 + im*c*x)))/2 + (b^2*d*PolyLog(3, -1 + 2/(1 + im*c*x)))/2]
    @test_int [((d + im*c*d*x)*(a + b*atan(c*x))^2)/x^2, x, 12, (-im)*c*d*(a + b*atan(c*x))^2 - (d*(a + b*atan(c*x))^2)/x + (2*im)*c*d*(a + b*atan(c*x))^2*atanh(1 - 2/(1 + im*c*x)) + 2*b*c*d*(a + b*atan(c*x))*log(2 - 2/(1 - im*c*x)) - im*b^2*c*d*PolyLog(2, -1 + 2/(1 - im*c*x)) + b*c*d*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)) - b*c*d*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 + im*c*x)) - (im/2)*b^2*c*d*PolyLog(3, 1 - 2/(1 + im*c*x)) + (im/2)*b^2*c*d*PolyLog(3, -1 + 2/(1 + im*c*x))]
    @test_int [((d + im*c*d*x)*(a + b*atan(c*x))^2)/x^3, x, 14, -((b*c*d*(a + b*atan(c*x)))/x) + (c^2*d*(a + b*atan(c*x))^2)/2 - (d*(a + b*atan(c*x))^2)/(2*x^2) - (im*c*d*(a + b*atan(c*x))^2)/x + b^2*c^2*d*log(x) - (b^2*c^2*d*log(1 + c^2*x^2))/2 + (2*im)*b*c^2*d*(a + b*atan(c*x))*log(2 - 2/(1 - im*c*x)) + b^2*c^2*d*PolyLog(2, -1 + 2/(1 - im*c*x))]
    @test_int [((d + im*c*d*x)*(a + b*atan(c*x))^2)/x^4, x, 18, -(b^2*c^2*d)/(3*x) - (b^2*c^3*d*atan(c*x))/3 - (b*c*d*(a + b*atan(c*x)))/(3*x^2) - (im*b*c^2*d*(a + b*atan(c*x)))/x - (im/6)*c^3*d*(a + b*atan(c*x))^2 - (d*(a + b*atan(c*x))^2)/(3*x^3) - ((im/2)*c*d*(a + b*atan(c*x))^2)/x^2 + im*b^2*c^3*d*log(x) - (im/2)*b^2*c^3*d*log(1 + c^2*x^2) - (2*b*c^3*d*(a + b*atan(c*x))*log(2 - 2/(1 - im*c*x)))/3 + (im/3)*b^2*c^3*d*PolyLog(2, -1 + 2/(1 - im*c*x))]

    @test_int [x^3*(d + im*c*d*x)^2*(a + b*atan(c*x))^2, x, 43, (5*a*b*d^2*x)/(6*c^3) - (((3*im)/5)*b^2*d^2*x)/c^3 + (31*b^2*d^2*x^2)/(180*c^2) + ((im/15)*b^2*d^2*x^3)/c - (b^2*d^2*x^4)/60 + (((3*im)/5)*b^2*d^2*atan(c*x))/c^4 + (5*b^2*d^2*x*atan(c*x))/(6*c^3) + (((2*im)/5)*b*d^2*x^2*(a + b*atan(c*x)))/c^2 - (5*b*d^2*x^3*(a + b*atan(c*x)))/(18*c) - (im/5)*b*d^2*x^4*(a + b*atan(c*x)) + (b*c*d^2*x^5*(a + b*atan(c*x)))/15 - (49*d^2*(a + b*atan(c*x))^2)/(60*c^4) + (d^2*x^4*(a + b*atan(c*x))^2)/4 + ((2*im)/5)*c*d^2*x^5*(a + b*atan(c*x))^2 - (c^2*d^2*x^6*(a + b*atan(c*x))^2)/6 + (((4*im)/5)*b*d^2*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/c^4 - (53*b^2*d^2*log(1 + c^2*x^2))/(90*c^4) - (2*b^2*d^2*PolyLog(2, 1 - 2/(1 + im*c*x)))/(5*c^4)]
    @test_int [x^2*(d + im*c*d*x)^2*(a + b*atan(c*x))^2, x, 36, (im*a*b*d^2*x)/c^2 + (19*b^2*d^2*x)/(30*c^2) + ((im/6)*b^2*d^2*x^2)/c - (b^2*d^2*x^3)/30 - (19*b^2*d^2*atan(c*x))/(30*c^3) + (im*b^2*d^2*x*atan(c*x))/c^2 - (8*b*d^2*x^2*(a + b*atan(c*x)))/(15*c) - (im/3)*b*d^2*x^3*(a + b*atan(c*x)) + (b*c*d^2*x^4*(a + b*atan(c*x)))/10 - (((31*im)/30)*d^2*(a + b*atan(c*x))^2)/c^3 + (d^2*x^3*(a + b*atan(c*x))^2)/3 + (im/2)*c*d^2*x^4*(a + b*atan(c*x))^2 - (c^2*d^2*x^5*(a + b*atan(c*x))^2)/5 - (16*b*d^2*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(15*c^3) - (((2*im)/3)*b^2*d^2*log(1 + c^2*x^2))/c^3 - (((8*im)/15)*b^2*d^2*PolyLog(2, 1 - 2/(1 + im*c*x)))/c^3]
    @test_int [x*(d + im*c*d*x)^2*(a + b*atan(c*x))^2, x, 28, (-3*a*b*d^2*x)/(2*c) + (((2*im)/3)*b^2*d^2*x)/c - (b^2*d^2*x^2)/12 - (((2*im)/3)*b^2*d^2*atan(c*x))/c^2 - (3*b^2*d^2*x*atan(c*x))/(2*c) - ((2*im)/3)*b*d^2*x^2*(a + b*atan(c*x)) + (b*c*d^2*x^3*(a + b*atan(c*x)))/6 + (17*d^2*(a + b*atan(c*x))^2)/(12*c^2) + (d^2*x^2*(a + b*atan(c*x))^2)/2 + ((2*im)/3)*c*d^2*x^3*(a + b*atan(c*x))^2 - (c^2*d^2*x^4*(a + b*atan(c*x))^2)/4 - (((4*im)/3)*b*d^2*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/c^2 + (5*b^2*d^2*log(1 + c^2*x^2))/(6*c^2) + (2*b^2*d^2*PolyLog(2, 1 - 2/(1 + im*c*x)))/(3*c^2)]
    @test_int [(d + im*c*d*x)^2*(a + b*atan(c*x))^2, x, 12, (-2*im)*a*b*d^2*x - (b^2*d^2*x)/3 + (b^2*d^2*atan(c*x))/(3*c) - (2*im)*b^2*d^2*x*atan(c*x) + (b*c*d^2*x^2*(a + b*atan(c*x)))/3 - ((im/3)*d^2*(1 + im*c*x)^3*(a + b*atan(c*x))^2)/c + (8*b*d^2*(a + b*atan(c*x))*log(2/(1 - im*c*x)))/(3*c) + (im*b^2*d^2*log(1 + c^2*x^2))/c - (((4*im)/3)*b^2*d^2*PolyLog(2, 1 - 2/(1 - im*c*x)))/c]
    @test_int [((d + im*c*d*x)^2*(a + b*atan(c*x))^2)/x, x, 19, a*b*c*d^2*x + b^2*c*d^2*x*atan(c*x) - (5*d^2*(a + b*atan(c*x))^2)/2 + (2*im)*c*d^2*x*(a + b*atan(c*x))^2 - (c^2*d^2*x^2*(a + b*atan(c*x))^2)/2 + 2*d^2*(a + b*atan(c*x))^2*atanh(1 - 2/(1 + im*c*x)) + (4*im)*b*d^2*(a + b*atan(c*x))*log(2/(1 + im*c*x)) - (b^2*d^2*log(1 + c^2*x^2))/2 - 2*b^2*d^2*PolyLog(2, 1 - 2/(1 + im*c*x)) - im*b*d^2*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)) + im*b*d^2*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 + im*c*x)) - (b^2*d^2*PolyLog(3, 1 - 2/(1 + im*c*x)))/2 + (b^2*d^2*PolyLog(3, -1 + 2/(1 + im*c*x)))/2]
    @test_int [((d + im*c*d*x)^2*(a + b*atan(c*x))^2)/x^2, x, 17, (-2*im)*c*d^2*(a + b*atan(c*x))^2 - (d^2*(a + b*atan(c*x))^2)/x - c^2*d^2*x*(a + b*atan(c*x))^2 + (4*im)*c*d^2*(a + b*atan(c*x))^2*atanh(1 - 2/(1 + im*c*x)) - 2*b*c*d^2*(a + b*atan(c*x))*log(2/(1 + im*c*x)) + 2*b*c*d^2*(a + b*atan(c*x))*log(2 - 2/(1 - im*c*x)) - im*b^2*c*d^2*PolyLog(2, -1 + 2/(1 - im*c*x)) - im*b^2*c*d^2*PolyLog(2, 1 - 2/(1 + im*c*x)) + 2*b*c*d^2*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)) - 2*b*c*d^2*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 + im*c*x)) - im*b^2*c*d^2*PolyLog(3, 1 - 2/(1 + im*c*x)) + im*b^2*c*d^2*PolyLog(3, -1 + 2/(1 + im*c*x))]
    @test_int [((d + im*c*d*x)^2*(a + b*atan(c*x))^2)/x^3, x, 20, -((b*c*d^2*(a + b*atan(c*x)))/x) + (3*c^2*d^2*(a + b*atan(c*x))^2)/2 - (d^2*(a + b*atan(c*x))^2)/(2*x^2) - ((2*im)*c*d^2*(a + b*atan(c*x))^2)/x - 2*c^2*d^2*(a + b*atan(c*x))^2*atanh(1 - 2/(1 + im*c*x)) + b^2*c^2*d^2*log(x) - (b^2*c^2*d^2*log(1 + c^2*x^2))/2 + (4*im)*b*c^2*d^2*(a + b*atan(c*x))*log(2 - 2/(1 - im*c*x)) + 2*b^2*c^2*d^2*PolyLog(2, -1 + 2/(1 - im*c*x)) + im*b*c^2*d^2*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)) - im*b*c^2*d^2*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 + im*c*x)) + (b^2*c^2*d^2*PolyLog(3, 1 - 2/(1 + im*c*x)))/2 - (b^2*c^2*d^2*PolyLog(3, -1 + 2/(1 + im*c*x)))/2]
    @test_int [((d + im*c*d*x)^2*(a + b*atan(c*x))^2)/x^4, x, 16, -(b^2*c^2*d^2)/(3*x) - (b^2*c^3*d^2*atan(c*x))/3 - (b*c*d^2*(a + b*atan(c*x)))/(3*x^2) - ((2*im)*b*c^2*d^2*(a + b*atan(c*x)))/x - (d^2*(1 + im*c*x)^3*(a + b*atan(c*x))^2)/(3*x^3) - (8*a*b*c^3*d^2*log(x))/3 + (2*im)*b^2*c^3*d^2*log(x) - (8*b*c^3*d^2*(a + b*atan(c*x))*log(2/(1 - im*c*x)))/3 - im*b^2*c^3*d^2*log(1 + c^2*x^2) - ((4*im)/3)*b^2*c^3*d^2*PolyLog(2, (-im)*c*x) + ((4*im)/3)*b^2*c^3*d^2*PolyLog(2, im*c*x) + ((4*im)/3)*b^2*c^3*d^2*PolyLog(2, 1 - 2/(1 - im*c*x))]

    @test_int [x^3*(d + im*c*d*x)^3*(a + b*atan(c*x))^2, x, 62, (3*a*b*d^3*x)/(2*c^3) - (((122*im)/105)*b^2*d^3*x)/c^3 + (7*b^2*d^3*x^2)/(20*c^2) + (((44*im)/315)*b^2*d^3*x^3)/c - (b^2*d^3*x^4)/20 - (im/105)*b^2*c*d^3*x^5 + (((122*im)/105)*b^2*d^3*atan(c*x))/c^4 + (3*b^2*d^3*x*atan(c*x))/(2*c^3) + (((26*im)/35)*b*d^3*x^2*(a + b*atan(c*x)))/c^2 - (b*d^3*x^3*(a + b*atan(c*x)))/(2*c) - ((13*im)/35)*b*d^3*x^4*(a + b*atan(c*x)) + (b*c*d^3*x^5*(a + b*atan(c*x)))/5 + (im/21)*b*c^2*d^3*x^6*(a + b*atan(c*x)) - (209*d^3*(a + b*atan(c*x))^2)/(140*c^4) + (d^3*x^4*(a + b*atan(c*x))^2)/4 + ((3*im)/5)*c*d^3*x^5*(a + b*atan(c*x))^2 - (c^2*d^3*x^6*(a + b*atan(c*x))^2)/2 - (im/7)*c^3*d^3*x^7*(a + b*atan(c*x))^2 + (((52*im)/35)*b*d^3*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/c^4 - (11*b^2*d^3*log(1 + c^2*x^2))/(10*c^4) - (26*b^2*d^3*PolyLog(2, 1 - 2/(1 + im*c*x)))/(35*c^4)]
    @test_int [x^2*(d + im*c*d*x)^3*(a + b*atan(c*x))^2, x, 52, (((11*im)/6)*a*b*d^3*x)/c^2 + (37*b^2*d^3*x)/(30*c^2) + (((61*im)/180)*b^2*d^3*x^2)/c - (b^2*d^3*x^3)/10 - (im/60)*b^2*c*d^3*x^4 - (37*b^2*d^3*atan(c*x))/(30*c^3) + (((11*im)/6)*b^2*d^3*x*atan(c*x))/c^2 - (14*b*d^3*x^2*(a + b*atan(c*x)))/(15*c) - ((11*im)/18)*b*d^3*x^3*(a + b*atan(c*x)) + (3*b*c*d^3*x^4*(a + b*atan(c*x)))/10 + (im/15)*b*c^2*d^3*x^5*(a + b*atan(c*x)) - (((37*im)/20)*d^3*(a + b*atan(c*x))^2)/c^3 + (d^3*x^3*(a + b*atan(c*x))^2)/3 + ((3*im)/4)*c*d^3*x^4*(a + b*atan(c*x))^2 - (3*c^2*d^3*x^5*(a + b*atan(c*x))^2)/5 - (im/6)*c^3*d^3*x^6*(a + b*atan(c*x))^2 - (28*b*d^3*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(15*c^3) - (((113*im)/90)*b^2*d^3*log(1 + c^2*x^2))/c^3 - (((14*im)/15)*b^2*d^3*PolyLog(2, 1 - 2/(1 + im*c*x)))/c^3]
    @test_int [x*(d + im*c*d*x)^3*(a + b*atan(c*x))^2, x, 38, (-5*a*b*d^3*x)/(2*c) + (((13*im)/10)*b^2*d^3*x)/c - (b^2*d^3*x^2)/4 - (im/30)*b^2*c*d^3*x^3 - (((13*im)/10)*b^2*d^3*atan(c*x))/c^2 - (5*b^2*d^3*x*atan(c*x))/(2*c) - ((6*im)/5)*b*d^3*x^2*(a + b*atan(c*x)) + (b*c*d^3*x^3*(a + b*atan(c*x)))/2 + (im/10)*b*c^2*d^3*x^4*(a + b*atan(c*x)) + (d^3*(1 + im*c*x)^4*(a + b*atan(c*x))^2)/(4*c^2) - (d^3*(1 + im*c*x)^5*(a + b*atan(c*x))^2)/(5*c^2) - (((12*im)/5)*b*d^3*(a + b*atan(c*x))*log(2/(1 - im*c*x)))/c^2 + (3*b^2*d^3*log(1 + c^2*x^2))/(2*c^2) - (6*b^2*d^3*PolyLog(2, 1 - 2/(1 - im*c*x)))/(5*c^2)]
    @test_int [(d + im*c*d*x)^3*(a + b*atan(c*x))^2, x, 16, ((-7*im)/2)*a*b*d^3*x - b^2*d^3*x - (im/12)*b^2*c*d^3*x^2 + (b^2*d^3*atan(c*x))/c - ((7*im)/2)*b^2*d^3*x*atan(c*x) + b*c*d^3*x^2*(a + b*atan(c*x)) + (im/6)*b*c^2*d^3*x^3*(a + b*atan(c*x)) - ((im/4)*d^3*(1 + im*c*x)^4*(a + b*atan(c*x))^2)/c + (4*b*d^3*(a + b*atan(c*x))*log(2/(1 - im*c*x)))/c + (((11*im)/6)*b^2*d^3*log(1 + c^2*x^2))/c - ((2*im)*b^2*d^3*PolyLog(2, 1 - 2/(1 - im*c*x)))/c]
    @test_int [((d + im*c*d*x)^3*(a + b*atan(c*x))^2)/x, x, 28, 3*a*b*c*d^3*x - (im/3)*b^2*c*d^3*x + (im/3)*b^2*d^3*atan(c*x) + 3*b^2*c*d^3*x*atan(c*x) + (im/3)*b*c^2*d^3*x^2*(a + b*atan(c*x)) - (29*d^3*(a + b*atan(c*x))^2)/6 + (3*im)*c*d^3*x*(a + b*atan(c*x))^2 - (3*c^2*d^3*x^2*(a + b*atan(c*x))^2)/2 - (im/3)*c^3*d^3*x^3*(a + b*atan(c*x))^2 + 2*d^3*(a + b*atan(c*x))^2*atanh(1 - 2/(1 + im*c*x)) + ((20*im)/3)*b*d^3*(a + b*atan(c*x))*log(2/(1 + im*c*x)) - (3*b^2*d^3*log(1 + c^2*x^2))/2 - (10*b^2*d^3*PolyLog(2, 1 - 2/(1 + im*c*x)))/3 - im*b*d^3*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)) + im*b*d^3*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 + im*c*x)) - (b^2*d^3*PolyLog(3, 1 - 2/(1 + im*c*x)))/2 + (b^2*d^3*PolyLog(3, -1 + 2/(1 + im*c*x)))/2]
    @test_int [((d + im*c*d*x)^3*(a + b*atan(c*x))^2)/x^2, x, 23, im*a*b*c^2*d^3*x + im*b^2*c^2*d^3*x*atan(c*x) - ((9*im)/2)*c*d^3*(a + b*atan(c*x))^2 - (d^3*(a + b*atan(c*x))^2)/x - 3*c^2*d^3*x*(a + b*atan(c*x))^2 - (im/2)*c^3*d^3*x^2*(a + b*atan(c*x))^2 + (6*im)*c*d^3*(a + b*atan(c*x))^2*atanh(1 - 2/(1 + im*c*x)) - 6*b*c*d^3*(a + b*atan(c*x))*log(2/(1 + im*c*x)) - (im/2)*b^2*c*d^3*log(1 + c^2*x^2) + 2*b*c*d^3*(a + b*atan(c*x))*log(2 - 2/(1 - im*c*x)) - im*b^2*c*d^3*PolyLog(2, -1 + 2/(1 - im*c*x)) - (3*im)*b^2*c*d^3*PolyLog(2, 1 - 2/(1 + im*c*x)) + 3*b*c*d^3*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)) - 3*b*c*d^3*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 + im*c*x)) - ((3*im)/2)*b^2*c*d^3*PolyLog(3, 1 - 2/(1 + im*c*x)) + ((3*im)/2)*b^2*c*d^3*PolyLog(3, -1 + 2/(1 + im*c*x))]
    @test_int [((d + im*c*d*x)^3*(a + b*atan(c*x))^2)/x^3, x, 25, -((b*c*d^3*(a + b*atan(c*x)))/x) + (7*c^2*d^3*(a + b*atan(c*x))^2)/2 - (d^3*(a + b*atan(c*x))^2)/(2*x^2) - ((3*im)*c*d^3*(a + b*atan(c*x))^2)/x - im*c^3*d^3*x*(a + b*atan(c*x))^2 - 6*c^2*d^3*(a + b*atan(c*x))^2*atanh(1 - 2/(1 + im*c*x)) + b^2*c^2*d^3*log(x) - (2*im)*b*c^2*d^3*(a + b*atan(c*x))*log(2/(1 + im*c*x)) - (b^2*c^2*d^3*log(1 + c^2*x^2))/2 + (6*im)*b*c^2*d^3*(a + b*atan(c*x))*log(2 - 2/(1 - im*c*x)) + 3*b^2*c^2*d^3*PolyLog(2, -1 + 2/(1 - im*c*x)) + b^2*c^2*d^3*PolyLog(2, 1 - 2/(1 + im*c*x)) + (3*im)*b*c^2*d^3*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)) - (3*im)*b*c^2*d^3*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 + im*c*x)) + (3*b^2*c^2*d^3*PolyLog(3, 1 - 2/(1 + im*c*x)))/2 - (3*b^2*c^2*d^3*PolyLog(3, -1 + 2/(1 + im*c*x)))/2]
    @test_int [((d + im*c*d*x)^3*(a + b*atan(c*x))^2)/x^4, x, 28, -(b^2*c^2*d^3)/(3*x) - (b^2*c^3*d^3*atan(c*x))/3 - (b*c*d^3*(a + b*atan(c*x)))/(3*x^2) - ((3*im)*b*c^2*d^3*(a + b*atan(c*x)))/x + ((11*im)/6)*c^3*d^3*(a + b*atan(c*x))^2 - (d^3*(a + b*atan(c*x))^2)/(3*x^3) - (((3*im)/2)*c*d^3*(a + b*atan(c*x))^2)/x^2 + (3*c^2*d^3*(a + b*atan(c*x))^2)/x - (2*im)*c^3*d^3*(a + b*atan(c*x))^2*atanh(1 - 2/(1 + im*c*x)) + (3*im)*b^2*c^3*d^3*log(x) - ((3*im)/2)*b^2*c^3*d^3*log(1 + c^2*x^2) - (20*b*c^3*d^3*(a + b*atan(c*x))*log(2 - 2/(1 - im*c*x)))/3 + ((10*im)/3)*b^2*c^3*d^3*PolyLog(2, -1 + 2/(1 - im*c*x)) - b*c^3*d^3*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)) + b*c^3*d^3*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 + im*c*x)) + (im/2)*b^2*c^3*d^3*PolyLog(3, 1 - 2/(1 + im*c*x)) - (im/2)*b^2*c^3*d^3*PolyLog(3, -1 + 2/(1 + im*c*x))]
    @test_int [((d + im*c*d*x)^3*(a + b*atan(c*x))^2)/x^5, x, 20, -(b^2*c^2*d^3)/(12*x^2) - (im*b^2*c^3*d^3)/x - im*b^2*c^4*d^3*atan(c*x) - (b*c*d^3*(a + b*atan(c*x)))/(6*x^3) - (im*b*c^2*d^3*(a + b*atan(c*x)))/x^2 + (7*b*c^3*d^3*(a + b*atan(c*x)))/(2*x) - (d^3*(1 + im*c*x)^4*(a + b*atan(c*x))^2)/(4*x^4) - (4*im)*a*b*c^4*d^3*log(x) - (11*b^2*c^4*d^3*log(x))/3 - (4*im)*b*c^4*d^3*(a + b*atan(c*x))*log(2/(1 - im*c*x)) + (11*b^2*c^4*d^3*log(1 + c^2*x^2))/6 + 2*b^2*c^4*d^3*PolyLog(2, (-im)*c*x) - 2*b^2*c^4*d^3*PolyLog(2, im*c*x) - 2*b^2*c^4*d^3*PolyLog(2, 1 - 2/(1 - im*c*x))]
    @test_int [((d + im*c*d*x)^3*(a + b*atan(c*x))^2)/x^6, x, 24, -(b^2*c^2*d^3)/(30*x^3) - ((im/4)*b^2*c^3*d^3)/x^2 + (13*b^2*c^4*d^3)/(10*x) + (13*b^2*c^5*d^3*atan(c*x))/10 - (b*c*d^3*(a + b*atan(c*x)))/(10*x^4) - ((im/2)*b*c^2*d^3*(a + b*atan(c*x)))/x^3 + (6*b*c^3*d^3*(a + b*atan(c*x)))/(5*x^2) + (((5*im)/2)*b*c^4*d^3*(a + b*atan(c*x)))/x - (d^3*(1 + im*c*x)^4*(a + b*atan(c*x))^2)/(5*x^5) + ((im/20)*c*d^3*(1 + im*c*x)^4*(a + b*atan(c*x))^2)/x^4 + (12*a*b*c^5*d^3*log(x))/5 - (3*im)*b^2*c^5*d^3*log(x) + (12*b*c^5*d^3*(a + b*atan(c*x))*log(2/(1 - im*c*x)))/5 + ((3*im)/2)*b^2*c^5*d^3*log(1 + c^2*x^2) + ((6*im)/5)*b^2*c^5*d^3*PolyLog(2, (-im)*c*x) - ((6*im)/5)*b^2*c^5*d^3*PolyLog(2, im*c*x) - ((6*im)/5)*b^2*c^5*d^3*PolyLog(2, 1 - 2/(1 - im*c*x))]
    @test_int [((d + im*c*d*x)^3*(a + b*atan(c*x))^2)/x^7, x, 31, -(b^2*c^2*d^3)/(60*x^4) - ((im/10)*b^2*c^3*d^3)/x^3 + (61*b^2*c^4*d^3)/(180*x^2) + (((37*im)/30)*b^2*c^5*d^3)/x + ((37*im)/30)*b^2*c^6*d^3*atan(c*x) - (b*c*d^3*(a + b*atan(c*x)))/(15*x^5) - (((3*im)/10)*b*c^2*d^3*(a + b*atan(c*x)))/x^4 + (11*b*c^3*d^3*(a + b*atan(c*x)))/(18*x^3) + (((14*im)/15)*b*c^4*d^3*(a + b*atan(c*x)))/x^2 - (11*b*c^5*d^3*(a + b*atan(c*x)))/(6*x) - (d^3*(a + b*atan(c*x))^2)/(6*x^6) - (((3*im)/5)*c*d^3*(a + b*atan(c*x))^2)/x^5 + (3*c^2*d^3*(a + b*atan(c*x))^2)/(4*x^4) + ((im/3)*c^3*d^3*(a + b*atan(c*x))^2)/x^3 + ((28*im)/15)*a*b*c^6*d^3*log(x) + (113*b^2*c^6*d^3*log(x))/45 + ((37*im)/20)*b*c^6*d^3*(a + b*atan(c*x))*log(2/(1 - im*c*x)) + (im/60)*b*c^6*d^3*(a + b*atan(c*x))*log(2/(1 + im*c*x)) - (113*b^2*c^6*d^3*log(1 + c^2*x^2))/90 - (14*b^2*c^6*d^3*PolyLog(2, (-im)*c*x))/15 + (14*b^2*c^6*d^3*PolyLog(2, im*c*x))/15 + (37*b^2*c^6*d^3*PolyLog(2, 1 - 2/(1 - im*c*x)))/40 - (b^2*c^6*d^3*PolyLog(2, 1 - 2/(1 + im*c*x)))/120]

    #= ::Subsubsection::Closed:: =#
    #=q<0=#

    @test_int [(x^3*(a + b*atan(c*x))^2)/(d + im*c*d*x), x, 26, -((a*b*x)/(c^3*d)) - ((im/3)*b^2*x)/(c^3*d) + ((im/3)*b^2*atan(c*x))/(c^4*d) - (b^2*x*atan(c*x))/(c^3*d) + ((im/3)*b*x^2*(a + b*atan(c*x)))/(c^2*d) - (5*(a + b*atan(c*x))^2)/(6*c^4*d) + (im*x*(a + b*atan(c*x))^2)/(c^3*d) + (x^2*(a + b*atan(c*x))^2)/(2*c^2*d) - ((im/3)*x^3*(a + b*atan(c*x))^2)/(c*d) + (((8*im)/3)*b*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(c^4*d) + ((a + b*atan(c*x))^2*log(2/(1 + im*c*x)))/(c^4*d) + (b^2*log(1 + c^2*x^2))/(2*c^4*d) - (4*b^2*PolyLog(2, 1 - 2/(1 + im*c*x)))/(3*c^4*d) + (im*b*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c^4*d) + (b^2*PolyLog(3, 1 - 2/(1 + im*c*x)))/(2*c^4*d)]
    @test_int [(x^2*(a + b*atan(c*x))^2)/(d + im*c*d*x), x, 16, (im*a*b*x)/(c^2*d) + (im*b^2*x*atan(c*x))/(c^2*d) + ((im/2)*(a + b*atan(c*x))^2)/(c^3*d) + (x*(a + b*atan(c*x))^2)/(c^2*d) - ((im/2)*x^2*(a + b*atan(c*x))^2)/(c*d) + (2*b*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(c^3*d) - (im*(a + b*atan(c*x))^2*log(2/(1 + im*c*x)))/(c^3*d) - ((im/2)*b^2*log(1 + c^2*x^2))/(c^3*d) + (im*b^2*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c^3*d) + (b*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c^3*d) - ((im/2)*b^2*PolyLog(3, 1 - 2/(1 + im*c*x)))/(c^3*d)]
    @test_int [(x*(a + b*atan(c*x))^2)/(d + im*c*d*x), x, 9, (a + b*atan(c*x))^2/(c^2*d) - (im*x*(a + b*atan(c*x))^2)/(c*d) - ((2*im)*b*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(c^2*d) - ((a + b*atan(c*x))^2*log(2/(1 + im*c*x)))/(c^2*d) + (b^2*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c^2*d) - (im*b*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c^2*d) - (b^2*PolyLog(3, 1 - 2/(1 + im*c*x)))/(2*c^2*d)]
    @test_int [(a + b*atan(c*x))^2/(d + im*c*d*x), x, 3, (im*(a + b*atan(c*x))^2*log(2/(1 + im*c*x)))/(c*d) - (b*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c*d) + ((im/2)*b^2*PolyLog(3, 1 - 2/(1 + im*c*x)))/(c*d)]
    @test_int [(a + b*atan(c*x))^2/(x*(d + im*c*d*x)), x, 3, ((a + b*atan(c*x))^2*log(2 - 2/(1 + im*c*x)))/d + (im*b*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 + im*c*x)))/d + (b^2*PolyLog(3, -1 + 2/(1 + im*c*x)))/(2*d)]
    @test_int [(a + b*atan(c*x))^2/(x^2*(d + im*c*d*x)), x, 8, ((-im)*c*(a + b*atan(c*x))^2)/d - (a + b*atan(c*x))^2/(d*x) + (2*b*c*(a + b*atan(c*x))*log(2 - 2/(1 - im*c*x)))/d - (im*c*(a + b*atan(c*x))^2*log(2 - 2/(1 + im*c*x)))/d - (im*b^2*c*PolyLog(2, -1 + 2/(1 - im*c*x)))/d + (b*c*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 + im*c*x)))/d - ((im/2)*b^2*c*PolyLog(3, -1 + 2/(1 + im*c*x)))/d]
    @test_int [(a + b*atan(c*x))^2/(x^3*(d + im*c*d*x)), x, 17, -((b*c*(a + b*atan(c*x)))/(d*x)) - (3*c^2*(a + b*atan(c*x))^2)/(2*d) - (a + b*atan(c*x))^2/(2*d*x^2) + (im*c*(a + b*atan(c*x))^2)/(d*x) + (b^2*c^2*log(x))/d - (b^2*c^2*log(1 + c^2*x^2))/(2*d) - ((2*im)*b*c^2*(a + b*atan(c*x))*log(2 - 2/(1 - im*c*x)))/d - (c^2*(a + b*atan(c*x))^2*log(2 - 2/(1 + im*c*x)))/d - (b^2*c^2*PolyLog(2, -1 + 2/(1 - im*c*x)))/d - (im*b*c^2*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 + im*c*x)))/d - (b^2*c^2*PolyLog(3, -1 + 2/(1 + im*c*x)))/(2*d)]
    @test_int [(a + b*atan(c*x))^2/(x^4*(d + im*c*d*x)), x, 26, -(b^2*c^2)/(3*d*x) - (b^2*c^3*atan(c*x))/(3*d) - (b*c*(a + b*atan(c*x)))/(3*d*x^2) + (im*b*c^2*(a + b*atan(c*x)))/(d*x) + (((11*im)/6)*c^3*(a + b*atan(c*x))^2)/d - (a + b*atan(c*x))^2/(3*d*x^3) + ((im/2)*c*(a + b*atan(c*x))^2)/(d*x^2) + (c^2*(a + b*atan(c*x))^2)/(d*x) - (im*b^2*c^3*log(x))/d + ((im/2)*b^2*c^3*log(1 + c^2*x^2))/d - (8*b*c^3*(a + b*atan(c*x))*log(2 - 2/(1 - im*c*x)))/(3*d) + (im*c^3*(a + b*atan(c*x))^2*log(2 - 2/(1 + im*c*x)))/d + (((4*im)/3)*b^2*c^3*PolyLog(2, -1 + 2/(1 - im*c*x)))/d - (b*c^3*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 + im*c*x)))/d + ((im/2)*b^2*c^3*PolyLog(3, -1 + 2/(1 + im*c*x)))/d]

    @test_int [(x^4*(a + b*atan(c*x))^2)/(d + im*c*d*x)^2, x, 33, ((2*im)*a*b*x)/(c^4*d^2) - (b^2*x)/(3*c^4*d^2) + b^2/(2*c^5*d^2*(im - c*x)) - (b^2*atan(c*x))/(6*c^5*d^2) + ((2*im)*b^2*x*atan(c*x))/(c^4*d^2) + (b*x^2*(a + b*atan(c*x)))/(3*c^3*d^2) + (im*b*(a + b*atan(c*x)))/(c^5*d^2*(im - c*x)) + (((11*im)/6)*(a + b*atan(c*x))^2)/(c^5*d^2) + (3*x*(a + b*atan(c*x))^2)/(c^4*d^2) - (im*x^2*(a + b*atan(c*x))^2)/(c^3*d^2) - (x^3*(a + b*atan(c*x))^2)/(3*c^2*d^2) - (a + b*atan(c*x))^2/(c^5*d^2*(im - c*x)) + (20*b*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(3*c^5*d^2) - ((4*im)*(a + b*atan(c*x))^2*log(2/(1 + im*c*x)))/(c^5*d^2) - (im*b^2*log(1 + c^2*x^2))/(c^5*d^2) + (((10*im)/3)*b^2*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c^5*d^2) + (4*b*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c^5*d^2) - ((2*im)*b^2*PolyLog(3, 1 - 2/(1 + im*c*x)))/(c^5*d^2)]
    @test_int [(x^3*(a + b*atan(c*x))^2)/(d + im*c*d*x)^2, x, 24, (a*b*x)/(c^3*d^2) - ((im/2)*b^2)/(c^4*d^2*(im - c*x)) + ((im/2)*b^2*atan(c*x))/(c^4*d^2) + (b^2*x*atan(c*x))/(c^3*d^2) + (b*(a + b*atan(c*x)))/(c^4*d^2*(im - c*x)) + (a + b*atan(c*x))^2/(c^4*d^2) - ((2*im)*x*(a + b*atan(c*x))^2)/(c^3*d^2) - (x^2*(a + b*atan(c*x))^2)/(2*c^2*d^2) + (im*(a + b*atan(c*x))^2)/(c^4*d^2*(im - c*x)) - ((4*im)*b*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(c^4*d^2) - (3*(a + b*atan(c*x))^2*log(2/(1 + im*c*x)))/(c^4*d^2) - (b^2*log(1 + c^2*x^2))/(2*c^4*d^2) + (2*b^2*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c^4*d^2) - ((3*im)*b*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c^4*d^2) - (3*b^2*PolyLog(3, 1 - 2/(1 + im*c*x)))/(2*c^4*d^2)]
    @test_int [(x^2*(a + b*atan(c*x))^2)/(d + im*c*d*x)^2, x, 18, -b^2/(2*c^3*d^2*(im - c*x)) + (b^2*atan(c*x))/(2*c^3*d^2) - (im*b*(a + b*atan(c*x)))/(c^3*d^2*(im - c*x)) - ((im/2)*(a + b*atan(c*x))^2)/(c^3*d^2) - (x*(a + b*atan(c*x))^2)/(c^2*d^2) + (a + b*atan(c*x))^2/(c^3*d^2*(im - c*x)) - (2*b*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(c^3*d^2) + ((2*im)*(a + b*atan(c*x))^2*log(2/(1 + im*c*x)))/(c^3*d^2) - (im*b^2*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c^3*d^2) - (2*b*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c^3*d^2) + (im*b^2*PolyLog(3, 1 - 2/(1 + im*c*x)))/(c^3*d^2)]
    @test_int [(x*(a + b*atan(c*x))^2)/(d + im*c*d*x)^2, x, 13, ((im/2)*b^2)/(c^2*d^2*(im - c*x)) - ((im/2)*b^2*atan(c*x))/(c^2*d^2) - (b*(a + b*atan(c*x)))/(c^2*d^2*(im - c*x)) + (a + b*atan(c*x))^2/(2*c^2*d^2) - (im*(a + b*atan(c*x))^2)/(c^2*d^2*(im - c*x)) + ((a + b*atan(c*x))^2*log(2/(1 + im*c*x)))/(c^2*d^2) + (im*b*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c^2*d^2) + (b^2*PolyLog(3, 1 - 2/(1 + im*c*x)))/(2*c^2*d^2)]
    @test_int [(a + b*atan(c*x))^2/(d + im*c*d*x)^2, x, 8, b^2/(2*c*d^2*(im - c*x)) - (b^2*atan(c*x))/(2*c*d^2) + (im*b*(a + b*atan(c*x)))/(c*d^2*(im - c*x)) - ((im/2)*(a + b*atan(c*x))^2)/(c*d^2) + (im*(a + b*atan(c*x))^2)/(c*d^2*(1 + im*c*x))]
    @test_int [(a + b*atan(c*x))^2/(x*(d + im*c*d*x)^2), x, 19, ((-im/2)*b^2)/(d^2*(im - c*x)) + ((im/2)*b^2*atan(c*x))/d^2 + (b*(a + b*atan(c*x)))/(d^2*(im - c*x)) - (a + b*atan(c*x))^2/(2*d^2) + (im*(a + b*atan(c*x))^2)/(d^2*(im - c*x)) + (2*(a + b*atan(c*x))^2*atanh(1 - 2/(1 + im*c*x)))/d^2 + ((a + b*atan(c*x))^2*log(2/(1 + im*c*x)))/d^2 + (im*b*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 + im*c*x)))/d^2 + (b^2*PolyLog(3, -1 + 2/(1 + im*c*x)))/(2*d^2)]
    @test_int [(a + b*atan(c*x))^2/(x^2*(d + im*c*d*x)^2), x, 23, -(b^2*c)/(2*d^2*(im - c*x)) + (b^2*c*atan(c*x))/(2*d^2) - (im*b*c*(a + b*atan(c*x)))/(d^2*(im - c*x)) - ((im/2)*c*(a + b*atan(c*x))^2)/d^2 - (a + b*atan(c*x))^2/(d^2*x) + (c*(a + b*atan(c*x))^2)/(d^2*(im - c*x)) - ((4*im)*c*(a + b*atan(c*x))^2*atanh(1 - 2/(1 + im*c*x)))/d^2 - ((2*im)*c*(a + b*atan(c*x))^2*log(2/(1 + im*c*x)))/d^2 + (2*b*c*(a + b*atan(c*x))*log(2 - 2/(1 - im*c*x)))/d^2 - (im*b^2*c*PolyLog(2, -1 + 2/(1 - im*c*x)))/d^2 + (2*b*c*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 + im*c*x)))/d^2 - (im*b^2*c*PolyLog(3, -1 + 2/(1 + im*c*x)))/d^2]
    @test_int [(a + b*atan(c*x))^2/(x^3*(d + im*c*d*x)^2), x, 31, ((im/2)*b^2*c^2)/(d^2*(im - c*x)) - ((im/2)*b^2*c^2*atan(c*x))/d^2 - (b*c*(a + b*atan(c*x)))/(d^2*x) - (b*c^2*(a + b*atan(c*x)))/(d^2*(im - c*x)) - (2*c^2*(a + b*atan(c*x))^2)/d^2 - (a + b*atan(c*x))^2/(2*d^2*x^2) + ((2*im)*c*(a + b*atan(c*x))^2)/(d^2*x) - (im*c^2*(a + b*atan(c*x))^2)/(d^2*(im - c*x)) - (6*c^2*(a + b*atan(c*x))^2*atanh(1 - 2/(1 + im*c*x)))/d^2 + (b^2*c^2*log(x))/d^2 - (3*c^2*(a + b*atan(c*x))^2*log(2/(1 + im*c*x)))/d^2 - (b^2*c^2*log(1 + c^2*x^2))/(2*d^2) - ((4*im)*b*c^2*(a + b*atan(c*x))*log(2 - 2/(1 - im*c*x)))/d^2 - (2*b^2*c^2*PolyLog(2, -1 + 2/(1 - im*c*x)))/d^2 - ((3*im)*b*c^2*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 + im*c*x)))/d^2 - (3*b^2*c^2*PolyLog(3, -1 + 2/(1 + im*c*x)))/(2*d^2)]

    @test_int [(x^4*(a + b*atan(c*x))^2)/(d + im*c*d*x)^3, x, 37, ((-im)*a*b*x)/(c^4*d^3) + ((im/16)*b^2)/(c^5*d^3*(im - c*x)^2) - (29*b^2)/(16*c^5*d^3*(im - c*x)) + (29*b^2*atan(c*x))/(16*c^5*d^3) - (im*b^2*x*atan(c*x))/(c^4*d^3) - (b*(a + b*atan(c*x)))/(4*c^5*d^3*(im - c*x)^2) - (((15*im)/4)*b*(a + b*atan(c*x)))/(c^5*d^3*(im - c*x)) - (((5*im)/8)*(a + b*atan(c*x))^2)/(c^5*d^3) - (3*x*(a + b*atan(c*x))^2)/(c^4*d^3) + ((im/2)*x^2*(a + b*atan(c*x))^2)/(c^3*d^3) - ((im/2)*(a + b*atan(c*x))^2)/(c^5*d^3*(im - c*x)^2) + (4*(a + b*atan(c*x))^2)/(c^5*d^3*(im - c*x)) - (6*b*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(c^5*d^3) + ((6*im)*(a + b*atan(c*x))^2*log(2/(1 + im*c*x)))/(c^5*d^3) + ((im/2)*b^2*log(1 + c^2*x^2))/(c^5*d^3) - ((3*im)*b^2*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c^5*d^3) - (6*b*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c^5*d^3) + ((3*im)*b^2*PolyLog(3, 1 - 2/(1 + im*c*x)))/(c^5*d^3)]
    @test_int [(x^3*(a + b*atan(c*x))^2)/(d + im*c*d*x)^3, x, 31, b^2/(16*c^4*d^3*(im - c*x)^2) + (((21*im)/16)*b^2)/(c^4*d^3*(im - c*x)) - (((21*im)/16)*b^2*atan(c*x))/(c^4*d^3) + ((im/4)*b*(a + b*atan(c*x)))/(c^4*d^3*(im - c*x)^2) - (11*b*(a + b*atan(c*x)))/(4*c^4*d^3*(im - c*x)) + (3*(a + b*atan(c*x))^2)/(8*c^4*d^3) + (im*x*(a + b*atan(c*x))^2)/(c^3*d^3) - (a + b*atan(c*x))^2/(2*c^4*d^3*(im - c*x)^2) - ((3*im)*(a + b*atan(c*x))^2)/(c^4*d^3*(im - c*x)) + ((2*im)*b*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(c^4*d^3) + (3*(a + b*atan(c*x))^2*log(2/(1 + im*c*x)))/(c^4*d^3) - (b^2*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c^4*d^3) + ((3*im)*b*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c^4*d^3) + (3*b^2*PolyLog(3, 1 - 2/(1 + im*c*x)))/(2*c^4*d^3)]
    @test_int [(x^2*(a + b*atan(c*x))^2)/(d + im*c*d*x)^3, x, 26, ((-im/16)*b^2)/(c^3*d^3*(im - c*x)^2) + (13*b^2)/(16*c^3*d^3*(im - c*x)) - (13*b^2*atan(c*x))/(16*c^3*d^3) + (b*(a + b*atan(c*x)))/(4*c^3*d^3*(im - c*x)^2) + (((7*im)/4)*b*(a + b*atan(c*x)))/(c^3*d^3*(im - c*x)) - (((7*im)/8)*(a + b*atan(c*x))^2)/(c^3*d^3) + ((im/2)*(a + b*atan(c*x))^2)/(c^3*d^3*(im - c*x)^2) - (2*(a + b*atan(c*x))^2)/(c^3*d^3*(im - c*x)) - (im*(a + b*atan(c*x))^2*log(2/(1 + im*c*x)))/(c^3*d^3) + (b*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c^3*d^3) - ((im/2)*b^2*PolyLog(3, 1 - 2/(1 + im*c*x)))/(c^3*d^3)]
    @test_int [(x*(a + b*atan(c*x))^2)/(d + im*c*d*x)^3, x, 13, -b^2/(16*c^2*d^3*(im - c*x)^2) - (((5*im)/16)*b^2)/(c^2*d^3*(im - c*x)) + (((5*im)/16)*b^2*atan(c*x))/(c^2*d^3) - ((im/4)*b*(a + b*atan(c*x)))/(c^2*d^3*(im - c*x)^2) + (3*b*(a + b*atan(c*x)))/(4*c^2*d^3*(im - c*x)) + (a + b*atan(c*x))^2/(8*c^2*d^3) + (x^2*(a + b*atan(c*x))^2)/(2*d^3*(1 + im*c*x)^2)]
    @test_int [(a + b*atan(c*x))^2/(d + im*c*d*x)^3, x, 13, ((im/16)*b^2)/(c*d^3*(im - c*x)^2) + (3*b^2)/(16*c*d^3*(im - c*x)) - (3*b^2*atan(c*x))/(16*c*d^3) - (b*(a + b*atan(c*x)))/(4*c*d^3*(im - c*x)^2) + ((im/4)*b*(a + b*atan(c*x)))/(c*d^3*(im - c*x)) - ((im/8)*(a + b*atan(c*x))^2)/(c*d^3) + ((im/2)*(a + b*atan(c*x))^2)/(c*d^3*(1 + im*c*x)^2)]
    @test_int [(a + b*atan(c*x))^2/(x*(d + im*c*d*x)^3), x, 32, b^2/(16*d^3*(im - c*x)^2) - (((11*im)/16)*b^2)/(d^3*(im - c*x)) + (((11*im)/16)*b^2*atan(c*x))/d^3 + ((im/4)*b*(a + b*atan(c*x)))/(d^3*(im - c*x)^2) + (5*b*(a + b*atan(c*x)))/(4*d^3*(im - c*x)) - (5*(a + b*atan(c*x))^2)/(8*d^3) - (a + b*atan(c*x))^2/(2*d^3*(im - c*x)^2) + (im*(a + b*atan(c*x))^2)/(d^3*(im - c*x)) + (2*(a + b*atan(c*x))^2*atanh(1 - 2/(1 + im*c*x)))/d^3 + ((a + b*atan(c*x))^2*log(2/(1 + im*c*x)))/d^3 + (im*b*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 + im*c*x)))/d^3 + (b^2*PolyLog(3, -1 + 2/(1 + im*c*x)))/(2*d^3)]
    @test_int [(a + b*atan(c*x))^2/(x^2*(d + im*c*d*x)^3), x, 36, ((-im/16)*b^2*c)/(d^3*(im - c*x)^2) - (19*b^2*c)/(16*d^3*(im - c*x)) + (19*b^2*c*atan(c*x))/(16*d^3) + (b*c*(a + b*atan(c*x)))/(4*d^3*(im - c*x)^2) - (((9*im)/4)*b*c*(a + b*atan(c*x)))/(d^3*(im - c*x)) + ((im/8)*c*(a + b*atan(c*x))^2)/d^3 - (a + b*atan(c*x))^2/(d^3*x) + ((im/2)*c*(a + b*atan(c*x))^2)/(d^3*(im - c*x)^2) + (2*c*(a + b*atan(c*x))^2)/(d^3*(im - c*x)) - ((6*im)*c*(a + b*atan(c*x))^2*atanh(1 - 2/(1 + im*c*x)))/d^3 - ((3*im)*c*(a + b*atan(c*x))^2*log(2/(1 + im*c*x)))/d^3 + (2*b*c*(a + b*atan(c*x))*log(2 - 2/(1 - im*c*x)))/d^3 - (im*b^2*c*PolyLog(2, -1 + 2/(1 - im*c*x)))/d^3 + (3*b*c*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 + im*c*x)))/d^3 - (((3*im)/2)*b^2*c*PolyLog(3, -1 + 2/(1 + im*c*x)))/d^3]

    @test_int [(a + b*atan(c*x))^2/(1 + im*c*x)^4, x, 18, -b^2/(54*c*(im - c*x)^3) + (((5*im)/144)*b^2)/(c*(im - c*x)^2) + (11*b^2)/(144*c*(im - c*x)) - (11*b^2*atan(c*x))/(144*c) - ((im/9)*b*(a + b*atan(c*x)))/(c*(im - c*x)^3) - (b*(a + b*atan(c*x)))/(12*c*(im - c*x)^2) + ((im/12)*b*(a + b*atan(c*x)))/(c*(im - c*x)) - ((im/24)*(a + b*atan(c*x))^2)/c + ((im/3)*(a + b*atan(c*x))^2)/(c*(1 + im*c*x)^3)]

    @test_int [atan(a*x)^2/(c*x - im*a*c*x^2), x, 4, (atan(a*x)^2*log(2 - 2/(1 - im*a*x)))/c - (im*atan(a*x)*PolyLog(2, -1 + 2/(1 - im*a*x)))/c + PolyLog(3, -1 + 2/(1 - im*a*x))/(2*c)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(d+e*x)^q*(a+b*atan(c*x))^3*with*c^2*d^2+e^2=0=#

    @test_int [(a + b*atan(c*x))^3*(d + im*c*d*x)^3, x, 26, -3*a*b^2*d^3*x + (1/4)*im*b^3*d^3*x - (im*b^3*d^3*atan(c*x))/(4*c) - 3*b^3*d^3*x*atan(c*x) - (1/4)*im*b^2*c*d^3*x^2*(a + b*atan(c*x)) + (7*b*d^3*(a + b*atan(c*x))^2)/c - (21/4)*im*b*d^3*x*(a + b*atan(c*x))^2 + (3/2)*b*c*d^3*x^2*(a + b*atan(c*x))^2 + (1/4)*im*b*c^2*d^3*x^3*(a + b*atan(c*x))^2 - (im*d^3*(1 + im*c*x)^4*(a + b*atan(c*x))^3)/(4*c) + (6*b*d^3*(a + b*atan(c*x))^2*log(2/(1 - im*c*x)))/c - (11*im*b^2*d^3*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/c + (3*b^3*d^3*log(1 + c^2*x^2))/(2*c) - (6*im*b^2*d^3*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 - im*c*x)))/c + (11*b^3*d^3*PolyLog(2, 1 - 2/(1 + im*c*x)))/(2*c) + (3*b^3*d^3*PolyLog(3, 1 - 2/(1 - im*c*x)))/c]
    @test_int [(a + b*atan(c*x))^3*(d + im*c*d*x)^2, x, 17, (-a)*b^2*d^2*x - b^3*d^2*x*atan(c*x) + (7*b*d^2*(a + b*atan(c*x))^2)/(2*c) - 3*im*b*d^2*x*(a + b*atan(c*x))^2 + (1/2)*b*c*d^2*x^2*(a + b*atan(c*x))^2 - (im*d^2*(1 + im*c*x)^3*(a + b*atan(c*x))^3)/(3*c) + (4*b*d^2*(a + b*atan(c*x))^2*log(2/(1 - im*c*x)))/c - (6*im*b^2*d^2*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/c + (b^3*d^2*log(1 + c^2*x^2))/(2*c) - (4*im*b^2*d^2*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 - im*c*x)))/c + (3*b^3*d^2*PolyLog(2, 1 - 2/(1 + im*c*x)))/c + (2*b^3*d^2*PolyLog(3, 1 - 2/(1 - im*c*x)))/c]
    @test_int [(a + b*atan(c*x))^3*(d + im*c*d*x)^1, x, 11, (3*b*d*(a + b*atan(c*x))^2)/(2*c) - (3/2)*im*b*d*x*(a + b*atan(c*x))^2 - (im*d*(1 + im*c*x)^2*(a + b*atan(c*x))^3)/(2*c) + (3*b*d*(a + b*atan(c*x))^2*log(2/(1 - im*c*x)))/c - (3*im*b^2*d*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/c - (3*im*b^2*d*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 - im*c*x)))/c + (3*b^3*d*PolyLog(2, 1 - 2/(1 + im*c*x)))/(2*c) + (3*b^3*d*PolyLog(3, 1 - 2/(1 - im*c*x)))/(2*c)]
    @test_int [(a + b*atan(c*x))^3/(d + im*c*d*x)^1, x, 4, (im*(a + b*atan(c*x))^3*log(2/(1 + im*c*x)))/(c*d) - (3*b*(a + b*atan(c*x))^2*PolyLog(2, 1 - 2/(1 + im*c*x)))/(2*c*d) + (3*im*b^2*(a + b*atan(c*x))*PolyLog(3, 1 - 2/(1 + im*c*x)))/(2*c*d) + (3*b^3*PolyLog(4, 1 - 2/(1 + im*c*x)))/(4*c*d)]
    @test_int [(a + b*atan(c*x))^3/(d + im*c*d*x)^2, x, 11, -((3*im*b^3)/(4*c*d^2*(im - c*x))) + (3*im*b^3*atan(c*x))/(4*c*d^2) + (3*b^2*(a + b*atan(c*x)))/(2*c*d^2*(im - c*x)) - (3*b*(a + b*atan(c*x))^2)/(4*c*d^2) + (3*im*b*(a + b*atan(c*x))^2)/(2*c*d^2*(im - c*x)) - (im*(a + b*atan(c*x))^3)/(2*c*d^2) + (im*(a + b*atan(c*x))^3)/(c*d^2*(1 + im*c*x))]
    @test_int [(a + b*atan(c*x))^3/(d + im*c*d*x)^3, x, 24, (3*b^3)/(64*c*d^3*(im - c*x)^2) - (21*im*b^3)/(64*c*d^3*(im - c*x)) + (21*im*b^3*atan(c*x))/(64*c*d^3) + (3*im*b^2*(a + b*atan(c*x)))/(16*c*d^3*(im - c*x)^2) + (9*b^2*(a + b*atan(c*x)))/(16*c*d^3*(im - c*x)) - (9*b*(a + b*atan(c*x))^2)/(32*c*d^3) - (3*b*(a + b*atan(c*x))^2)/(8*c*d^3*(im - c*x)^2) + (3*im*b*(a + b*atan(c*x))^2)/(8*c*d^3*(im - c*x)) - (im*(a + b*atan(c*x))^3)/(8*c*d^3) + (im*(a + b*atan(c*x))^3)/(2*c*d^3*(1 + im*c*x)^2)]
    @test_int [(a + b*atan(c*x))^3/(d + im*c*d*x)^4, x, 42, (im*b^3)/(108*c*d^4*(im - c*x)^3) + (19*b^3)/(576*c*d^4*(im - c*x)^2) - (85*im*b^3)/(576*c*d^4*(im - c*x)) + (85*im*b^3*atan(c*x))/(576*c*d^4) - (b^2*(a + b*atan(c*x)))/(18*c*d^4*(im - c*x)^3) + (5*im*b^2*(a + b*atan(c*x)))/(48*c*d^4*(im - c*x)^2) + (11*b^2*(a + b*atan(c*x)))/(48*c*d^4*(im - c*x)) - (11*b*(a + b*atan(c*x))^2)/(96*c*d^4) - (im*b*(a + b*atan(c*x))^2)/(6*c*d^4*(im - c*x)^3) - (b*(a + b*atan(c*x))^2)/(8*c*d^4*(im - c*x)^2) + (im*b*(a + b*atan(c*x))^2)/(8*c*d^4*(im - c*x)) - (im*(a + b*atan(c*x))^3)/(24*c*d^4) + (im*(a + b*atan(c*x))^3)/(3*c*d^4*(1 + im*c*x)^3)]

    @test_int [x^2*(a + b*atan(c*x))^3/(d + im*c*d*x), x, 19, (-3*b*(a + b*atan(c*x))^2)/(2*c^3*d) + (((3*im)/2)*b*x*(a + b*atan(c*x))^2)/(c^2*d) + ((im/2)*(a + b*atan(c*x))^3)/(c^3*d) + (x*(a + b*atan(c*x))^3)/(c^2*d) - ((im/2)*x^2*(a + b*atan(c*x))^3)/(c*d) + ((3*im)*b^2*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(c^3*d) + (3*b*(a + b*atan(c*x))^2*log(2/(1 + im*c*x)))/(c^3*d) - (im*(a + b*atan(c*x))^3*log(2/(1 + im*c*x)))/(c^3*d) - (3*b^3*PolyLog(2, 1 - 2/(1 + im*c*x)))/(2*c^3*d) + ((3*im)*b^2*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c^3*d) + (3*b*(a + b*atan(c*x))^2*PolyLog(2, 1 - 2/(1 + im*c*x)))/(2*c^3*d) + (3*b^3*PolyLog(3, 1 - 2/(1 + im*c*x)))/(2*c^3*d) - (((3*im)/2)*b^2*(a + b*atan(c*x))*PolyLog(3, 1 - 2/(1 + im*c*x)))/(c^3*d) - (3*b^3*PolyLog(4, 1 - 2/(1 + im*c*x)))/(4*c^3*d)]
    @test_int [x^1*(a + b*atan(c*x))^3/(d + im*c*d*x), x, 10, (a + b*atan(c*x))^3/(c^2*d) - (im*x*(a + b*atan(c*x))^3)/(c*d) - ((3*im)*b*(a + b*atan(c*x))^2*log(2/(1 + im*c*x)))/(c^2*d) - ((a + b*atan(c*x))^3*log(2/(1 + im*c*x)))/(c^2*d) + (3*b^2*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c^2*d) - (((3*im)/2)*b*(a + b*atan(c*x))^2*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c^2*d) - (((3*im)/2)*b^3*PolyLog(3, 1 - 2/(1 + im*c*x)))/(c^2*d) - (3*b^2*(a + b*atan(c*x))*PolyLog(3, 1 - 2/(1 + im*c*x)))/(2*c^2*d) + (((3*im)/4)*b^3*PolyLog(4, 1 - 2/(1 + im*c*x)))/(c^2*d)]
    @test_int [x^0*(a + b*atan(c*x))^3/(d + im*c*d*x), x, 4, (im*(a + b*atan(c*x))^3*log(2/(1 + im*c*x)))/(c*d) - (3*b*(a + b*atan(c*x))^2*PolyLog(2, 1 - 2/(1 + im*c*x)))/(2*c*d) + (((3*im)/2)*b^2*(a + b*atan(c*x))*PolyLog(3, 1 - 2/(1 + im*c*x)))/(c*d) + (3*b^3*PolyLog(4, 1 - 2/(1 + im*c*x)))/(4*c*d)]
    @test_int [(a + b*atan(c*x))^3/(x^1*(d + im*c*d*x)), x, 4, ((a + b*atan(c*x))^3*log(2 - 2/(1 + im*c*x)))/d + (((3*im)/2)*b*(a + b*atan(c*x))^2*PolyLog(2, -1 + 2/(1 + im*c*x)))/d + (3*b^2*(a + b*atan(c*x))*PolyLog(3, -1 + 2/(1 + im*c*x)))/(2*d) - (((3*im)/4)*b^3*PolyLog(4, -1 + 2/(1 + im*c*x)))/d]
    @test_int [(a + b*atan(c*x))^3/(x^2*(d + im*c*d*x)), x, 10, ((-im)*c*(a + b*atan(c*x))^3)/d - (a + b*atan(c*x))^3/(d*x) + (3*b*c*(a + b*atan(c*x))^2*log(2 - 2/(1 - im*c*x)))/d - (im*c*(a + b*atan(c*x))^3*log(2 - 2/(1 + im*c*x)))/d - ((3*im)*b^2*c*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 - im*c*x)))/d + (3*b*c*(a + b*atan(c*x))^2*PolyLog(2, -1 + 2/(1 + im*c*x)))/(2*d) + (3*b^3*c*PolyLog(3, -1 + 2/(1 - im*c*x)))/(2*d) - (((3*im)/2)*b^2*c*(a + b*atan(c*x))*PolyLog(3, -1 + 2/(1 + im*c*x)))/d - (3*b^3*c*PolyLog(4, -1 + 2/(1 + im*c*x)))/(4*d)]
    @test_int [(a + b*atan(c*x))^3/(x^3*(d + im*c*d*x)), x, 18, (((-3*im)/2)*b*c^2*(a + b*atan(c*x))^2)/d - (3*b*c*(a + b*atan(c*x))^2)/(2*d*x) - (3*c^2*(a + b*atan(c*x))^3)/(2*d) - (a + b*atan(c*x))^3/(2*d*x^2) + (im*c*(a + b*atan(c*x))^3)/(d*x) + (3*b^2*c^2*(a + b*atan(c*x))*log(2 - 2/(1 - im*c*x)))/d - ((3*im)*b*c^2*(a + b*atan(c*x))^2*log(2 - 2/(1 - im*c*x)))/d - (c^2*(a + b*atan(c*x))^3*log(2 - 2/(1 + im*c*x)))/d - (((3*im)/2)*b^3*c^2*PolyLog(2, -1 + 2/(1 - im*c*x)))/d - (3*b^2*c^2*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 - im*c*x)))/d - (((3*im)/2)*b*c^2*(a + b*atan(c*x))^2*PolyLog(2, -1 + 2/(1 + im*c*x)))/d - (((3*im)/2)*b^3*c^2*PolyLog(3, -1 + 2/(1 - im*c*x)))/d - (3*b^2*c^2*(a + b*atan(c*x))*PolyLog(3, -1 + 2/(1 + im*c*x)))/(2*d) + (((3*im)/4)*b^3*c^2*PolyLog(4, -1 + 2/(1 + im*c*x)))/d]

    #= ::Subsection:: =#
    #=Integrands*of*the*form*x^m*(d+e*x)^q*(a+b*atan(c*x))^4*with*c^2*d^2+e^2=0=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(d+e*x)^q*(a+b*atan(c*x))^-1*with*c^2*d^2+e^2=0=#

    @test_int [1/((d + im*c*d*x)*(a + b*atan(c*x))), x, 0, Unintegrable(1/((d + im*c*d*x)*(a + b*atan(c*x))), x)]

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

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

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

    @test_int [x^3*(a + b*atan(c*x))/(d + e*x), x, 16, (a*d^2*x)/e^3 + (b*d*x)/(2*c*e^2) - (b*x^2)/(6*c*e) - (b*d*atan(c*x))/(2*c^2*e^2) + (b*d^2*x*atan(c*x))/e^3 - (d*x^2*(a + b*atan(c*x)))/(2*e^2) + (x^3*(a + b*atan(c*x)))/(3*e) + (d^3*(a + b*atan(c*x))*log(2/(1 - im*c*x)))/e^4 - (d^3*(a + b*atan(c*x))*log((2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/e^4 - (b*d^2*log(1 + c^2*x^2))/(2*c*e^3) + (b*log(1 + c^2*x^2))/(6*c^3*e) - (im*b*d^3*PolyLog(2, 1 - 2/(1 - im*c*x)))/(2*e^4) + (im*b*d^3*PolyLog(2, 1 - (2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/(2*e^4)]
    @test_int [x^2*(a + b*atan(c*x))/(d + e*x), x, 12, -((a*d*x)/e^2) - (b*x)/(2*c*e) + (b*atan(c*x))/(2*c^2*e) - (b*d*x*atan(c*x))/e^2 + (x^2*(a + b*atan(c*x)))/(2*e) - (d^2*(a + b*atan(c*x))*log(2/(1 - im*c*x)))/e^3 + (d^2*(a + b*atan(c*x))*log((2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/e^3 + (b*d*log(1 + c^2*x^2))/(2*c*e^2) + (im*b*d^2*PolyLog(2, 1 - 2/(1 - im*c*x)))/(2*e^3) - (im*b*d^2*PolyLog(2, 1 - (2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/(2*e^3)]
    @test_int [x^1*(a + b*atan(c*x))/(d + e*x), x, 9, (a*x)/e + (b*x*atan(c*x))/e + (d*(a + b*atan(c*x))*log(2/(1 - im*c*x)))/e^2 - (d*(a + b*atan(c*x))*log((2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/e^2 - (b*log(1 + c^2*x^2))/(2*c*e) - (im*b*d*PolyLog(2, 1 - 2/(1 - im*c*x)))/(2*e^2) + (im*b*d*PolyLog(2, 1 - (2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/(2*e^2)]
    @test_int [x^0*(a + b*atan(c*x))/(d + e*x), x, 4, -(((a + b*atan(c*x))*log(2/(1 - im*c*x)))/e) + ((a + b*atan(c*x))*log((2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/e + (im*b*PolyLog(2, 1 - 2/(1 - im*c*x)))/(2*e) - (im*b*PolyLog(2, 1 - (2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/(2*e)]
    @test_int [(a + b*atan(c*x))/(x^1*(d + e*x)), x, 9, (a*log(x))/d + ((a + b*atan(c*x))*log(2/(1 - im*c*x)))/d - ((a + b*atan(c*x))*log((2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/d + (im*b*PolyLog(2, (-im)*c*x))/(2*d) - (im*b*PolyLog(2, im*c*x))/(2*d) - (im*b*PolyLog(2, 1 - 2/(1 - im*c*x)))/(2*d) + (im*b*PolyLog(2, 1 - (2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/(2*d)]
    @test_int [(a + b*atan(c*x))/(x^2*(d + e*x)), x, 14, -((a + b*atan(c*x))/(d*x)) + (b*c*log(x))/d - (a*e*log(x))/d^2 - (e*(a + b*atan(c*x))*log(2/(1 - im*c*x)))/d^2 + (e*(a + b*atan(c*x))*log((2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/d^2 - (b*c*log(1 + c^2*x^2))/(2*d) - (im*b*e*PolyLog(2, (-im)*c*x))/(2*d^2) + (im*b*e*PolyLog(2, im*c*x))/(2*d^2) + (im*b*e*PolyLog(2, 1 - 2/(1 - im*c*x)))/(2*d^2) - (im*b*e*PolyLog(2, 1 - (2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/(2*d^2)]
    @test_int [(a + b*atan(c*x))/(x^3*(d + e*x)), x, 17, -((b*c)/(2*d*x)) - (b*c^2*atan(c*x))/(2*d) - (a + b*atan(c*x))/(2*d*x^2) + (e*(a + b*atan(c*x)))/(d^2*x) - (b*c*e*log(x))/d^2 + (a*e^2*log(x))/d^3 + (e^2*(a + b*atan(c*x))*log(2/(1 - im*c*x)))/d^3 - (e^2*(a + b*atan(c*x))*log((2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/d^3 + (b*c*e*log(1 + c^2*x^2))/(2*d^2) + (im*b*e^2*PolyLog(2, (-im)*c*x))/(2*d^3) - (im*b*e^2*PolyLog(2, im*c*x))/(2*d^3) - (im*b*e^2*PolyLog(2, 1 - 2/(1 - im*c*x)))/(2*d^3) + (im*b*e^2*PolyLog(2, 1 - (2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/(2*d^3)]

    @test_int [x^3*(a + b*atan(c*x))^2/(d + e*x), x, 23, (a*b*d*x)/(c*e^2) + (b^2*x)/(3*c^2*e) - (b^2*atan(c*x))/(3*c^3*e) + (b^2*d*x*atan(c*x))/(c*e^2) - (b*x^2*(a + b*atan(c*x)))/(3*c*e) + (im*d^2*(a + b*atan(c*x))^2)/(c*e^3) - (d*(a + b*atan(c*x))^2)/(2*c^2*e^2) - (im*(a + b*atan(c*x))^2)/(3*c^3*e) + (d^2*x*(a + b*atan(c*x))^2)/e^3 - (d*x^2*(a + b*atan(c*x))^2)/(2*e^2) + (x^3*(a + b*atan(c*x))^2)/(3*e) + (d^3*(a + b*atan(c*x))^2*log(2/(1 - im*c*x)))/e^4 + (2*b*d^2*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(c*e^3) - (2*b*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(3*c^3*e) - (d^3*(a + b*atan(c*x))^2*log((2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/e^4 - (b^2*d*log(1 + c^2*x^2))/(2*c^2*e^2) - (im*b*d^3*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 - im*c*x)))/e^4 + (im*b^2*d^2*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c*e^3) - (im*b^2*PolyLog(2, 1 - 2/(1 + im*c*x)))/(3*c^3*e) + (im*b*d^3*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/e^4 + (b^2*d^3*PolyLog(3, 1 - 2/(1 - im*c*x)))/(2*e^4) - (b^2*d^3*PolyLog(3, 1 - (2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/(2*e^4)]
    @test_int [x^2*(a + b*atan(c*x))^2/(d + e*x), x, 14, -((a*b*x)/(c*e)) - (b^2*x*atan(c*x))/(c*e) - (im*d*(a + b*atan(c*x))^2)/(c*e^2) + (a + b*atan(c*x))^2/(2*c^2*e) - (d*x*(a + b*atan(c*x))^2)/e^2 + (x^2*(a + b*atan(c*x))^2)/(2*e) - (d^2*(a + b*atan(c*x))^2*log(2/(1 - im*c*x)))/e^3 - (2*b*d*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(c*e^2) + (d^2*(a + b*atan(c*x))^2*log((2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/e^3 + (b^2*log(1 + c^2*x^2))/(2*c^2*e) + (im*b*d^2*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 - im*c*x)))/e^3 - (im*b^2*d*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c*e^2) - (im*b*d^2*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/e^3 - (b^2*d^2*PolyLog(3, 1 - 2/(1 - im*c*x)))/(2*e^3) + (b^2*d^2*PolyLog(3, 1 - (2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/(2*e^3)]
    @test_int [x^1*(a + b*atan(c*x))^2/(d + e*x), x, 8, (im*(a + b*atan(c*x))^2)/(c*e) + (x*(a + b*atan(c*x))^2)/e + (d*(a + b*atan(c*x))^2*log(2/(1 - im*c*x)))/e^2 + (2*b*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(c*e) - (d*(a + b*atan(c*x))^2*log((2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/e^2 - (im*b*d*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 - im*c*x)))/e^2 + (im*b^2*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c*e) + (im*b*d*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/e^2 + (b^2*d*PolyLog(3, 1 - 2/(1 - im*c*x)))/(2*e^2) - (b^2*d*PolyLog(3, 1 - (2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/(2*e^2)]
    @test_int [x^0*(a + b*atan(c*x))^2/(d + e*x), x, 1, -(((a + b*atan(c*x))^2*log(2/(1 - im*c*x)))/e) + ((a + b*atan(c*x))^2*log((2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/e + (im*b*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 - im*c*x)))/e - (im*b*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/e - (b^2*PolyLog(3, 1 - 2/(1 - im*c*x)))/(2*e) + (b^2*PolyLog(3, 1 - (2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/(2*e)]
    @test_int [(a + b*atan(c*x))^2/(x^1*(d + e*x)), x, 9, (2*(a + b*atan(c*x))^2*atanh(1 - 2/(1 + im*c*x)))/d + ((a + b*atan(c*x))^2*log(2/(1 - im*c*x)))/d - ((a + b*atan(c*x))^2*log((2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/d - (im*b*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 - im*c*x)))/d - (im*b*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)))/d + (im*b*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 + im*c*x)))/d + (im*b*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/d + (b^2*PolyLog(3, 1 - 2/(1 - im*c*x)))/(2*d) - (b^2*PolyLog(3, 1 - 2/(1 + im*c*x)))/(2*d) + (b^2*PolyLog(3, -1 + 2/(1 + im*c*x)))/(2*d) - (b^2*PolyLog(3, 1 - (2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/(2*d)]
    @test_int [(a + b*atan(c*x))^2/(x^2*(d + e*x)), x, 13, -((im*c*(a + b*atan(c*x))^2)/d) - (a + b*atan(c*x))^2/(d*x) - (2*e*(a + b*atan(c*x))^2*atanh(1 - 2/(1 + im*c*x)))/d^2 - (e*(a + b*atan(c*x))^2*log(2/(1 - im*c*x)))/d^2 + (e*(a + b*atan(c*x))^2*log((2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/d^2 + (2*b*c*(a + b*atan(c*x))*log(2 - 2/(1 - im*c*x)))/d + (im*b*e*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 - im*c*x)))/d^2 - (im*b^2*c*PolyLog(2, -1 + 2/(1 - im*c*x)))/d + (im*b*e*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)))/d^2 - (im*b*e*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 + im*c*x)))/d^2 - (im*b*e*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/d^2 - (b^2*e*PolyLog(3, 1 - 2/(1 - im*c*x)))/(2*d^2) + (b^2*e*PolyLog(3, 1 - 2/(1 + im*c*x)))/(2*d^2) - (b^2*e*PolyLog(3, -1 + 2/(1 + im*c*x)))/(2*d^2) + (b^2*e*PolyLog(3, 1 - (2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/(2*d^2)]
    @test_int [(a + b*atan(c*x))^2/(x^3*(d + e*x)), x, 21, -((b*c*(a + b*atan(c*x)))/(d*x)) - (c^2*(a + b*atan(c*x))^2)/(2*d) + (im*c*e*(a + b*atan(c*x))^2)/d^2 - (a + b*atan(c*x))^2/(2*d*x^2) + (e*(a + b*atan(c*x))^2)/(d^2*x) + (2*e^2*(a + b*atan(c*x))^2*atanh(1 - 2/(1 + im*c*x)))/d^3 + (b^2*c^2*log(x))/d + (e^2*(a + b*atan(c*x))^2*log(2/(1 - im*c*x)))/d^3 - (e^2*(a + b*atan(c*x))^2*log((2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/d^3 - (b^2*c^2*log(1 + c^2*x^2))/(2*d) - (2*b*c*e*(a + b*atan(c*x))*log(2 - 2/(1 - im*c*x)))/d^2 - (im*b*e^2*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 - im*c*x)))/d^3 + (im*b^2*c*e*PolyLog(2, -1 + 2/(1 - im*c*x)))/d^2 - (im*b*e^2*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)))/d^3 + (im*b*e^2*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 + im*c*x)))/d^3 + (im*b*e^2*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/d^3 + (b^2*e^2*PolyLog(3, 1 - 2/(1 - im*c*x)))/(2*d^3) - (b^2*e^2*PolyLog(3, 1 - 2/(1 + im*c*x)))/(2*d^3) + (b^2*e^2*PolyLog(3, -1 + 2/(1 + im*c*x)))/(2*d^3) - (b^2*e^2*PolyLog(3, 1 - (2*c*(d + e*x))/((c*d + im*e)*(1 - im*c*x))))/(2*d^3)]

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

    @test_int [1/((d + e*x)*(a + b*atan(c*x))), x, 0, Unintegrable(1/((d + e*x)*(a + b*atan(c*x))), x)]

    #= ::Title::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d+e*x^2)^q*(a+b*atan(c*x))^p*with*e=c^2*d=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d+c^2*d*x^2)^q*(a+b*atan(c*x))^1=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x^2)^p*atan(a*x)^1*with*d=a^2*c=#

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

    @test_int [x^3*(c + a^2*c*x^2)*atan(a*x), x, 9, (c*x)/(12*a^3) - (c*x^3)/(36*a) - (a*c*x^5)/30 - (c*atan(a*x))/(12*a^4) + (c*x^4*atan(a*x))/4 + (a^2*c*x^6*atan(a*x))/6]
    @test_int [x^2*(c + a^2*c*x^2)*atan(a*x), x, 9, -(c*x^2)/(15*a) - (a*c*x^4)/20 + (c*x^3*atan(a*x))/3 + (a^2*c*x^5*atan(a*x))/5 + (c*log(1 + a^2*x^2))/(15*a^3)]
    @test_int [x^1*(c + a^2*c*x^2)*atan(a*x), x, 2, -(c*x)/(4*a) - (a*c*x^3)/12 + (c*(1 + a^2*x^2)^2*atan(a*x))/(4*a^2)]
    @test_int [x^0*(c + a^2*c*x^2)*atan(a*x), x, 3, (-(1/6))*a*c*x^2 + c*x*atan(a*x) + (1/3)*a^2*c*x^3*atan(a*x) - (c*log(1 + a^2*x^2))/(3*a), -((c*(1 + a^2*x^2))/(6*a)) + (2/3)*c*x*atan(a*x) + (1/3)*c*x*(1 + a^2*x^2)*atan(a*x) - (c*log(1 + a^2*x^2))/(3*a)]
    @test_int [((c + a^2*c*x^2)*atan(a*x))/x^1, x, 7, -(a*c*x)/2 + (c*atan(a*x))/2 + (a^2*c*x^2*atan(a*x))/2 + (im/2)*c*PolyLog(2, (-im)*a*x) - (im/2)*c*PolyLog(2, im*a*x)]
    @test_int [((c + a^2*c*x^2)*atan(a*x))/x^2, x, 8, -((c*atan(a*x))/x) + a^2*c*x*atan(a*x) + a*c*log(x) - a*c*log(1 + a^2*x^2)]
    @test_int [((c + a^2*c*x^2)*atan(a*x))/x^3, x, 7, -(a*c)/(2*x) - (a^2*c*atan(a*x))/2 - (c*atan(a*x))/(2*x^2) + (im/2)*a^2*c*PolyLog(2, (-im)*a*x) - (im/2)*a^2*c*PolyLog(2, im*a*x)]
    @test_int [((c + a^2*c*x^2)*atan(a*x))/x^4, x, 10, -((a*c)/(6*x^2)) - (c*atan(a*x))/(3*x^3) - (a^2*c*atan(a*x))/x + (2/3)*a^3*c*log(x) - (1/3)*a^3*c*log(1 + a^2*x^2)]

    @test_int [x^3*(c + a^2*c*x^2)^2*atan(a*x), x, 14, (c^2*x)/(24*a^3) - (c^2*x^3)/(72*a) - (a*c^2*x^5)/24 - (a^3*c^2*x^7)/56 - (c^2*atan(a*x))/(24*a^4) + (c^2*x^4*atan(a*x))/4 + (a^2*c^2*x^6*atan(a*x))/3 + (a^4*c^2*x^8*atan(a*x))/8]
    @test_int [x^2*(c + a^2*c*x^2)^2*atan(a*x), x, 14, (-4*c^2*x^2)/(105*a) - (9*a*c^2*x^4)/140 - (a^3*c^2*x^6)/42 + (c^2*x^3*atan(a*x))/3 + (2*a^2*c^2*x^5*atan(a*x))/5 + (a^4*c^2*x^7*atan(a*x))/7 + (4*c^2*log(1 + a^2*x^2))/(105*a^3)]
    @test_int [x*(c + a^2*c*x^2)^2*atan(a*x), x, 3, -(c^2*x)/(6*a) - (a*c^2*x^3)/9 - (a^3*c^2*x^5)/30 + (c^2*(1 + a^2*x^2)^3*atan(a*x))/(6*a^2)]
    @test_int [(c + a^2*c*x^2)^2*atan(a*x), x, 4, (-2*c^2*(1 + a^2*x^2))/(15*a) - (c^2*(1 + a^2*x^2)^2)/(20*a) + (8*c^2*x*atan(a*x))/15 + (4*c^2*x*(1 + a^2*x^2)*atan(a*x))/15 + (c^2*x*(1 + a^2*x^2)^2*atan(a*x))/5 - (4*c^2*log(1 + a^2*x^2))/(15*a)]
    @test_int [((c + a^2*c*x^2)^2*atan(a*x))/x, x, 12, (-3*a*c^2*x)/4 - (a^3*c^2*x^3)/12 + (3*c^2*atan(a*x))/4 + a^2*c^2*x^2*atan(a*x) + (a^4*c^2*x^4*atan(a*x))/4 + (im/2)*c^2*PolyLog(2, (-im)*a*x) - (im/2)*c^2*PolyLog(2, im*a*x)]
    @test_int [((c + a^2*c*x^2)^2*atan(a*x))/x^2, x, 13, (-(1/6))*a^3*c^2*x^2 - (c^2*atan(a*x))/x + 2*a^2*c^2*x*atan(a*x) + (1/3)*a^4*c^2*x^3*atan(a*x) + a*c^2*log(x) - (4/3)*a*c^2*log(1 + a^2*x^2)]
    @test_int [((c + a^2*c*x^2)^2*atan(a*x))/x^3, x, 11, -(a*c^2)/(2*x) - (a^3*c^2*x)/2 - (c^2*atan(a*x))/(2*x^2) + (a^4*c^2*x^2*atan(a*x))/2 + im*a^2*c^2*PolyLog(2, (-im)*a*x) - im*a^2*c^2*PolyLog(2, im*a*x)]
    @test_int [((c + a^2*c*x^2)^2*atan(a*x))/x^4, x, 13, -((a*c^2)/(6*x^2)) - (c^2*atan(a*x))/(3*x^3) - (2*a^2*c^2*atan(a*x))/x + a^4*c^2*x*atan(a*x) + (5/3)*a^3*c^2*log(x) - (4/3)*a^3*c^2*log(1 + a^2*x^2)]

    @test_int [x^3*(c + a^2*c*x^2)^3*atan(a*x), x, 18, (c^3*x)/(40*a^3) - (c^3*x^3)/(120*a) - (9*a*c^3*x^5)/200 - (11*a^3*c^3*x^7)/280 - (a^5*c^3*x^9)/90 - (c^3*atan(a*x))/(40*a^4) + (c^3*x^4*atan(a*x))/4 + (a^2*c^3*x^6*atan(a*x))/2 + (3*a^4*c^3*x^8*atan(a*x))/8 + (a^6*c^3*x^10*atan(a*x))/10]
    @test_int [x^2*(c + a^2*c*x^2)^3*atan(a*x), x, 18, (-8*c^3*x^2)/(315*a) - (89*a*c^3*x^4)/1260 - (10*a^3*c^3*x^6)/189 - (a^5*c^3*x^8)/72 + (c^3*x^3*atan(a*x))/3 + (3*a^2*c^3*x^5*atan(a*x))/5 + (3*a^4*c^3*x^7*atan(a*x))/7 + (a^6*c^3*x^9*atan(a*x))/9 + (8*c^3*log(1 + a^2*x^2))/(315*a^3)]
    @test_int [x*(c + a^2*c*x^2)^3*atan(a*x), x, 3, -(c^3*x)/(8*a) - (a*c^3*x^3)/8 - (3*a^3*c^3*x^5)/40 - (a^5*c^3*x^7)/56 + (c^3*(1 + a^2*x^2)^4*atan(a*x))/(8*a^2)]
    @test_int [(c + a^2*c*x^2)^3*atan(a*x), x, 5, (-4*c^3*(1 + a^2*x^2))/(35*a) - (3*c^3*(1 + a^2*x^2)^2)/(70*a) - (c^3*(1 + a^2*x^2)^3)/(42*a) + (16*c^3*x*atan(a*x))/35 + (8*c^3*x*(1 + a^2*x^2)*atan(a*x))/35 + (6*c^3*x*(1 + a^2*x^2)^2*atan(a*x))/35 + (c^3*x*(1 + a^2*x^2)^3*atan(a*x))/7 - (8*c^3*log(1 + a^2*x^2))/(35*a)]
    @test_int [((c + a^2*c*x^2)^3*atan(a*x))/x, x, 16, (-11*a*c^3*x)/12 - (7*a^3*c^3*x^3)/36 - (a^5*c^3*x^5)/30 + (11*c^3*atan(a*x))/12 + (3*a^2*c^3*x^2*atan(a*x))/2 + (3*a^4*c^3*x^4*atan(a*x))/4 + (a^6*c^3*x^6*atan(a*x))/6 + (im/2)*c^3*PolyLog(2, (-im)*a*x) - (im/2)*c^3*PolyLog(2, im*a*x)]
    @test_int [((c + a^2*c*x^2)^3*atan(a*x))/x^2, x, 17, (-(2/5))*a^3*c^3*x^2 - (1/20)*a^5*c^3*x^4 - (c^3*atan(a*x))/x + 3*a^2*c^3*x*atan(a*x) + a^4*c^3*x^3*atan(a*x) + (1/5)*a^6*c^3*x^5*atan(a*x) + a*c^3*log(x) - (8/5)*a*c^3*log(1 + a^2*x^2)]
    @test_int [((c + a^2*c*x^2)^3*atan(a*x))/x^3, x, 15, -(a*c^3)/(2*x) - (5*a^3*c^3*x)/4 - (a^5*c^3*x^3)/12 + (3*a^2*c^3*atan(a*x))/4 - (c^3*atan(a*x))/(2*x^2) + (3*a^4*c^3*x^2*atan(a*x))/2 + (a^6*c^3*x^4*atan(a*x))/4 + ((3*im)/2)*a^2*c^3*PolyLog(2, (-im)*a*x) - ((3*im)/2)*a^2*c^3*PolyLog(2, im*a*x)]
    @test_int [((c + a^2*c*x^2)^3*atan(a*x))/x^4, x, 17, -((a*c^3)/(6*x^2)) - (1/6)*a^5*c^3*x^2 - (c^3*atan(a*x))/(3*x^3) - (3*a^2*c^3*atan(a*x))/x + 3*a^4*c^3*x*atan(a*x) + (1/3)*a^6*c^3*x^3*atan(a*x) + (8/3)*a^3*c^3*log(x) - (8/3)*a^3*c^3*log(1 + a^2*x^2)]

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

    @test_int [x^4*atan(a*x)/(c + a^2*c*x^2), x, 9, -(x^2/(6*a^3*c)) - (x*atan(a*x))/(a^4*c) + (x^3*atan(a*x))/(3*a^2*c) + atan(a*x)^2/(2*a^5*c) + (2*log(1 + a^2*x^2))/(3*a^5*c)]
    @test_int [x^3*atan(a*x)/(c + a^2*c*x^2), x, 8, -x/(2*a^3*c) + atan(a*x)/(2*a^4*c) + (x^2*atan(a*x))/(2*a^2*c) + ((im/2)*atan(a*x)^2)/(a^4*c) + (atan(a*x)*log(2/(1 + im*a*x)))/(a^4*c) + ((im/2)*PolyLog(2, 1 - 2/(1 + im*a*x)))/(a^4*c)]
    @test_int [x^2*atan(a*x)/(c + a^2*c*x^2), x, 4, (x*atan(a*x))/(a^2*c) - atan(a*x)^2/(2*a^3*c) - log(1 + a^2*x^2)/(2*a^3*c)]
    @test_int [x*atan(a*x)/(c + a^2*c*x^2), x, 4, ((-im/2)*atan(a*x)^2)/(a^2*c) - (atan(a*x)*log(2/(1 + im*a*x)))/(a^2*c) - ((im/2)*PolyLog(2, 1 - 2/(1 + im*a*x)))/(a^2*c)]
    @test_int [atan(a*x)/(c + a^2*c*x^2), x, 1, atan(a*x)^2/(2*a*c)]
    @test_int [atan(a*x)/(x*(c + a^2*c*x^2)), x, 3, ((-im/2)*atan(a*x)^2)/c + (atan(a*x)*log(2 - 2/(1 - im*a*x)))/c - ((im/2)*PolyLog(2, -1 + 2/(1 - im*a*x)))/c]
    @test_int [atan(a*x)/(x^2*(c + a^2*c*x^2)), x, 7, -(atan(a*x)/(c*x)) - (a*atan(a*x)^2)/(2*c) + (a*log(x))/c - (a*log(1 + a^2*x^2))/(2*c)]
    @test_int [atan(a*x)/(x^3*(c + a^2*c*x^2)), x, 7, -a/(2*c*x) - (a^2*atan(a*x))/(2*c) - atan(a*x)/(2*c*x^2) + ((im/2)*a^2*atan(a*x)^2)/c - (a^2*atan(a*x)*log(2 - 2/(1 - im*a*x)))/c + ((im/2)*a^2*PolyLog(2, -1 + 2/(1 - im*a*x)))/c]
    @test_int [atan(a*x)/(x^4*(c + a^2*c*x^2)), x, 12, -(a/(6*c*x^2)) - atan(a*x)/(3*c*x^3) + (a^2*atan(a*x))/(c*x) + (a^3*atan(a*x)^2)/(2*c) - (4*a^3*log(x))/(3*c) + (2*a^3*log(1 + a^2*x^2))/(3*c)]

    @test_int [x^5*atan(a*x)/(c + a^2*c*x^2)^2, x, 17, -(x/(2*a^5*c^2)) + x/(4*a^5*c^2*(1 + a^2*x^2)) + (3*atan(a*x))/(4*a^6*c^2) + (x^2*atan(a*x))/(2*a^4*c^2) - atan(a*x)/(2*a^6*c^2*(1 + a^2*x^2)) + (im*atan(a*x)^2)/(a^6*c^2) + (2*atan(a*x)*log(2/(1 + im*a*x)))/(a^6*c^2) + (im*PolyLog(2, 1 - 2/(1 + im*a*x)))/(a^6*c^2)]
    @test_int [x^4*atan(a*x)/(c + a^2*c*x^2)^2, x, 7, 1/(4*a^5*c^2*(1 + a^2*x^2)) + (x*atan(a*x))/(a^4*c^2) + (x*atan(a*x))/(2*a^4*c^2*(1 + a^2*x^2)) - (3*atan(a*x)^2)/(4*a^5*c^2) - log(1 + a^2*x^2)/(2*a^5*c^2)]
    @test_int [x^3*atan(a*x)/(c + a^2*c*x^2)^2, x, 8, -x/(4*a^3*c^2*(1 + a^2*x^2)) - atan(a*x)/(4*a^4*c^2) + atan(a*x)/(2*a^4*c^2*(1 + a^2*x^2)) - ((im/2)*atan(a*x)^2)/(a^4*c^2) - (atan(a*x)*log(2/(1 + im*a*x)))/(a^4*c^2) - ((im/2)*PolyLog(2, 1 - 2/(1 + im*a*x)))/(a^4*c^2)]
    @test_int [x^2*atan(a*x)/(c + a^2*c*x^2)^2, x, 2, -(1/(4*a^3*c^2*(1 + a^2*x^2))) - (x*atan(a*x))/(2*a^2*c^2*(1 + a^2*x^2)) + atan(a*x)^2/(4*a^3*c^2)]
    @test_int [x*atan(a*x)/(c + a^2*c*x^2)^2, x, 3, x/(4*a*c^2*(1 + a^2*x^2)) + atan(a*x)/(4*a^2*c^2) - atan(a*x)/(2*a^2*c^2*(1 + a^2*x^2))]
    @test_int [atan(a*x)/(c + a^2*c*x^2)^2, x, 2, 1/(4*a*c^2*(1 + a^2*x^2)) + (x*atan(a*x))/(2*c^2*(1 + a^2*x^2)) + atan(a*x)^2/(4*a*c^2)]
    @test_int [atan(a*x)/(x*(c + a^2*c*x^2)^2), x, 7, -(a*x)/(4*c^2*(1 + a^2*x^2)) - atan(a*x)/(4*c^2) + atan(a*x)/(2*c^2*(1 + a^2*x^2)) - ((im/2)*atan(a*x)^2)/c^2 + (atan(a*x)*log(2 - 2/(1 - im*a*x)))/c^2 - ((im/2)*PolyLog(2, -1 + 2/(1 - im*a*x)))/c^2]
    @test_int [atan(a*x)/(x^2*(c + a^2*c*x^2)^2), x, 10, -(a/(4*c^2*(1 + a^2*x^2))) - atan(a*x)/(c^2*x) - (a^2*x*atan(a*x))/(2*c^2*(1 + a^2*x^2)) - (3*a*atan(a*x)^2)/(4*c^2) + (a*log(x))/c^2 - (a*log(1 + a^2*x^2))/(2*c^2)]
    @test_int [atan(a*x)/(x^3*(c + a^2*c*x^2)^2), x, 15, -a/(2*c^2*x) + (a^3*x)/(4*c^2*(1 + a^2*x^2)) - (a^2*atan(a*x))/(4*c^2) - atan(a*x)/(2*c^2*x^2) - (a^2*atan(a*x))/(2*c^2*(1 + a^2*x^2)) + (im*a^2*atan(a*x)^2)/c^2 - (2*a^2*atan(a*x)*log(2 - 2/(1 - im*a*x)))/c^2 + (im*a^2*PolyLog(2, -1 + 2/(1 - im*a*x)))/c^2]
    @test_int [atan(a*x)/(x^4*(c + a^2*c*x^2)^2), x, 23, -(a/(6*c^2*x^2)) + a^3/(4*c^2*(1 + a^2*x^2)) - atan(a*x)/(3*c^2*x^3) + (2*a^2*atan(a*x))/(c^2*x) + (a^4*x*atan(a*x))/(2*c^2*(1 + a^2*x^2)) + (5*a^3*atan(a*x)^2)/(4*c^2) - (7*a^3*log(x))/(3*c^2) + (7*a^3*log(1 + a^2*x^2))/(6*c^2)]

    @test_int [(x^3*atan(a*x))/(c + a^2*c*x^2)^3, x, 4, x^3/(16*a*c^3*(1 + a^2*x^2)^2) + (3*x)/(32*a^3*c^3*(1 + a^2*x^2)) - (3*atan(a*x))/(32*a^4*c^3) + (x^4*atan(a*x))/(4*c^3*(1 + a^2*x^2)^2)]
    @test_int [(x^2*atan(a*x))/(c + a^2*c*x^2)^3, x, 3, -1/(16*a^3*c^3*(1 + a^2*x^2)^2) + 1/(16*a^3*c^3*(1 + a^2*x^2)) - (x*atan(a*x))/(4*a^2*c^3*(1 + a^2*x^2)^2) + (x*atan(a*x))/(8*a^2*c^3*(1 + a^2*x^2)) + atan(a*x)^2/(16*a^3*c^3)]
    @test_int [(x*atan(a*x))/(c + a^2*c*x^2)^3, x, 4, x/(16*a*c^3*(1 + a^2*x^2)^2) + (3*x)/(32*a*c^3*(1 + a^2*x^2)) + (3*atan(a*x))/(32*a^2*c^3) - atan(a*x)/(4*a^2*c^3*(1 + a^2*x^2)^2)]
    @test_int [atan(a*x)/(c + a^2*c*x^2)^3, x, 3, 1/(16*a*c^3*(1 + a^2*x^2)^2) + 3/(16*a*c^3*(1 + a^2*x^2)) + (x*atan(a*x))/(4*c^3*(1 + a^2*x^2)^2) + (3*x*atan(a*x))/(8*c^3*(1 + a^2*x^2)) + (3*atan(a*x)^2)/(16*a*c^3)]
    @test_int [atan(a*x)/(x*(c + a^2*c*x^2)^3), x, 12, -(a*x)/(16*c^3*(1 + a^2*x^2)^2) - (11*a*x)/(32*c^3*(1 + a^2*x^2)) - (11*atan(a*x))/(32*c^3) + atan(a*x)/(4*c^3*(1 + a^2*x^2)^2) + atan(a*x)/(2*c^3*(1 + a^2*x^2)) - ((im/2)*atan(a*x)^2)/c^3 + (atan(a*x)*log(2 - 2/(1 - im*a*x)))/c^3 - ((im/2)*PolyLog(2, -1 + 2/(1 - im*a*x)))/c^3]
    @test_int [atan(a*x)/(x^2*(c + a^2*c*x^2)^3), x, 14, -(a/(16*c^3*(1 + a^2*x^2)^2)) - (7*a)/(16*c^3*(1 + a^2*x^2)) - atan(a*x)/(c^3*x) - (a^2*x*atan(a*x))/(4*c^3*(1 + a^2*x^2)^2) - (7*a^2*x*atan(a*x))/(8*c^3*(1 + a^2*x^2)) - (15*a*atan(a*x)^2)/(16*c^3) + (a*log(x))/c^3 - (a*log(1 + a^2*x^2))/(2*c^3)]
    @test_int [atan(a*x)/(x^3*(c + a^2*c*x^2)^3), x, 28, -a/(2*c^3*x) + (a^3*x)/(16*c^3*(1 + a^2*x^2)^2) + (19*a^3*x)/(32*c^3*(1 + a^2*x^2)) + (3*a^2*atan(a*x))/(32*c^3) - atan(a*x)/(2*c^3*x^2) - (a^2*atan(a*x))/(4*c^3*(1 + a^2*x^2)^2) - (a^2*atan(a*x))/(c^3*(1 + a^2*x^2)) + (((3*im)/2)*a^2*atan(a*x)^2)/c^3 - (3*a^2*atan(a*x)*log(2 - 2/(1 - im*a*x)))/c^3 + (((3*im)/2)*a^2*PolyLog(2, -1 + 2/(1 - im*a*x)))/c^3]
    @test_int [atan(a*x)/(x^4*(c + a^2*c*x^2)^3), x, 38, -(a/(6*c^3*x^2)) + a^3/(16*c^3*(1 + a^2*x^2)^2) + (11*a^3)/(16*c^3*(1 + a^2*x^2)) - atan(a*x)/(3*c^3*x^3) + (3*a^2*atan(a*x))/(c^3*x) + (a^4*x*atan(a*x))/(4*c^3*(1 + a^2*x^2)^2) + (11*a^4*x*atan(a*x))/(8*c^3*(1 + a^2*x^2)) + (35*a^3*atan(a*x)^2)/(16*c^3) - (10*a^3*log(x))/(3*c^3) + (5*a^3*log(1 + a^2*x^2))/(3*c^3)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x^2)^(p/2)*atan(a*x)^1*with*d=a^2*c=#

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

    @test_int [x^3*sqrt(c + a^2*c*x^2)*atan(a*x), x, 12, (x*sqrt(c + a^2*c*x^2))/(24*a^3) - (x^3*sqrt(c + a^2*c*x^2))/(20*a) - (2*sqrt(c + a^2*c*x^2)*atan(a*x))/(15*a^4) + (x^2*sqrt(c + a^2*c*x^2)*atan(a*x))/(15*a^2) + (x^4*sqrt(c + a^2*c*x^2)*atan(a*x))/5 + (11*sqrt(c)*atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2)))/(120*a^4)]
    @test_int [x^2*sqrt(c + a^2*c*x^2)*atan(a*x), x, 8, sqrt(c + a^2*c*x^2)/(8*a^3) - (c + a^2*c*x^2)^(3/2)/(12*a^3*c) + (x*sqrt(c + a^2*c*x^2)*atan(a*x))/(8*a^2) + (1/4)*x^3*sqrt(c + a^2*c*x^2)*atan(a*x) + (im*c*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(4*a^3*sqrt(c + a^2*c*x^2)) - (im*c*sqrt(1 + a^2*x^2)*PolyLog(2, -((im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x))))/(8*a^3*sqrt(c + a^2*c*x^2)) + (im*c*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(8*a^3*sqrt(c + a^2*c*x^2))]
    @test_int [x*sqrt(c + a^2*c*x^2)*atan(a*x), x, 4, -(x*sqrt(c + a^2*c*x^2))/(6*a) + ((c + a^2*c*x^2)^(3/2)*atan(a*x))/(3*a^2*c) - (sqrt(c)*atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2)))/(6*a^2)]
    @test_int [sqrt(c + a^2*c*x^2)*atan(a*x), x, 3, -sqrt(c + a^2*c*x^2)/(2*a) + (x*sqrt(c + a^2*c*x^2)*atan(a*x))/2 - (im*c*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(a*sqrt(c + a^2*c*x^2)) + ((im/2)*c*sqrt(1 + a^2*x^2)*PolyLog(2, ((-im)*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(a*sqrt(c + a^2*c*x^2)) - ((im/2)*c*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(a*sqrt(c + a^2*c*x^2))]
    @test_int [(sqrt(c + a^2*c*x^2)*atan(a*x))/x, x, 5, sqrt(c + a^2*c*x^2)*atan(a*x) - (2*c*sqrt(1 + a^2*x^2)*atan(a*x)*atanh(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - sqrt(c)*atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2)) + (im*c*sqrt(1 + a^2*x^2)*PolyLog(2, -(sqrt(1 + im*a*x)/sqrt(1 - im*a*x))))/sqrt(c + a^2*c*x^2) - (im*c*sqrt(1 + a^2*x^2)*PolyLog(2, sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2)]
    @test_int [(sqrt(c + a^2*c*x^2)*atan(a*x))/x^2, x, 7, -((sqrt(c + a^2*c*x^2)*atan(a*x))/x) - ((2*im)*a*c*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - a*sqrt(c)*atanh(sqrt(c + a^2*c*x^2)/sqrt(c)) + (im*a*c*sqrt(1 + a^2*x^2)*PolyLog(2, ((-im)*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (im*a*c*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2)]
    @test_int [(sqrt(c + a^2*c*x^2)*atan(a*x))/x^3, x, 6, -(a*sqrt(c + a^2*c*x^2))/(2*x) - (sqrt(c + a^2*c*x^2)*atan(a*x))/(2*x^2) - (a^2*c*sqrt(1 + a^2*x^2)*atan(a*x)*atanh(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) + ((im/2)*a^2*c*sqrt(1 + a^2*x^2)*PolyLog(2, -(sqrt(1 + im*a*x)/sqrt(1 - im*a*x))))/sqrt(c + a^2*c*x^2) - ((im/2)*a^2*c*sqrt(1 + a^2*x^2)*PolyLog(2, sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2)]
    @test_int [(sqrt(c + a^2*c*x^2)*atan(a*x))/x^4, x, 5, -(a*sqrt(c + a^2*c*x^2))/(6*x^2) - ((c + a^2*c*x^2)^(3/2)*atan(a*x))/(3*c*x^3) - (a^3*sqrt(c)*atanh(sqrt(c + a^2*c*x^2)/sqrt(c)))/6]

    @test_int [x^3*(c + a^2*c*x^2)^(3/2)*atan(a*x), x, 31, (3*c*x*sqrt(c + a^2*c*x^2))/(112*a^3) - (23*c*x^3*sqrt(c + a^2*c*x^2))/(840*a) - (a*c*x^5*sqrt(c + a^2*c*x^2))/42 - (2*c*sqrt(c + a^2*c*x^2)*atan(a*x))/(35*a^4) + (c*x^2*sqrt(c + a^2*c*x^2)*atan(a*x))/(35*a^2) + (8*c*x^4*sqrt(c + a^2*c*x^2)*atan(a*x))/35 + (a^2*c*x^6*sqrt(c + a^2*c*x^2)*atan(a*x))/7 + (17*c^(3/2)*atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2)))/(560*a^4)]
    @test_int [x^2*(c + a^2*c*x^2)^(3/2)*atan(a*x), x, 21, (c*sqrt(c + a^2*c*x^2))/(16*a^3) + (c + a^2*c*x^2)^(3/2)/(72*a^3) - (c + a^2*c*x^2)^(5/2)/(30*a^3*c) + (c*x*sqrt(c + a^2*c*x^2)*atan(a*x))/(16*a^2) + (7/24)*c*x^3*sqrt(c + a^2*c*x^2)*atan(a*x) + (1/6)*a^2*c*x^5*sqrt(c + a^2*c*x^2)*atan(a*x) + (im*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(8*a^3*sqrt(c + a^2*c*x^2)) - (im*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, -((im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x))))/(16*a^3*sqrt(c + a^2*c*x^2)) + (im*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(16*a^3*sqrt(c + a^2*c*x^2))]
    @test_int [x*(c + a^2*c*x^2)^(3/2)*atan(a*x), x, 5, (-3*c*x*sqrt(c + a^2*c*x^2))/(40*a) - (x*(c + a^2*c*x^2)^(3/2))/(20*a) + ((c + a^2*c*x^2)^(5/2)*atan(a*x))/(5*a^2*c) - (3*c^(3/2)*atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2)))/(40*a^2)]
    @test_int [(c + a^2*c*x^2)^(3/2)*atan(a*x), x, 4, (-3*c*sqrt(c + a^2*c*x^2))/(8*a) - (c + a^2*c*x^2)^(3/2)/(12*a) + (3*c*x*sqrt(c + a^2*c*x^2)*atan(a*x))/8 + (x*(c + a^2*c*x^2)^(3/2)*atan(a*x))/4 - (((3*im)/4)*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(a*sqrt(c + a^2*c*x^2)) + (((3*im)/8)*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, ((-im)*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(a*sqrt(c + a^2*c*x^2)) - (((3*im)/8)*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(a*sqrt(c + a^2*c*x^2))]
    @test_int [((c + a^2*c*x^2)^(3/2)*atan(a*x))/x, x, 10, -(a*c*x*sqrt(c + a^2*c*x^2))/6 + c*sqrt(c + a^2*c*x^2)*atan(a*x) + ((c + a^2*c*x^2)^(3/2)*atan(a*x))/3 - (2*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*atanh(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (7*c^(3/2)*atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2)))/6 + (im*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, -(sqrt(1 + im*a*x)/sqrt(1 - im*a*x))))/sqrt(c + a^2*c*x^2) - (im*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2)]
    @test_int [((c + a^2*c*x^2)^(3/2)*atan(a*x))/x^2, x, 11, -(a*c*sqrt(c + a^2*c*x^2))/2 - (c*sqrt(c + a^2*c*x^2)*atan(a*x))/x + (a^2*c*x*sqrt(c + a^2*c*x^2)*atan(a*x))/2 - ((3*im)*a*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - a*c^(3/2)*atanh(sqrt(c + a^2*c*x^2)/sqrt(c)) + (((3*im)/2)*a*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, ((-im)*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (((3*im)/2)*a*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2)]
    @test_int [((c + a^2*c*x^2)^(3/2)*atan(a*x))/x^3, x, 12, -(a*c*sqrt(c + a^2*c*x^2))/(2*x) + a^2*c*sqrt(c + a^2*c*x^2)*atan(a*x) - (c*sqrt(c + a^2*c*x^2)*atan(a*x))/(2*x^2) - (3*a^2*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*atanh(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - a^2*c^(3/2)*atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2)) + (((3*im)/2)*a^2*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, -(sqrt(1 + im*a*x)/sqrt(1 - im*a*x))))/sqrt(c + a^2*c*x^2) - (((3*im)/2)*a^2*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2)]
    @test_int [((c + a^2*c*x^2)^(3/2)*atan(a*x))/x^4, x, 13, -(a*c*sqrt(c + a^2*c*x^2))/(6*x^2) - (a^2*c*sqrt(c + a^2*c*x^2)*atan(a*x))/x - ((c + a^2*c*x^2)^(3/2)*atan(a*x))/(3*x^3) - ((2*im)*a^3*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (7*a^3*c^(3/2)*atanh(sqrt(c + a^2*c*x^2)/sqrt(c)))/6 + (im*a^3*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, ((-im)*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (im*a^3*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2)]

    @test_int [x^3*(c + a^2*c*x^2)^(5/2)*atan(a*x), x, 76, (47*c^2*x*sqrt(c + a^2*c*x^2))/(2688*a^3) - (205*c^2*x^3*sqrt(c + a^2*c*x^2))/(12096*a) - (103*a*c^2*x^5*sqrt(c + a^2*c*x^2))/3024 - (a^3*c^2*x^7*sqrt(c + a^2*c*x^2))/72 - (2*c^2*sqrt(c + a^2*c*x^2)*atan(a*x))/(63*a^4) + (c^2*x^2*sqrt(c + a^2*c*x^2)*atan(a*x))/(63*a^2) + (5*c^2*x^4*sqrt(c + a^2*c*x^2)*atan(a*x))/21 + (19*a^2*c^2*x^6*sqrt(c + a^2*c*x^2)*atan(a*x))/63 + (a^4*c^2*x^8*sqrt(c + a^2*c*x^2)*atan(a*x))/9 + (115*c^(5/2)*atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2)))/(8064*a^4)]
    @test_int [x^2*(c + a^2*c*x^2)^(5/2)*atan(a*x), x, 51, (5*c^2*sqrt(c + a^2*c*x^2))/(128*a^3) + (5*c*(c + a^2*c*x^2)^(3/2))/(576*a^3) + (c + a^2*c*x^2)^(5/2)/(240*a^3) - (c + a^2*c*x^2)^(7/2)/(56*a^3*c) + (5*c^2*x*sqrt(c + a^2*c*x^2)*atan(a*x))/(128*a^2) + (59/192)*c^2*x^3*sqrt(c + a^2*c*x^2)*atan(a*x) + (17/48)*a^2*c^2*x^5*sqrt(c + a^2*c*x^2)*atan(a*x) + (1/8)*a^4*c^2*x^7*sqrt(c + a^2*c*x^2)*atan(a*x) + (5*im*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(64*a^3*sqrt(c + a^2*c*x^2)) - (5*im*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, -((im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x))))/(128*a^3*sqrt(c + a^2*c*x^2)) + (5*im*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(128*a^3*sqrt(c + a^2*c*x^2))]
    @test_int [x*(c + a^2*c*x^2)^(5/2)*atan(a*x), x, 6, (-5*c^2*x*sqrt(c + a^2*c*x^2))/(112*a) - (5*c*x*(c + a^2*c*x^2)^(3/2))/(168*a) - (x*(c + a^2*c*x^2)^(5/2))/(42*a) + ((c + a^2*c*x^2)^(7/2)*atan(a*x))/(7*a^2*c) - (5*c^(5/2)*atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2)))/(112*a^2)]
    @test_int [(c + a^2*c*x^2)^(5/2)*atan(a*x), x, 5, (-5*c^2*sqrt(c + a^2*c*x^2))/(16*a) - (5*c*(c + a^2*c*x^2)^(3/2))/(72*a) - (c + a^2*c*x^2)^(5/2)/(30*a) + (5*c^2*x*sqrt(c + a^2*c*x^2)*atan(a*x))/16 + (5*c*x*(c + a^2*c*x^2)^(3/2)*atan(a*x))/24 + (x*(c + a^2*c*x^2)^(5/2)*atan(a*x))/6 - (((5*im)/8)*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(a*sqrt(c + a^2*c*x^2)) + (((5*im)/16)*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, ((-im)*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(a*sqrt(c + a^2*c*x^2)) - (((5*im)/16)*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(a*sqrt(c + a^2*c*x^2))]
    @test_int [((c + a^2*c*x^2)^(5/2)*atan(a*x))/x, x, 16, (-29*a*c^2*x*sqrt(c + a^2*c*x^2))/120 - (a*c*x*(c + a^2*c*x^2)^(3/2))/20 + c^2*sqrt(c + a^2*c*x^2)*atan(a*x) + (c*(c + a^2*c*x^2)^(3/2)*atan(a*x))/3 + ((c + a^2*c*x^2)^(5/2)*atan(a*x))/5 - (2*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*atanh(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (149*c^(5/2)*atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2)))/120 + (im*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, -(sqrt(1 + im*a*x)/sqrt(1 - im*a*x))))/sqrt(c + a^2*c*x^2) - (im*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2)]
    @test_int [((c + a^2*c*x^2)^(5/2)*atan(a*x))/x^2, x, 16, (-7*a*c^2*sqrt(c + a^2*c*x^2))/8 - (a*c*(c + a^2*c*x^2)^(3/2))/12 - (c^2*sqrt(c + a^2*c*x^2)*atan(a*x))/x + (7*a^2*c^2*x*sqrt(c + a^2*c*x^2)*atan(a*x))/8 + (a^2*c*x*(c + a^2*c*x^2)^(3/2)*atan(a*x))/4 - (((15*im)/4)*a*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - a*c^(5/2)*atanh(sqrt(c + a^2*c*x^2)/sqrt(c)) + (((15*im)/8)*a*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, ((-im)*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (((15*im)/8)*a*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2)]
    @test_int [((c + a^2*c*x^2)^(5/2)*atan(a*x))/x^3, x, 23, -(a*c^2*sqrt(c + a^2*c*x^2))/(2*x) - (a^3*c^2*x*sqrt(c + a^2*c*x^2))/6 + 2*a^2*c^2*sqrt(c + a^2*c*x^2)*atan(a*x) - (c^2*sqrt(c + a^2*c*x^2)*atan(a*x))/(2*x^2) + (a^2*c*(c + a^2*c*x^2)^(3/2)*atan(a*x))/3 - (5*a^2*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*atanh(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (13*a^2*c^(5/2)*atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2)))/6 + (((5*im)/2)*a^2*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, -(sqrt(1 + im*a*x)/sqrt(1 - im*a*x))))/sqrt(c + a^2*c*x^2) - (((5*im)/2)*a^2*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2)]
    @test_int [((c + a^2*c*x^2)^(5/2)*atan(a*x))/x^4, x, 25, -(a^3*c^2*sqrt(c + a^2*c*x^2))/2 - (a*c^2*sqrt(c + a^2*c*x^2))/(6*x^2) - (2*a^2*c^2*sqrt(c + a^2*c*x^2)*atan(a*x))/x + (a^4*c^2*x*sqrt(c + a^2*c*x^2)*atan(a*x))/2 - (c*(c + a^2*c*x^2)^(3/2)*atan(a*x))/(3*x^3) - ((5*im)*a^3*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (13*a^3*c^(5/2)*atanh(sqrt(c + a^2*c*x^2)/sqrt(c)))/6 + (((5*im)/2)*a^3*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, ((-im)*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (((5*im)/2)*a^3*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2)]

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

    @test_int [(x^3*atan(a*x))/sqrt(c + a^2*c*x^2), x, 7, -(x*sqrt(c + a^2*c*x^2))/(6*a^3*c) - (2*sqrt(c + a^2*c*x^2)*atan(a*x))/(3*a^4*c) + (x^2*sqrt(c + a^2*c*x^2)*atan(a*x))/(3*a^2*c) + (5*atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2)))/(6*a^4*sqrt(c))]
    @test_int [(x^2*atan(a*x))/sqrt(c + a^2*c*x^2), x, 4, -(sqrt(c + a^2*c*x^2)/(2*a^3*c)) + (x*sqrt(c + a^2*c*x^2)*atan(a*x))/(2*a^2*c) + (im*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(a^3*sqrt(c + a^2*c*x^2)) - (im*sqrt(1 + a^2*x^2)*PolyLog(2, -((im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x))))/(2*a^3*sqrt(c + a^2*c*x^2)) + (im*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(2*a^3*sqrt(c + a^2*c*x^2))]
    @test_int [(x*atan(a*x))/sqrt(c + a^2*c*x^2), x, 3, (sqrt(c + a^2*c*x^2)*atan(a*x))/(a^2*c) - atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2))/(a^2*sqrt(c))]
    @test_int [atan(a*x)/sqrt(c + a^2*c*x^2), x, 2, ((-2*im)*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(a*sqrt(c + a^2*c*x^2)) + (im*sqrt(1 + a^2*x^2)*PolyLog(2, ((-im)*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(a*sqrt(c + a^2*c*x^2)) - (im*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(a*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)/(x*sqrt(c + a^2*c*x^2)), x, 2, (-2*sqrt(1 + a^2*x^2)*atan(a*x)*atanh(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) + (im*sqrt(1 + a^2*x^2)*PolyLog(2, -(sqrt(1 + im*a*x)/sqrt(1 - im*a*x))))/sqrt(c + a^2*c*x^2) - (im*sqrt(1 + a^2*x^2)*PolyLog(2, sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2)]
    @test_int [atan(a*x)/(x^2*sqrt(c + a^2*c*x^2)), x, 4, -((sqrt(c + a^2*c*x^2)*atan(a*x))/(c*x)) - (a*atanh(sqrt(c + a^2*c*x^2)/sqrt(c)))/sqrt(c)]
    @test_int [atan(a*x)/(x^3*sqrt(c + a^2*c*x^2)), x, 4, -(a*sqrt(c + a^2*c*x^2))/(2*c*x) - (sqrt(c + a^2*c*x^2)*atan(a*x))/(2*c*x^2) + (a^2*sqrt(1 + a^2*x^2)*atan(a*x)*atanh(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - ((im/2)*a^2*sqrt(1 + a^2*x^2)*PolyLog(2, -(sqrt(1 + im*a*x)/sqrt(1 - im*a*x))))/sqrt(c + a^2*c*x^2) + ((im/2)*a^2*sqrt(1 + a^2*x^2)*PolyLog(2, sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2)]
    @test_int [atan(a*x)/(x^4*sqrt(c + a^2*c*x^2)), x, 9, -(a*sqrt(c + a^2*c*x^2))/(6*c*x^2) - (sqrt(c + a^2*c*x^2)*atan(a*x))/(3*c*x^3) + (2*a^2*sqrt(c + a^2*c*x^2)*atan(a*x))/(3*c*x) + (5*a^3*atanh(sqrt(c + a^2*c*x^2)/sqrt(c)))/(6*sqrt(c))]

    @test_int [(x^3*atan(a*x))/(c + a^2*c*x^2)^(3/2), x, 6, -(x/(a^3*c*sqrt(c + a^2*c*x^2))) + atan(a*x)/(a^4*c*sqrt(c + a^2*c*x^2)) + (sqrt(c + a^2*c*x^2)*atan(a*x))/(a^4*c^2) - atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2))/(a^4*c^(3/2))]
    @test_int [(x^2*atan(a*x))/(c + a^2*c*x^2)^(3/2), x, 3, -(1/(a^3*c*sqrt(c + a^2*c*x^2))) - (x*atan(a*x))/(a^2*c*sqrt(c + a^2*c*x^2)) - ((2*im)*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(a^3*c*sqrt(c + a^2*c*x^2)) + (im*sqrt(1 + a^2*x^2)*PolyLog(2, ((-im)*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(a^3*c*sqrt(c + a^2*c*x^2)) - (im*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(a^3*c*sqrt(c + a^2*c*x^2))]
    @test_int [(x*atan(a*x))/(c + a^2*c*x^2)^(3/2), x, 2, x/(a*c*sqrt(c + a^2*c*x^2)) - atan(a*x)/(a^2*c*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)/(c + a^2*c*x^2)^(3/2), x, 1, 1/(a*c*sqrt(c + a^2*c*x^2)) + (x*atan(a*x))/(c*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)/(x*(c + a^2*c*x^2)^(3/2)), x, 5, -((a*x)/(c*sqrt(c + a^2*c*x^2))) + atan(a*x)/(c*sqrt(c + a^2*c*x^2)) - (2*sqrt(1 + a^2*x^2)*atan(a*x)*atanh(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(c*sqrt(c + a^2*c*x^2)) + (im*sqrt(1 + a^2*x^2)*PolyLog(2, -(sqrt(1 + im*a*x)/sqrt(1 - im*a*x))))/(c*sqrt(c + a^2*c*x^2)) - (im*sqrt(1 + a^2*x^2)*PolyLog(2, sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(c*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)/(x^2*(c + a^2*c*x^2)^(3/2)), x, 6, -(a/(c*sqrt(c + a^2*c*x^2))) - (a^2*x*atan(a*x))/(c*sqrt(c + a^2*c*x^2)) - (sqrt(c + a^2*c*x^2)*atan(a*x))/(c^2*x) - (a*atanh(sqrt(c + a^2*c*x^2)/sqrt(c)))/c^(3/2)]
    @test_int [atan(a*x)/(x^3*(c + a^2*c*x^2)^(3/2)), x, 10, (a^3*x)/(c*sqrt(c + a^2*c*x^2)) - (a*sqrt(c + a^2*c*x^2))/(2*c^2*x) - (a^2*atan(a*x))/(c*sqrt(c + a^2*c*x^2)) - (sqrt(c + a^2*c*x^2)*atan(a*x))/(2*c^2*x^2) + (3*a^2*sqrt(1 + a^2*x^2)*atan(a*x)*atanh(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(c*sqrt(c + a^2*c*x^2)) - (((3*im)/2)*a^2*sqrt(1 + a^2*x^2)*PolyLog(2, -(sqrt(1 + im*a*x)/sqrt(1 - im*a*x))))/(c*sqrt(c + a^2*c*x^2)) + (((3*im)/2)*a^2*sqrt(1 + a^2*x^2)*PolyLog(2, sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(c*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)/(x^4*(c + a^2*c*x^2)^(3/2)), x, 16, a^3/(c*sqrt(c + a^2*c*x^2)) - (a*sqrt(c + a^2*c*x^2))/(6*c^2*x^2) + (a^4*x*atan(a*x))/(c*sqrt(c + a^2*c*x^2)) - (sqrt(c + a^2*c*x^2)*atan(a*x))/(3*c^2*x^3) + (5*a^2*sqrt(c + a^2*c*x^2)*atan(a*x))/(3*c^2*x) + (11*a^3*atanh(sqrt(c + a^2*c*x^2)/sqrt(c)))/(6*c^(3/2))]

    @test_int [(x^5*atan(a*x))/(c + a^2*c*x^2)^(5/2), x, 10, -(x^3/(9*a^3*c*(c + a^2*c*x^2)^(3/2))) - (5*x)/(3*a^5*c^2*sqrt(c + a^2*c*x^2)) + (x^2*atan(a*x))/(3*a^4*c*(c + a^2*c*x^2)^(3/2)) + (5*atan(a*x))/(3*a^6*c^2*sqrt(c + a^2*c*x^2)) + (sqrt(c + a^2*c*x^2)*atan(a*x))/(a^6*c^3) - atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2))/(a^6*c^(5/2))]
    @test_int [(x^4*atan(a*x))/(c + a^2*c*x^2)^(5/2), x, 8, 1/(9*a^5*c*(c + a^2*c*x^2)^(3/2)) - 4/(3*a^5*c^2*sqrt(c + a^2*c*x^2)) - (x^3*atan(a*x))/(3*a^2*c*(c + a^2*c*x^2)^(3/2)) - (x*atan(a*x))/(a^4*c^2*sqrt(c + a^2*c*x^2)) - (2*im*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(a^5*c^2*sqrt(c + a^2*c*x^2)) + (im*sqrt(1 + a^2*x^2)*PolyLog(2, -((im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x))))/(a^5*c^2*sqrt(c + a^2*c*x^2)) - (im*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(a^5*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [(x^3*atan(a*x))/(c + a^2*c*x^2)^(5/2), x, 3, x^3/(9*a*c*(c + a^2*c*x^2)^(3/2)) + (2*x)/(3*a^3*c^2*sqrt(c + a^2*c*x^2)) - (x^2*atan(a*x))/(3*a^2*c*(c + a^2*c*x^2)^(3/2)) - (2*atan(a*x))/(3*a^4*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [(x^2*atan(a*x))/(c + a^2*c*x^2)^(5/2), x, 4, -(1/(9*a^3*c*(c + a^2*c*x^2)^(3/2))) + 1/(3*a^3*c^2*sqrt(c + a^2*c*x^2)) + (x^3*atan(a*x))/(3*c*(c + a^2*c*x^2)^(3/2))]
    @test_int [(x*atan(a*x))/(c + a^2*c*x^2)^(5/2), x, 3, x/(9*a*c*(c + a^2*c*x^2)^(3/2)) + (2*x)/(9*a*c^2*sqrt(c + a^2*c*x^2)) - atan(a*x)/(3*a^2*c*(c + a^2*c*x^2)^(3/2))]
    @test_int [atan(a*x)/(c + a^2*c*x^2)^(5/2), x, 2, 1/(9*a*c*(c + a^2*c*x^2)^(3/2)) + 2/(3*a*c^2*sqrt(c + a^2*c*x^2)) + (x*atan(a*x))/(3*c*(c + a^2*c*x^2)^(3/2)) + (2*x*atan(a*x))/(3*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)/(x*(c + a^2*c*x^2)^(5/2)), x, 9, -(a*x)/(9*c*(c + a^2*c*x^2)^(3/2)) - (11*a*x)/(9*c^2*sqrt(c + a^2*c*x^2)) + atan(a*x)/(3*c*(c + a^2*c*x^2)^(3/2)) + atan(a*x)/(c^2*sqrt(c + a^2*c*x^2)) - (2*sqrt(1 + a^2*x^2)*atan(a*x)*atanh(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(c^2*sqrt(c + a^2*c*x^2)) + (im*sqrt(1 + a^2*x^2)*PolyLog(2, -(sqrt(1 + im*a*x)/sqrt(1 - im*a*x))))/(c^2*sqrt(c + a^2*c*x^2)) - (im*sqrt(1 + a^2*x^2)*PolyLog(2, sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(c^2*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)/(x^2*(c + a^2*c*x^2)^(5/2)), x, 9, -a/(9*c*(c + a^2*c*x^2)^(3/2)) - (5*a)/(3*c^2*sqrt(c + a^2*c*x^2)) - (a^2*x*atan(a*x))/(3*c*(c + a^2*c*x^2)^(3/2)) - (5*a^2*x*atan(a*x))/(3*c^2*sqrt(c + a^2*c*x^2)) - (sqrt(c + a^2*c*x^2)*atan(a*x))/(c^3*x) - (a*atanh(sqrt(c + a^2*c*x^2)/sqrt(c)))/c^(5/2)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x^2)^p*atan(a*x)^1*with*d=a^2*c*and*m*symbolic=#

    @test_int [x^m*(c + a^2*c*x^2)^3*atan(a*x), x, 10, (c^3*x^(1 + m)*atan(a*x))/(1 + m) + (3*a^2*c^3*x^(3 + m)*atan(a*x))/(3 + m) + (3*a^4*c^3*x^(5 + m)*atan(a*x))/(5 + m) + (a^6*c^3*x^(7 + m)*atan(a*x))/(7 + m) - (a*c^3*x^(2 + m)*HypergeometricFunctions._₂F₁(1, (2 + m)/2, (4 + m)/2, (-a^2)*x^2))/(2 + 3*m + m^2) - (3*a^3*c^3*x^(4 + m)*HypergeometricFunctions._₂F₁(1, (4 + m)/2, (6 + m)/2, (-a^2)*x^2))/(12 + 7*m + m^2) - (3*a^5*c^3*x^(6 + m)*HypergeometricFunctions._₂F₁(1, (6 + m)/2, (8 + m)/2, (-a^2)*x^2))/((5 + m)*(6 + m)) - (a^7*c^3*x^(8 + m)*HypergeometricFunctions._₂F₁(1, (8 + m)/2, (10 + m)/2, (-a^2)*x^2))/((7 + m)*(8 + m))]
    @test_int [x^m*(c + a^2*c*x^2)^2*atan(a*x), x, 8, (c^2*x^(1 + m)*atan(a*x))/(1 + m) + (2*a^2*c^2*x^(3 + m)*atan(a*x))/(3 + m) + (a^4*c^2*x^(5 + m)*atan(a*x))/(5 + m) - (a*c^2*x^(2 + m)*HypergeometricFunctions._₂F₁(1, (2 + m)/2, (4 + m)/2, (-a^2)*x^2))/(2 + 3*m + m^2) - (2*a^3*c^2*x^(4 + m)*HypergeometricFunctions._₂F₁(1, (4 + m)/2, (6 + m)/2, (-a^2)*x^2))/(12 + 7*m + m^2) - (a^5*c^2*x^(6 + m)*HypergeometricFunctions._₂F₁(1, (6 + m)/2, (8 + m)/2, (-a^2)*x^2))/((5 + m)*(6 + m))]
    @test_int [x^m*(c + a^2*c*x^2)*atan(a*x), x, 5, (c*x^(1 + m)*atan(a*x))/(1 + m) + (a^2*c*x^(3 + m)*atan(a*x))/(3 + m) - (a*c*x^(2 + m)*HypergeometricFunctions._₂F₁(1, (2 + m)/2, (4 + m)/2, (-a^2)*x^2))/(2 + 3*m + m^2) - (a^3*c*x^(4 + m)*HypergeometricFunctions._₂F₁(1, (4 + m)/2, (6 + m)/2, (-a^2)*x^2))/(12 + 7*m + m^2)]
    @test_int [(x^m*atan(a*x))/(c + a^2*c*x^2), x, 0, Unintegrable((x^m*atan(a*x))/(c + a^2*c*x^2), x)]
    @test_int [(x^m*atan(a*x))/(c + a^2*c*x^2)^2, x, 0, Unintegrable((x^m*atan(a*x))/(c + a^2*c*x^2)^2, x)]

    @test_int [x^m*(c + a^2*c*x^2)^(5/2)*atan(a*x), x, 0, Unintegrable(x^m*(c + a^2*c*x^2)^(5/2)*atan(a*x), x)]
    @test_int [x^m*(c + a^2*c*x^2)^(3/2)*atan(a*x), x, 0, Unintegrable(x^m*(c + a^2*c*x^2)^(3/2)*atan(a*x), x)]
    @test_int [x^m*(c + a^2*c*x^2)^(1/2)*atan(a*x), x, 3, (x^(1 + m)*sqrt(c + a^2*c*x^2)*atan(a*x))/(2 + m) - (a*x^(2 + m)*sqrt(c + a^2*c*x^2)*HypergeometricFunctions._₂F₁(1, (3 + m)/2, (4 + m)/2, (-a^2)*x^2))/(2 + m)^2 + (c*Unintegrable((x^m*atan(a*x))/sqrt(c + a^2*c*x^2), x))/(2 + m), (x^(1 + m)*sqrt(c + a^2*c*x^2)*atan(a*x))/(2 + m) - (a*c*x^(2 + m)*sqrt(1 + a^2*x^2)*HypergeometricFunctions._₂F₁(1/2, (2 + m)/2, (4 + m)/2, (-a^2)*x^2))/((2 + m)^2*sqrt(c + a^2*c*x^2)) + (c*Unintegrable((x^m*atan(a*x))/sqrt(c + a^2*c*x^2), x))/(2 + m)]
    @test_int [(x^m*atan(a*x))/(c + a^2*c*x^2)^(1/2), x, 0, Unintegrable((x^m*atan(a*x))/sqrt(c + a^2*c*x^2), x)]
    @test_int [(x^m*atan(a*x))/(c + a^2*c*x^2)^(3/2), x, 0, Unintegrable((x^m*atan(a*x))/(c + a^2*c*x^2)^(3/2), x)]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d+c^2*d*x^2)^q*(a+b*atan(c*x))^2=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x^2)^p*atan(a*x)^2*with*d=a^2*c=#

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

    @test_int [x^3*(c + a^2*c*x^2)*atan(a*x)^2, x, 26, -(c*x^2)/(180*a^2) + (c*x^4)/60 + (c*x*atan(a*x))/(6*a^3) - (c*x^3*atan(a*x))/(18*a) - (a*c*x^5*atan(a*x))/15 - (c*atan(a*x)^2)/(12*a^4) + (c*x^4*atan(a*x)^2)/4 + (a^2*c*x^6*atan(a*x)^2)/6 - (7*c*log(1 + a^2*x^2))/(90*a^4)]
    @test_int [x^2*(c + a^2*c*x^2)*atan(a*x)^2, x, 24, (c*x)/(30*a^2) + (c*x^3)/30 - (c*atan(a*x))/(30*a^3) - (2*c*x^2*atan(a*x))/(15*a) - (a*c*x^4*atan(a*x))/10 - (((2*im)/15)*c*atan(a*x)^2)/a^3 + (c*x^3*atan(a*x)^2)/3 + (a^2*c*x^5*atan(a*x)^2)/5 - (4*c*atan(a*x)*log(2/(1 + im*a*x)))/(15*a^3) - (((2*im)/15)*c*PolyLog(2, 1 - 2/(1 + im*a*x)))/a^3]
    @test_int [x*(c + a^2*c*x^2)*atan(a*x)^2, x, 4, (c*(1 + a^2*x^2))/(12*a^2) - (c*x*atan(a*x))/(3*a) - (c*x*(1 + a^2*x^2)*atan(a*x))/(6*a) + (c*(1 + a^2*x^2)^2*atan(a*x)^2)/(4*a^2) + (c*log(1 + a^2*x^2))/(6*a^2)]
    @test_int [(c + a^2*c*x^2)*atan(a*x)^2, x, 7, (c*x)/3 - (c*(1 + a^2*x^2)*atan(a*x))/(3*a) + (((2*im)/3)*c*atan(a*x)^2)/a + (2*c*x*atan(a*x)^2)/3 + (c*x*(1 + a^2*x^2)*atan(a*x)^2)/3 + (4*c*atan(a*x)*log(2/(1 + im*a*x)))/(3*a) + (((2*im)/3)*c*PolyLog(2, 1 - 2/(1 + im*a*x)))/a]
    @test_int [((c + a^2*c*x^2)*atan(a*x)^2)/x, x, 12, -(a*c*x*atan(a*x)) + (c*atan(a*x)^2)/2 + (a^2*c*x^2*atan(a*x)^2)/2 + 2*c*atan(a*x)^2*atanh(1 - 2/(1 + im*a*x)) + (c*log(1 + a^2*x^2))/2 - im*c*atan(a*x)*PolyLog(2, 1 - 2/(1 + im*a*x)) + im*c*atan(a*x)*PolyLog(2, -1 + 2/(1 + im*a*x)) - (c*PolyLog(3, 1 - 2/(1 + im*a*x)))/2 + (c*PolyLog(3, -1 + 2/(1 + im*a*x)))/2]
    @test_int [((c + a^2*c*x^2)*atan(a*x)^2)/x^2, x, 10, -((c*atan(a*x)^2)/x) + a^2*c*x*atan(a*x)^2 + 2*a*c*atan(a*x)*log(2/(1 + im*a*x)) + 2*a*c*atan(a*x)*log(2 - 2/(1 - im*a*x)) - im*a*c*PolyLog(2, -1 + 2/(1 - im*a*x)) + im*a*c*PolyLog(2, 1 - 2/(1 + im*a*x))]
    @test_int [((c + a^2*c*x^2)*atan(a*x)^2)/x^3, x, 15, -((a*c*atan(a*x))/x) - (1/2)*a^2*c*atan(a*x)^2 - (c*atan(a*x)^2)/(2*x^2) + 2*a^2*c*atan(a*x)^2*atanh(1 - 2/(1 + im*a*x)) + a^2*c*log(x) - (1/2)*a^2*c*log(1 + a^2*x^2) - im*a^2*c*atan(a*x)*PolyLog(2, 1 - 2/(1 + im*a*x)) + im*a^2*c*atan(a*x)*PolyLog(2, -1 + 2/(1 + im*a*x)) - (1/2)*a^2*c*PolyLog(3, 1 - 2/(1 + im*a*x)) + (1/2)*a^2*c*PolyLog(3, -1 + 2/(1 + im*a*x))]
    @test_int [((c + a^2*c*x^2)*atan(a*x)^2)/x^4, x, 13, -(a^2*c)/(3*x) - (a^3*c*atan(a*x))/3 - (a*c*atan(a*x))/(3*x^2) - ((2*im)/3)*a^3*c*atan(a*x)^2 - (c*atan(a*x)^2)/(3*x^3) - (a^2*c*atan(a*x)^2)/x + (4*a^3*c*atan(a*x)*log(2 - 2/(1 - im*a*x)))/3 - ((2*im)/3)*a^3*c*PolyLog(2, -1 + 2/(1 - im*a*x))]

    @test_int [x^3*(c + a^2*c*x^2)^2*atan(a*x)^2, x, 47, (-5*c^2*x^2)/(504*a^2) + (c^2*x^4)/84 + (a^2*c^2*x^6)/168 + (c^2*x*atan(a*x))/(12*a^3) - (c^2*x^3*atan(a*x))/(36*a) - (a*c^2*x^5*atan(a*x))/12 - (a^3*c^2*x^7*atan(a*x))/28 - (c^2*atan(a*x)^2)/(24*a^4) + (c^2*x^4*atan(a*x)^2)/4 + (a^2*c^2*x^6*atan(a*x)^2)/3 + (a^4*c^2*x^8*atan(a*x)^2)/8 - (2*c^2*log(1 + a^2*x^2))/(63*a^4)]
    @test_int [x^2*(c + a^2*c*x^2)^2*atan(a*x)^2, x, 44, -(c^2*x)/(210*a^2) + (17*c^2*x^3)/630 + (a^2*c^2*x^5)/105 + (c^2*atan(a*x))/(210*a^3) - (8*c^2*x^2*atan(a*x))/(105*a) - (9*a*c^2*x^4*atan(a*x))/70 - (a^3*c^2*x^6*atan(a*x))/21 - (((8*im)/105)*c^2*atan(a*x)^2)/a^3 + (c^2*x^3*atan(a*x)^2)/3 + (2*a^2*c^2*x^5*atan(a*x)^2)/5 + (a^4*c^2*x^7*atan(a*x)^2)/7 - (16*c^2*atan(a*x)*log(2/(1 + im*a*x)))/(105*a^3) - (((8*im)/105)*c^2*PolyLog(2, 1 - 2/(1 + im*a*x)))/a^3]
    @test_int [x*(c + a^2*c*x^2)^2*atan(a*x)^2, x, 5, (2*c^2*(1 + a^2*x^2))/(45*a^2) + (c^2*(1 + a^2*x^2)^2)/(60*a^2) - (8*c^2*x*atan(a*x))/(45*a) - (4*c^2*x*(1 + a^2*x^2)*atan(a*x))/(45*a) - (c^2*x*(1 + a^2*x^2)^2*atan(a*x))/(15*a) + (c^2*(1 + a^2*x^2)^3*atan(a*x)^2)/(6*a^2) + (4*c^2*log(1 + a^2*x^2))/(45*a^2)]
    @test_int [(c + a^2*c*x^2)^2*atan(a*x)^2, x, 9, (11*c^2*x)/30 + (a^2*c^2*x^3)/30 - (4*c^2*(1 + a^2*x^2)*atan(a*x))/(15*a) - (c^2*(1 + a^2*x^2)^2*atan(a*x))/(10*a) + (((8*im)/15)*c^2*atan(a*x)^2)/a + (8*c^2*x*atan(a*x)^2)/15 + (4*c^2*x*(1 + a^2*x^2)*atan(a*x)^2)/15 + (c^2*x*(1 + a^2*x^2)^2*atan(a*x)^2)/5 + (16*c^2*atan(a*x)*log(2/(1 + im*a*x)))/(15*a) + (((8*im)/15)*c^2*PolyLog(2, 1 - 2/(1 + im*a*x)))/a]
    @test_int [((c + a^2*c*x^2)^2*atan(a*x)^2)/x, x, 23, (a^2*c^2*x^2)/12 - (3*a*c^2*x*atan(a*x))/2 - (a^3*c^2*x^3*atan(a*x))/6 + (3*c^2*atan(a*x)^2)/4 + a^2*c^2*x^2*atan(a*x)^2 + (a^4*c^2*x^4*atan(a*x)^2)/4 + 2*c^2*atan(a*x)^2*atanh(1 - 2/(1 + im*a*x)) + (2*c^2*log(1 + a^2*x^2))/3 - im*c^2*atan(a*x)*PolyLog(2, 1 - 2/(1 + im*a*x)) + im*c^2*atan(a*x)*PolyLog(2, -1 + 2/(1 + im*a*x)) - (c^2*PolyLog(3, 1 - 2/(1 + im*a*x)))/2 + (c^2*PolyLog(3, -1 + 2/(1 + im*a*x)))/2]
    @test_int [((c + a^2*c*x^2)^2*atan(a*x)^2)/x^2, x, 20, (a^2*c^2*x)/3 - (a*c^2*atan(a*x))/3 - (a^3*c^2*x^2*atan(a*x))/3 + ((2*im)/3)*a*c^2*atan(a*x)^2 - (c^2*atan(a*x)^2)/x + 2*a^2*c^2*x*atan(a*x)^2 + (a^4*c^2*x^3*atan(a*x)^2)/3 + (10*a*c^2*atan(a*x)*log(2/(1 + im*a*x)))/3 + 2*a*c^2*atan(a*x)*log(2 - 2/(1 - im*a*x)) - im*a*c^2*PolyLog(2, -1 + 2/(1 - im*a*x)) + ((5*im)/3)*a*c^2*PolyLog(2, 1 - 2/(1 + im*a*x))]
    @test_int [((c + a^2*c*x^2)^2*atan(a*x)^2)/x^3, x, 21, -((a*c^2*atan(a*x))/x) - a^3*c^2*x*atan(a*x) - (c^2*atan(a*x)^2)/(2*x^2) + (1/2)*a^4*c^2*x^2*atan(a*x)^2 + 4*a^2*c^2*atan(a*x)^2*atanh(1 - 2/(1 + im*a*x)) + a^2*c^2*log(x) - 2*im*a^2*c^2*atan(a*x)*PolyLog(2, 1 - 2/(1 + im*a*x)) + 2*im*a^2*c^2*atan(a*x)*PolyLog(2, -1 + 2/(1 + im*a*x)) - a^2*c^2*PolyLog(3, 1 - 2/(1 + im*a*x)) + a^2*c^2*PolyLog(3, -1 + 2/(1 + im*a*x))]
    @test_int [((c + a^2*c*x^2)^2*atan(a*x)^2)/x^4, x, 19, -(a^2*c^2)/(3*x) - (a^3*c^2*atan(a*x))/3 - (a*c^2*atan(a*x))/(3*x^2) - ((2*im)/3)*a^3*c^2*atan(a*x)^2 - (c^2*atan(a*x)^2)/(3*x^3) - (2*a^2*c^2*atan(a*x)^2)/x + a^4*c^2*x*atan(a*x)^2 + 2*a^3*c^2*atan(a*x)*log(2/(1 + im*a*x)) + (10*a^3*c^2*atan(a*x)*log(2 - 2/(1 - im*a*x)))/3 - ((5*im)/3)*a^3*c^2*PolyLog(2, -1 + 2/(1 - im*a*x)) + im*a^3*c^2*PolyLog(2, 1 - 2/(1 + im*a*x))]

    @test_int [x^3*(c + a^2*c*x^2)^3*atan(a*x)^2, x, 72, (-107*c^3*x^2)/(12600*a^2) + (53*c^3*x^4)/6300 + (71*a^2*c^3*x^6)/7560 + (a^4*c^3*x^8)/360 + (c^3*x*atan(a*x))/(20*a^3) - (c^3*x^3*atan(a*x))/(60*a) - (9*a*c^3*x^5*atan(a*x))/100 - (11*a^3*c^3*x^7*atan(a*x))/140 - (a^5*c^3*x^9*atan(a*x))/45 - (c^3*atan(a*x)^2)/(40*a^4) + (c^3*x^4*atan(a*x)^2)/4 + (a^2*c^3*x^6*atan(a*x)^2)/2 + (3*a^4*c^3*x^8*atan(a*x)^2)/8 + (a^6*c^3*x^10*atan(a*x)^2)/10 - (26*c^3*log(1 + a^2*x^2))/(1575*a^4)]
    @test_int [x^2*(c + a^2*c*x^2)^3*atan(a*x)^2, x, 68, (-47*c^3*x)/(3780*a^2) + (239*c^3*x^3)/11340 + (59*a^2*c^3*x^5)/3780 + (a^4*c^3*x^7)/252 + (47*c^3*atan(a*x))/(3780*a^3) - (16*c^3*x^2*atan(a*x))/(315*a) - (89*a*c^3*x^4*atan(a*x))/630 - (20*a^3*c^3*x^6*atan(a*x))/189 - (a^5*c^3*x^8*atan(a*x))/36 - (((16*im)/315)*c^3*atan(a*x)^2)/a^3 + (c^3*x^3*atan(a*x)^2)/3 + (3*a^2*c^3*x^5*atan(a*x)^2)/5 + (3*a^4*c^3*x^7*atan(a*x)^2)/7 + (a^6*c^3*x^9*atan(a*x)^2)/9 - (32*c^3*atan(a*x)*log(2/(1 + im*a*x)))/(315*a^3) - (((16*im)/315)*c^3*PolyLog(2, 1 - 2/(1 + im*a*x)))/a^3]
    @test_int [x*(c + a^2*c*x^2)^3*atan(a*x)^2, x, 6, (c^3*(1 + a^2*x^2))/(35*a^2) + (3*c^3*(1 + a^2*x^2)^2)/(280*a^2) + (c^3*(1 + a^2*x^2)^3)/(168*a^2) - (4*c^3*x*atan(a*x))/(35*a) - (2*c^3*x*(1 + a^2*x^2)*atan(a*x))/(35*a) - (3*c^3*x*(1 + a^2*x^2)^2*atan(a*x))/(70*a) - (c^3*x*(1 + a^2*x^2)^3*atan(a*x))/(28*a) + (c^3*(1 + a^2*x^2)^4*atan(a*x)^2)/(8*a^2) + (2*c^3*log(1 + a^2*x^2))/(35*a^2)]
    @test_int [(c + a^2*c*x^2)^3*atan(a*x)^2, x, 12, (38*c^3*x)/105 + (19*a^2*c^3*x^3)/315 + (a^4*c^3*x^5)/105 - (8*c^3*(1 + a^2*x^2)*atan(a*x))/(35*a) - (3*c^3*(1 + a^2*x^2)^2*atan(a*x))/(35*a) - (c^3*(1 + a^2*x^2)^3*atan(a*x))/(21*a) + (((16*im)/35)*c^3*atan(a*x)^2)/a + (16*c^3*x*atan(a*x)^2)/35 + (8*c^3*x*(1 + a^2*x^2)*atan(a*x)^2)/35 + (6*c^3*x*(1 + a^2*x^2)^2*atan(a*x)^2)/35 + (c^3*x*(1 + a^2*x^2)^3*atan(a*x)^2)/7 + (32*c^3*atan(a*x)*log(2/(1 + im*a*x)))/(35*a) + (((16*im)/35)*c^3*PolyLog(2, 1 - 2/(1 + im*a*x)))/a]
    @test_int [((c + a^2*c*x^2)^3*atan(a*x)^2)/x, x, 38, (29*a^2*c^3*x^2)/180 + (a^4*c^3*x^4)/60 - (11*a*c^3*x*atan(a*x))/6 - (7*a^3*c^3*x^3*atan(a*x))/18 - (a^5*c^3*x^5*atan(a*x))/15 + (11*c^3*atan(a*x)^2)/12 + (3*a^2*c^3*x^2*atan(a*x)^2)/2 + (3*a^4*c^3*x^4*atan(a*x)^2)/4 + (a^6*c^3*x^6*atan(a*x)^2)/6 + 2*c^3*atan(a*x)^2*atanh(1 - 2/(1 + im*a*x)) + (34*c^3*log(1 + a^2*x^2))/45 - im*c^3*atan(a*x)*PolyLog(2, 1 - 2/(1 + im*a*x)) + im*c^3*atan(a*x)*PolyLog(2, -1 + 2/(1 + im*a*x)) - (c^3*PolyLog(3, 1 - 2/(1 + im*a*x)))/2 + (c^3*PolyLog(3, -1 + 2/(1 + im*a*x)))/2]
    @test_int [((c + a^2*c*x^2)^3*atan(a*x)^2)/x^2, x, 34, (7*a^2*c^3*x)/10 + (a^4*c^3*x^3)/30 - (7*a*c^3*atan(a*x))/10 - (4*a^3*c^3*x^2*atan(a*x))/5 - (a^5*c^3*x^4*atan(a*x))/10 + ((6*im)/5)*a*c^3*atan(a*x)^2 - (c^3*atan(a*x)^2)/x + 3*a^2*c^3*x*atan(a*x)^2 + a^4*c^3*x^3*atan(a*x)^2 + (a^6*c^3*x^5*atan(a*x)^2)/5 + (22*a*c^3*atan(a*x)*log(2/(1 + im*a*x)))/5 + 2*a*c^3*atan(a*x)*log(2 - 2/(1 - im*a*x)) - im*a*c^3*PolyLog(2, -1 + 2/(1 - im*a*x)) + ((11*im)/5)*a*c^3*PolyLog(2, 1 - 2/(1 + im*a*x))]
    @test_int [((c + a^2*c*x^2)^3*atan(a*x)^2)/x^3, x, 31, (1/12)*a^4*c^3*x^2 - (a*c^3*atan(a*x))/x - (5/2)*a^3*c^3*x*atan(a*x) - (1/6)*a^5*c^3*x^3*atan(a*x) + (3/4)*a^2*c^3*atan(a*x)^2 - (c^3*atan(a*x)^2)/(2*x^2) + (3/2)*a^4*c^3*x^2*atan(a*x)^2 + (1/4)*a^6*c^3*x^4*atan(a*x)^2 + 6*a^2*c^3*atan(a*x)^2*atanh(1 - 2/(1 + im*a*x)) + a^2*c^3*log(x) + (2/3)*a^2*c^3*log(1 + a^2*x^2) - 3*im*a^2*c^3*atan(a*x)*PolyLog(2, 1 - 2/(1 + im*a*x)) + 3*im*a^2*c^3*atan(a*x)*PolyLog(2, -1 + 2/(1 + im*a*x)) - (3/2)*a^2*c^3*PolyLog(3, 1 - 2/(1 + im*a*x)) + (3/2)*a^2*c^3*PolyLog(3, -1 + 2/(1 + im*a*x))]
    @test_int [((c + a^2*c*x^2)^3*atan(a*x)^2)/x^4, x, 28, -(a^2*c^3)/(3*x) + (a^4*c^3*x)/3 - (2*a^3*c^3*atan(a*x))/3 - (a*c^3*atan(a*x))/(3*x^2) - (a^5*c^3*x^2*atan(a*x))/3 - (c^3*atan(a*x)^2)/(3*x^3) - (3*a^2*c^3*atan(a*x)^2)/x + 3*a^4*c^3*x*atan(a*x)^2 + (a^6*c^3*x^3*atan(a*x)^2)/3 + (16*a^3*c^3*atan(a*x)*log(2/(1 + im*a*x)))/3 + (16*a^3*c^3*atan(a*x)*log(2 - 2/(1 - im*a*x)))/3 - ((8*im)/3)*a^3*c^3*PolyLog(2, -1 + 2/(1 - im*a*x)) + ((8*im)/3)*a^3*c^3*PolyLog(2, 1 - 2/(1 + im*a*x))]

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

    @test_int [x^4*atan(a*x)^2/(c + a^2*c*x^2), x, 17, x/(3*a^4*c) - atan(a*x)/(3*a^5*c) - (x^2*atan(a*x))/(3*a^3*c) - (4*im*atan(a*x)^2)/(3*a^5*c) - (x*atan(a*x)^2)/(a^4*c) + (x^3*atan(a*x)^2)/(3*a^2*c) + atan(a*x)^3/(3*a^5*c) - (8*atan(a*x)*log(2/(1 + im*a*x)))/(3*a^5*c) - (4*im*PolyLog(2, 1 - 2/(1 + im*a*x)))/(3*a^5*c)]
    @test_int [x^3*atan(a*x)^2/(c + a^2*c*x^2), x, 10, -((x*atan(a*x))/(a^3*c)) + atan(a*x)^2/(2*a^4*c) + (x^2*atan(a*x)^2)/(2*a^2*c) + ((im/3)*atan(a*x)^3)/(a^4*c) + (atan(a*x)^2*log(2/(1 + im*a*x)))/(a^4*c) + log(1 + a^2*x^2)/(2*a^4*c) + (im*atan(a*x)*PolyLog(2, 1 - 2/(1 + im*a*x)))/(a^4*c) + PolyLog(3, 1 - 2/(1 + im*a*x))/(2*a^4*c)]
    @test_int [x^2*atan(a*x)^2/(c + a^2*c*x^2), x, 7, (im*atan(a*x)^2)/(a^3*c) + (x*atan(a*x)^2)/(a^2*c) - atan(a*x)^3/(3*a^3*c) + (2*atan(a*x)*log(2/(1 + im*a*x)))/(a^3*c) + (im*PolyLog(2, 1 - 2/(1 + im*a*x)))/(a^3*c)]
    @test_int [x*atan(a*x)^2/(c + a^2*c*x^2), x, 4, ((-im/3)*atan(a*x)^3)/(a^2*c) - (atan(a*x)^2*log(2/(1 + im*a*x)))/(a^2*c) - (im*atan(a*x)*PolyLog(2, 1 - 2/(1 + im*a*x)))/(a^2*c) - PolyLog(3, 1 - 2/(1 + im*a*x))/(2*a^2*c)]
    @test_int [atan(a*x)^2/(c + a^2*c*x^2), x, 1, atan(a*x)^3/(3*a*c)]
    @test_int [atan(a*x)^2/(x*(c + a^2*c*x^2)), x, 4, ((-im/3)*atan(a*x)^3)/c + (atan(a*x)^2*log(2 - 2/(1 - im*a*x)))/c - (im*atan(a*x)*PolyLog(2, -1 + 2/(1 - im*a*x)))/c + PolyLog(3, -1 + 2/(1 - im*a*x))/(2*c)]
    @test_int [atan(a*x)^2/(x^2*(c + a^2*c*x^2)), x, 6, ((-im)*a*atan(a*x)^2)/c - atan(a*x)^2/(c*x) - (a*atan(a*x)^3)/(3*c) + (2*a*atan(a*x)*log(2 - 2/(1 - im*a*x)))/c - (im*a*PolyLog(2, -1 + 2/(1 - im*a*x)))/c]
    @test_int [atan(a*x)^2/(x^3*(c + a^2*c*x^2)), x, 13, -((a*atan(a*x))/(c*x)) - (a^2*atan(a*x)^2)/(2*c) - atan(a*x)^2/(2*c*x^2) + (im*a^2*atan(a*x)^3)/(3*c) + (a^2*log(x))/c - (a^2*atan(a*x)^2*log(2 - 2/(1 - im*a*x)))/c - (a^2*log(1 + a^2*x^2))/(2*c) + (im*a^2*atan(a*x)*PolyLog(2, -1 + 2/(1 - im*a*x)))/c - (a^2*PolyLog(3, -1 + 2/(1 - im*a*x)))/(2*c)]
    @test_int [atan(a*x)^2/(x^4*(c + a^2*c*x^2)), x, 15, -a^2/(3*c*x) - (a^3*atan(a*x))/(3*c) - (a*atan(a*x))/(3*c*x^2) + (((4*im)/3)*a^3*atan(a*x)^2)/c - atan(a*x)^2/(3*c*x^3) + (a^2*atan(a*x)^2)/(c*x) + (a^3*atan(a*x)^3)/(3*c) - (8*a^3*atan(a*x)*log(2 - 2/(1 - im*a*x)))/(3*c) + (((4*im)/3)*a^3*PolyLog(2, -1 + 2/(1 - im*a*x)))/c]

    @test_int [(x^3*atan(a*x)^2)/(c + a^2*c*x^2)^2, x, 8, -1/(4*a^4*c^2*(1 + a^2*x^2)) - (x*atan(a*x))/(2*a^3*c^2*(1 + a^2*x^2)) - atan(a*x)^2/(4*a^4*c^2) + atan(a*x)^2/(2*a^4*c^2*(1 + a^2*x^2)) - ((im/3)*atan(a*x)^3)/(a^4*c^2) - (atan(a*x)^2*log(2/(1 + im*a*x)))/(a^4*c^2) - (im*atan(a*x)*PolyLog(2, 1 - 2/(1 + im*a*x)))/(a^4*c^2) - PolyLog(3, 1 - 2/(1 + im*a*x))/(2*a^4*c^2)]
    @test_int [(x^2*atan(a*x)^2)/(c + a^2*c*x^2)^2, x, 4, x/(4*a^2*c^2*(1 + a^2*x^2)) + atan(a*x)/(4*a^3*c^2) - atan(a*x)/(2*a^3*c^2*(1 + a^2*x^2)) - (x*atan(a*x)^2)/(2*a^2*c^2*(1 + a^2*x^2)) + atan(a*x)^3/(6*a^3*c^2)]
    @test_int [(x*atan(a*x)^2)/(c + a^2*c*x^2)^2, x, 3, 1/(4*a^2*c^2*(1 + a^2*x^2)) + (x*atan(a*x))/(2*a*c^2*(1 + a^2*x^2)) + atan(a*x)^2/(4*a^2*c^2) - atan(a*x)^2/(2*a^2*c^2*(1 + a^2*x^2))]
    @test_int [atan(a*x)^2/(c + a^2*c*x^2)^2, x, 4, -x/(4*c^2*(1 + a^2*x^2)) - atan(a*x)/(4*a*c^2) + atan(a*x)/(2*a*c^2*(1 + a^2*x^2)) + (x*atan(a*x)^2)/(2*c^2*(1 + a^2*x^2)) + atan(a*x)^3/(6*a*c^2)]
    @test_int [atan(a*x)^2/(x*(c + a^2*c*x^2)^2), x, 8, -1/(4*c^2*(1 + a^2*x^2)) - (a*x*atan(a*x))/(2*c^2*(1 + a^2*x^2)) - atan(a*x)^2/(4*c^2) + atan(a*x)^2/(2*c^2*(1 + a^2*x^2)) - ((im/3)*atan(a*x)^3)/c^2 + (atan(a*x)^2*log(2 - 2/(1 - im*a*x)))/c^2 - (im*atan(a*x)*PolyLog(2, -1 + 2/(1 - im*a*x)))/c^2 + PolyLog(3, -1 + 2/(1 - im*a*x))/(2*c^2)]
    @test_int [atan(a*x)^2/(x^2*(c + a^2*c*x^2)^2), x, 11, (a^2*x)/(4*c^2*(1 + a^2*x^2)) + (a*atan(a*x))/(4*c^2) - (a*atan(a*x))/(2*c^2*(1 + a^2*x^2)) - (im*a*atan(a*x)^2)/c^2 - atan(a*x)^2/(c^2*x) - (a^2*x*atan(a*x)^2)/(2*c^2*(1 + a^2*x^2)) - (a*atan(a*x)^3)/(2*c^2) + (2*a*atan(a*x)*log(2 - 2/(1 - im*a*x)))/c^2 - (im*a*PolyLog(2, -1 + 2/(1 - im*a*x)))/c^2]
    @test_int [atan(a*x)^2/(x^3*(c + a^2*c*x^2)^2), x, 22, a^2/(4*c^2*(1 + a^2*x^2)) - (a*atan(a*x))/(c^2*x) + (a^3*x*atan(a*x))/(2*c^2*(1 + a^2*x^2)) - (a^2*atan(a*x)^2)/(4*c^2) - atan(a*x)^2/(2*c^2*x^2) - (a^2*atan(a*x)^2)/(2*c^2*(1 + a^2*x^2)) + (2*im*a^2*atan(a*x)^3)/(3*c^2) + (a^2*log(x))/c^2 - (2*a^2*atan(a*x)^2*log(2 - 2/(1 - im*a*x)))/c^2 - (a^2*log(1 + a^2*x^2))/(2*c^2) + (2*im*a^2*atan(a*x)*PolyLog(2, -1 + 2/(1 - im*a*x)))/c^2 - (a^2*PolyLog(3, -1 + 2/(1 - im*a*x)))/c^2]
    @test_int [atan(a*x)^2/(x^4*(c + a^2*c*x^2)^2), x, 27, -a^2/(3*c^2*x) - (a^4*x)/(4*c^2*(1 + a^2*x^2)) - (7*a^3*atan(a*x))/(12*c^2) - (a*atan(a*x))/(3*c^2*x^2) + (a^3*atan(a*x))/(2*c^2*(1 + a^2*x^2)) + (((7*im)/3)*a^3*atan(a*x)^2)/c^2 - atan(a*x)^2/(3*c^2*x^3) + (2*a^2*atan(a*x)^2)/(c^2*x) + (a^4*x*atan(a*x)^2)/(2*c^2*(1 + a^2*x^2)) + (5*a^3*atan(a*x)^3)/(6*c^2) - (14*a^3*atan(a*x)*log(2 - 2/(1 - im*a*x)))/(3*c^2) + (((7*im)/3)*a^3*PolyLog(2, -1 + 2/(1 - im*a*x)))/c^2]

    @test_int [(x^3*atan(a*x)^2)/(c + a^2*c*x^2)^3, x, 4, -(x^4/(32*c^3*(1 + a^2*x^2)^2)) + 3/(32*a^4*c^3*(1 + a^2*x^2)) + (x^3*atan(a*x))/(8*a*c^3*(1 + a^2*x^2)^2) + (3*x*atan(a*x))/(16*a^3*c^3*(1 + a^2*x^2)) - (3*atan(a*x)^2)/(32*a^4*c^3) + (x^4*atan(a*x)^2)/(4*c^3*(1 + a^2*x^2)^2)]
    @test_int [(x^2*atan(a*x)^2)/(c + a^2*c*x^2)^3, x, 13, x/(32*a^2*c^3*(1 + a^2*x^2)^2) - x/(64*a^2*c^3*(1 + a^2*x^2)) - atan(a*x)/(64*a^3*c^3) - atan(a*x)/(8*a^3*c^3*(1 + a^2*x^2)^2) + atan(a*x)/(8*a^3*c^3*(1 + a^2*x^2)) - (x*atan(a*x)^2)/(4*a^2*c^3*(1 + a^2*x^2)^2) + (x*atan(a*x)^2)/(8*a^2*c^3*(1 + a^2*x^2)) + atan(a*x)^3/(24*a^3*c^3)]
    @test_int [(x*atan(a*x)^2)/(c + a^2*c*x^2)^3, x, 4, 1/(32*a^2*c^3*(1 + a^2*x^2)^2) + 3/(32*a^2*c^3*(1 + a^2*x^2)) + (x*atan(a*x))/(8*a*c^3*(1 + a^2*x^2)^2) + (3*x*atan(a*x))/(16*a*c^3*(1 + a^2*x^2)) + (3*atan(a*x)^2)/(32*a^2*c^3) - atan(a*x)^2/(4*a^2*c^3*(1 + a^2*x^2)^2)]
    @test_int [atan(a*x)^2/(c + a^2*c*x^2)^3, x, 8, -x/(32*c^3*(1 + a^2*x^2)^2) - (15*x)/(64*c^3*(1 + a^2*x^2)) - (15*atan(a*x))/(64*a*c^3) + atan(a*x)/(8*a*c^3*(1 + a^2*x^2)^2) + (3*atan(a*x))/(8*a*c^3*(1 + a^2*x^2)) + (x*atan(a*x)^2)/(4*c^3*(1 + a^2*x^2)^2) + (3*x*atan(a*x)^2)/(8*c^3*(1 + a^2*x^2)) + atan(a*x)^3/(8*a*c^3)]
    @test_int [atan(a*x)^2/(x*(c + a^2*c*x^2)^3), x, 13, -1/(32*c^3*(1 + a^2*x^2)^2) - 11/(32*c^3*(1 + a^2*x^2)) - (a*x*atan(a*x))/(8*c^3*(1 + a^2*x^2)^2) - (11*a*x*atan(a*x))/(16*c^3*(1 + a^2*x^2)) - (11*atan(a*x)^2)/(32*c^3) + atan(a*x)^2/(4*c^3*(1 + a^2*x^2)^2) + atan(a*x)^2/(2*c^3*(1 + a^2*x^2)) - ((im/3)*atan(a*x)^3)/c^3 + (atan(a*x)^2*log(2 - 2/(1 - im*a*x)))/c^3 - (im*atan(a*x)*PolyLog(2, -1 + 2/(1 - im*a*x)))/c^3 + PolyLog(3, -1 + 2/(1 - im*a*x))/(2*c^3)]
    @test_int [atan(a*x)^2/(x^2*(c + a^2*c*x^2)^3), x, 20, (a^2*x)/(32*c^3*(1 + a^2*x^2)^2) + (31*a^2*x)/(64*c^3*(1 + a^2*x^2)) + (31*a*atan(a*x))/(64*c^3) - (a*atan(a*x))/(8*c^3*(1 + a^2*x^2)^2) - (7*a*atan(a*x))/(8*c^3*(1 + a^2*x^2)) - (im*a*atan(a*x)^2)/c^3 - atan(a*x)^2/(c^3*x) - (a^2*x*atan(a*x)^2)/(4*c^3*(1 + a^2*x^2)^2) - (7*a^2*x*atan(a*x)^2)/(8*c^3*(1 + a^2*x^2)) - (5*a*atan(a*x)^3)/(8*c^3) + (2*a*atan(a*x)*log(2 - 2/(1 - im*a*x)))/c^3 - (im*a*PolyLog(2, -1 + 2/(1 - im*a*x)))/c^3]
    @test_int [atan(a*x)^2/(x^3*(c + a^2*c*x^2)^3), x, 36, a^2/(32*c^3*(1 + a^2*x^2)^2) + (19*a^2)/(32*c^3*(1 + a^2*x^2)) - (a*atan(a*x))/(c^3*x) + (a^3*x*atan(a*x))/(8*c^3*(1 + a^2*x^2)^2) + (19*a^3*x*atan(a*x))/(16*c^3*(1 + a^2*x^2)) + (3*a^2*atan(a*x)^2)/(32*c^3) - atan(a*x)^2/(2*c^3*x^2) - (a^2*atan(a*x)^2)/(4*c^3*(1 + a^2*x^2)^2) - (a^2*atan(a*x)^2)/(c^3*(1 + a^2*x^2)) + (im*a^2*atan(a*x)^3)/c^3 + (a^2*log(x))/c^3 - (3*a^2*atan(a*x)^2*log(2 - 2/(1 - im*a*x)))/c^3 - (a^2*log(1 + a^2*x^2))/(2*c^3) + (3*im*a^2*atan(a*x)*PolyLog(2, -1 + 2/(1 - im*a*x)))/c^3 - (3*a^2*PolyLog(3, -1 + 2/(1 - im*a*x)))/(2*c^3)]
    @test_int [atan(a*x)^2/(x^4*(c + a^2*c*x^2)^3), x, 48, -a^2/(3*c^3*x) - (a^4*x)/(32*c^3*(1 + a^2*x^2)^2) - (47*a^4*x)/(64*c^3*(1 + a^2*x^2)) - (205*a^3*atan(a*x))/(192*c^3) - (a*atan(a*x))/(3*c^3*x^2) + (a^3*atan(a*x))/(8*c^3*(1 + a^2*x^2)^2) + (11*a^3*atan(a*x))/(8*c^3*(1 + a^2*x^2)) + (((10*im)/3)*a^3*atan(a*x)^2)/c^3 - atan(a*x)^2/(3*c^3*x^3) + (3*a^2*atan(a*x)^2)/(c^3*x) + (a^4*x*atan(a*x)^2)/(4*c^3*(1 + a^2*x^2)^2) + (11*a^4*x*atan(a*x)^2)/(8*c^3*(1 + a^2*x^2)) + (35*a^3*atan(a*x)^3)/(24*c^3) - (20*a^3*atan(a*x)*log(2 - 2/(1 - im*a*x)))/(3*c^3) + (((10*im)/3)*a^3*PolyLog(2, -1 + 2/(1 - im*a*x)))/c^3]

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

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

    @test_int [x^3*sqrt(c + a^2*c*x^2)*atan(a*x)^2, x, 26, -((11*sqrt(c + a^2*c*x^2))/(60*a^4)) + (c + a^2*c*x^2)^(3/2)/(30*a^4*c) + (x*sqrt(c + a^2*c*x^2)*atan(a*x))/(12*a^3) - (x^3*sqrt(c + a^2*c*x^2)*atan(a*x))/(10*a) - (2*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(15*a^4) + (x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(15*a^2) + (1/5)*x^4*sqrt(c + a^2*c*x^2)*atan(a*x)^2 - (11*im*c*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(30*a^4*sqrt(c + a^2*c*x^2)) + (11*im*c*sqrt(1 + a^2*x^2)*PolyLog(2, -((im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x))))/(60*a^4*sqrt(c + a^2*c*x^2)) - (11*im*c*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(60*a^4*sqrt(c + a^2*c*x^2))]
    @test_int [x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2, x, 35, (x*sqrt(c + a^2*c*x^2))/(12*a^2) + (sqrt(c + a^2*c*x^2)*atan(a*x))/(12*a^3) - (x^2*sqrt(c + a^2*c*x^2)*atan(a*x))/(6*a) + (x*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(8*a^2) + (1/4)*x^3*sqrt(c + a^2*c*x^2)*atan(a*x)^2 + (im*c*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^2)/(4*a^3*sqrt(c + a^2*c*x^2)) - (sqrt(c)*atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2)))/(6*a^3) - (im*c*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/(4*a^3*sqrt(c + a^2*c*x^2)) + (im*c*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, im*ℯ^(im*atan(a*x))))/(4*a^3*sqrt(c + a^2*c*x^2)) + (c*sqrt(1 + a^2*x^2)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(4*a^3*sqrt(c + a^2*c*x^2)) - (c*sqrt(1 + a^2*x^2)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(4*a^3*sqrt(c + a^2*c*x^2))]
    @test_int [x*sqrt(c + a^2*c*x^2)*atan(a*x)^2, x, 4, sqrt(c + a^2*c*x^2)/(3*a^2) - (x*sqrt(c + a^2*c*x^2)*atan(a*x))/(3*a) + ((c + a^2*c*x^2)^(3/2)*atan(a*x)^2)/(3*a^2*c) + (((2*im)/3)*c*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(a^2*sqrt(c + a^2*c*x^2)) - ((im/3)*c*sqrt(1 + a^2*x^2)*PolyLog(2, ((-im)*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(a^2*sqrt(c + a^2*c*x^2)) + ((im/3)*c*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(a^2*sqrt(c + a^2*c*x^2))]
    @test_int [sqrt(c + a^2*c*x^2)*atan(a*x)^2, x, 12, -((sqrt(c + a^2*c*x^2)*atan(a*x))/a) + (x*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/2 - (im*c*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^2)/(a*sqrt(c + a^2*c*x^2)) + (sqrt(c)*atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2)))/a + (im*c*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2)) - (im*c*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, im*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2)) - (c*sqrt(1 + a^2*x^2)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2)) + (c*sqrt(1 + a^2*x^2)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2))]
    @test_int [(sqrt(c + a^2*c*x^2)*atan(a*x)^2)/x, x, 13, sqrt(c + a^2*c*x^2)*atan(a*x)^2 + ((4*im)*c*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (2*c*sqrt(1 + a^2*x^2)*atan(a*x)^2*atanh(ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((2*im)*c*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((2*im)*c*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((2*im)*c*sqrt(1 + a^2*x^2)*PolyLog(2, ((-im)*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) + ((2*im)*c*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (2*c*sqrt(1 + a^2*x^2)*PolyLog(3, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (2*c*sqrt(1 + a^2*x^2)*PolyLog(3, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2)]
    @test_int [(sqrt(c + a^2*c*x^2)*atan(a*x)^2)/x^2, x, 13, -((sqrt(c + a^2*c*x^2)*atan(a*x)^2)/x) - ((2*im)*a*c*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^2)/sqrt(c + a^2*c*x^2) - (4*a*c*sqrt(1 + a^2*x^2)*atan(a*x)*atanh(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) + ((2*im)*a*c*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((2*im)*a*c*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((2*im)*a*c*sqrt(1 + a^2*x^2)*PolyLog(2, -(sqrt(1 + im*a*x)/sqrt(1 - im*a*x))))/sqrt(c + a^2*c*x^2) - ((2*im)*a*c*sqrt(1 + a^2*x^2)*PolyLog(2, sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (2*a*c*sqrt(1 + a^2*x^2)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (2*a*c*sqrt(1 + a^2*x^2)*PolyLog(3, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2)]
    @test_int [(sqrt(c + a^2*c*x^2)*atan(a*x)^2)/x^3, x, 24, -((a*sqrt(c + a^2*c*x^2)*atan(a*x))/x) - (sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(2*x^2) - (a^2*c*sqrt(1 + a^2*x^2)*atan(a*x)^2*atanh(ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - a^2*sqrt(c)*atanh(sqrt(c + a^2*c*x^2)/sqrt(c)) + (im*a^2*c*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (im*a^2*c*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (a^2*c*sqrt(1 + a^2*x^2)*PolyLog(3, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (a^2*c*sqrt(1 + a^2*x^2)*PolyLog(3, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2)]
    @test_int [(sqrt(c + a^2*c*x^2)*atan(a*x)^2)/x^4, x, 7, -(a^2*sqrt(c + a^2*c*x^2))/(3*x) - (a*sqrt(c + a^2*c*x^2)*atan(a*x))/(3*x^2) - ((c + a^2*c*x^2)^(3/2)*atan(a*x)^2)/(3*c*x^3) - (2*a^3*c*sqrt(1 + a^2*x^2)*atan(a*x)*atanh(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(3*sqrt(c + a^2*c*x^2)) + ((im/3)*a^3*c*sqrt(1 + a^2*x^2)*PolyLog(2, -(sqrt(1 + im*a*x)/sqrt(1 - im*a*x))))/sqrt(c + a^2*c*x^2) - ((im/3)*a^3*c*sqrt(1 + a^2*x^2)*PolyLog(2, sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2)]

    @test_int [x^3*(c + a^2*c*x^2)^(3/2)*atan(a*x)^2, x, 75, -((17*c*sqrt(c + a^2*c*x^2))/(280*a^4)) - (17*(c + a^2*c*x^2)^(3/2))/(1260*a^4) + (c + a^2*c*x^2)^(5/2)/(105*a^4*c) + (3*c*x*sqrt(c + a^2*c*x^2)*atan(a*x))/(56*a^3) - (23*c*x^3*sqrt(c + a^2*c*x^2)*atan(a*x))/(420*a) - (1/21)*a*c*x^5*sqrt(c + a^2*c*x^2)*atan(a*x) - (2*c*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(35*a^4) + (c*x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(35*a^2) + (8/35)*c*x^4*sqrt(c + a^2*c*x^2)*atan(a*x)^2 + (1/7)*a^2*c*x^6*sqrt(c + a^2*c*x^2)*atan(a*x)^2 - (17*im*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(140*a^4*sqrt(c + a^2*c*x^2)) + (17*im*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, -((im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x))))/(280*a^4*sqrt(c + a^2*c*x^2)) - (17*im*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(280*a^4*sqrt(c + a^2*c*x^2))]
    @test_int [x^2*(c + a^2*c*x^2)^(3/2)*atan(a*x)^2, x, 92, (c*x*sqrt(c + a^2*c*x^2))/(36*a^2) + (1/60)*c*x^3*sqrt(c + a^2*c*x^2) + (31*c*sqrt(c + a^2*c*x^2)*atan(a*x))/(360*a^3) - (19*c*x^2*sqrt(c + a^2*c*x^2)*atan(a*x))/(180*a) - (1/15)*a*c*x^4*sqrt(c + a^2*c*x^2)*atan(a*x) + (c*x*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(16*a^2) + (7/24)*c*x^3*sqrt(c + a^2*c*x^2)*atan(a*x)^2 + (1/6)*a^2*c*x^5*sqrt(c + a^2*c*x^2)*atan(a*x)^2 + (im*c^2*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^2)/(8*a^3*sqrt(c + a^2*c*x^2)) - (41*c^(3/2)*atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2)))/(360*a^3) - (im*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/(8*a^3*sqrt(c + a^2*c*x^2)) + (im*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, im*ℯ^(im*atan(a*x))))/(8*a^3*sqrt(c + a^2*c*x^2)) + (c^2*sqrt(1 + a^2*x^2)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(8*a^3*sqrt(c + a^2*c*x^2)) - (c^2*sqrt(1 + a^2*x^2)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(8*a^3*sqrt(c + a^2*c*x^2))]
    @test_int [x*(c + a^2*c*x^2)^(3/2)*atan(a*x)^2, x, 5, (3*c*sqrt(c + a^2*c*x^2))/(20*a^2) + (c + a^2*c*x^2)^(3/2)/(30*a^2) - (3*c*x*sqrt(c + a^2*c*x^2)*atan(a*x))/(20*a) - (x*(c + a^2*c*x^2)^(3/2)*atan(a*x))/(10*a) + ((c + a^2*c*x^2)^(5/2)*atan(a*x)^2)/(5*a^2*c) + (((3*im)/10)*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(a^2*sqrt(c + a^2*c*x^2)) - (((3*im)/20)*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, ((-im)*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(a^2*sqrt(c + a^2*c*x^2)) + (((3*im)/20)*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(a^2*sqrt(c + a^2*c*x^2))]
    @test_int [(c + a^2*c*x^2)^(3/2)*atan(a*x)^2, x, 16, (c*x*sqrt(c + a^2*c*x^2))/12 - (3*c*sqrt(c + a^2*c*x^2)*atan(a*x))/(4*a) - ((c + a^2*c*x^2)^(3/2)*atan(a*x))/(6*a) + (3*c*x*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/8 + (x*(c + a^2*c*x^2)^(3/2)*atan(a*x)^2)/4 - (((3*im)/4)*c^2*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^2)/(a*sqrt(c + a^2*c*x^2)) + (5*c^(3/2)*atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2)))/(6*a) + (((3*im)/4)*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2)) - (((3*im)/4)*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, im*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2)) - (3*c^2*sqrt(1 + a^2*x^2)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(4*a*sqrt(c + a^2*c*x^2)) + (3*c^2*sqrt(1 + a^2*x^2)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(4*a*sqrt(c + a^2*c*x^2))]
    @test_int [((c + a^2*c*x^2)^(3/2)*atan(a*x)^2)/x, x, 18, (c*sqrt(c + a^2*c*x^2))/3 - (a*c*x*sqrt(c + a^2*c*x^2)*atan(a*x))/3 + c*sqrt(c + a^2*c*x^2)*atan(a*x)^2 + ((c + a^2*c*x^2)^(3/2)*atan(a*x)^2)/3 + (((14*im)/3)*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (2*c^2*sqrt(1 + a^2*x^2)*atan(a*x)^2*atanh(ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((2*im)*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((2*im)*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (((7*im)/3)*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, ((-im)*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) + (((7*im)/3)*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (2*c^2*sqrt(1 + a^2*x^2)*PolyLog(3, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (2*c^2*sqrt(1 + a^2*x^2)*PolyLog(3, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2)]
    @test_int [((c + a^2*c*x^2)^(3/2)*atan(a*x)^2)/x^2, x, 26, -(a*c*sqrt(c + a^2*c*x^2)*atan(a*x)) - (c*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/x + (a^2*c*x*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/2 - ((3*im)*a*c^2*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^2)/sqrt(c + a^2*c*x^2) - (4*a*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*atanh(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) + a*c^(3/2)*atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2)) + ((3*im)*a*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((3*im)*a*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((2*im)*a*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, -(sqrt(1 + im*a*x)/sqrt(1 - im*a*x))))/sqrt(c + a^2*c*x^2) - ((2*im)*a*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (3*a*c^2*sqrt(1 + a^2*x^2)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (3*a*c^2*sqrt(1 + a^2*x^2)*PolyLog(3, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2)]
    @test_int [((c + a^2*c*x^2)^(3/2)*atan(a*x)^2)/x^3, x, 38, -((a*c*sqrt(c + a^2*c*x^2)*atan(a*x))/x) + a^2*c*sqrt(c + a^2*c*x^2)*atan(a*x)^2 - (c*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(2*x^2) + ((4*im)*a^2*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (3*a^2*c^2*sqrt(1 + a^2*x^2)*atan(a*x)^2*atanh(ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - a^2*c^(3/2)*atanh(sqrt(c + a^2*c*x^2)/sqrt(c)) + ((3*im)*a^2*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((3*im)*a^2*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((2*im)*a^2*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, ((-im)*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) + ((2*im)*a^2*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (3*a^2*c^2*sqrt(1 + a^2*x^2)*PolyLog(3, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (3*a^2*c^2*sqrt(1 + a^2*x^2)*PolyLog(3, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2)]
    @test_int [((c + a^2*c*x^2)^(3/2)*atan(a*x)^2)/x^4, x, 21, -(a^2*c*sqrt(c + a^2*c*x^2))/(3*x) - (a*c*sqrt(c + a^2*c*x^2)*atan(a*x))/(3*x^2) - (a^2*c*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/x - ((c + a^2*c*x^2)^(3/2)*atan(a*x)^2)/(3*x^3) - ((2*im)*a^3*c^2*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^2)/sqrt(c + a^2*c*x^2) - (14*a^3*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*atanh(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(3*sqrt(c + a^2*c*x^2)) + ((2*im)*a^3*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((2*im)*a^3*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (((7*im)/3)*a^3*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, -(sqrt(1 + im*a*x)/sqrt(1 - im*a*x))))/sqrt(c + a^2*c*x^2) - (((7*im)/3)*a^3*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (2*a^3*c^2*sqrt(1 + a^2*x^2)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (2*a^3*c^2*sqrt(1 + a^2*x^2)*PolyLog(3, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2)]

    @test_int [x^3*(c + a^2*c*x^2)^(5/2)*atan(a*x)^2, x, 203, -((115*c^2*sqrt(c + a^2*c*x^2))/(4032*a^4)) - (115*c*(c + a^2*c*x^2)^(3/2))/(18144*a^4) - (23*(c + a^2*c*x^2)^(5/2))/(7560*a^4) + (c + a^2*c*x^2)^(7/2)/(252*a^4*c) + (47*c^2*x*sqrt(c + a^2*c*x^2)*atan(a*x))/(1344*a^3) - (205*c^2*x^3*sqrt(c + a^2*c*x^2)*atan(a*x))/(6048*a) - (103*a*c^2*x^5*sqrt(c + a^2*c*x^2)*atan(a*x))/1512 - (1/36)*a^3*c^2*x^7*sqrt(c + a^2*c*x^2)*atan(a*x) - (2*c^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(63*a^4) + (c^2*x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(63*a^2) + (5/21)*c^2*x^4*sqrt(c + a^2*c*x^2)*atan(a*x)^2 + (19/63)*a^2*c^2*x^6*sqrt(c + a^2*c*x^2)*atan(a*x)^2 + (1/9)*a^4*c^2*x^8*sqrt(c + a^2*c*x^2)*atan(a*x)^2 - (115*im*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(2016*a^4*sqrt(c + a^2*c*x^2)) + (115*im*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, -((im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x))))/(4032*a^4*sqrt(c + a^2*c*x^2)) - (115*im*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(4032*a^4*sqrt(c + a^2*c*x^2))]
    @test_int [x^2*(c + a^2*c*x^2)^(5/2)*atan(a*x)^2, x, 238, (43*c^2*x*sqrt(c + a^2*c*x^2))/(4032*a^2) + (29*c^2*x^3*sqrt(c + a^2*c*x^2))/1680 + (1/168)*a^2*c^2*x^5*sqrt(c + a^2*c*x^2) + (1373*c^2*sqrt(c + a^2*c*x^2)*atan(a*x))/(20160*a^3) - (737*c^2*x^2*sqrt(c + a^2*c*x^2)*atan(a*x))/(10080*a) - (83/840)*a*c^2*x^4*sqrt(c + a^2*c*x^2)*atan(a*x) - (1/28)*a^3*c^2*x^6*sqrt(c + a^2*c*x^2)*atan(a*x) + (5*c^2*x*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(128*a^2) + (59/192)*c^2*x^3*sqrt(c + a^2*c*x^2)*atan(a*x)^2 + (17/48)*a^2*c^2*x^5*sqrt(c + a^2*c*x^2)*atan(a*x)^2 + (1/8)*a^4*c^2*x^7*sqrt(c + a^2*c*x^2)*atan(a*x)^2 + (5*im*c^3*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^2)/(64*a^3*sqrt(c + a^2*c*x^2)) - (397*c^(5/2)*atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2)))/(5040*a^3) - (5*im*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/(64*a^3*sqrt(c + a^2*c*x^2)) + (5*im*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, im*ℯ^(im*atan(a*x))))/(64*a^3*sqrt(c + a^2*c*x^2)) + (5*c^3*sqrt(1 + a^2*x^2)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(64*a^3*sqrt(c + a^2*c*x^2)) - (5*c^3*sqrt(1 + a^2*x^2)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(64*a^3*sqrt(c + a^2*c*x^2))]
    @test_int [x*(c + a^2*c*x^2)^(5/2)*atan(a*x)^2, x, 6, (5*c^2*sqrt(c + a^2*c*x^2))/(56*a^2) + (5*c*(c + a^2*c*x^2)^(3/2))/(252*a^2) + (c + a^2*c*x^2)^(5/2)/(105*a^2) - (5*c^2*x*sqrt(c + a^2*c*x^2)*atan(a*x))/(56*a) - (5*c*x*(c + a^2*c*x^2)^(3/2)*atan(a*x))/(84*a) - (x*(c + a^2*c*x^2)^(5/2)*atan(a*x))/(21*a) + ((c + a^2*c*x^2)^(7/2)*atan(a*x)^2)/(7*a^2*c) + (((5*im)/28)*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(a^2*sqrt(c + a^2*c*x^2)) - (((5*im)/56)*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, ((-im)*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(a^2*sqrt(c + a^2*c*x^2)) + (((5*im)/56)*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(a^2*sqrt(c + a^2*c*x^2))]
    @test_int [(c + a^2*c*x^2)^(5/2)*atan(a*x)^2, x, 21, (17*c^2*x*sqrt(c + a^2*c*x^2))/180 + (c*x*(c + a^2*c*x^2)^(3/2))/60 - (5*c^2*sqrt(c + a^2*c*x^2)*atan(a*x))/(8*a) - (5*c*(c + a^2*c*x^2)^(3/2)*atan(a*x))/(36*a) - ((c + a^2*c*x^2)^(5/2)*atan(a*x))/(15*a) + (5*c^2*x*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/16 + (5*c*x*(c + a^2*c*x^2)^(3/2)*atan(a*x)^2)/24 + (x*(c + a^2*c*x^2)^(5/2)*atan(a*x)^2)/6 - (((5*im)/8)*c^3*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^2)/(a*sqrt(c + a^2*c*x^2)) + (259*c^(5/2)*atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2)))/(360*a) + (((5*im)/8)*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2)) - (((5*im)/8)*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, im*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2)) - (5*c^3*sqrt(1 + a^2*x^2)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(8*a*sqrt(c + a^2*c*x^2)) + (5*c^3*sqrt(1 + a^2*x^2)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(8*a*sqrt(c + a^2*c*x^2))]
    @test_int [((c + a^2*c*x^2)^(5/2)*atan(a*x)^2)/x, x, 24, (29*c^2*sqrt(c + a^2*c*x^2))/60 + (c*(c + a^2*c*x^2)^(3/2))/30 - (29*a*c^2*x*sqrt(c + a^2*c*x^2)*atan(a*x))/60 - (a*c*x*(c + a^2*c*x^2)^(3/2)*atan(a*x))/10 + c^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2 + (c*(c + a^2*c*x^2)^(3/2)*atan(a*x)^2)/3 + ((c + a^2*c*x^2)^(5/2)*atan(a*x)^2)/5 + (((149*im)/30)*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (2*c^3*sqrt(1 + a^2*x^2)*atan(a*x)^2*atanh(ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((2*im)*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((2*im)*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (((149*im)/60)*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, ((-im)*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) + (((149*im)/60)*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (2*c^3*sqrt(1 + a^2*x^2)*PolyLog(3, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (2*c^3*sqrt(1 + a^2*x^2)*PolyLog(3, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2)]
    @test_int [((c + a^2*c*x^2)^(5/2)*atan(a*x)^2)/x^2, x, 43, (a^2*c^2*x*sqrt(c + a^2*c*x^2))/12 - (7*a*c^2*sqrt(c + a^2*c*x^2)*atan(a*x))/4 - (a*c*(c + a^2*c*x^2)^(3/2)*atan(a*x))/6 - (c^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/x + (7*a^2*c^2*x*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/8 + (a^2*c*x*(c + a^2*c*x^2)^(3/2)*atan(a*x)^2)/4 - (((15*im)/4)*a*c^3*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^2)/sqrt(c + a^2*c*x^2) - (4*a*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*atanh(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) + (11*a*c^(5/2)*atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2)))/6 + (((15*im)/4)*a*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (((15*im)/4)*a*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((2*im)*a*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, -(sqrt(1 + im*a*x)/sqrt(1 - im*a*x))))/sqrt(c + a^2*c*x^2) - ((2*im)*a*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (15*a*c^3*sqrt(1 + a^2*x^2)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(4*sqrt(c + a^2*c*x^2)) + (15*a*c^3*sqrt(1 + a^2*x^2)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(4*sqrt(c + a^2*c*x^2))]
    @test_int [((c + a^2*c*x^2)^(5/2)*atan(a*x)^2)/x^3, x, 57, (a^2*c^2*sqrt(c + a^2*c*x^2))/3 - (a*c^2*sqrt(c + a^2*c*x^2)*atan(a*x))/x - (a^3*c^2*x*sqrt(c + a^2*c*x^2)*atan(a*x))/3 + 2*a^2*c^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2 - (c^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(2*x^2) + (a^2*c*(c + a^2*c*x^2)^(3/2)*atan(a*x)^2)/3 + (((26*im)/3)*a^2*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (5*a^2*c^3*sqrt(1 + a^2*x^2)*atan(a*x)^2*atanh(ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - a^2*c^(5/2)*atanh(sqrt(c + a^2*c*x^2)/sqrt(c)) + ((5*im)*a^2*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((5*im)*a^2*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (((13*im)/3)*a^2*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, ((-im)*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) + (((13*im)/3)*a^2*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (5*a^2*c^3*sqrt(1 + a^2*x^2)*PolyLog(3, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (5*a^2*c^3*sqrt(1 + a^2*x^2)*PolyLog(3, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2)]
    @test_int [((c + a^2*c*x^2)^(5/2)*atan(a*x)^2)/x^4, x, 48, -(a^2*c^2*sqrt(c + a^2*c*x^2))/(3*x) - a^3*c^2*sqrt(c + a^2*c*x^2)*atan(a*x) - (a*c^2*sqrt(c + a^2*c*x^2)*atan(a*x))/(3*x^2) - (2*a^2*c^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/x + (a^4*c^2*x*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/2 - (c*(c + a^2*c*x^2)^(3/2)*atan(a*x)^2)/(3*x^3) - ((5*im)*a^3*c^3*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^2)/sqrt(c + a^2*c*x^2) - (26*a^3*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*atanh(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(3*sqrt(c + a^2*c*x^2)) + a^3*c^(5/2)*atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2)) + ((5*im)*a^3*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((5*im)*a^3*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (((13*im)/3)*a^3*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, -(sqrt(1 + im*a*x)/sqrt(1 - im*a*x))))/sqrt(c + a^2*c*x^2) - (((13*im)/3)*a^3*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (5*a^3*c^3*sqrt(1 + a^2*x^2)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (5*a^3*c^3*sqrt(1 + a^2*x^2)*PolyLog(3, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2)]

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

    @test_int [(x^3*atan(a*x)^2)/sqrt(c + a^2*c*x^2), x, 8, sqrt(c + a^2*c*x^2)/(3*a^4*c) - (x*sqrt(c + a^2*c*x^2)*atan(a*x))/(3*a^3*c) - (2*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(3*a^4*c) + (x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(3*a^2*c) - (10*im*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(3*a^4*sqrt(c + a^2*c*x^2)) + (5*im*sqrt(1 + a^2*x^2)*PolyLog(2, -((im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x))))/(3*a^4*sqrt(c + a^2*c*x^2)) - (5*im*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(3*a^4*sqrt(c + a^2*c*x^2))]
    @test_int [(x^2*atan(a*x)^2)/sqrt(c + a^2*c*x^2), x, 13, -((sqrt(c + a^2*c*x^2)*atan(a*x))/(a^3*c)) + (x*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(2*a^2*c) + (im*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^2)/(a^3*sqrt(c + a^2*c*x^2)) + atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2))/(a^3*sqrt(c)) - (im*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/(a^3*sqrt(c + a^2*c*x^2)) + (im*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, im*ℯ^(im*atan(a*x))))/(a^3*sqrt(c + a^2*c*x^2)) + (sqrt(1 + a^2*x^2)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(a^3*sqrt(c + a^2*c*x^2)) - (sqrt(1 + a^2*x^2)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(a^3*sqrt(c + a^2*c*x^2))]
    @test_int [(x*atan(a*x)^2)/sqrt(c + a^2*c*x^2), x, 3, (sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(a^2*c) + ((4*im)*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(a^2*sqrt(c + a^2*c*x^2)) - ((2*im)*sqrt(1 + a^2*x^2)*PolyLog(2, ((-im)*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(a^2*sqrt(c + a^2*c*x^2)) + ((2*im)*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(a^2*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)^2/sqrt(c + a^2*c*x^2), x, 9, ((-2*im)*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^2)/(a*sqrt(c + a^2*c*x^2)) + ((2*im)*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2)) - ((2*im)*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, im*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2)) - (2*sqrt(1 + a^2*x^2)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2)) + (2*sqrt(1 + a^2*x^2)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)^2/(x*sqrt(c + a^2*c*x^2)), x, 9, (-2*sqrt(1 + a^2*x^2)*atan(a*x)^2*atanh(ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((2*im)*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((2*im)*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (2*sqrt(1 + a^2*x^2)*PolyLog(3, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (2*sqrt(1 + a^2*x^2)*PolyLog(3, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2)]
    @test_int [atan(a*x)^2/(x^2*sqrt(c + a^2*c*x^2)), x, 3, -((sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(c*x)) - (4*a*sqrt(1 + a^2*x^2)*atan(a*x)*atanh(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) + ((2*im)*a*sqrt(1 + a^2*x^2)*PolyLog(2, -(sqrt(1 + im*a*x)/sqrt(1 - im*a*x))))/sqrt(c + a^2*c*x^2) - ((2*im)*a*sqrt(1 + a^2*x^2)*PolyLog(2, sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2)]
    @test_int [atan(a*x)^2/(x^3*sqrt(c + a^2*c*x^2)), x, 14, -((a*sqrt(c + a^2*c*x^2)*atan(a*x))/(c*x)) - (sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(2*c*x^2) + (a^2*sqrt(1 + a^2*x^2)*atan(a*x)^2*atanh(ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (a^2*atanh(sqrt(c + a^2*c*x^2)/sqrt(c)))/sqrt(c) - (im*a^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (im*a^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (a^2*sqrt(1 + a^2*x^2)*PolyLog(3, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (a^2*sqrt(1 + a^2*x^2)*PolyLog(3, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2)]
    @test_int [atan(a*x)^2/(x^4*sqrt(c + a^2*c*x^2)), x, 8, -(a^2*sqrt(c + a^2*c*x^2))/(3*c*x) - (a*sqrt(c + a^2*c*x^2)*atan(a*x))/(3*c*x^2) - (sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(3*c*x^3) + (2*a^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(3*c*x) + (10*a^3*sqrt(1 + a^2*x^2)*atan(a*x)*atanh(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(3*sqrt(c + a^2*c*x^2)) - (((5*im)/3)*a^3*sqrt(1 + a^2*x^2)*PolyLog(2, -(sqrt(1 + im*a*x)/sqrt(1 - im*a*x))))/sqrt(c + a^2*c*x^2) + (((5*im)/3)*a^3*sqrt(1 + a^2*x^2)*PolyLog(2, sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2)]

    @test_int [(x^3*atan(a*x)^2)/(c + a^2*c*x^2)^(3/2), x, 6, -2/(a^4*c*sqrt(c + a^2*c*x^2)) - (2*x*atan(a*x))/(a^3*c*sqrt(c + a^2*c*x^2)) + atan(a*x)^2/(a^4*c*sqrt(c + a^2*c*x^2)) + (sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(a^4*c^2) + ((4*im)*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(a^4*c*sqrt(c + a^2*c*x^2)) - ((2*im)*sqrt(1 + a^2*x^2)*PolyLog(2, ((-im)*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(a^4*c*sqrt(c + a^2*c*x^2)) + ((2*im)*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(a^4*c*sqrt(c + a^2*c*x^2))]
    @test_int [(x^2*atan(a*x)^2)/(c + a^2*c*x^2)^(3/2), x, 12, (2*x)/(a^2*c*sqrt(c + a^2*c*x^2)) - (2*atan(a*x))/(a^3*c*sqrt(c + a^2*c*x^2)) - (x*atan(a*x)^2)/(a^2*c*sqrt(c + a^2*c*x^2)) - ((2*im)*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^2)/(a^3*c*sqrt(c + a^2*c*x^2)) + ((2*im)*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/(a^3*c*sqrt(c + a^2*c*x^2)) - ((2*im)*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, im*ℯ^(im*atan(a*x))))/(a^3*c*sqrt(c + a^2*c*x^2)) - (2*sqrt(1 + a^2*x^2)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(a^3*c*sqrt(c + a^2*c*x^2)) + (2*sqrt(1 + a^2*x^2)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(a^3*c*sqrt(c + a^2*c*x^2))]
    @test_int [(x*atan(a*x)^2)/(c + a^2*c*x^2)^(3/2), x, 2, 2/(a^2*c*sqrt(c + a^2*c*x^2)) + (2*x*atan(a*x))/(a*c*sqrt(c + a^2*c*x^2)) - atan(a*x)^2/(a^2*c*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)^2/(c + a^2*c*x^2)^(3/2), x, 2, (-2*x)/(c*sqrt(c + a^2*c*x^2)) + (2*atan(a*x))/(a*c*sqrt(c + a^2*c*x^2)) + (x*atan(a*x)^2)/(c*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)^2/(x*(c + a^2*c*x^2)^(3/2)), x, 12, -2/(c*sqrt(c + a^2*c*x^2)) - (2*a*x*atan(a*x))/(c*sqrt(c + a^2*c*x^2)) + atan(a*x)^2/(c*sqrt(c + a^2*c*x^2)) - (2*sqrt(1 + a^2*x^2)*atan(a*x)^2*atanh(ℯ^(im*atan(a*x))))/(c*sqrt(c + a^2*c*x^2)) + ((2*im)*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, -ℯ^(im*atan(a*x))))/(c*sqrt(c + a^2*c*x^2)) - ((2*im)*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, ℯ^(im*atan(a*x))))/(c*sqrt(c + a^2*c*x^2)) - (2*sqrt(1 + a^2*x^2)*PolyLog(3, -ℯ^(im*atan(a*x))))/(c*sqrt(c + a^2*c*x^2)) + (2*sqrt(1 + a^2*x^2)*PolyLog(3, ℯ^(im*atan(a*x))))/(c*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)^2/(x^2*(c + a^2*c*x^2)^(3/2)), x, 6, (2*a^2*x)/(c*sqrt(c + a^2*c*x^2)) - (2*a*atan(a*x))/(c*sqrt(c + a^2*c*x^2)) - (a^2*x*atan(a*x)^2)/(c*sqrt(c + a^2*c*x^2)) - (sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(c^2*x) - (4*a*sqrt(1 + a^2*x^2)*atan(a*x)*atanh(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(c*sqrt(c + a^2*c*x^2)) + ((2*im)*a*sqrt(1 + a^2*x^2)*PolyLog(2, -(sqrt(1 + im*a*x)/sqrt(1 - im*a*x))))/(c*sqrt(c + a^2*c*x^2)) - ((2*im)*a*sqrt(1 + a^2*x^2)*PolyLog(2, sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(c*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)^2/(x^3*(c + a^2*c*x^2)^(3/2)), x, 27, (2*a^2)/(c*sqrt(c + a^2*c*x^2)) + (2*a^3*x*atan(a*x))/(c*sqrt(c + a^2*c*x^2)) - (a*sqrt(c + a^2*c*x^2)*atan(a*x))/(c^2*x) - (a^2*atan(a*x)^2)/(c*sqrt(c + a^2*c*x^2)) - (sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(2*c^2*x^2) + (3*a^2*sqrt(1 + a^2*x^2)*atan(a*x)^2*atanh(ℯ^(im*atan(a*x))))/(c*sqrt(c + a^2*c*x^2)) - (a^2*atanh(sqrt(c + a^2*c*x^2)/sqrt(c)))/c^(3/2) - ((3*im)*a^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, -ℯ^(im*atan(a*x))))/(c*sqrt(c + a^2*c*x^2)) + ((3*im)*a^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, ℯ^(im*atan(a*x))))/(c*sqrt(c + a^2*c*x^2)) + (3*a^2*sqrt(1 + a^2*x^2)*PolyLog(3, -ℯ^(im*atan(a*x))))/(c*sqrt(c + a^2*c*x^2)) - (3*a^2*sqrt(1 + a^2*x^2)*PolyLog(3, ℯ^(im*atan(a*x))))/(c*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)^2/(x^4*(c + a^2*c*x^2)^(3/2)), x, 15, (-2*a^4*x)/(c*sqrt(c + a^2*c*x^2)) - (a^2*sqrt(c + a^2*c*x^2))/(3*c^2*x) + (2*a^3*atan(a*x))/(c*sqrt(c + a^2*c*x^2)) - (a*sqrt(c + a^2*c*x^2)*atan(a*x))/(3*c^2*x^2) + (a^4*x*atan(a*x)^2)/(c*sqrt(c + a^2*c*x^2)) - (sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(3*c^2*x^3) + (5*a^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(3*c^2*x) + (22*a^3*sqrt(1 + a^2*x^2)*atan(a*x)*atanh(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(3*c*sqrt(c + a^2*c*x^2)) - (((11*im)/3)*a^3*sqrt(1 + a^2*x^2)*PolyLog(2, -(sqrt(1 + im*a*x)/sqrt(1 - im*a*x))))/(c*sqrt(c + a^2*c*x^2)) + (((11*im)/3)*a^3*sqrt(1 + a^2*x^2)*PolyLog(2, sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(c*sqrt(c + a^2*c*x^2))]

    @test_int [(x^5*atan(a*x)^2)/(c + a^2*c*x^2)^(5/2), x, 13, 2/(27*a^6*c*(c + a^2*c*x^2)^(3/2)) - 32/(9*a^6*c^2*sqrt(c + a^2*c*x^2)) - (2*x^3*atan(a*x))/(9*a^3*c*(c + a^2*c*x^2)^(3/2)) - (10*x*atan(a*x))/(3*a^5*c^2*sqrt(c + a^2*c*x^2)) + (x^2*atan(a*x)^2)/(3*a^4*c*(c + a^2*c*x^2)^(3/2)) + (5*atan(a*x)^2)/(3*a^6*c^2*sqrt(c + a^2*c*x^2)) + (sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(a^6*c^3) + (4*im*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(a^6*c^2*sqrt(c + a^2*c*x^2)) - (2*im*sqrt(1 + a^2*x^2)*PolyLog(2, -((im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x))))/(a^6*c^2*sqrt(c + a^2*c*x^2)) + (2*im*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(a^6*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [(x^4*atan(a*x)^2)/(c + a^2*c*x^2)^(5/2), x, 17, (2*x^3)/(27*a^2*c*(c + a^2*c*x^2)^(3/2)) + (22*x)/(9*a^4*c^2*sqrt(c + a^2*c*x^2)) - (2*x^2*atan(a*x))/(9*a^3*c*(c + a^2*c*x^2)^(3/2)) - (22*atan(a*x))/(9*a^5*c^2*sqrt(c + a^2*c*x^2)) - (x^3*atan(a*x)^2)/(3*a^2*c*(c + a^2*c*x^2)^(3/2)) - (x*atan(a*x)^2)/(a^4*c^2*sqrt(c + a^2*c*x^2)) - (2*im*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^2)/(a^5*c^2*sqrt(c + a^2*c*x^2)) + (2*im*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/(a^5*c^2*sqrt(c + a^2*c*x^2)) - (2*im*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, im*ℯ^(im*atan(a*x))))/(a^5*c^2*sqrt(c + a^2*c*x^2)) - (2*sqrt(1 + a^2*x^2)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(a^5*c^2*sqrt(c + a^2*c*x^2)) + (2*sqrt(1 + a^2*x^2)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(a^5*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [(x^3*atan(a*x)^2)/(c + a^2*c*x^2)^(5/2), x, 6, -(2/(27*a^4*c*(c + a^2*c*x^2)^(3/2))) + 14/(9*a^4*c^2*sqrt(c + a^2*c*x^2)) + (2*x^3*atan(a*x))/(9*a*c*(c + a^2*c*x^2)^(3/2)) + (4*x*atan(a*x))/(3*a^3*c^2*sqrt(c + a^2*c*x^2)) - (x^2*atan(a*x)^2)/(3*a^2*c*(c + a^2*c*x^2)^(3/2)) - (2*atan(a*x)^2)/(3*a^4*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [(x^2*atan(a*x)^2)/(c + a^2*c*x^2)^(5/2), x, 4, -((2*x^3)/(27*c*(c + a^2*c*x^2)^(3/2))) - (4*x)/(9*a^2*c^2*sqrt(c + a^2*c*x^2)) + (2*x^2*atan(a*x))/(9*a*c*(c + a^2*c*x^2)^(3/2)) + (4*atan(a*x))/(9*a^3*c^2*sqrt(c + a^2*c*x^2)) + (x^3*atan(a*x)^2)/(3*c*(c + a^2*c*x^2)^(3/2))]
    @test_int [(x*atan(a*x)^2)/(c + a^2*c*x^2)^(5/2), x, 3, 2/(27*a^2*c*(c + a^2*c*x^2)^(3/2)) + 4/(9*a^2*c^2*sqrt(c + a^2*c*x^2)) + (2*x*atan(a*x))/(9*a*c*(c + a^2*c*x^2)^(3/2)) + (4*x*atan(a*x))/(9*a*c^2*sqrt(c + a^2*c*x^2)) - atan(a*x)^2/(3*a^2*c*(c + a^2*c*x^2)^(3/2))]
    @test_int [atan(a*x)^2/(c + a^2*c*x^2)^(5/2), x, 5, (-2*x)/(27*c*(c + a^2*c*x^2)^(3/2)) - (40*x)/(27*c^2*sqrt(c + a^2*c*x^2)) + (2*atan(a*x))/(9*a*c*(c + a^2*c*x^2)^(3/2)) + (4*atan(a*x))/(3*a*c^2*sqrt(c + a^2*c*x^2)) + (x*atan(a*x)^2)/(3*c*(c + a^2*c*x^2)^(3/2)) + (2*x*atan(a*x)^2)/(3*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)^2/(x*(c + a^2*c*x^2)^(5/2)), x, 16, -2/(27*c*(c + a^2*c*x^2)^(3/2)) - 22/(9*c^2*sqrt(c + a^2*c*x^2)) - (2*a*x*atan(a*x))/(9*c*(c + a^2*c*x^2)^(3/2)) - (22*a*x*atan(a*x))/(9*c^2*sqrt(c + a^2*c*x^2)) + atan(a*x)^2/(3*c*(c + a^2*c*x^2)^(3/2)) + atan(a*x)^2/(c^2*sqrt(c + a^2*c*x^2)) - (2*sqrt(1 + a^2*x^2)*atan(a*x)^2*atanh(ℯ^(im*atan(a*x))))/(c^2*sqrt(c + a^2*c*x^2)) + ((2*im)*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, -ℯ^(im*atan(a*x))))/(c^2*sqrt(c + a^2*c*x^2)) - ((2*im)*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, ℯ^(im*atan(a*x))))/(c^2*sqrt(c + a^2*c*x^2)) - (2*sqrt(1 + a^2*x^2)*PolyLog(3, -ℯ^(im*atan(a*x))))/(c^2*sqrt(c + a^2*c*x^2)) + (2*sqrt(1 + a^2*x^2)*PolyLog(3, ℯ^(im*atan(a*x))))/(c^2*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)^2/(x^2*(c + a^2*c*x^2)^(5/2)), x, 12, (2*a^2*x)/(27*c*(c + a^2*c*x^2)^(3/2)) + (94*a^2*x)/(27*c^2*sqrt(c + a^2*c*x^2)) - (2*a*atan(a*x))/(9*c*(c + a^2*c*x^2)^(3/2)) - (10*a*atan(a*x))/(3*c^2*sqrt(c + a^2*c*x^2)) - (a^2*x*atan(a*x)^2)/(3*c*(c + a^2*c*x^2)^(3/2)) - (5*a^2*x*atan(a*x)^2)/(3*c^2*sqrt(c + a^2*c*x^2)) - (sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(c^3*x) - (4*a*sqrt(1 + a^2*x^2)*atan(a*x)*atanh(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(c^2*sqrt(c + a^2*c*x^2)) + ((2*im)*a*sqrt(1 + a^2*x^2)*PolyLog(2, -(sqrt(1 + im*a*x)/sqrt(1 - im*a*x))))/(c^2*sqrt(c + a^2*c*x^2)) - ((2*im)*a*sqrt(1 + a^2*x^2)*PolyLog(2, sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(c^2*sqrt(c + a^2*c*x^2))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x^2)^p*atan(a*x)^2*with*d=a^2*c*and*m*symbolic=#

    @test_int [x^m*(c + a^2*c*x^2)^2*atan(a*x)^2, x, 0, Unintegrable(x^m*(c + a^2*c*x^2)^2*atan(a*x)^2, x)]
    @test_int [x^m*(c + a^2*c*x^2)^1*atan(a*x)^2, x, 0, Unintegrable(x^m*(c + a^2*c*x^2)*atan(a*x)^2, x)]
    @test_int [(x^m*atan(a*x)^2)/(c + a^2*c*x^2)^1, x, 0, Unintegrable((x^m*atan(a*x)^2)/(c + a^2*c*x^2), x)]
    @test_int [(x^m*atan(a*x)^2)/(c + a^2*c*x^2)^2, x, 0, Unintegrable((x^m*atan(a*x)^2)/(c + a^2*c*x^2)^2, x)]

    @test_int [x^m*(c + a^2*c*x^2)^(3/2)*atan(a*x)^2, x, 0, Unintegrable(x^m*(c + a^2*c*x^2)^(3/2)*atan(a*x)^2, x)]
    @test_int [x^m*(c + a^2*c*x^2)^(1/2)*atan(a*x)^2, x, 0, Unintegrable(x^m*sqrt(c + a^2*c*x^2)*atan(a*x)^2, x)]
    @test_int [(x^m*atan(a*x)^2)/(c + a^2*c*x^2)^(1/2), x, 0, Unintegrable((x^m*atan(a*x)^2)/sqrt(c + a^2*c*x^2), x)]
    @test_int [(x^m*atan(a*x)^2)/(c + a^2*c*x^2)^(3/2), x, 0, Unintegrable((x^m*atan(a*x)^2)/(c + a^2*c*x^2)^(3/2), x)]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d+c^2*d*x^2)^q*(a+b*atan(c*x))^3=#

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

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

    @test_int [x^3*(c + a^2*c*x^2)*atan(a*x)^3, x, 52, (c*x)/(15*a^3) - (c*x^3)/(60*a) - (c*atan(a*x))/(15*a^4) - (c*x^2*atan(a*x))/(60*a^2) + (c*x^4*atan(a*x))/20 + (((7*im)/30)*c*atan(a*x)^2)/a^4 + (c*x*atan(a*x)^2)/(4*a^3) - (c*x^3*atan(a*x)^2)/(12*a) - (a*c*x^5*atan(a*x)^2)/10 - (c*atan(a*x)^3)/(12*a^4) + (c*x^4*atan(a*x)^3)/4 + (a^2*c*x^6*atan(a*x)^3)/6 + (7*c*atan(a*x)*log(2/(1 + im*a*x)))/(15*a^4) + (((7*im)/30)*c*PolyLog(2, 1 - 2/(1 + im*a*x)))/a^4]
    @test_int [x^2*(c + a^2*c*x^2)*atan(a*x)^3, x, 34, -(c*x^2)/(20*a) + (c*x*atan(a*x))/(10*a^2) + (c*x^3*atan(a*x))/10 - (c*atan(a*x)^2)/(20*a^3) - (c*x^2*atan(a*x)^2)/(5*a) - (3*a*c*x^4*atan(a*x)^2)/20 - (((2*im)/15)*c*atan(a*x)^3)/a^3 + (c*x^3*atan(a*x)^3)/3 + (a^2*c*x^5*atan(a*x)^3)/5 - (2*c*atan(a*x)^2*log(2/(1 + im*a*x)))/(5*a^3) - (((2*im)/5)*c*atan(a*x)*PolyLog(2, 1 - 2/(1 + im*a*x)))/a^3 - (c*PolyLog(3, 1 - 2/(1 + im*a*x)))/(5*a^3)]
    @test_int [x*(c + a^2*c*x^2)*atan(a*x)^3, x, 8, -(c*x)/(4*a) + (c*(1 + a^2*x^2)*atan(a*x))/(4*a^2) - ((im/2)*c*atan(a*x)^2)/a^2 - (c*x*atan(a*x)^2)/(2*a) - (c*x*(1 + a^2*x^2)*atan(a*x)^2)/(4*a) + (c*(1 + a^2*x^2)^2*atan(a*x)^3)/(4*a^2) - (c*atan(a*x)*log(2/(1 + im*a*x)))/a^2 - ((im/2)*c*PolyLog(2, 1 - 2/(1 + im*a*x)))/a^2]
    @test_int [(c + a^2*c*x^2)*atan(a*x)^3, x, 8, c*x*atan(a*x) - (c*(1 + a^2*x^2)*atan(a*x)^2)/(2*a) + (((2*im)/3)*c*atan(a*x)^3)/a + (2*c*x*atan(a*x)^3)/3 + (c*x*(1 + a^2*x^2)*atan(a*x)^3)/3 + (2*c*atan(a*x)^2*log(2/(1 + im*a*x)))/a - (c*log(1 + a^2*x^2))/(2*a) + ((2*im)*c*atan(a*x)*PolyLog(2, 1 - 2/(1 + im*a*x)))/a + (c*PolyLog(3, 1 - 2/(1 + im*a*x)))/a]
    @test_int [((c + a^2*c*x^2)*atan(a*x)^3)/x, x, 17, ((-3*im)/2)*c*atan(a*x)^2 - (3*a*c*x*atan(a*x)^2)/2 + (c*atan(a*x)^3)/2 + (a^2*c*x^2*atan(a*x)^3)/2 + 2*c*atan(a*x)^3*atanh(1 - 2/(1 + im*a*x)) - 3*c*atan(a*x)*log(2/(1 + im*a*x)) - ((3*im)/2)*c*PolyLog(2, 1 - 2/(1 + im*a*x)) - ((3*im)/2)*c*atan(a*x)^2*PolyLog(2, 1 - 2/(1 + im*a*x)) + ((3*im)/2)*c*atan(a*x)^2*PolyLog(2, -1 + 2/(1 + im*a*x)) - (3*c*atan(a*x)*PolyLog(3, 1 - 2/(1 + im*a*x)))/2 + (3*c*atan(a*x)*PolyLog(3, -1 + 2/(1 + im*a*x)))/2 + ((3*im)/4)*c*PolyLog(4, 1 - 2/(1 + im*a*x)) - ((3*im)/4)*c*PolyLog(4, -1 + 2/(1 + im*a*x))]
    @test_int [((c + a^2*c*x^2)*atan(a*x)^3)/x^2, x, 11, -((c*atan(a*x)^3)/x) + a^2*c*x*atan(a*x)^3 + 3*a*c*atan(a*x)^2*log(2/(1 + im*a*x)) + 3*a*c*atan(a*x)^2*log(2 - 2/(1 - im*a*x)) - (3*im)*a*c*atan(a*x)*PolyLog(2, -1 + 2/(1 - im*a*x)) + (3*im)*a*c*atan(a*x)*PolyLog(2, 1 - 2/(1 + im*a*x)) + (3*a*c*PolyLog(3, -1 + 2/(1 - im*a*x)))/2 + (3*a*c*PolyLog(3, 1 - 2/(1 + im*a*x)))/2]
    @test_int [((c + a^2*c*x^2)*atan(a*x)^3)/x^3, x, 16, ((-3*im)/2)*a^2*c*atan(a*x)^2 - (3*a*c*atan(a*x)^2)/(2*x) - (a^2*c*atan(a*x)^3)/2 - (c*atan(a*x)^3)/(2*x^2) + 2*a^2*c*atan(a*x)^3*atanh(1 - 2/(1 + im*a*x)) + 3*a^2*c*atan(a*x)*log(2 - 2/(1 - im*a*x)) - ((3*im)/2)*a^2*c*PolyLog(2, -1 + 2/(1 - im*a*x)) - ((3*im)/2)*a^2*c*atan(a*x)^2*PolyLog(2, 1 - 2/(1 + im*a*x)) + ((3*im)/2)*a^2*c*atan(a*x)^2*PolyLog(2, -1 + 2/(1 + im*a*x)) - (3*a^2*c*atan(a*x)*PolyLog(3, 1 - 2/(1 + im*a*x)))/2 + (3*a^2*c*atan(a*x)*PolyLog(3, -1 + 2/(1 + im*a*x)))/2 + ((3*im)/4)*a^2*c*PolyLog(4, 1 - 2/(1 + im*a*x)) - ((3*im)/4)*a^2*c*PolyLog(4, -1 + 2/(1 + im*a*x))]
    @test_int [((c + a^2*c*x^2)*atan(a*x)^3)/x^4, x, 20, -((a^2*c*atan(a*x))/x) - (1/2)*a^3*c*atan(a*x)^2 - (a*c*atan(a*x)^2)/(2*x^2) - (2/3)*im*a^3*c*atan(a*x)^3 - (c*atan(a*x)^3)/(3*x^3) - (a^2*c*atan(a*x)^3)/x + a^3*c*log(x) + 2*a^3*c*atan(a*x)^2*log(2 - 2/(1 - im*a*x)) - (1/2)*a^3*c*log(1 + a^2*x^2) - 2*im*a^3*c*atan(a*x)*PolyLog(2, -1 + 2/(1 - im*a*x)) + a^3*c*PolyLog(3, -1 + 2/(1 - im*a*x))]

    @test_int [x^3*(c + a^2*c*x^2)^2*atan(a*x)^3, x, 106, (c^2*x)/(21*a^3) - (c^2*x^3)/(168*a) - (a*c^2*x^5)/280 - (c^2*atan(a*x))/(21*a^4) - (5*c^2*x^2*atan(a*x))/(168*a^2) + (c^2*x^4*atan(a*x))/28 + (a^2*c^2*x^6*atan(a*x))/56 + (((2*im)/21)*c^2*atan(a*x)^2)/a^4 + (c^2*x*atan(a*x)^2)/(8*a^3) - (c^2*x^3*atan(a*x)^2)/(24*a) - (a*c^2*x^5*atan(a*x)^2)/8 - (3*a^3*c^2*x^7*atan(a*x)^2)/56 - (c^2*atan(a*x)^3)/(24*a^4) + (c^2*x^4*atan(a*x)^3)/4 + (a^2*c^2*x^6*atan(a*x)^3)/3 + (a^4*c^2*x^8*atan(a*x)^3)/8 + (4*c^2*atan(a*x)*log(2/(1 + im*a*x)))/(21*a^4) + (((2*im)/21)*c^2*PolyLog(2, 1 - 2/(1 + im*a*x)))/a^4]
    @test_int [x^2*(c + a^2*c*x^2)^2*atan(a*x)^3, x, 73, (-11*c^2*x^2)/(420*a) - (a*c^2*x^4)/140 - (c^2*x*atan(a*x))/(70*a^2) + (17*c^2*x^3*atan(a*x))/210 + (a^2*c^2*x^5*atan(a*x))/35 + (c^2*atan(a*x)^2)/(140*a^3) - (4*c^2*x^2*atan(a*x)^2)/(35*a) - (27*a*c^2*x^4*atan(a*x)^2)/140 - (a^3*c^2*x^6*atan(a*x)^2)/14 - (((8*im)/105)*c^2*atan(a*x)^3)/a^3 + (c^2*x^3*atan(a*x)^3)/3 + (2*a^2*c^2*x^5*atan(a*x)^3)/5 + (a^4*c^2*x^7*atan(a*x)^3)/7 - (8*c^2*atan(a*x)^2*log(2/(1 + im*a*x)))/(35*a^3) + (c^2*log(1 + a^2*x^2))/(30*a^3) - (((8*im)/35)*c^2*atan(a*x)*PolyLog(2, 1 - 2/(1 + im*a*x)))/a^3 - (4*c^2*PolyLog(3, 1 - 2/(1 + im*a*x)))/(35*a^3)]
    @test_int [x*(c + a^2*c*x^2)^2*atan(a*x)^3, x, 10, (-11*c^2*x)/(60*a) - (a*c^2*x^3)/60 + (2*c^2*(1 + a^2*x^2)*atan(a*x))/(15*a^2) + (c^2*(1 + a^2*x^2)^2*atan(a*x))/(20*a^2) - (((4*im)/15)*c^2*atan(a*x)^2)/a^2 - (4*c^2*x*atan(a*x)^2)/(15*a) - (2*c^2*x*(1 + a^2*x^2)*atan(a*x)^2)/(15*a) - (c^2*x*(1 + a^2*x^2)^2*atan(a*x)^2)/(10*a) + (c^2*(1 + a^2*x^2)^3*atan(a*x)^3)/(6*a^2) - (8*c^2*atan(a*x)*log(2/(1 + im*a*x)))/(15*a^2) - (((4*im)/15)*c^2*PolyLog(2, 1 - 2/(1 + im*a*x)))/a^2]
    @test_int [(c + a^2*c*x^2)^2*atan(a*x)^3, x, 12, -(c^2*(1 + a^2*x^2))/(20*a) + c^2*x*atan(a*x) + (c^2*x*(1 + a^2*x^2)*atan(a*x))/10 - (2*c^2*(1 + a^2*x^2)*atan(a*x)^2)/(5*a) - (3*c^2*(1 + a^2*x^2)^2*atan(a*x)^2)/(20*a) + (((8*im)/15)*c^2*atan(a*x)^3)/a + (8*c^2*x*atan(a*x)^3)/15 + (4*c^2*x*(1 + a^2*x^2)*atan(a*x)^3)/15 + (c^2*x*(1 + a^2*x^2)^2*atan(a*x)^3)/5 + (8*c^2*atan(a*x)^2*log(2/(1 + im*a*x)))/(5*a) - (c^2*log(1 + a^2*x^2))/(2*a) + (((8*im)/5)*c^2*atan(a*x)*PolyLog(2, 1 - 2/(1 + im*a*x)))/a + (4*c^2*PolyLog(3, 1 - 2/(1 + im*a*x)))/(5*a)]
    @test_int [((c + a^2*c*x^2)^2*atan(a*x)^3)/x, x, 36, -(a*c^2*x)/4 + (c^2*atan(a*x))/4 + (a^2*c^2*x^2*atan(a*x))/4 - (2*im)*c^2*atan(a*x)^2 - (9*a*c^2*x*atan(a*x)^2)/4 - (a^3*c^2*x^3*atan(a*x)^2)/4 + (3*c^2*atan(a*x)^3)/4 + a^2*c^2*x^2*atan(a*x)^3 + (a^4*c^2*x^4*atan(a*x)^3)/4 + 2*c^2*atan(a*x)^3*atanh(1 - 2/(1 + im*a*x)) - 4*c^2*atan(a*x)*log(2/(1 + im*a*x)) - (2*im)*c^2*PolyLog(2, 1 - 2/(1 + im*a*x)) - ((3*im)/2)*c^2*atan(a*x)^2*PolyLog(2, 1 - 2/(1 + im*a*x)) + ((3*im)/2)*c^2*atan(a*x)^2*PolyLog(2, -1 + 2/(1 + im*a*x)) - (3*c^2*atan(a*x)*PolyLog(3, 1 - 2/(1 + im*a*x)))/2 + (3*c^2*atan(a*x)*PolyLog(3, -1 + 2/(1 + im*a*x)))/2 + ((3*im)/4)*c^2*PolyLog(4, 1 - 2/(1 + im*a*x)) - ((3*im)/4)*c^2*PolyLog(4, -1 + 2/(1 + im*a*x))]
    @test_int [((c + a^2*c*x^2)^2*atan(a*x)^3)/x^2, x, 23, a^2*c^2*x*atan(a*x) - (a*c^2*atan(a*x)^2)/2 - (a^3*c^2*x^2*atan(a*x)^2)/2 + ((2*im)/3)*a*c^2*atan(a*x)^3 - (c^2*atan(a*x)^3)/x + 2*a^2*c^2*x*atan(a*x)^3 + (a^4*c^2*x^3*atan(a*x)^3)/3 + 5*a*c^2*atan(a*x)^2*log(2/(1 + im*a*x)) + 3*a*c^2*atan(a*x)^2*log(2 - 2/(1 - im*a*x)) - (a*c^2*log(1 + a^2*x^2))/2 - (3*im)*a*c^2*atan(a*x)*PolyLog(2, -1 + 2/(1 - im*a*x)) + (5*im)*a*c^2*atan(a*x)*PolyLog(2, 1 - 2/(1 + im*a*x)) + (3*a*c^2*PolyLog(3, -1 + 2/(1 - im*a*x)))/2 + (5*a*c^2*PolyLog(3, 1 - 2/(1 + im*a*x)))/2]
    @test_int [((c + a^2*c*x^2)^2*atan(a*x)^3)/x^3, x, 25, (-3*im)*a^2*c^2*atan(a*x)^2 - (3*a*c^2*atan(a*x)^2)/(2*x) - (3*a^3*c^2*x*atan(a*x)^2)/2 - (c^2*atan(a*x)^3)/(2*x^2) + (a^4*c^2*x^2*atan(a*x)^3)/2 + 4*a^2*c^2*atan(a*x)^3*atanh(1 - 2/(1 + im*a*x)) - 3*a^2*c^2*atan(a*x)*log(2/(1 + im*a*x)) + 3*a^2*c^2*atan(a*x)*log(2 - 2/(1 - im*a*x)) - ((3*im)/2)*a^2*c^2*PolyLog(2, -1 + 2/(1 - im*a*x)) - ((3*im)/2)*a^2*c^2*PolyLog(2, 1 - 2/(1 + im*a*x)) - (3*im)*a^2*c^2*atan(a*x)^2*PolyLog(2, 1 - 2/(1 + im*a*x)) + (3*im)*a^2*c^2*atan(a*x)^2*PolyLog(2, -1 + 2/(1 + im*a*x)) - 3*a^2*c^2*atan(a*x)*PolyLog(3, 1 - 2/(1 + im*a*x)) + 3*a^2*c^2*atan(a*x)*PolyLog(3, -1 + 2/(1 + im*a*x)) + ((3*im)/2)*a^2*c^2*PolyLog(4, 1 - 2/(1 + im*a*x)) - ((3*im)/2)*a^2*c^2*PolyLog(4, -1 + 2/(1 + im*a*x))]
    @test_int [((c + a^2*c*x^2)^2*atan(a*x)^3)/x^4, x, 26, -((a^2*c^2*atan(a*x))/x) - (1/2)*a^3*c^2*atan(a*x)^2 - (a*c^2*atan(a*x)^2)/(2*x^2) - (2/3)*im*a^3*c^2*atan(a*x)^3 - (c^2*atan(a*x)^3)/(3*x^3) - (2*a^2*c^2*atan(a*x)^3)/x + a^4*c^2*x*atan(a*x)^3 + a^3*c^2*log(x) + 3*a^3*c^2*atan(a*x)^2*log(2/(1 + im*a*x)) + 5*a^3*c^2*atan(a*x)^2*log(2 - 2/(1 - im*a*x)) - (1/2)*a^3*c^2*log(1 + a^2*x^2) - 5*im*a^3*c^2*atan(a*x)*PolyLog(2, -1 + 2/(1 - im*a*x)) + 3*im*a^3*c^2*atan(a*x)*PolyLog(2, 1 - 2/(1 + im*a*x)) + (5/2)*a^3*c^2*PolyLog(3, -1 + 2/(1 - im*a*x)) + (3/2)*a^3*c^2*PolyLog(3, 1 - 2/(1 + im*a*x))]

    @test_int [x^3*(c + a^2*c*x^2)^3*atan(a*x)^3, x, 184, (389*c^3*x)/(12600*a^3) - (17*c^3*x^3)/(9450*a) - (a*c^3*x^5)/252 - (a^3*c^3*x^7)/840 - (389*c^3*atan(a*x))/(12600*a^4) - (107*c^3*x^2*atan(a*x))/(4200*a^2) + (53*c^3*x^4*atan(a*x))/2100 + (71*a^2*c^3*x^6*atan(a*x))/2520 + (a^4*c^3*x^8*atan(a*x))/120 + (((26*im)/525)*c^3*atan(a*x)^2)/a^4 + (3*c^3*x*atan(a*x)^2)/(40*a^3) - (c^3*x^3*atan(a*x)^2)/(40*a) - (27*a*c^3*x^5*atan(a*x)^2)/200 - (33*a^3*c^3*x^7*atan(a*x)^2)/280 - (a^5*c^3*x^9*atan(a*x)^2)/30 - (c^3*atan(a*x)^3)/(40*a^4) + (c^3*x^4*atan(a*x)^3)/4 + (a^2*c^3*x^6*atan(a*x)^3)/2 + (3*a^4*c^3*x^8*atan(a*x)^3)/8 + (a^6*c^3*x^10*atan(a*x)^3)/10 + (52*c^3*atan(a*x)*log(2/(1 + im*a*x)))/(525*a^4) + (((26*im)/525)*c^3*PolyLog(2, 1 - 2/(1 + im*a*x)))/a^4]
    @test_int [x^2*(c + a^2*c*x^2)^3*atan(a*x)^3, x, 132, (-107*c^3*x^2)/(7560*a) - (11*a*c^3*x^4)/1260 - (a^3*c^3*x^6)/504 - (47*c^3*x*atan(a*x))/(1260*a^2) + (239*c^3*x^3*atan(a*x))/3780 + (59*a^2*c^3*x^5*atan(a*x))/1260 + (a^4*c^3*x^7*atan(a*x))/84 + (47*c^3*atan(a*x)^2)/(2520*a^3) - (8*c^3*x^2*atan(a*x)^2)/(105*a) - (89*a*c^3*x^4*atan(a*x)^2)/420 - (10*a^3*c^3*x^6*atan(a*x)^2)/63 - (a^5*c^3*x^8*atan(a*x)^2)/24 - (((16*im)/315)*c^3*atan(a*x)^3)/a^3 + (c^3*x^3*atan(a*x)^3)/3 + (3*a^2*c^3*x^5*atan(a*x)^3)/5 + (3*a^4*c^3*x^7*atan(a*x)^3)/7 + (a^6*c^3*x^9*atan(a*x)^3)/9 - (16*c^3*atan(a*x)^2*log(2/(1 + im*a*x)))/(105*a^3) + (31*c^3*log(1 + a^2*x^2))/(945*a^3) - (((16*im)/105)*c^3*atan(a*x)*PolyLog(2, 1 - 2/(1 + im*a*x)))/a^3 - (8*c^3*PolyLog(3, 1 - 2/(1 + im*a*x)))/(105*a^3)]
    @test_int [x*(c + a^2*c*x^2)^3*atan(a*x)^3, x, 13, (-19*c^3*x)/(140*a) - (19*a*c^3*x^3)/840 - (a^3*c^3*x^5)/280 + (3*c^3*(1 + a^2*x^2)*atan(a*x))/(35*a^2) + (9*c^3*(1 + a^2*x^2)^2*atan(a*x))/(280*a^2) + (c^3*(1 + a^2*x^2)^3*atan(a*x))/(56*a^2) - (((6*im)/35)*c^3*atan(a*x)^2)/a^2 - (6*c^3*x*atan(a*x)^2)/(35*a) - (3*c^3*x*(1 + a^2*x^2)*atan(a*x)^2)/(35*a) - (9*c^3*x*(1 + a^2*x^2)^2*atan(a*x)^2)/(140*a) - (3*c^3*x*(1 + a^2*x^2)^3*atan(a*x)^2)/(56*a) + (c^3*(1 + a^2*x^2)^4*atan(a*x)^3)/(8*a^2) - (12*c^3*atan(a*x)*log(2/(1 + im*a*x)))/(35*a^2) - (((6*im)/35)*c^3*PolyLog(2, 1 - 2/(1 + im*a*x)))/a^2]
    @test_int [(c + a^2*c*x^2)^3*atan(a*x)^3, x, 17, (-13*c^3*(1 + a^2*x^2))/(210*a) - (c^3*(1 + a^2*x^2)^2)/(140*a) + (14*c^3*x*atan(a*x))/15 + (13*c^3*x*(1 + a^2*x^2)*atan(a*x))/105 + (c^3*x*(1 + a^2*x^2)^2*atan(a*x))/35 - (12*c^3*(1 + a^2*x^2)*atan(a*x)^2)/(35*a) - (9*c^3*(1 + a^2*x^2)^2*atan(a*x)^2)/(70*a) - (c^3*(1 + a^2*x^2)^3*atan(a*x)^2)/(14*a) + (((16*im)/35)*c^3*atan(a*x)^3)/a + (16*c^3*x*atan(a*x)^3)/35 + (8*c^3*x*(1 + a^2*x^2)*atan(a*x)^3)/35 + (6*c^3*x*(1 + a^2*x^2)^2*atan(a*x)^3)/35 + (c^3*x*(1 + a^2*x^2)^3*atan(a*x)^3)/7 + (48*c^3*atan(a*x)^2*log(2/(1 + im*a*x)))/(35*a) - (7*c^3*log(1 + a^2*x^2))/(15*a) + (((48*im)/35)*c^3*atan(a*x)*PolyLog(2, 1 - 2/(1 + im*a*x)))/a + (24*c^3*PolyLog(3, 1 - 2/(1 + im*a*x)))/(35*a)]
    @test_int [((c + a^2*c*x^2)^3*atan(a*x)^3)/x, x, 69, (-13*a*c^3*x)/30 - (a^3*c^3*x^3)/60 + (13*c^3*atan(a*x))/30 + (29*a^2*c^3*x^2*atan(a*x))/60 + (a^4*c^3*x^4*atan(a*x))/20 - ((34*im)/15)*c^3*atan(a*x)^2 - (11*a*c^3*x*atan(a*x)^2)/4 - (7*a^3*c^3*x^3*atan(a*x)^2)/12 - (a^5*c^3*x^5*atan(a*x)^2)/10 + (11*c^3*atan(a*x)^3)/12 + (3*a^2*c^3*x^2*atan(a*x)^3)/2 + (3*a^4*c^3*x^4*atan(a*x)^3)/4 + (a^6*c^3*x^6*atan(a*x)^3)/6 + 2*c^3*atan(a*x)^3*atanh(1 - 2/(1 + im*a*x)) - (68*c^3*atan(a*x)*log(2/(1 + im*a*x)))/15 - ((34*im)/15)*c^3*PolyLog(2, 1 - 2/(1 + im*a*x)) - ((3*im)/2)*c^3*atan(a*x)^2*PolyLog(2, 1 - 2/(1 + im*a*x)) + ((3*im)/2)*c^3*atan(a*x)^2*PolyLog(2, -1 + 2/(1 + im*a*x)) - (3*c^3*atan(a*x)*PolyLog(3, 1 - 2/(1 + im*a*x)))/2 + (3*c^3*atan(a*x)*PolyLog(3, -1 + 2/(1 + im*a*x)))/2 + ((3*im)/4)*c^3*PolyLog(4, 1 - 2/(1 + im*a*x)) - ((3*im)/4)*c^3*PolyLog(4, -1 + 2/(1 + im*a*x))]
    @test_int [((c + a^2*c*x^2)^3*atan(a*x)^3)/x^2, x, 45, -(a^3*c^3*x^2)/20 + (21*a^2*c^3*x*atan(a*x))/10 + (a^4*c^3*x^3*atan(a*x))/10 - (21*a*c^3*atan(a*x)^2)/20 - (6*a^3*c^3*x^2*atan(a*x)^2)/5 - (3*a^5*c^3*x^4*atan(a*x)^2)/20 + ((6*im)/5)*a*c^3*atan(a*x)^3 - (c^3*atan(a*x)^3)/x + 3*a^2*c^3*x*atan(a*x)^3 + a^4*c^3*x^3*atan(a*x)^3 + (a^6*c^3*x^5*atan(a*x)^3)/5 + (33*a*c^3*atan(a*x)^2*log(2/(1 + im*a*x)))/5 + 3*a*c^3*atan(a*x)^2*log(2 - 2/(1 - im*a*x)) - a*c^3*log(1 + a^2*x^2) - (3*im)*a*c^3*atan(a*x)*PolyLog(2, -1 + 2/(1 - im*a*x)) + ((33*im)/5)*a*c^3*atan(a*x)*PolyLog(2, 1 - 2/(1 + im*a*x)) + (3*a*c^3*PolyLog(3, -1 + 2/(1 - im*a*x)))/2 + (33*a*c^3*PolyLog(3, 1 - 2/(1 + im*a*x)))/10]
    @test_int [((c + a^2*c*x^2)^3*atan(a*x)^3)/x^3, x, 43, -(a^3*c^3*x)/4 + (a^2*c^3*atan(a*x))/4 + (a^4*c^3*x^2*atan(a*x))/4 - (5*im)*a^2*c^3*atan(a*x)^2 - (3*a*c^3*atan(a*x)^2)/(2*x) - (15*a^3*c^3*x*atan(a*x)^2)/4 - (a^5*c^3*x^3*atan(a*x)^2)/4 + (3*a^2*c^3*atan(a*x)^3)/4 - (c^3*atan(a*x)^3)/(2*x^2) + (3*a^4*c^3*x^2*atan(a*x)^3)/2 + (a^6*c^3*x^4*atan(a*x)^3)/4 + 6*a^2*c^3*atan(a*x)^3*atanh(1 - 2/(1 + im*a*x)) - 7*a^2*c^3*atan(a*x)*log(2/(1 + im*a*x)) + 3*a^2*c^3*atan(a*x)*log(2 - 2/(1 - im*a*x)) - ((3*im)/2)*a^2*c^3*PolyLog(2, -1 + 2/(1 - im*a*x)) - ((7*im)/2)*a^2*c^3*PolyLog(2, 1 - 2/(1 + im*a*x)) - ((9*im)/2)*a^2*c^3*atan(a*x)^2*PolyLog(2, 1 - 2/(1 + im*a*x)) + ((9*im)/2)*a^2*c^3*atan(a*x)^2*PolyLog(2, -1 + 2/(1 + im*a*x)) - (9*a^2*c^3*atan(a*x)*PolyLog(3, 1 - 2/(1 + im*a*x)))/2 + (9*a^2*c^3*atan(a*x)*PolyLog(3, -1 + 2/(1 + im*a*x)))/2 + ((9*im)/4)*a^2*c^3*PolyLog(4, 1 - 2/(1 + im*a*x)) - ((9*im)/4)*a^2*c^3*PolyLog(4, -1 + 2/(1 + im*a*x))]
    @test_int [((c + a^2*c*x^2)^3*atan(a*x)^3)/x^4, x, 37, -((a^2*c^3*atan(a*x))/x) + a^4*c^3*x*atan(a*x) - a^3*c^3*atan(a*x)^2 - (a*c^3*atan(a*x)^2)/(2*x^2) - (1/2)*a^5*c^3*x^2*atan(a*x)^2 - (c^3*atan(a*x)^3)/(3*x^3) - (3*a^2*c^3*atan(a*x)^3)/x + 3*a^4*c^3*x*atan(a*x)^3 + (1/3)*a^6*c^3*x^3*atan(a*x)^3 + a^3*c^3*log(x) + 8*a^3*c^3*atan(a*x)^2*log(2/(1 + im*a*x)) + 8*a^3*c^3*atan(a*x)^2*log(2 - 2/(1 - im*a*x)) - a^3*c^3*log(1 + a^2*x^2) - 8*im*a^3*c^3*atan(a*x)*PolyLog(2, -1 + 2/(1 - im*a*x)) + 8*im*a^3*c^3*atan(a*x)*PolyLog(2, 1 - 2/(1 + im*a*x)) + 4*a^3*c^3*PolyLog(3, -1 + 2/(1 - im*a*x)) + 4*a^3*c^3*PolyLog(3, 1 - 2/(1 + im*a*x))]

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

    @test_int [x^4*atan(a*x)^3/(c + a^2*c*x^2), x, 19, (x*atan(a*x))/(a^4*c) - atan(a*x)^2/(2*a^5*c) - (x^2*atan(a*x)^2)/(2*a^3*c) - (4*im*atan(a*x)^3)/(3*a^5*c) - (x*atan(a*x)^3)/(a^4*c) + (x^3*atan(a*x)^3)/(3*a^2*c) + atan(a*x)^4/(4*a^5*c) - (4*atan(a*x)^2*log(2/(1 + im*a*x)))/(a^5*c) - log(1 + a^2*x^2)/(2*a^5*c) - (4*im*atan(a*x)*PolyLog(2, 1 - 2/(1 + im*a*x)))/(a^5*c) - (2*PolyLog(3, 1 - 2/(1 + im*a*x)))/(a^5*c)]
    @test_int [x^3*atan(a*x)^3/(c + a^2*c*x^2), x, 14, (((-3*im)/2)*atan(a*x)^2)/(a^4*c) - (3*x*atan(a*x)^2)/(2*a^3*c) + atan(a*x)^3/(2*a^4*c) + (x^2*atan(a*x)^3)/(2*a^2*c) + ((im/4)*atan(a*x)^4)/(a^4*c) - (3*atan(a*x)*log(2/(1 + im*a*x)))/(a^4*c) + (atan(a*x)^3*log(2/(1 + im*a*x)))/(a^4*c) - (((3*im)/2)*PolyLog(2, 1 - 2/(1 + im*a*x)))/(a^4*c) + (((3*im)/2)*atan(a*x)^2*PolyLog(2, 1 - 2/(1 + im*a*x)))/(a^4*c) + (3*atan(a*x)*PolyLog(3, 1 - 2/(1 + im*a*x)))/(2*a^4*c) - (((3*im)/4)*PolyLog(4, 1 - 2/(1 + im*a*x)))/(a^4*c)]
    @test_int [x^2*atan(a*x)^3/(c + a^2*c*x^2), x, 7, (im*atan(a*x)^3)/(a^3*c) + (x*atan(a*x)^3)/(a^2*c) - atan(a*x)^4/(4*a^3*c) + (3*atan(a*x)^2*log(2/(1 + im*a*x)))/(a^3*c) + ((3*im)*atan(a*x)*PolyLog(2, 1 - 2/(1 + im*a*x)))/(a^3*c) + (3*PolyLog(3, 1 - 2/(1 + im*a*x)))/(2*a^3*c)]
    @test_int [x*atan(a*x)^3/(c + a^2*c*x^2), x, 5, ((-im/4)*atan(a*x)^4)/(a^2*c) - (atan(a*x)^3*log(2/(1 + im*a*x)))/(a^2*c) - (((3*im)/2)*atan(a*x)^2*PolyLog(2, 1 - 2/(1 + im*a*x)))/(a^2*c) - (3*atan(a*x)*PolyLog(3, 1 - 2/(1 + im*a*x)))/(2*a^2*c) + (((3*im)/4)*PolyLog(4, 1 - 2/(1 + im*a*x)))/(a^2*c)]
    @test_int [atan(a*x)^3/(c + a^2*c*x^2), x, 1, atan(a*x)^4/(4*a*c)]
    @test_int [atan(a*x)^3/(x*(c + a^2*c*x^2)), x, 5, ((-im/4)*atan(a*x)^4)/c + (atan(a*x)^3*log(2 - 2/(1 - im*a*x)))/c - (((3*im)/2)*atan(a*x)^2*PolyLog(2, -1 + 2/(1 - im*a*x)))/c + (3*atan(a*x)*PolyLog(3, -1 + 2/(1 - im*a*x)))/(2*c) + (((3*im)/4)*PolyLog(4, -1 + 2/(1 - im*a*x)))/c]
    @test_int [atan(a*x)^3/(x^2*(c + a^2*c*x^2)), x, 7, ((-im)*a*atan(a*x)^3)/c - atan(a*x)^3/(c*x) - (a*atan(a*x)^4)/(4*c) + (3*a*atan(a*x)^2*log(2 - 2/(1 - im*a*x)))/c - ((3*im)*a*atan(a*x)*PolyLog(2, -1 + 2/(1 - im*a*x)))/c + (3*a*PolyLog(3, -1 + 2/(1 - im*a*x)))/(2*c)]
    @test_int [atan(a*x)^3/(x^3*(c + a^2*c*x^2)), x, 13, (((-3*im)/2)*a^2*atan(a*x)^2)/c - (3*a*atan(a*x)^2)/(2*c*x) - (a^2*atan(a*x)^3)/(2*c) - atan(a*x)^3/(2*c*x^2) + ((im/4)*a^2*atan(a*x)^4)/c + (3*a^2*atan(a*x)*log(2 - 2/(1 - im*a*x)))/c - (a^2*atan(a*x)^3*log(2 - 2/(1 - im*a*x)))/c - (((3*im)/2)*a^2*PolyLog(2, -1 + 2/(1 - im*a*x)))/c + (((3*im)/2)*a^2*atan(a*x)^2*PolyLog(2, -1 + 2/(1 - im*a*x)))/c - (3*a^2*atan(a*x)*PolyLog(3, -1 + 2/(1 - im*a*x)))/(2*c) - (((3*im)/4)*a^2*PolyLog(4, -1 + 2/(1 - im*a*x)))/c]
    @test_int [atan(a*x)^3/(x^4*(c + a^2*c*x^2)), x, 22, -((a^2*atan(a*x))/(c*x)) - (a^3*atan(a*x)^2)/(2*c) - (a*atan(a*x)^2)/(2*c*x^2) + (4*im*a^3*atan(a*x)^3)/(3*c) - atan(a*x)^3/(3*c*x^3) + (a^2*atan(a*x)^3)/(c*x) + (a^3*atan(a*x)^4)/(4*c) + (a^3*log(x))/c - (4*a^3*atan(a*x)^2*log(2 - 2/(1 - im*a*x)))/c - (a^3*log(1 + a^2*x^2))/(2*c) + (4*im*a^3*atan(a*x)*PolyLog(2, -1 + 2/(1 - im*a*x)))/c - (2*a^3*PolyLog(3, -1 + 2/(1 - im*a*x)))/c]

    @test_int [(x^3*atan(a*x)^3)/(c + a^2*c*x^2)^2, x, 11, (3*x)/(8*a^3*c^2*(1 + a^2*x^2)) + (3*atan(a*x))/(8*a^4*c^2) - (3*atan(a*x))/(4*a^4*c^2*(1 + a^2*x^2)) - (3*x*atan(a*x)^2)/(4*a^3*c^2*(1 + a^2*x^2)) - atan(a*x)^3/(4*a^4*c^2) + atan(a*x)^3/(2*a^4*c^2*(1 + a^2*x^2)) - ((im/4)*atan(a*x)^4)/(a^4*c^2) - (atan(a*x)^3*log(2/(1 + im*a*x)))/(a^4*c^2) - (((3*im)/2)*atan(a*x)^2*PolyLog(2, 1 - 2/(1 + im*a*x)))/(a^4*c^2) - (3*atan(a*x)*PolyLog(3, 1 - 2/(1 + im*a*x)))/(2*a^4*c^2) + (((3*im)/4)*PolyLog(4, 1 - 2/(1 + im*a*x)))/(a^4*c^2)]
    @test_int [(x^2*atan(a*x)^3)/(c + a^2*c*x^2)^2, x, 4, 3/(8*a^3*c^2*(1 + a^2*x^2)) + (3*x*atan(a*x))/(4*a^2*c^2*(1 + a^2*x^2)) + (3*atan(a*x)^2)/(8*a^3*c^2) - (3*atan(a*x)^2)/(4*a^3*c^2*(1 + a^2*x^2)) - (x*atan(a*x)^3)/(2*a^2*c^2*(1 + a^2*x^2)) + atan(a*x)^4/(8*a^3*c^2)]
    @test_int [(x*atan(a*x)^3)/(c + a^2*c*x^2)^2, x, 5, (-3*x)/(8*a*c^2*(1 + a^2*x^2)) - (3*atan(a*x))/(8*a^2*c^2) + (3*atan(a*x))/(4*a^2*c^2*(1 + a^2*x^2)) + (3*x*atan(a*x)^2)/(4*a*c^2*(1 + a^2*x^2)) + atan(a*x)^3/(4*a^2*c^2) - atan(a*x)^3/(2*a^2*c^2*(1 + a^2*x^2))]
    @test_int [atan(a*x)^3/(c + a^2*c*x^2)^2, x, 4, -3/(8*a*c^2*(1 + a^2*x^2)) - (3*x*atan(a*x))/(4*c^2*(1 + a^2*x^2)) - (3*atan(a*x)^2)/(8*a*c^2) + (3*atan(a*x)^2)/(4*a*c^2*(1 + a^2*x^2)) + (x*atan(a*x)^3)/(2*c^2*(1 + a^2*x^2)) + atan(a*x)^4/(8*a*c^2)]
    @test_int [atan(a*x)^3/(x*(c + a^2*c*x^2)^2), x, 11, (3*a*x)/(8*c^2*(1 + a^2*x^2)) + (3*atan(a*x))/(8*c^2) - (3*atan(a*x))/(4*c^2*(1 + a^2*x^2)) - (3*a*x*atan(a*x)^2)/(4*c^2*(1 + a^2*x^2)) - atan(a*x)^3/(4*c^2) + atan(a*x)^3/(2*c^2*(1 + a^2*x^2)) - ((im/4)*atan(a*x)^4)/c^2 + (atan(a*x)^3*log(2 - 2/(1 - im*a*x)))/c^2 - (((3*im)/2)*atan(a*x)^2*PolyLog(2, -1 + 2/(1 - im*a*x)))/c^2 + (3*atan(a*x)*PolyLog(3, -1 + 2/(1 - im*a*x)))/(2*c^2) + (((3*im)/4)*PolyLog(4, -1 + 2/(1 - im*a*x)))/c^2]
    @test_int [atan(a*x)^3/(x^2*(c + a^2*c*x^2)^2), x, 12, (3*a)/(8*c^2*(1 + a^2*x^2)) + (3*a^2*x*atan(a*x))/(4*c^2*(1 + a^2*x^2)) + (3*a*atan(a*x)^2)/(8*c^2) - (3*a*atan(a*x)^2)/(4*c^2*(1 + a^2*x^2)) - (im*a*atan(a*x)^3)/c^2 - atan(a*x)^3/(c^2*x) - (a^2*x*atan(a*x)^3)/(2*c^2*(1 + a^2*x^2)) - (3*a*atan(a*x)^4)/(8*c^2) + (3*a*atan(a*x)^2*log(2 - 2/(1 - im*a*x)))/c^2 - ((3*im)*a*atan(a*x)*PolyLog(2, -1 + 2/(1 - im*a*x)))/c^2 + (3*a*PolyLog(3, -1 + 2/(1 - im*a*x)))/(2*c^2)]
    @test_int [atan(a*x)^3/(x^3*(c + a^2*c*x^2)^2), x, 25, (-3*a^3*x)/(8*c^2*(1 + a^2*x^2)) - (3*a^2*atan(a*x))/(8*c^2) + (3*a^2*atan(a*x))/(4*c^2*(1 + a^2*x^2)) - (((3*im)/2)*a^2*atan(a*x)^2)/c^2 - (3*a*atan(a*x)^2)/(2*c^2*x) + (3*a^3*x*atan(a*x)^2)/(4*c^2*(1 + a^2*x^2)) - (a^2*atan(a*x)^3)/(4*c^2) - atan(a*x)^3/(2*c^2*x^2) - (a^2*atan(a*x)^3)/(2*c^2*(1 + a^2*x^2)) + ((im/2)*a^2*atan(a*x)^4)/c^2 + (3*a^2*atan(a*x)*log(2 - 2/(1 - im*a*x)))/c^2 - (2*a^2*atan(a*x)^3*log(2 - 2/(1 - im*a*x)))/c^2 - (((3*im)/2)*a^2*PolyLog(2, -1 + 2/(1 - im*a*x)))/c^2 + ((3*im)*a^2*atan(a*x)^2*PolyLog(2, -1 + 2/(1 - im*a*x)))/c^2 - (3*a^2*atan(a*x)*PolyLog(3, -1 + 2/(1 - im*a*x)))/c^2 - (((3*im)/2)*a^2*PolyLog(4, -1 + 2/(1 - im*a*x)))/c^2]
    @test_int [atan(a*x)^3/(x^4*(c + a^2*c*x^2)^2), x, 35, -((3*a^3)/(8*c^2*(1 + a^2*x^2))) - (a^2*atan(a*x))/(c^2*x) - (3*a^4*x*atan(a*x))/(4*c^2*(1 + a^2*x^2)) - (7*a^3*atan(a*x)^2)/(8*c^2) - (a*atan(a*x)^2)/(2*c^2*x^2) + (3*a^3*atan(a*x)^2)/(4*c^2*(1 + a^2*x^2)) + (7*im*a^3*atan(a*x)^3)/(3*c^2) - atan(a*x)^3/(3*c^2*x^3) + (2*a^2*atan(a*x)^3)/(c^2*x) + (a^4*x*atan(a*x)^3)/(2*c^2*(1 + a^2*x^2)) + (5*a^3*atan(a*x)^4)/(8*c^2) + (a^3*log(x))/c^2 - (7*a^3*atan(a*x)^2*log(2 - 2/(1 - im*a*x)))/c^2 - (a^3*log(1 + a^2*x^2))/(2*c^2) + (7*im*a^3*atan(a*x)*PolyLog(2, -1 + 2/(1 - im*a*x)))/c^2 - (7*a^3*PolyLog(3, -1 + 2/(1 - im*a*x)))/(2*c^2)]

    @test_int [(x^3*atan(a*x)^3)/(c + a^2*c*x^2)^3, x, 9, -((3*x^3)/(128*a*c^3*(1 + a^2*x^2)^2)) - (45*x)/(256*a^3*c^3*(1 + a^2*x^2)) - (27*atan(a*x))/(256*a^4*c^3) - (3*x^4*atan(a*x))/(32*c^3*(1 + a^2*x^2)^2) + (9*atan(a*x))/(32*a^4*c^3*(1 + a^2*x^2)) + (3*x^3*atan(a*x)^2)/(16*a*c^3*(1 + a^2*x^2)^2) + (9*x*atan(a*x)^2)/(32*a^3*c^3*(1 + a^2*x^2)) - (3*atan(a*x)^3)/(32*a^4*c^3) + (x^4*atan(a*x)^3)/(4*c^3*(1 + a^2*x^2)^2)]
    @test_int [(x^2*atan(a*x)^3)/(c + a^2*c*x^2)^3, x, 13, 3/(128*a^3*c^3*(1 + a^2*x^2)^2) - 3/(128*a^3*c^3*(1 + a^2*x^2)) + (3*x*atan(a*x))/(32*a^2*c^3*(1 + a^2*x^2)^2) - (3*x*atan(a*x))/(64*a^2*c^3*(1 + a^2*x^2)) - (3*atan(a*x)^2)/(128*a^3*c^3) - (3*atan(a*x)^2)/(16*a^3*c^3*(1 + a^2*x^2)^2) + (3*atan(a*x)^2)/(16*a^3*c^3*(1 + a^2*x^2)) - (x*atan(a*x)^3)/(4*a^2*c^3*(1 + a^2*x^2)^2) + (x*atan(a*x)^3)/(8*a^2*c^3*(1 + a^2*x^2)) + atan(a*x)^4/(32*a^3*c^3)]
    @test_int [(x*atan(a*x)^3)/(c + a^2*c*x^2)^3, x, 9, (-3*x)/(128*a*c^3*(1 + a^2*x^2)^2) - (45*x)/(256*a*c^3*(1 + a^2*x^2)) - (45*atan(a*x))/(256*a^2*c^3) + (3*atan(a*x))/(32*a^2*c^3*(1 + a^2*x^2)^2) + (9*atan(a*x))/(32*a^2*c^3*(1 + a^2*x^2)) + (3*x*atan(a*x)^2)/(16*a*c^3*(1 + a^2*x^2)^2) + (9*x*atan(a*x)^2)/(32*a*c^3*(1 + a^2*x^2)) + (3*atan(a*x)^3)/(32*a^2*c^3) - atan(a*x)^3/(4*a^2*c^3*(1 + a^2*x^2)^2)]
    @test_int [atan(a*x)^3/(c + a^2*c*x^2)^3, x, 8, -3/(128*a*c^3*(1 + a^2*x^2)^2) - 45/(128*a*c^3*(1 + a^2*x^2)) - (3*x*atan(a*x))/(32*c^3*(1 + a^2*x^2)^2) - (45*x*atan(a*x))/(64*c^3*(1 + a^2*x^2)) - (45*atan(a*x)^2)/(128*a*c^3) + (3*atan(a*x)^2)/(16*a*c^3*(1 + a^2*x^2)^2) + (9*atan(a*x)^2)/(16*a*c^3*(1 + a^2*x^2)) + (x*atan(a*x)^3)/(4*c^3*(1 + a^2*x^2)^2) + (3*x*atan(a*x)^3)/(8*c^3*(1 + a^2*x^2)) + (3*atan(a*x)^4)/(32*a*c^3)]
    @test_int [atan(a*x)^3/(x*(c + a^2*c*x^2)^3), x, 21, (3*a*x)/(128*c^3*(1 + a^2*x^2)^2) + (141*a*x)/(256*c^3*(1 + a^2*x^2)) + (141*atan(a*x))/(256*c^3) - (3*atan(a*x))/(32*c^3*(1 + a^2*x^2)^2) - (33*atan(a*x))/(32*c^3*(1 + a^2*x^2)) - (3*a*x*atan(a*x)^2)/(16*c^3*(1 + a^2*x^2)^2) - (33*a*x*atan(a*x)^2)/(32*c^3*(1 + a^2*x^2)) - (11*atan(a*x)^3)/(32*c^3) + atan(a*x)^3/(4*c^3*(1 + a^2*x^2)^2) + atan(a*x)^3/(2*c^3*(1 + a^2*x^2)) - ((im/4)*atan(a*x)^4)/c^3 + (atan(a*x)^3*log(2 - 2/(1 - im*a*x)))/c^3 - (((3*im)/2)*atan(a*x)^2*PolyLog(2, -1 + 2/(1 - im*a*x)))/c^3 + (3*atan(a*x)*PolyLog(3, -1 + 2/(1 - im*a*x)))/(2*c^3) + (((3*im)/4)*PolyLog(4, -1 + 2/(1 - im*a*x)))/c^3]
    @test_int [atan(a*x)^3/(x^2*(c + a^2*c*x^2)^3), x, 21, (3*a)/(128*c^3*(1 + a^2*x^2)^2) + (93*a)/(128*c^3*(1 + a^2*x^2)) + (3*a^2*x*atan(a*x))/(32*c^3*(1 + a^2*x^2)^2) + (93*a^2*x*atan(a*x))/(64*c^3*(1 + a^2*x^2)) + (93*a*atan(a*x)^2)/(128*c^3) - (3*a*atan(a*x)^2)/(16*c^3*(1 + a^2*x^2)^2) - (21*a*atan(a*x)^2)/(16*c^3*(1 + a^2*x^2)) - (im*a*atan(a*x)^3)/c^3 - atan(a*x)^3/(c^3*x) - (a^2*x*atan(a*x)^3)/(4*c^3*(1 + a^2*x^2)^2) - (7*a^2*x*atan(a*x)^3)/(8*c^3*(1 + a^2*x^2)) - (15*a*atan(a*x)^4)/(32*c^3) + (3*a*atan(a*x)^2*log(2 - 2/(1 - im*a*x)))/c^3 - ((3*im)*a*atan(a*x)*PolyLog(2, -1 + 2/(1 - im*a*x)))/c^3 + (3*a*PolyLog(3, -1 + 2/(1 - im*a*x)))/(2*c^3)]
    @test_int [atan(a*x)^3/(x^3*(c + a^2*c*x^2)^3), x, 47, (-3*a^3*x)/(128*c^3*(1 + a^2*x^2)^2) - (237*a^3*x)/(256*c^3*(1 + a^2*x^2)) - (237*a^2*atan(a*x))/(256*c^3) + (3*a^2*atan(a*x))/(32*c^3*(1 + a^2*x^2)^2) + (57*a^2*atan(a*x))/(32*c^3*(1 + a^2*x^2)) - (((3*im)/2)*a^2*atan(a*x)^2)/c^3 - (3*a*atan(a*x)^2)/(2*c^3*x) + (3*a^3*x*atan(a*x)^2)/(16*c^3*(1 + a^2*x^2)^2) + (57*a^3*x*atan(a*x)^2)/(32*c^3*(1 + a^2*x^2)) + (3*a^2*atan(a*x)^3)/(32*c^3) - atan(a*x)^3/(2*c^3*x^2) - (a^2*atan(a*x)^3)/(4*c^3*(1 + a^2*x^2)^2) - (a^2*atan(a*x)^3)/(c^3*(1 + a^2*x^2)) + (((3*im)/4)*a^2*atan(a*x)^4)/c^3 + (3*a^2*atan(a*x)*log(2 - 2/(1 - im*a*x)))/c^3 - (3*a^2*atan(a*x)^3*log(2 - 2/(1 - im*a*x)))/c^3 - (((3*im)/2)*a^2*PolyLog(2, -1 + 2/(1 - im*a*x)))/c^3 + (((9*im)/2)*a^2*atan(a*x)^2*PolyLog(2, -1 + 2/(1 - im*a*x)))/c^3 - (9*a^2*atan(a*x)*PolyLog(3, -1 + 2/(1 - im*a*x)))/(2*c^3) - (((9*im)/4)*a^2*PolyLog(4, -1 + 2/(1 - im*a*x)))/c^3]
    @test_int [atan(a*x)^3/(x^4*(c + a^2*c*x^2)^3), x, 57, -((3*a^3)/(128*c^3*(1 + a^2*x^2)^2)) - (141*a^3)/(128*c^3*(1 + a^2*x^2)) - (a^2*atan(a*x))/(c^3*x) - (3*a^4*x*atan(a*x))/(32*c^3*(1 + a^2*x^2)^2) - (141*a^4*x*atan(a*x))/(64*c^3*(1 + a^2*x^2)) - (205*a^3*atan(a*x)^2)/(128*c^3) - (a*atan(a*x)^2)/(2*c^3*x^2) + (3*a^3*atan(a*x)^2)/(16*c^3*(1 + a^2*x^2)^2) + (33*a^3*atan(a*x)^2)/(16*c^3*(1 + a^2*x^2)) + (10*im*a^3*atan(a*x)^3)/(3*c^3) - atan(a*x)^3/(3*c^3*x^3) + (3*a^2*atan(a*x)^3)/(c^3*x) + (a^4*x*atan(a*x)^3)/(4*c^3*(1 + a^2*x^2)^2) + (11*a^4*x*atan(a*x)^3)/(8*c^3*(1 + a^2*x^2)) + (35*a^3*atan(a*x)^4)/(32*c^3) + (a^3*log(x))/c^3 - (10*a^3*atan(a*x)^2*log(2 - 2/(1 - im*a*x)))/c^3 - (a^3*log(1 + a^2*x^2))/(2*c^3) + (10*im*a^3*atan(a*x)*PolyLog(2, -1 + 2/(1 - im*a*x)))/c^3 - (5*a^3*PolyLog(3, -1 + 2/(1 - im*a*x)))/c^3]

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

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

    @test_int [x^3*sqrt(c + a^2*c*x^2)*atan(a*x)^3, x, 71, -((x*sqrt(c + a^2*c*x^2))/(20*a^3)) - (9*sqrt(c + a^2*c*x^2)*atan(a*x))/(20*a^4) + (x^2*sqrt(c + a^2*c*x^2)*atan(a*x))/(10*a^2) + (x*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(8*a^3) - (3*x^3*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(20*a) - (11*im*c*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^2)/(20*a^4*sqrt(c + a^2*c*x^2)) - (2*sqrt(c + a^2*c*x^2)*atan(a*x)^3)/(15*a^4) + (x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^3)/(15*a^2) + (1/5)*x^4*sqrt(c + a^2*c*x^2)*atan(a*x)^3 + (sqrt(c)*atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2)))/(2*a^4) + (11*im*c*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/(20*a^4*sqrt(c + a^2*c*x^2)) - (11*im*c*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, im*ℯ^(im*atan(a*x))))/(20*a^4*sqrt(c + a^2*c*x^2)) - (11*c*sqrt(1 + a^2*x^2)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(20*a^4*sqrt(c + a^2*c*x^2)) + (11*c*sqrt(1 + a^2*x^2)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(20*a^4*sqrt(c + a^2*c*x^2))]
    @test_int [x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^3, x, 40, -(sqrt(c + a^2*c*x^2)/(4*a^3)) + (x*sqrt(c + a^2*c*x^2)*atan(a*x))/(4*a^2) + (sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(8*a^3) - (x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(4*a) + (x*sqrt(c + a^2*c*x^2)*atan(a*x)^3)/(8*a^2) + (1/4)*x^3*sqrt(c + a^2*c*x^2)*atan(a*x)^3 + (im*c*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^3)/(4*a^3*sqrt(c + a^2*c*x^2)) + (im*c*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(a^3*sqrt(c + a^2*c*x^2)) - (3*im*c*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/(8*a^3*sqrt(c + a^2*c*x^2)) + (3*im*c*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, im*ℯ^(im*atan(a*x))))/(8*a^3*sqrt(c + a^2*c*x^2)) - (im*c*sqrt(1 + a^2*x^2)*PolyLog(2, -((im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x))))/(2*a^3*sqrt(c + a^2*c*x^2)) + (im*c*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(2*a^3*sqrt(c + a^2*c*x^2)) + (3*c*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(4*a^3*sqrt(c + a^2*c*x^2)) - (3*c*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(4*a^3*sqrt(c + a^2*c*x^2)) + (3*im*c*sqrt(1 + a^2*x^2)*PolyLog(4, (-im)*ℯ^(im*atan(a*x))))/(4*a^3*sqrt(c + a^2*c*x^2)) - (3*im*c*sqrt(1 + a^2*x^2)*PolyLog(4, im*ℯ^(im*atan(a*x))))/(4*a^3*sqrt(c + a^2*c*x^2))]
    @test_int [x*sqrt(c + a^2*c*x^2)*atan(a*x)^3, x, 13, (sqrt(c + a^2*c*x^2)*atan(a*x))/a^2 - (x*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(2*a) + (im*c*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^2)/(a^2*sqrt(c + a^2*c*x^2)) + ((c + a^2*c*x^2)^(3/2)*atan(a*x)^3)/(3*a^2*c) - (sqrt(c)*atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2)))/a^2 - (im*c*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/(a^2*sqrt(c + a^2*c*x^2)) + (im*c*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, im*ℯ^(im*atan(a*x))))/(a^2*sqrt(c + a^2*c*x^2)) + (c*sqrt(1 + a^2*x^2)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(a^2*sqrt(c + a^2*c*x^2)) - (c*sqrt(1 + a^2*x^2)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(a^2*sqrt(c + a^2*c*x^2))]
    @test_int [sqrt(c + a^2*c*x^2)*atan(a*x)^3, x, 14, (-3*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(2*a) + (x*sqrt(c + a^2*c*x^2)*atan(a*x)^3)/2 - (im*c*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^3)/(a*sqrt(c + a^2*c*x^2)) - ((6*im)*c*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(a*sqrt(c + a^2*c*x^2)) + (((3*im)/2)*c*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2)) - (((3*im)/2)*c*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, im*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2)) + ((3*im)*c*sqrt(1 + a^2*x^2)*PolyLog(2, ((-im)*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(a*sqrt(c + a^2*c*x^2)) - ((3*im)*c*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(a*sqrt(c + a^2*c*x^2)) - (3*c*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2)) + (3*c*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2)) - ((3*im)*c*sqrt(1 + a^2*x^2)*PolyLog(4, (-im)*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2)) + ((3*im)*c*sqrt(1 + a^2*x^2)*PolyLog(4, im*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2))]
    @test_int [(sqrt(c + a^2*c*x^2)*atan(a*x)^3)/x, x, 22, ((6*im)*c*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^2)/sqrt(c + a^2*c*x^2) + sqrt(c + a^2*c*x^2)*atan(a*x)^3 - (2*c*sqrt(1 + a^2*x^2)*atan(a*x)^3*atanh(ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((3*im)*c*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((6*im)*c*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((6*im)*c*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((3*im)*c*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (6*c*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (6*c*sqrt(1 + a^2*x^2)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (6*c*sqrt(1 + a^2*x^2)*PolyLog(3, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (6*c*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((6*im)*c*sqrt(1 + a^2*x^2)*PolyLog(4, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((6*im)*c*sqrt(1 + a^2*x^2)*PolyLog(4, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2)]
    @test_int [(sqrt(c + a^2*c*x^2)*atan(a*x)^3)/x^2, x, 22, -((sqrt(c + a^2*c*x^2)*atan(a*x)^3)/x) - ((2*im)*a*c*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^3)/sqrt(c + a^2*c*x^2) - (6*a*c*sqrt(1 + a^2*x^2)*atan(a*x)^2*atanh(ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((6*im)*a*c*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((3*im)*a*c*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((3*im)*a*c*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((6*im)*a*c*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (6*a*c*sqrt(1 + a^2*x^2)*PolyLog(3, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (6*a*c*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (6*a*c*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (6*a*c*sqrt(1 + a^2*x^2)*PolyLog(3, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((6*im)*a*c*sqrt(1 + a^2*x^2)*PolyLog(4, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((6*im)*a*c*sqrt(1 + a^2*x^2)*PolyLog(4, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2)]
    @test_int [(sqrt(c + a^2*c*x^2)*atan(a*x)^3)/x^3, x, 27, (-3*a*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(2*x) - (sqrt(c + a^2*c*x^2)*atan(a*x)^3)/(2*x^2) - (a^2*c*sqrt(1 + a^2*x^2)*atan(a*x)^3*atanh(ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (6*a^2*c*sqrt(1 + a^2*x^2)*atan(a*x)*atanh(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) + (((3*im)/2)*a^2*c*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (((3*im)/2)*a^2*c*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((3*im)*a^2*c*sqrt(1 + a^2*x^2)*PolyLog(2, -(sqrt(1 + im*a*x)/sqrt(1 - im*a*x))))/sqrt(c + a^2*c*x^2) - ((3*im)*a^2*c*sqrt(1 + a^2*x^2)*PolyLog(2, sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (3*a^2*c*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (3*a^2*c*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((3*im)*a^2*c*sqrt(1 + a^2*x^2)*PolyLog(4, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((3*im)*a^2*c*sqrt(1 + a^2*x^2)*PolyLog(4, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2)]
    @test_int [(sqrt(c + a^2*c*x^2)*atan(a*x)^3)/x^4, x, 25, -((a^2*sqrt(c + a^2*c*x^2)*atan(a*x))/x) - (a*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(2*x^2) - ((c + a^2*c*x^2)^(3/2)*atan(a*x)^3)/(3*c*x^3) - (a^3*c*sqrt(1 + a^2*x^2)*atan(a*x)^2*atanh(ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - a^3*sqrt(c)*atanh(sqrt(c + a^2*c*x^2)/sqrt(c)) + (im*a^3*c*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (im*a^3*c*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (a^3*c*sqrt(1 + a^2*x^2)*PolyLog(3, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (a^3*c*sqrt(1 + a^2*x^2)*PolyLog(3, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2)]

    @test_int [x^3*(c + a^2*c*x^2)^(3/2)*atan(a*x)^3, x, 200, (c*x*sqrt(c + a^2*c*x^2))/(420*a^3) - (c*x^3*sqrt(c + a^2*c*x^2))/(140*a) - (163*c*sqrt(c + a^2*c*x^2)*atan(a*x))/(840*a^4) + (c*x^2*sqrt(c + a^2*c*x^2)*atan(a*x))/(60*a^2) + (1/35)*c*x^4*sqrt(c + a^2*c*x^2)*atan(a*x) + (9*c*x*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(112*a^3) - (23*c*x^3*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(280*a) - (1/14)*a*c*x^5*sqrt(c + a^2*c*x^2)*atan(a*x)^2 - (51*im*c^2*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^2)/(280*a^4*sqrt(c + a^2*c*x^2)) - (2*c*sqrt(c + a^2*c*x^2)*atan(a*x)^3)/(35*a^4) + (c*x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^3)/(35*a^2) + (8/35)*c*x^4*sqrt(c + a^2*c*x^2)*atan(a*x)^3 + (1/7)*a^2*c*x^6*sqrt(c + a^2*c*x^2)*atan(a*x)^3 + (23*c^(3/2)*atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2)))/(120*a^4) + (51*im*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/(280*a^4*sqrt(c + a^2*c*x^2)) - (51*im*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, im*ℯ^(im*atan(a*x))))/(280*a^4*sqrt(c + a^2*c*x^2)) - (51*c^2*sqrt(1 + a^2*x^2)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(280*a^4*sqrt(c + a^2*c*x^2)) + (51*c^2*sqrt(1 + a^2*x^2)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(280*a^4*sqrt(c + a^2*c*x^2))]
    @test_int [x^2*(c + a^2*c*x^2)^(3/2)*atan(a*x)^3, x, 108, -((c*sqrt(c + a^2*c*x^2))/(30*a^3)) - (c + a^2*c*x^2)^(3/2)/(60*a^3) + (c*x*sqrt(c + a^2*c*x^2)*atan(a*x))/(12*a^2) + (1/20)*c*x^3*sqrt(c + a^2*c*x^2)*atan(a*x) + (31*c*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(240*a^3) - (19*c*x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(120*a) - (1/10)*a*c*x^4*sqrt(c + a^2*c*x^2)*atan(a*x)^2 + (c*x*sqrt(c + a^2*c*x^2)*atan(a*x)^3)/(16*a^2) + (7/24)*c*x^3*sqrt(c + a^2*c*x^2)*atan(a*x)^3 + (1/6)*a^2*c*x^5*sqrt(c + a^2*c*x^2)*atan(a*x)^3 + (im*c^2*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^3)/(8*a^3*sqrt(c + a^2*c*x^2)) + (41*im*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(60*a^3*sqrt(c + a^2*c*x^2)) - (3*im*c^2*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/(16*a^3*sqrt(c + a^2*c*x^2)) + (3*im*c^2*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, im*ℯ^(im*atan(a*x))))/(16*a^3*sqrt(c + a^2*c*x^2)) - (41*im*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, -((im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x))))/(120*a^3*sqrt(c + a^2*c*x^2)) + (41*im*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(120*a^3*sqrt(c + a^2*c*x^2)) + (3*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(8*a^3*sqrt(c + a^2*c*x^2)) - (3*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(8*a^3*sqrt(c + a^2*c*x^2)) + (3*im*c^2*sqrt(1 + a^2*x^2)*PolyLog(4, (-im)*ℯ^(im*atan(a*x))))/(8*a^3*sqrt(c + a^2*c*x^2)) - (3*im*c^2*sqrt(1 + a^2*x^2)*PolyLog(4, im*ℯ^(im*atan(a*x))))/(8*a^3*sqrt(c + a^2*c*x^2))]
    @test_int [x*(c + a^2*c*x^2)^(3/2)*atan(a*x)^3, x, 17, -(c*x*sqrt(c + a^2*c*x^2))/(20*a) + (9*c*sqrt(c + a^2*c*x^2)*atan(a*x))/(20*a^2) + ((c + a^2*c*x^2)^(3/2)*atan(a*x))/(10*a^2) - (9*c*x*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(40*a) - (3*x*(c + a^2*c*x^2)^(3/2)*atan(a*x)^2)/(20*a) + (((9*im)/20)*c^2*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^2)/(a^2*sqrt(c + a^2*c*x^2)) + ((c + a^2*c*x^2)^(5/2)*atan(a*x)^3)/(5*a^2*c) - (c^(3/2)*atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2)))/(2*a^2) - (((9*im)/20)*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/(a^2*sqrt(c + a^2*c*x^2)) + (((9*im)/20)*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, im*ℯ^(im*atan(a*x))))/(a^2*sqrt(c + a^2*c*x^2)) + (9*c^2*sqrt(1 + a^2*x^2)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(20*a^2*sqrt(c + a^2*c*x^2)) - (9*c^2*sqrt(1 + a^2*x^2)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(20*a^2*sqrt(c + a^2*c*x^2))]
    @test_int [(c + a^2*c*x^2)^(3/2)*atan(a*x)^3, x, 18, -(c*sqrt(c + a^2*c*x^2))/(4*a) + (c*x*sqrt(c + a^2*c*x^2)*atan(a*x))/4 - (9*c*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(8*a) - ((c + a^2*c*x^2)^(3/2)*atan(a*x)^2)/(4*a) + (3*c*x*sqrt(c + a^2*c*x^2)*atan(a*x)^3)/8 + (x*(c + a^2*c*x^2)^(3/2)*atan(a*x)^3)/4 - (((3*im)/4)*c^2*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^3)/(a*sqrt(c + a^2*c*x^2)) - ((5*im)*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(a*sqrt(c + a^2*c*x^2)) + (((9*im)/8)*c^2*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2)) - (((9*im)/8)*c^2*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, im*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2)) + (((5*im)/2)*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, ((-im)*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(a*sqrt(c + a^2*c*x^2)) - (((5*im)/2)*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(a*sqrt(c + a^2*c*x^2)) - (9*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(4*a*sqrt(c + a^2*c*x^2)) + (9*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(4*a*sqrt(c + a^2*c*x^2)) - (((9*im)/4)*c^2*sqrt(1 + a^2*x^2)*PolyLog(4, (-im)*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2)) + (((9*im)/4)*c^2*sqrt(1 + a^2*x^2)*PolyLog(4, im*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2))]
    @test_int [((c + a^2*c*x^2)^(3/2)*atan(a*x)^3)/x, x, 36, c*sqrt(c + a^2*c*x^2)*atan(a*x) - (a*c*x*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/2 + ((7*im)*c^2*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^2)/sqrt(c + a^2*c*x^2) + c*sqrt(c + a^2*c*x^2)*atan(a*x)^3 + ((c + a^2*c*x^2)^(3/2)*atan(a*x)^3)/3 - (2*c^2*sqrt(1 + a^2*x^2)*atan(a*x)^3*atanh(ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - c^(3/2)*atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2)) + ((3*im)*c^2*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((7*im)*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((7*im)*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((3*im)*c^2*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (6*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (7*c^2*sqrt(1 + a^2*x^2)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (7*c^2*sqrt(1 + a^2*x^2)*PolyLog(3, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (6*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((6*im)*c^2*sqrt(1 + a^2*x^2)*PolyLog(4, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((6*im)*c^2*sqrt(1 + a^2*x^2)*PolyLog(4, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2)]
    @test_int [((c + a^2*c*x^2)^(3/2)*atan(a*x)^3)/x^2, x, 37, (-3*a*c*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/2 - (c*sqrt(c + a^2*c*x^2)*atan(a*x)^3)/x + (a^2*c*x*sqrt(c + a^2*c*x^2)*atan(a*x)^3)/2 - ((3*im)*a*c^2*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^3)/sqrt(c + a^2*c*x^2) - ((6*im)*a*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (6*a*c^2*sqrt(1 + a^2*x^2)*atan(a*x)^2*atanh(ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((6*im)*a*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (((9*im)/2)*a*c^2*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (((9*im)/2)*a*c^2*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((6*im)*a*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((3*im)*a*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, ((-im)*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - ((3*im)*a*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (6*a*c^2*sqrt(1 + a^2*x^2)*PolyLog(3, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (9*a*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (9*a*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (6*a*c^2*sqrt(1 + a^2*x^2)*PolyLog(3, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((9*im)*a*c^2*sqrt(1 + a^2*x^2)*PolyLog(4, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((9*im)*a*c^2*sqrt(1 + a^2*x^2)*PolyLog(4, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2)]
    @test_int [((c + a^2*c*x^2)^(3/2)*atan(a*x)^3)/x^3, x, 50, (-3*a*c*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(2*x) + ((6*im)*a^2*c^2*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^2)/sqrt(c + a^2*c*x^2) + a^2*c*sqrt(c + a^2*c*x^2)*atan(a*x)^3 - (c*sqrt(c + a^2*c*x^2)*atan(a*x)^3)/(2*x^2) - (3*a^2*c^2*sqrt(1 + a^2*x^2)*atan(a*x)^3*atanh(ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (6*a^2*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*atanh(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) + (((9*im)/2)*a^2*c^2*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((6*im)*a^2*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((6*im)*a^2*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (((9*im)/2)*a^2*c^2*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((3*im)*a^2*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, -(sqrt(1 + im*a*x)/sqrt(1 - im*a*x))))/sqrt(c + a^2*c*x^2) - ((3*im)*a^2*c^2*sqrt(1 + a^2*x^2)*PolyLog(2, sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (9*a^2*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (6*a^2*c^2*sqrt(1 + a^2*x^2)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (6*a^2*c^2*sqrt(1 + a^2*x^2)*PolyLog(3, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (9*a^2*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((9*im)*a^2*c^2*sqrt(1 + a^2*x^2)*PolyLog(4, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((9*im)*a^2*c^2*sqrt(1 + a^2*x^2)*PolyLog(4, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2)]
    @test_int [((c + a^2*c*x^2)^(3/2)*atan(a*x)^3)/x^4, x, 48, -((a^2*c*sqrt(c + a^2*c*x^2)*atan(a*x))/x) - (a*c*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(2*x^2) - (a^2*c*sqrt(c + a^2*c*x^2)*atan(a*x)^3)/x - ((c + a^2*c*x^2)^(3/2)*atan(a*x)^3)/(3*x^3) - ((2*im)*a^3*c^2*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^3)/sqrt(c + a^2*c*x^2) - (7*a^3*c^2*sqrt(1 + a^2*x^2)*atan(a*x)^2*atanh(ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - a^3*c^(3/2)*atanh(sqrt(c + a^2*c*x^2)/sqrt(c)) + ((7*im)*a^3*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((3*im)*a^3*c^2*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((3*im)*a^3*c^2*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((7*im)*a^3*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (7*a^3*c^2*sqrt(1 + a^2*x^2)*PolyLog(3, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (6*a^3*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (6*a^3*c^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (7*a^3*c^2*sqrt(1 + a^2*x^2)*PolyLog(3, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((6*im)*a^3*c^2*sqrt(1 + a^2*x^2)*PolyLog(4, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((6*im)*a^3*c^2*sqrt(1 + a^2*x^2)*PolyLog(4, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2)]

    @test_int [x^3*(c + a^2*c*x^2)^(5/2)*atan(a*x)^3, x, 547, (85*c^2*x*sqrt(c + a^2*c*x^2))/(12096*a^3) - (c^2*x^3*sqrt(c + a^2*c*x^2))/(240*a) - (1/504)*a*c^2*x^5*sqrt(c + a^2*c*x^2) - (6157*c^2*sqrt(c + a^2*c*x^2)*atan(a*x))/(60480*a^4) - (47*c^2*x^2*sqrt(c + a^2*c*x^2)*atan(a*x))/(30240*a^2) + (67*c^2*x^4*sqrt(c + a^2*c*x^2)*atan(a*x))/2520 + (1/84)*a^2*c^2*x^6*sqrt(c + a^2*c*x^2)*atan(a*x) + (47*c^2*x*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(896*a^3) - (205*c^2*x^3*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(4032*a) - (103*a*c^2*x^5*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/1008 - (1/24)*a^3*c^2*x^7*sqrt(c + a^2*c*x^2)*atan(a*x)^2 - (115*im*c^3*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^2)/(1344*a^4*sqrt(c + a^2*c*x^2)) - (2*c^2*sqrt(c + a^2*c*x^2)*atan(a*x)^3)/(63*a^4) + (c^2*x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^3)/(63*a^2) + (5/21)*c^2*x^4*sqrt(c + a^2*c*x^2)*atan(a*x)^3 + (19/63)*a^2*c^2*x^6*sqrt(c + a^2*c*x^2)*atan(a*x)^3 + (1/9)*a^4*c^2*x^8*sqrt(c + a^2*c*x^2)*atan(a*x)^3 + (1433*c^(5/2)*atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2)))/(15120*a^4) + (115*im*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/(1344*a^4*sqrt(c + a^2*c*x^2)) - (115*im*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, im*ℯ^(im*atan(a*x))))/(1344*a^4*sqrt(c + a^2*c*x^2)) - (115*c^3*sqrt(1 + a^2*x^2)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(1344*a^4*sqrt(c + a^2*c*x^2)) + (115*c^3*sqrt(1 + a^2*x^2)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(1344*a^4*sqrt(c + a^2*c*x^2))]
    @test_int [x^2*(c + a^2*c*x^2)^(5/2)*atan(a*x)^3, x, 293, (13*c^2*sqrt(c + a^2*c*x^2))/(6720*a^3) - (3*c*(c + a^2*c*x^2)^(3/2))/(560*a^3) - (c + a^2*c*x^2)^(5/2)/(280*a^3) + (43*c^2*x*sqrt(c + a^2*c*x^2)*atan(a*x))/(1344*a^2) + (29/560)*c^2*x^3*sqrt(c + a^2*c*x^2)*atan(a*x) + (1/56)*a^2*c^2*x^5*sqrt(c + a^2*c*x^2)*atan(a*x) + (1373*c^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(13440*a^3) - (737*c^2*x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(6720*a) - (83/560)*a*c^2*x^4*sqrt(c + a^2*c*x^2)*atan(a*x)^2 - (3/56)*a^3*c^2*x^6*sqrt(c + a^2*c*x^2)*atan(a*x)^2 + (5*c^2*x*sqrt(c + a^2*c*x^2)*atan(a*x)^3)/(128*a^2) + (59/192)*c^2*x^3*sqrt(c + a^2*c*x^2)*atan(a*x)^3 + (17/48)*a^2*c^2*x^5*sqrt(c + a^2*c*x^2)*atan(a*x)^3 + (1/8)*a^4*c^2*x^7*sqrt(c + a^2*c*x^2)*atan(a*x)^3 + (5*im*c^3*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^3)/(64*a^3*sqrt(c + a^2*c*x^2)) + (397*im*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(840*a^3*sqrt(c + a^2*c*x^2)) - (15*im*c^3*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/(128*a^3*sqrt(c + a^2*c*x^2)) + (15*im*c^3*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, im*ℯ^(im*atan(a*x))))/(128*a^3*sqrt(c + a^2*c*x^2)) - (397*im*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, -((im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x))))/(1680*a^3*sqrt(c + a^2*c*x^2)) + (397*im*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(1680*a^3*sqrt(c + a^2*c*x^2)) + (15*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(64*a^3*sqrt(c + a^2*c*x^2)) - (15*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(64*a^3*sqrt(c + a^2*c*x^2)) + (15*im*c^3*sqrt(1 + a^2*x^2)*PolyLog(4, (-im)*ℯ^(im*atan(a*x))))/(64*a^3*sqrt(c + a^2*c*x^2)) - (15*im*c^3*sqrt(1 + a^2*x^2)*PolyLog(4, im*ℯ^(im*atan(a*x))))/(64*a^3*sqrt(c + a^2*c*x^2))]
    @test_int [x*(c + a^2*c*x^2)^(5/2)*atan(a*x)^3, x, 22, (-17*c^2*x*sqrt(c + a^2*c*x^2))/(420*a) - (c*x*(c + a^2*c*x^2)^(3/2))/(140*a) + (15*c^2*sqrt(c + a^2*c*x^2)*atan(a*x))/(56*a^2) + (5*c*(c + a^2*c*x^2)^(3/2)*atan(a*x))/(84*a^2) + ((c + a^2*c*x^2)^(5/2)*atan(a*x))/(35*a^2) - (15*c^2*x*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(112*a) - (5*c*x*(c + a^2*c*x^2)^(3/2)*atan(a*x)^2)/(56*a) - (x*(c + a^2*c*x^2)^(5/2)*atan(a*x)^2)/(14*a) + (((15*im)/56)*c^3*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^2)/(a^2*sqrt(c + a^2*c*x^2)) + ((c + a^2*c*x^2)^(7/2)*atan(a*x)^3)/(7*a^2*c) - (37*c^(5/2)*atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2)))/(120*a^2) - (((15*im)/56)*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/(a^2*sqrt(c + a^2*c*x^2)) + (((15*im)/56)*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, im*ℯ^(im*atan(a*x))))/(a^2*sqrt(c + a^2*c*x^2)) + (15*c^3*sqrt(1 + a^2*x^2)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(56*a^2*sqrt(c + a^2*c*x^2)) - (15*c^3*sqrt(1 + a^2*x^2)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(56*a^2*sqrt(c + a^2*c*x^2))]
    @test_int [(c + a^2*c*x^2)^(5/2)*atan(a*x)^3, x, 23, (-17*c^2*sqrt(c + a^2*c*x^2))/(60*a) - (c*(c + a^2*c*x^2)^(3/2))/(60*a) + (17*c^2*x*sqrt(c + a^2*c*x^2)*atan(a*x))/60 + (c*x*(c + a^2*c*x^2)^(3/2)*atan(a*x))/20 - (15*c^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(16*a) - (5*c*(c + a^2*c*x^2)^(3/2)*atan(a*x)^2)/(24*a) - ((c + a^2*c*x^2)^(5/2)*atan(a*x)^2)/(10*a) + (5*c^2*x*sqrt(c + a^2*c*x^2)*atan(a*x)^3)/16 + (5*c*x*(c + a^2*c*x^2)^(3/2)*atan(a*x)^3)/24 + (x*(c + a^2*c*x^2)^(5/2)*atan(a*x)^3)/6 - (((5*im)/8)*c^3*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^3)/(a*sqrt(c + a^2*c*x^2)) - (((259*im)/60)*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(a*sqrt(c + a^2*c*x^2)) + (((15*im)/16)*c^3*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2)) - (((15*im)/16)*c^3*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, im*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2)) + (((259*im)/120)*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, ((-im)*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(a*sqrt(c + a^2*c*x^2)) - (((259*im)/120)*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(a*sqrt(c + a^2*c*x^2)) - (15*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(8*a*sqrt(c + a^2*c*x^2)) + (15*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(8*a*sqrt(c + a^2*c*x^2)) - (((15*im)/8)*c^3*sqrt(1 + a^2*x^2)*PolyLog(4, (-im)*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2)) + (((15*im)/8)*c^3*sqrt(1 + a^2*x^2)*PolyLog(4, im*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2))]
    @test_int [((c + a^2*c*x^2)^(5/2)*atan(a*x)^3)/x, x, 54, -(a*c^2*x*sqrt(c + a^2*c*x^2))/20 + (29*c^2*sqrt(c + a^2*c*x^2)*atan(a*x))/20 + (c*(c + a^2*c*x^2)^(3/2)*atan(a*x))/10 - (29*a*c^2*x*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/40 - (3*a*c*x*(c + a^2*c*x^2)^(3/2)*atan(a*x)^2)/20 + (((149*im)/20)*c^3*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^2)/sqrt(c + a^2*c*x^2) + c^2*sqrt(c + a^2*c*x^2)*atan(a*x)^3 + (c*(c + a^2*c*x^2)^(3/2)*atan(a*x)^3)/3 + ((c + a^2*c*x^2)^(5/2)*atan(a*x)^3)/5 - (2*c^3*sqrt(1 + a^2*x^2)*atan(a*x)^3*atanh(ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (3*c^(5/2)*atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2)))/2 + ((3*im)*c^3*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (((149*im)/20)*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (((149*im)/20)*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((3*im)*c^3*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (6*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (149*c^3*sqrt(1 + a^2*x^2)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(20*sqrt(c + a^2*c*x^2)) - (149*c^3*sqrt(1 + a^2*x^2)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(20*sqrt(c + a^2*c*x^2)) + (6*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((6*im)*c^3*sqrt(1 + a^2*x^2)*PolyLog(4, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((6*im)*c^3*sqrt(1 + a^2*x^2)*PolyLog(4, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2)]
    @test_int [((c + a^2*c*x^2)^(5/2)*atan(a*x)^3)/x^2, x, 56, -(a*c^2*sqrt(c + a^2*c*x^2))/4 + (a^2*c^2*x*sqrt(c + a^2*c*x^2)*atan(a*x))/4 - (21*a*c^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/8 - (a*c*(c + a^2*c*x^2)^(3/2)*atan(a*x)^2)/4 - (c^2*sqrt(c + a^2*c*x^2)*atan(a*x)^3)/x + (7*a^2*c^2*x*sqrt(c + a^2*c*x^2)*atan(a*x)^3)/8 + (a^2*c*x*(c + a^2*c*x^2)^(3/2)*atan(a*x)^3)/4 - (((15*im)/4)*a*c^3*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^3)/sqrt(c + a^2*c*x^2) - ((11*im)*a*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (6*a*c^3*sqrt(1 + a^2*x^2)*atan(a*x)^2*atanh(ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((6*im)*a*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (((45*im)/8)*a*c^3*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (((45*im)/8)*a*c^3*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((6*im)*a*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (((11*im)/2)*a*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, ((-im)*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (((11*im)/2)*a*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (6*a*c^3*sqrt(1 + a^2*x^2)*PolyLog(3, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (45*a*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(4*sqrt(c + a^2*c*x^2)) + (45*a*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(4*sqrt(c + a^2*c*x^2)) + (6*a*c^3*sqrt(1 + a^2*x^2)*PolyLog(3, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (((45*im)/4)*a*c^3*sqrt(1 + a^2*x^2)*PolyLog(4, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (((45*im)/4)*a*c^3*sqrt(1 + a^2*x^2)*PolyLog(4, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2)]
    @test_int [((c + a^2*c*x^2)^(5/2)*atan(a*x)^3)/x^3, x, 87, a^2*c^2*sqrt(c + a^2*c*x^2)*atan(a*x) - (3*a*c^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(2*x) - (a^3*c^2*x*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/2 + ((13*im)*a^2*c^3*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^2)/sqrt(c + a^2*c*x^2) + 2*a^2*c^2*sqrt(c + a^2*c*x^2)*atan(a*x)^3 - (c^2*sqrt(c + a^2*c*x^2)*atan(a*x)^3)/(2*x^2) + (a^2*c*(c + a^2*c*x^2)^(3/2)*atan(a*x)^3)/3 - (5*a^2*c^3*sqrt(1 + a^2*x^2)*atan(a*x)^3*atanh(ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (6*a^2*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*atanh(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - a^2*c^(5/2)*atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2)) + (((15*im)/2)*a^2*c^3*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((13*im)*a^2*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((13*im)*a^2*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (((15*im)/2)*a^2*c^3*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((3*im)*a^2*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, -(sqrt(1 + im*a*x)/sqrt(1 - im*a*x))))/sqrt(c + a^2*c*x^2) - ((3*im)*a^2*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (15*a^2*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (13*a^2*c^3*sqrt(1 + a^2*x^2)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (13*a^2*c^3*sqrt(1 + a^2*x^2)*PolyLog(3, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (15*a^2*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((15*im)*a^2*c^3*sqrt(1 + a^2*x^2)*PolyLog(4, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((15*im)*a^2*c^3*sqrt(1 + a^2*x^2)*PolyLog(4, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2)]
    @test_int [((c + a^2*c*x^2)^(5/2)*atan(a*x)^3)/x^4, x, 86, -((a^2*c^2*sqrt(c + a^2*c*x^2)*atan(a*x))/x) - (3*a^3*c^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/2 - (a*c^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(2*x^2) - (2*a^2*c^2*sqrt(c + a^2*c*x^2)*atan(a*x)^3)/x + (a^4*c^2*x*sqrt(c + a^2*c*x^2)*atan(a*x)^3)/2 - (c*(c + a^2*c*x^2)^(3/2)*atan(a*x)^3)/(3*x^3) - ((5*im)*a^3*c^3*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^3)/sqrt(c + a^2*c*x^2) - ((6*im)*a^3*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (13*a^3*c^3*sqrt(1 + a^2*x^2)*atan(a*x)^2*atanh(ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - a^3*c^(5/2)*atanh(sqrt(c + a^2*c*x^2)/sqrt(c)) + ((13*im)*a^3*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (((15*im)/2)*a^3*c^3*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (((15*im)/2)*a^3*c^3*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((13*im)*a^3*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((3*im)*a^3*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, ((-im)*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - ((3*im)*a^3*c^3*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (13*a^3*c^3*sqrt(1 + a^2*x^2)*PolyLog(3, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (15*a^3*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (15*a^3*c^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (13*a^3*c^3*sqrt(1 + a^2*x^2)*PolyLog(3, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((15*im)*a^3*c^3*sqrt(1 + a^2*x^2)*PolyLog(4, (-im)*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((15*im)*a^3*c^3*sqrt(1 + a^2*x^2)*PolyLog(4, im*ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2)]

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

    @test_int [(x^3*atan(a*x)^3)/sqrt(c + a^2*c*x^2), x, 24, (sqrt(c + a^2*c*x^2)*atan(a*x))/(a^4*c) - (x*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(2*a^3*c) - (5*im*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^2)/(a^4*sqrt(c + a^2*c*x^2)) - (2*sqrt(c + a^2*c*x^2)*atan(a*x)^3)/(3*a^4*c) + (x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^3)/(3*a^2*c) - atanh((a*sqrt(c)*x)/sqrt(c + a^2*c*x^2))/(a^4*sqrt(c)) + (5*im*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/(a^4*sqrt(c + a^2*c*x^2)) - (5*im*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, im*ℯ^(im*atan(a*x))))/(a^4*sqrt(c + a^2*c*x^2)) - (5*sqrt(1 + a^2*x^2)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(a^4*sqrt(c + a^2*c*x^2)) + (5*sqrt(1 + a^2*x^2)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(a^4*sqrt(c + a^2*c*x^2))]
    @test_int [(x^2*atan(a*x)^3)/sqrt(c + a^2*c*x^2), x, 15, -((3*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(2*a^3*c)) + (x*sqrt(c + a^2*c*x^2)*atan(a*x)^3)/(2*a^2*c) + (im*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^3)/(a^3*sqrt(c + a^2*c*x^2)) - (6*im*sqrt(1 + a^2*x^2)*atan(a*x)*atan(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/(a^3*sqrt(c + a^2*c*x^2)) - (3*im*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/(2*a^3*sqrt(c + a^2*c*x^2)) + (3*im*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, im*ℯ^(im*atan(a*x))))/(2*a^3*sqrt(c + a^2*c*x^2)) + (3*im*sqrt(1 + a^2*x^2)*PolyLog(2, -((im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x))))/(a^3*sqrt(c + a^2*c*x^2)) - (3*im*sqrt(1 + a^2*x^2)*PolyLog(2, (im*sqrt(1 + im*a*x))/sqrt(1 - im*a*x)))/(a^3*sqrt(c + a^2*c*x^2)) + (3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(a^3*sqrt(c + a^2*c*x^2)) - (3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(a^3*sqrt(c + a^2*c*x^2)) + (3*im*sqrt(1 + a^2*x^2)*PolyLog(4, (-im)*ℯ^(im*atan(a*x))))/(a^3*sqrt(c + a^2*c*x^2)) - (3*im*sqrt(1 + a^2*x^2)*PolyLog(4, im*ℯ^(im*atan(a*x))))/(a^3*sqrt(c + a^2*c*x^2))]
    @test_int [(x*atan(a*x)^3)/sqrt(c + a^2*c*x^2), x, 10, ((6*im)*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^2)/(a^2*sqrt(c + a^2*c*x^2)) + (sqrt(c + a^2*c*x^2)*atan(a*x)^3)/(a^2*c) - ((6*im)*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/(a^2*sqrt(c + a^2*c*x^2)) + ((6*im)*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, im*ℯ^(im*atan(a*x))))/(a^2*sqrt(c + a^2*c*x^2)) + (6*sqrt(1 + a^2*x^2)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(a^2*sqrt(c + a^2*c*x^2)) - (6*sqrt(1 + a^2*x^2)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(a^2*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)^3/sqrt(c + a^2*c*x^2), x, 11, ((-2*im)*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^3)/(a*sqrt(c + a^2*c*x^2)) + ((3*im)*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2)) - ((3*im)*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, im*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2)) - (6*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2)) + (6*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2)) - ((6*im)*sqrt(1 + a^2*x^2)*PolyLog(4, (-im)*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2)) + ((6*im)*sqrt(1 + a^2*x^2)*PolyLog(4, im*ℯ^(im*atan(a*x))))/(a*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)^3/(x*sqrt(c + a^2*c*x^2)), x, 11, (-2*sqrt(1 + a^2*x^2)*atan(a*x)^3*atanh(ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((3*im)*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((3*im)*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (6*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (6*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((6*im)*sqrt(1 + a^2*x^2)*PolyLog(4, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((6*im)*sqrt(1 + a^2*x^2)*PolyLog(4, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2)]
    @test_int [atan(a*x)^3/(x^2*sqrt(c + a^2*c*x^2)), x, 10, -((sqrt(c + a^2*c*x^2)*atan(a*x)^3)/(c*x)) - (6*a*sqrt(1 + a^2*x^2)*atan(a*x)^2*atanh(ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((6*im)*a*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((6*im)*a*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (6*a*sqrt(1 + a^2*x^2)*PolyLog(3, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (6*a*sqrt(1 + a^2*x^2)*PolyLog(3, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2)]
    @test_int [atan(a*x)^3/(x^3*sqrt(c + a^2*c*x^2)), x, 15, (-3*a*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(2*c*x) - (sqrt(c + a^2*c*x^2)*atan(a*x)^3)/(2*c*x^2) + (a^2*sqrt(1 + a^2*x^2)*atan(a*x)^3*atanh(ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (6*a^2*sqrt(1 + a^2*x^2)*atan(a*x)*atanh(sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) - (((3*im)/2)*a^2*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (((3*im)/2)*a^2*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((3*im)*a^2*sqrt(1 + a^2*x^2)*PolyLog(2, -(sqrt(1 + im*a*x)/sqrt(1 - im*a*x))))/sqrt(c + a^2*c*x^2) - ((3*im)*a^2*sqrt(1 + a^2*x^2)*PolyLog(2, sqrt(1 + im*a*x)/sqrt(1 - im*a*x)))/sqrt(c + a^2*c*x^2) + (3*a^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (3*a^2*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((3*im)*a^2*sqrt(1 + a^2*x^2)*PolyLog(4, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - ((3*im)*a^2*sqrt(1 + a^2*x^2)*PolyLog(4, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2)]
    @test_int [atan(a*x)^3/(x^4*sqrt(c + a^2*c*x^2)), x, 25, -((a^2*sqrt(c + a^2*c*x^2)*atan(a*x))/(c*x)) - (a*sqrt(c + a^2*c*x^2)*atan(a*x)^2)/(2*c*x^2) - (sqrt(c + a^2*c*x^2)*atan(a*x)^3)/(3*c*x^3) + (2*a^2*sqrt(c + a^2*c*x^2)*atan(a*x)^3)/(3*c*x) + (5*a^3*sqrt(1 + a^2*x^2)*atan(a*x)^2*atanh(ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (a^3*atanh(sqrt(c + a^2*c*x^2)/sqrt(c)))/sqrt(c) - ((5*im)*a^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + ((5*im)*a^3*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) + (5*a^3*sqrt(1 + a^2*x^2)*PolyLog(3, -ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2) - (5*a^3*sqrt(1 + a^2*x^2)*PolyLog(3, ℯ^(im*atan(a*x))))/sqrt(c + a^2*c*x^2)]

    @test_int [(x^3*atan(a*x)^3)/(c + a^2*c*x^2)^(3/2), x, 14, (6*x)/(a^3*c*sqrt(c + a^2*c*x^2)) - (6*atan(a*x))/(a^4*c*sqrt(c + a^2*c*x^2)) - (3*x*atan(a*x)^2)/(a^3*c*sqrt(c + a^2*c*x^2)) + ((6*im)*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^2)/(a^4*c*sqrt(c + a^2*c*x^2)) + atan(a*x)^3/(a^4*c*sqrt(c + a^2*c*x^2)) + (sqrt(c + a^2*c*x^2)*atan(a*x)^3)/(a^4*c^2) - ((6*im)*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/(a^4*c*sqrt(c + a^2*c*x^2)) + ((6*im)*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, im*ℯ^(im*atan(a*x))))/(a^4*c*sqrt(c + a^2*c*x^2)) + (6*sqrt(1 + a^2*x^2)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(a^4*c*sqrt(c + a^2*c*x^2)) - (6*sqrt(1 + a^2*x^2)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(a^4*c*sqrt(c + a^2*c*x^2))]
    @test_int [(x^2*atan(a*x)^3)/(c + a^2*c*x^2)^(3/2), x, 14, 6/(a^3*c*sqrt(c + a^2*c*x^2)) + (6*x*atan(a*x))/(a^2*c*sqrt(c + a^2*c*x^2)) - (3*atan(a*x)^2)/(a^3*c*sqrt(c + a^2*c*x^2)) - (x*atan(a*x)^3)/(a^2*c*sqrt(c + a^2*c*x^2)) - ((2*im)*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^3)/(a^3*c*sqrt(c + a^2*c*x^2)) + ((3*im)*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/(a^3*c*sqrt(c + a^2*c*x^2)) - ((3*im)*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, im*ℯ^(im*atan(a*x))))/(a^3*c*sqrt(c + a^2*c*x^2)) - (6*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(a^3*c*sqrt(c + a^2*c*x^2)) + (6*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(a^3*c*sqrt(c + a^2*c*x^2)) - ((6*im)*sqrt(1 + a^2*x^2)*PolyLog(4, (-im)*ℯ^(im*atan(a*x))))/(a^3*c*sqrt(c + a^2*c*x^2)) + ((6*im)*sqrt(1 + a^2*x^2)*PolyLog(4, im*ℯ^(im*atan(a*x))))/(a^3*c*sqrt(c + a^2*c*x^2))]
    @test_int [(x*atan(a*x)^3)/(c + a^2*c*x^2)^(3/2), x, 3, (-6*x)/(a*c*sqrt(c + a^2*c*x^2)) + (6*atan(a*x))/(a^2*c*sqrt(c + a^2*c*x^2)) + (3*x*atan(a*x)^2)/(a*c*sqrt(c + a^2*c*x^2)) - atan(a*x)^3/(a^2*c*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)^3/(c + a^2*c*x^2)^(3/2), x, 2, -6/(a*c*sqrt(c + a^2*c*x^2)) - (6*x*atan(a*x))/(c*sqrt(c + a^2*c*x^2)) + (3*atan(a*x)^2)/(a*c*sqrt(c + a^2*c*x^2)) + (x*atan(a*x)^3)/(c*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)^3/(x*(c + a^2*c*x^2)^(3/2)), x, 15, (6*a*x)/(c*sqrt(c + a^2*c*x^2)) - (6*atan(a*x))/(c*sqrt(c + a^2*c*x^2)) - (3*a*x*atan(a*x)^2)/(c*sqrt(c + a^2*c*x^2)) + atan(a*x)^3/(c*sqrt(c + a^2*c*x^2)) - (2*sqrt(1 + a^2*x^2)*atan(a*x)^3*atanh(ℯ^(im*atan(a*x))))/(c*sqrt(c + a^2*c*x^2)) + ((3*im)*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, -ℯ^(im*atan(a*x))))/(c*sqrt(c + a^2*c*x^2)) - ((3*im)*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, ℯ^(im*atan(a*x))))/(c*sqrt(c + a^2*c*x^2)) - (6*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, -ℯ^(im*atan(a*x))))/(c*sqrt(c + a^2*c*x^2)) + (6*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, ℯ^(im*atan(a*x))))/(c*sqrt(c + a^2*c*x^2)) - ((6*im)*sqrt(1 + a^2*x^2)*PolyLog(4, -ℯ^(im*atan(a*x))))/(c*sqrt(c + a^2*c*x^2)) + ((6*im)*sqrt(1 + a^2*x^2)*PolyLog(4, ℯ^(im*atan(a*x))))/(c*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)^3/(x^2*(c + a^2*c*x^2)^(3/2)), x, 13, (6*a)/(c*sqrt(c + a^2*c*x^2)) + (6*a^2*x*atan(a*x))/(c*sqrt(c + a^2*c*x^2)) - (3*a*atan(a*x)^2)/(c*sqrt(c + a^2*c*x^2)) - (a^2*x*atan(a*x)^3)/(c*sqrt(c + a^2*c*x^2)) - (sqrt(c + a^2*c*x^2)*atan(a*x)^3)/(c^2*x) - (6*a*sqrt(1 + a^2*x^2)*atan(a*x)^2*atanh(ℯ^(im*atan(a*x))))/(c*sqrt(c + a^2*c*x^2)) + ((6*im)*a*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, -ℯ^(im*atan(a*x))))/(c*sqrt(c + a^2*c*x^2)) - ((6*im)*a*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, ℯ^(im*atan(a*x))))/(c*sqrt(c + a^2*c*x^2)) - (6*a*sqrt(1 + a^2*x^2)*PolyLog(3, -ℯ^(im*atan(a*x))))/(c*sqrt(c + a^2*c*x^2)) + (6*a*sqrt(1 + a^2*x^2)*PolyLog(3, ℯ^(im*atan(a*x))))/(c*sqrt(c + a^2*c*x^2))]

    @test_int [(x^5*atan(a*x)^3)/(c + a^2*c*x^2)^(5/2), x, 22, (2*x^3)/(27*a^3*c*(c + a^2*c*x^2)^(3/2)) + (94*x)/(9*a^5*c^2*sqrt(c + a^2*c*x^2)) - (2*x^2*atan(a*x))/(9*a^4*c*(c + a^2*c*x^2)^(3/2)) - (94*atan(a*x))/(9*a^6*c^2*sqrt(c + a^2*c*x^2)) - (x^3*atan(a*x)^2)/(3*a^3*c*(c + a^2*c*x^2)^(3/2)) - (5*x*atan(a*x)^2)/(a^5*c^2*sqrt(c + a^2*c*x^2)) + (6*im*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^2)/(a^6*c^2*sqrt(c + a^2*c*x^2)) + (x^2*atan(a*x)^3)/(3*a^4*c*(c + a^2*c*x^2)^(3/2)) + (5*atan(a*x)^3)/(3*a^6*c^2*sqrt(c + a^2*c*x^2)) + (sqrt(c + a^2*c*x^2)*atan(a*x)^3)/(a^6*c^3) - (6*im*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/(a^6*c^2*sqrt(c + a^2*c*x^2)) + (6*im*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, im*ℯ^(im*atan(a*x))))/(a^6*c^2*sqrt(c + a^2*c*x^2)) + (6*sqrt(1 + a^2*x^2)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(a^6*c^2*sqrt(c + a^2*c*x^2)) - (6*sqrt(1 + a^2*x^2)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(a^6*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [(x^4*atan(a*x)^3)/(c + a^2*c*x^2)^(5/2), x, 22, -(2/(27*a^5*c*(c + a^2*c*x^2)^(3/2))) + 68/(9*a^5*c^2*sqrt(c + a^2*c*x^2)) + (2*x^3*atan(a*x))/(9*a^2*c*(c + a^2*c*x^2)^(3/2)) + (22*x*atan(a*x))/(3*a^4*c^2*sqrt(c + a^2*c*x^2)) - (x^2*atan(a*x)^2)/(3*a^3*c*(c + a^2*c*x^2)^(3/2)) - (11*atan(a*x)^2)/(3*a^5*c^2*sqrt(c + a^2*c*x^2)) - (x^3*atan(a*x)^3)/(3*a^2*c*(c + a^2*c*x^2)^(3/2)) - (x*atan(a*x)^3)/(a^4*c^2*sqrt(c + a^2*c*x^2)) - (2*im*sqrt(1 + a^2*x^2)*atan(ℯ^(im*atan(a*x)))*atan(a*x)^3)/(a^5*c^2*sqrt(c + a^2*c*x^2)) + (3*im*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, (-im)*ℯ^(im*atan(a*x))))/(a^5*c^2*sqrt(c + a^2*c*x^2)) - (3*im*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, im*ℯ^(im*atan(a*x))))/(a^5*c^2*sqrt(c + a^2*c*x^2)) - (6*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, (-im)*ℯ^(im*atan(a*x))))/(a^5*c^2*sqrt(c + a^2*c*x^2)) + (6*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, im*ℯ^(im*atan(a*x))))/(a^5*c^2*sqrt(c + a^2*c*x^2)) - (6*im*sqrt(1 + a^2*x^2)*PolyLog(4, (-im)*ℯ^(im*atan(a*x))))/(a^5*c^2*sqrt(c + a^2*c*x^2)) + (6*im*sqrt(1 + a^2*x^2)*PolyLog(4, im*ℯ^(im*atan(a*x))))/(a^5*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [(x^3*atan(a*x)^3)/(c + a^2*c*x^2)^(5/2), x, 7, -((2*x^3)/(27*a*c*(c + a^2*c*x^2)^(3/2))) - (40*x)/(9*a^3*c^2*sqrt(c + a^2*c*x^2)) + (2*x^2*atan(a*x))/(9*a^2*c*(c + a^2*c*x^2)^(3/2)) + (40*atan(a*x))/(9*a^4*c^2*sqrt(c + a^2*c*x^2)) + (x^3*atan(a*x)^2)/(3*a*c*(c + a^2*c*x^2)^(3/2)) + (2*x*atan(a*x)^2)/(a^3*c^2*sqrt(c + a^2*c*x^2)) - (x^2*atan(a*x)^3)/(3*a^2*c*(c + a^2*c*x^2)^(3/2)) - (2*atan(a*x)^3)/(3*a^4*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [(x^2*atan(a*x)^3)/(c + a^2*c*x^2)^(5/2), x, 7, 2/(27*a^3*c*(c + a^2*c*x^2)^(3/2)) - 14/(9*a^3*c^2*sqrt(c + a^2*c*x^2)) - (2*x^3*atan(a*x))/(9*c*(c + a^2*c*x^2)^(3/2)) - (4*x*atan(a*x))/(3*a^2*c^2*sqrt(c + a^2*c*x^2)) + (x^2*atan(a*x)^2)/(3*a*c*(c + a^2*c*x^2)^(3/2)) + (2*atan(a*x)^2)/(3*a^3*c^2*sqrt(c + a^2*c*x^2)) + (x^3*atan(a*x)^3)/(3*c*(c + a^2*c*x^2)^(3/2))]
    @test_int [(x*atan(a*x)^3)/(c + a^2*c*x^2)^(5/2), x, 6, (-2*x)/(27*a*c*(c + a^2*c*x^2)^(3/2)) - (40*x)/(27*a*c^2*sqrt(c + a^2*c*x^2)) + (2*atan(a*x))/(9*a^2*c*(c + a^2*c*x^2)^(3/2)) + (4*atan(a*x))/(3*a^2*c^2*sqrt(c + a^2*c*x^2)) + (x*atan(a*x)^2)/(3*a*c*(c + a^2*c*x^2)^(3/2)) + (2*x*atan(a*x)^2)/(3*a*c^2*sqrt(c + a^2*c*x^2)) - atan(a*x)^3/(3*a^2*c*(c + a^2*c*x^2)^(3/2))]
    @test_int [atan(a*x)^3/(c + a^2*c*x^2)^(5/2), x, 5, -2/(27*a*c*(c + a^2*c*x^2)^(3/2)) - 40/(9*a*c^2*sqrt(c + a^2*c*x^2)) - (2*x*atan(a*x))/(9*c*(c + a^2*c*x^2)^(3/2)) - (40*x*atan(a*x))/(9*c^2*sqrt(c + a^2*c*x^2)) + atan(a*x)^2/(3*a*c*(c + a^2*c*x^2)^(3/2)) + (2*atan(a*x)^2)/(a*c^2*sqrt(c + a^2*c*x^2)) + (x*atan(a*x)^3)/(3*c*(c + a^2*c*x^2)^(3/2)) + (2*x*atan(a*x)^3)/(3*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)^3/(x*(c + a^2*c*x^2)^(5/2)), x, 22, (2*a*x)/(27*c*(c + a^2*c*x^2)^(3/2)) + (202*a*x)/(27*c^2*sqrt(c + a^2*c*x^2)) - (2*atan(a*x))/(9*c*(c + a^2*c*x^2)^(3/2)) - (22*atan(a*x))/(3*c^2*sqrt(c + a^2*c*x^2)) - (a*x*atan(a*x)^2)/(3*c*(c + a^2*c*x^2)^(3/2)) - (11*a*x*atan(a*x)^2)/(3*c^2*sqrt(c + a^2*c*x^2)) + atan(a*x)^3/(3*c*(c + a^2*c*x^2)^(3/2)) + atan(a*x)^3/(c^2*sqrt(c + a^2*c*x^2)) - (2*sqrt(1 + a^2*x^2)*atan(a*x)^3*atanh(ℯ^(im*atan(a*x))))/(c^2*sqrt(c + a^2*c*x^2)) + ((3*im)*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, -ℯ^(im*atan(a*x))))/(c^2*sqrt(c + a^2*c*x^2)) - ((3*im)*sqrt(1 + a^2*x^2)*atan(a*x)^2*PolyLog(2, ℯ^(im*atan(a*x))))/(c^2*sqrt(c + a^2*c*x^2)) - (6*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, -ℯ^(im*atan(a*x))))/(c^2*sqrt(c + a^2*c*x^2)) + (6*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(3, ℯ^(im*atan(a*x))))/(c^2*sqrt(c + a^2*c*x^2)) - ((6*im)*sqrt(1 + a^2*x^2)*PolyLog(4, -ℯ^(im*atan(a*x))))/(c^2*sqrt(c + a^2*c*x^2)) + ((6*im)*sqrt(1 + a^2*x^2)*PolyLog(4, ℯ^(im*atan(a*x))))/(c^2*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)^3/(x^2*(c + a^2*c*x^2)^(5/2)), x, 19, (2*a)/(27*c*(c + a^2*c*x^2)^(3/2)) + (94*a)/(9*c^2*sqrt(c + a^2*c*x^2)) + (2*a^2*x*atan(a*x))/(9*c*(c + a^2*c*x^2)^(3/2)) + (94*a^2*x*atan(a*x))/(9*c^2*sqrt(c + a^2*c*x^2)) - (a*atan(a*x)^2)/(3*c*(c + a^2*c*x^2)^(3/2)) - (5*a*atan(a*x)^2)/(c^2*sqrt(c + a^2*c*x^2)) - (a^2*x*atan(a*x)^3)/(3*c*(c + a^2*c*x^2)^(3/2)) - (5*a^2*x*atan(a*x)^3)/(3*c^2*sqrt(c + a^2*c*x^2)) - (sqrt(c + a^2*c*x^2)*atan(a*x)^3)/(c^3*x) - (6*a*sqrt(1 + a^2*x^2)*atan(a*x)^2*atanh(ℯ^(im*atan(a*x))))/(c^2*sqrt(c + a^2*c*x^2)) + ((6*im)*a*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, -ℯ^(im*atan(a*x))))/(c^2*sqrt(c + a^2*c*x^2)) - ((6*im)*a*sqrt(1 + a^2*x^2)*atan(a*x)*PolyLog(2, ℯ^(im*atan(a*x))))/(c^2*sqrt(c + a^2*c*x^2)) - (6*a*sqrt(1 + a^2*x^2)*PolyLog(3, -ℯ^(im*atan(a*x))))/(c^2*sqrt(c + a^2*c*x^2)) + (6*a*sqrt(1 + a^2*x^2)*PolyLog(3, ℯ^(im*atan(a*x))))/(c^2*sqrt(c + a^2*c*x^2))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x^2)^p*atan(a*x)^3*with*d=a^2*c*and*m*symbolic=#

    @test_int [x^m*(c + a^2*c*x^2)^2*atan(a*x)^3, x, 0, Unintegrable(x^m*(c + a^2*c*x^2)^2*atan(a*x)^3, x)]
    @test_int [x^m*(c + a^2*c*x^2)^1*atan(a*x)^3, x, 0, Unintegrable(x^m*(c + a^2*c*x^2)*atan(a*x)^3, x)]
    @test_int [(x^m*atan(a*x)^3)/(c + a^2*c*x^2)^1, x, 0, Unintegrable((x^m*atan(a*x)^3)/(c + a^2*c*x^2), x)]
    @test_int [(x^m*atan(a*x)^3)/(c + a^2*c*x^2)^2, x, 0, Unintegrable((x^m*atan(a*x)^3)/(c + a^2*c*x^2)^2, x)]

    @test_int [x^m*(c + a^2*c*x^2)^(3/2)*atan(a*x)^3, x, 0, Unintegrable(x^m*(c + a^2*c*x^2)^(3/2)*atan(a*x)^3, x)]
    @test_int [x^m*sqrt(c + a^2*c*x^2)*atan(a*x)^3, x, 0, Unintegrable(x^m*sqrt(c + a^2*c*x^2)*atan(a*x)^3, x)]
    @test_int [(x^m*atan(a*x)^3)/sqrt(c + a^2*c*x^2), x, 0, Unintegrable((x^m*atan(a*x)^3)/sqrt(c + a^2*c*x^2), x)]
    @test_int [(x^m*atan(a*x)^3)/(c + a^2*c*x^2)^(3/2), x, 0, Unintegrable((x^m*atan(a*x)^3)/(c + a^2*c*x^2)^(3/2), x)]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d+c^2*d*x^2)^q*(a+b*atan(c*x))^-1=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x^2)^p / atan(a*x)^1*with*d=a^2*c=#

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

    @test_int [(x*(c + a^2*c*x^2))/atan(a*x), x, 0, Unintegrable((x*(c + a^2*c*x^2))/atan(a*x), x)]
    @test_int [(c + a^2*c*x^2)/atan(a*x), x, 0, Unintegrable((c + a^2*c*x^2)/atan(a*x), x)]
    @test_int [(c + a^2*c*x^2)/(x*atan(a*x)), x, 0, Unintegrable((c + a^2*c*x^2)/(x*atan(a*x)), x)]

    @test_int [(x*(c + a^2*c*x^2)^2)/atan(a*x), x, 0, Unintegrable((x*(c + a^2*c*x^2)^2)/atan(a*x), x)]
    @test_int [(c + a^2*c*x^2)^2/atan(a*x), x, 0, Unintegrable((c + a^2*c*x^2)^2/atan(a*x), x)]
    @test_int [(c + a^2*c*x^2)^2/(x*atan(a*x)), x, 0, Unintegrable((c + a^2*c*x^2)^2/(x*atan(a*x)), x)]

    @test_int [(x*(c + a^2*c*x^2)^3)/atan(a*x), x, 0, Unintegrable((x*(c + a^2*c*x^2)^3)/atan(a*x), x)]
    @test_int [(c + a^2*c*x^2)^3/atan(a*x), x, 0, Unintegrable((c + a^2*c*x^2)^3/atan(a*x), x)]
    @test_int [(c + a^2*c*x^2)^3/(x*atan(a*x)), x, 0, Unintegrable((c + a^2*c*x^2)^3/(x*atan(a*x)), x)]

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

    @test_int [x^2/((c + a^2*c*x^2)*atan(a*x)), x, 0, Unintegrable(x^2/((c + a^2*c*x^2)*atan(a*x)), x)]
    @test_int [x/((c + a^2*c*x^2)*atan(a*x)), x, 0, Unintegrable(x/((c + a^2*c*x^2)*atan(a*x)), x)]
    @test_int [1/((c + a^2*c*x^2)*atan(a*x)), x, 1, log(atan(a*x))/(a*c)]
    @test_int [1/(x*(c + a^2*c*x^2)*atan(a*x)), x, 0, Unintegrable(1/(x*(c + a^2*c*x^2)*atan(a*x)), x)]
    @test_int [1/(x^2*(c + a^2*c*x^2)*atan(a*x)), x, 0, Unintegrable(1/(x^2*(c + a^2*c*x^2)*atan(a*x)), x)]

    @test_int [x^4/((c + a^2*c*x^2)^2*atan(a*x)), x, 0, Unintegrable(x^4/((c + a^2*c*x^2)^2*atan(a*x)), x)]
    @test_int [x^3/((c + a^2*c*x^2)^2*atan(a*x)), x, 0, Unintegrable(x^3/((c + a^2*c*x^2)^2*atan(a*x)), x)]
    @test_int [x^2/((c + a^2*c*x^2)^2*atan(a*x)), x, 4, -CosIntegral(2*atan(a*x))/(2*a^3*c^2) + log(atan(a*x))/(2*a^3*c^2)]
    @test_int [x/((c + a^2*c*x^2)^2*atan(a*x)), x, 4, SinIntegral(2*atan(a*x))/(2*a^2*c^2)]
    @test_int [1/((c + a^2*c*x^2)^2*atan(a*x)), x, 4, CosIntegral(2*atan(a*x))/(2*a*c^2) + log(atan(a*x))/(2*a*c^2)]
    @test_int [1/(x*(c + a^2*c*x^2)^2*atan(a*x)), x, 0, Unintegrable(1/(x*(c + a^2*c*x^2)^2*atan(a*x)), x)]
    @test_int [1/(x^2*(c + a^2*c*x^2)^2*atan(a*x)), x, 0, Unintegrable(1/(x^2*(c + a^2*c*x^2)^2*atan(a*x)), x)]

    @test_int [x^6/((c + a^2*c*x^2)^3*atan(a*x)), x, 0, Unintegrable(x^6/((c + a^2*c*x^2)^3*atan(a*x)), x)]
    @test_int [x^5/((c + a^2*c*x^2)^3*atan(a*x)), x, 0, Unintegrable(x^5/((c + a^2*c*x^2)^3*atan(a*x)), x)]
    @test_int [x^4/((c + a^2*c*x^2)^3*atan(a*x)), x, 5, -(CosIntegral(2*atan(a*x))/(2*a^5*c^3)) + CosIntegral(4*atan(a*x))/(8*a^5*c^3) + (3*log(atan(a*x)))/(8*a^5*c^3)]
    @test_int [x^3/((c + a^2*c*x^2)^3*atan(a*x)), x, 5, SinIntegral(2*atan(a*x))/(4*a^4*c^3) - SinIntegral(4*atan(a*x))/(8*a^4*c^3)]
    @test_int [x^2/((c + a^2*c*x^2)^3*atan(a*x)), x, 4, -CosIntegral(4*atan(a*x))/(8*a^3*c^3) + log(atan(a*x))/(8*a^3*c^3)]
    @test_int [x/((c + a^2*c*x^2)^3*atan(a*x)), x, 5, SinIntegral(2*atan(a*x))/(4*a^2*c^3) + SinIntegral(4*atan(a*x))/(8*a^2*c^3)]
    @test_int [1/((c + a^2*c*x^2)^3*atan(a*x)), x, 5, CosIntegral(2*atan(a*x))/(2*a*c^3) + CosIntegral(4*atan(a*x))/(8*a*c^3) + (3*log(atan(a*x)))/(8*a*c^3)]
    @test_int [1/(x*(c + a^2*c*x^2)^3*atan(a*x)), x, 0, Unintegrable(1/(x*(c + a^2*c*x^2)^3*atan(a*x)), x)]
    @test_int [1/(x^2*(c + a^2*c*x^2)^3*atan(a*x)), x, 0, Unintegrable(1/(x^2*(c + a^2*c*x^2)^3*atan(a*x)), x)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x^2)^(p/2) / atan(a*x)^1*with*d=a^2*c=#

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

    @test_int [(x*sqrt(c + a^2*c*x^2))/atan(a*x), x, 0, Unintegrable((x*sqrt(c + a^2*c*x^2))/atan(a*x), x)]
    @test_int [sqrt(c + a^2*c*x^2)/atan(a*x), x, 0, Unintegrable(sqrt(c + a^2*c*x^2)/atan(a*x), x)]
    @test_int [sqrt(c + a^2*c*x^2)/(x*atan(a*x)), x, 0, Unintegrable(sqrt(c + a^2*c*x^2)/(x*atan(a*x)), x)]

    @test_int [(x*(c + a^2*c*x^2)^(3/2))/atan(a*x), x, 0, Unintegrable((x*(c + a^2*c*x^2)^(3/2))/atan(a*x), x)]
    @test_int [(c + a^2*c*x^2)^(3/2)/atan(a*x), x, 0, Unintegrable((c + a^2*c*x^2)^(3/2)/atan(a*x), x)]
    @test_int [(c + a^2*c*x^2)^(3/2)/(x*atan(a*x)), x, 0, Unintegrable((c + a^2*c*x^2)^(3/2)/(x*atan(a*x)), x)]

    @test_int [(x*(c + a^2*c*x^2)^(5/2))/atan(a*x), x, 0, Unintegrable((x*(c + a^2*c*x^2)^(5/2))/atan(a*x), x)]
    @test_int [(c + a^2*c*x^2)^(5/2)/atan(a*x), x, 0, Unintegrable((c + a^2*c*x^2)^(5/2)/atan(a*x), x)]
    @test_int [(c + a^2*c*x^2)^(5/2)/(x*atan(a*x)), x, 0, Unintegrable((c + a^2*c*x^2)^(5/2)/(x*atan(a*x)), x)]

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

    @test_int [x/(sqrt(c + a^2*c*x^2)*atan(a*x)), x, 0, Unintegrable(x/(sqrt(c + a^2*c*x^2)*atan(a*x)), x)]
    @test_int [1/(sqrt(c + a^2*c*x^2)*atan(a*x)), x, 0, Unintegrable(1/(sqrt(c + a^2*c*x^2)*atan(a*x)), x)]
    @test_int [1/(x*sqrt(c + a^2*c*x^2)*atan(a*x)), x, 0, Unintegrable(1/(x*sqrt(c + a^2*c*x^2)*atan(a*x)), x)]

    @test_int [x^3/((c + a^2*c*x^2)^(3/2)*atan(a*x)), x, 0, Unintegrable(x^3/((c + a^2*c*x^2)^(3/2)*atan(a*x)), x)]
    @test_int [x^2/((c + a^2*c*x^2)^(3/2)*atan(a*x)), x, 0, Unintegrable(x^2/((c + a^2*c*x^2)^(3/2)*atan(a*x)), x)]
    @test_int [x/((c + a^2*c*x^2)^(3/2)*atan(a*x)), x, 3, (sqrt(1 + a^2*x^2)*SinIntegral(atan(a*x)))/(a^2*c*sqrt(c + a^2*c*x^2))]
    @test_int [1/((c + a^2*c*x^2)^(3/2)*atan(a*x)), x, 3, (sqrt(1 + a^2*x^2)*CosIntegral(atan(a*x)))/(a*c*sqrt(c + a^2*c*x^2))]
    @test_int [1/(x*(c + a^2*c*x^2)^(3/2)*atan(a*x)), x, 0, Unintegrable(1/(x*(c + a^2*c*x^2)^(3/2)*atan(a*x)), x)]
    @test_int [1/(x^2*(c + a^2*c*x^2)^(3/2)*atan(a*x)), x, 0, Unintegrable(1/(x^2*(c + a^2*c*x^2)^(3/2)*atan(a*x)), x)]

    @test_int [x^5/((c + a^2*c*x^2)^(5/2)*atan(a*x)), x, 0, Unintegrable(x^5/((c + a^2*c*x^2)^(5/2)*atan(a*x)), x)]
    @test_int [x^4/((c + a^2*c*x^2)^(5/2)*atan(a*x)), x, 0, Unintegrable(x^4/((c + a^2*c*x^2)^(5/2)*atan(a*x)), x)]
    @test_int [x^3/((c + a^2*c*x^2)^(5/2)*atan(a*x)), x, 6, (3*sqrt(1 + a^2*x^2)*SinIntegral(atan(a*x)))/(4*a^4*c^2*sqrt(c + a^2*c*x^2)) - (sqrt(1 + a^2*x^2)*SinIntegral(3*atan(a*x)))/(4*a^4*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [x^2/((c + a^2*c*x^2)^(5/2)*atan(a*x)), x, 6, (sqrt(1 + a^2*x^2)*CosIntegral(atan(a*x)))/(4*a^3*c^2*sqrt(c + a^2*c*x^2)) - (sqrt(1 + a^2*x^2)*CosIntegral(3*atan(a*x)))/(4*a^3*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [x/((c + a^2*c*x^2)^(5/2)*atan(a*x)), x, 6, (sqrt(1 + a^2*x^2)*SinIntegral(atan(a*x)))/(4*a^2*c^2*sqrt(c + a^2*c*x^2)) + (sqrt(1 + a^2*x^2)*SinIntegral(3*atan(a*x)))/(4*a^2*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [1/((c + a^2*c*x^2)^(5/2)*atan(a*x)), x, 6, (3*sqrt(1 + a^2*x^2)*CosIntegral(atan(a*x)))/(4*a*c^2*sqrt(c + a^2*c*x^2)) + (sqrt(1 + a^2*x^2)*CosIntegral(3*atan(a*x)))/(4*a*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [1/(x*(c + a^2*c*x^2)^(5/2)*atan(a*x)), x, 0, Unintegrable(1/(x*(c + a^2*c*x^2)^(5/2)*atan(a*x)), x)]
    @test_int [1/(x^2*(c + a^2*c*x^2)^(5/2)*atan(a*x)), x, 0, Unintegrable(1/(x^2*(c + a^2*c*x^2)^(5/2)*atan(a*x)), x)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x^2)^p / atan(a*x)^1*with*d=a^2*c*and*m*symbolic=#

    @test_int [(x^m*(c + a^2*c*x^2)^3)/atan(a*x), x, 0, Unintegrable((x^m*(c + a^2*c*x^2)^3)/atan(a*x), x)]
    @test_int [(x^m*(c + a^2*c*x^2)^2)/atan(a*x), x, 0, Unintegrable((x^m*(c + a^2*c*x^2)^2)/atan(a*x), x)]
    @test_int [(x^m*(c + a^2*c*x^2))/atan(a*x), x, 0, Unintegrable((x^m*(c + a^2*c*x^2))/atan(a*x), x)]
    @test_int [x^m/((c + a^2*c*x^2)*atan(a*x)), x, 0, Unintegrable(x^m/((c + a^2*c*x^2)*atan(a*x)), x)]
    @test_int [x^m/((c + a^2*c*x^2)^2*atan(a*x)), x, 0, Unintegrable(x^m/((c + a^2*c*x^2)^2*atan(a*x)), x)]
    @test_int [x^m/((c + a^2*c*x^2)^3*atan(a*x)), x, 0, Unintegrable(x^m/((c + a^2*c*x^2)^3*atan(a*x)), x)]

    @test_int [(x^m*(c + a^2*c*x^2)^(5/2))/atan(a*x), x, 0, Unintegrable((x^m*(c + a^2*c*x^2)^(5/2))/atan(a*x), x)]
    @test_int [(x^m*(c + a^2*c*x^2)^(3/2))/atan(a*x), x, 0, Unintegrable((x^m*(c + a^2*c*x^2)^(3/2))/atan(a*x), x)]
    @test_int [(x^m*sqrt(c + a^2*c*x^2))/atan(a*x), x, 0, Unintegrable((x^m*sqrt(c + a^2*c*x^2))/atan(a*x), x)]
    @test_int [x^m/(sqrt(c + a^2*c*x^2)*atan(a*x)), x, 0, Unintegrable(x^m/(sqrt(c + a^2*c*x^2)*atan(a*x)), x)]
    @test_int [x^m/((c + a^2*c*x^2)^(3/2)*atan(a*x)), x, 0, Unintegrable(x^m/((c + a^2*c*x^2)^(3/2)*atan(a*x)), x)]
    @test_int [x^m/((c + a^2*c*x^2)^(5/2)*atan(a*x)), x, 0, Unintegrable(x^m/((c + a^2*c*x^2)^(5/2)*atan(a*x)), x)]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d+c^2*d*x^2)^q*(a+b*atan(c*x))^-2=#

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

    #= ::Subsubsection::Closed:: =#
    #=q>0=#

    @test_int [(x*(c + a^2*c*x^2))/atan(a*x)^2, x, 0, Unintegrable((x*(c + a^2*c*x^2))/atan(a*x)^2, x)]
    @test_int [(c + a^2*c*x^2)/atan(a*x)^2, x, 0, Unintegrable((c + a^2*c*x^2)/atan(a*x)^2, x)]
    @test_int [(c + a^2*c*x^2)/(x*atan(a*x)^2), x, 0, Unintegrable((c + a^2*c*x^2)/(x*atan(a*x)^2), x)]

    @test_int [(x*(c + a^2*c*x^2)^2)/atan(a*x)^2, x, 0, Unintegrable((x*(c + a^2*c*x^2)^2)/atan(a*x)^2, x)]
    @test_int [(c + a^2*c*x^2)^2/atan(a*x)^2, x, 0, Unintegrable((c + a^2*c*x^2)^2/atan(a*x)^2, x)]
    @test_int [(c + a^2*c*x^2)^2/(x*atan(a*x)^2), x, 0, Unintegrable((c + a^2*c*x^2)^2/(x*atan(a*x)^2), x)]

    @test_int [(x*(c + a^2*c*x^2)^3)/atan(a*x)^2, x, 0, Unintegrable((x*(c + a^2*c*x^2)^3)/atan(a*x)^2, x)]
    @test_int [(c + a^2*c*x^2)^3/atan(a*x)^2, x, 0, Unintegrable((c + a^2*c*x^2)^3/atan(a*x)^2, x)]
    @test_int [(c + a^2*c*x^2)^3/(x*atan(a*x)^2), x, 0, Unintegrable((c + a^2*c*x^2)^3/(x*atan(a*x)^2), x)]

    #= ::Subsubsection::Closed:: =#
    #=q<0=#

    @test_int [x^3/((c + a^2*c*x^2)*atan(a*x)^2), x, 1, -(x^3/(a*c*atan(a*x))) + (3*Unintegrable(x^2/atan(a*x), x))/(a*c)]
    @test_int [x^2/((c + a^2*c*x^2)*atan(a*x)^2), x, 1, -(x^2/(a*c*atan(a*x))) + (2*Unintegrable(x/atan(a*x), x))/(a*c)]
    @test_int [x/((c + a^2*c*x^2)*atan(a*x)^2), x, 1, -(x/(a*c*atan(a*x))) + Unintegrable(atan(a*x)^(-1), x)/(a*c)]
    @test_int [1/((c + a^2*c*x^2)*atan(a*x)^2), x, 1, -(1/(a*c*atan(a*x)))]
    @test_int [1/(x*(c + a^2*c*x^2)*atan(a*x)^2), x, 1, -(1/(a*c*x*atan(a*x))) - Unintegrable(1/(x^2*atan(a*x)), x)/(a*c)]
    @test_int [1/(x^2*(c + a^2*c*x^2)*atan(a*x)^2), x, 1, -(1/(a*c*x^2*atan(a*x))) - (2*Unintegrable(1/(x^3*atan(a*x)), x))/(a*c)]
    @test_int [1/(x^3*(c + a^2*c*x^2)*atan(a*x)^2), x, 1, -(1/(a*c*x^3*atan(a*x))) - (3*Unintegrable(1/(x^4*atan(a*x)), x))/(a*c)]
    @test_int [1/(x^4*(c + a^2*c*x^2)*atan(a*x)^2), x, 1, -(1/(a*c*x^4*atan(a*x))) - (4*Unintegrable(1/(x^5*atan(a*x)), x))/(a*c)]

    @test_int [x^3/((c + a^2*c*x^2)^2*atan(a*x)^2), x, 11, -(x/(a^3*c^2*atan(a*x))) + x/(a^3*c^2*(1 + a^2*x^2)*atan(a*x)) - CosIntegral(2*atan(a*x))/(a^4*c^2) + Unintegrable(atan(a*x)^(-1), x)/(a^3*c^2)]
    @test_int [x^2/((c + a^2*c*x^2)^2*atan(a*x)^2), x, 5, -(x^2/(a*c^2*(1 + a^2*x^2)*atan(a*x))) + SinIntegral(2*atan(a*x))/(a^3*c^2)]
    @test_int [x/((c + a^2*c*x^2)^2*atan(a*x)^2), x, 9, -(x/(a*c^2*(1 + a^2*x^2)*atan(a*x))) + CosIntegral(2*atan(a*x))/(a^2*c^2)]
    @test_int [1/((c + a^2*c*x^2)^2*atan(a*x)^2), x, 5, -(1/(a*c^2*(1 + a^2*x^2)*atan(a*x))) - SinIntegral(2*atan(a*x))/(a*c^2)]
    @test_int [1/(x*(c + a^2*c*x^2)^2*atan(a*x)^2), x, 11, -(1/(a*c^2*x*atan(a*x))) + (a*x)/(c^2*(1 + a^2*x^2)*atan(a*x)) - CosIntegral(2*atan(a*x))/c^2 - Unintegrable(1/(x^2*atan(a*x)), x)/(a*c^2)]
    @test_int [1/(x^2*(c + a^2*c*x^2)^2*atan(a*x)^2), x, 7, -(1/(a*c^2*x^2*atan(a*x))) + a/(c^2*(1 + a^2*x^2)*atan(a*x)) + (a*SinIntegral(2*atan(a*x)))/c^2 - (2*Unintegrable(1/(x^3*atan(a*x)), x))/(a*c^2)]
    @test_int [1/(x^3*(c + a^2*c*x^2)^2*atan(a*x)^2), x, 13, -(1/(a*c^2*x^3*atan(a*x))) + a/(c^2*x*atan(a*x)) - (a^3*x)/(c^2*(1 + a^2*x^2)*atan(a*x)) + (a^2*CosIntegral(2*atan(a*x)))/c^2 - (3*Unintegrable(1/(x^4*atan(a*x)), x))/(a*c^2) + (a*Unintegrable(1/(x^2*atan(a*x)), x))/c^2]
    @test_int [1/(x^4*(c + a^2*c*x^2)^2*atan(a*x)^2), x, 9, -(1/(a*c^2*x^4*atan(a*x))) + a/(c^2*x^2*atan(a*x)) - a^3/(c^2*(1 + a^2*x^2)*atan(a*x)) - (a^3*SinIntegral(2*atan(a*x)))/c^2 - (4*Unintegrable(1/(x^5*atan(a*x)), x))/(a*c^2) + (2*a*Unintegrable(1/(x^3*atan(a*x)), x))/c^2]

    @test_int [x^3/((c + a^2*c*x^2)^3*atan(a*x)^2), x, 20, x/(a^3*c^3*(1 + a^2*x^2)^2*atan(a*x)) - x/(a^3*c^3*(1 + a^2*x^2)*atan(a*x)) + CosIntegral(2*atan(a*x))/(2*a^4*c^3) - CosIntegral(4*atan(a*x))/(2*a^4*c^3)]
    @test_int [x^2/((c + a^2*c*x^2)^3*atan(a*x)^2), x, 12, 1/(a^3*c^3*(1 + a^2*x^2)^2*atan(a*x)) - 1/(a^3*c^3*(1 + a^2*x^2)*atan(a*x)) + SinIntegral(4*atan(a*x))/(2*a^3*c^3)]
    @test_int [x/((c + a^2*c*x^2)^3*atan(a*x)^2), x, 10, -(x/(a*c^3*(1 + a^2*x^2)^2*atan(a*x))) + CosIntegral(2*atan(a*x))/(2*a^2*c^3) + CosIntegral(4*atan(a*x))/(2*a^2*c^3)]
    @test_int [1/((c + a^2*c*x^2)^3*atan(a*x)^2), x, 6, -(1/(a*c^3*(1 + a^2*x^2)^2*atan(a*x))) - SinIntegral(2*atan(a*x))/(a*c^3) - SinIntegral(4*atan(a*x))/(2*a*c^3)]
    @test_int [1/(x*(c + a^2*c*x^2)^3*atan(a*x)^2), x, 22, -(1/(a*c^3*x*atan(a*x))) + (a*x)/(c^3*(1 + a^2*x^2)^2*atan(a*x)) + (a*x)/(c^3*(1 + a^2*x^2)*atan(a*x)) - (3*CosIntegral(2*atan(a*x)))/(2*c^3) - CosIntegral(4*atan(a*x))/(2*c^3) - Unintegrable(1/(x^2*atan(a*x)), x)/(a*c^3)]
    @test_int [1/(x^2*(c + a^2*c*x^2)^3*atan(a*x)^2), x, 14, -(1/(a*c^3*x^2*atan(a*x))) + a/(c^3*(1 + a^2*x^2)^2*atan(a*x)) + a/(c^3*(1 + a^2*x^2)*atan(a*x)) + (2*a*SinIntegral(2*atan(a*x)))/c^3 + (a*SinIntegral(4*atan(a*x)))/(2*c^3) - (2*Unintegrable(1/(x^3*atan(a*x)), x))/(a*c^3)]
    @test_int [1/(x^3*(c + a^2*c*x^2)^3*atan(a*x)^2), x, 36, -(1/(a*c^3*x^3*atan(a*x))) + (2*a)/(c^3*x*atan(a*x)) - (a^3*x)/(c^3*(1 + a^2*x^2)^2*atan(a*x)) - (2*a^3*x)/(c^3*(1 + a^2*x^2)*atan(a*x)) + (5*a^2*CosIntegral(2*atan(a*x)))/(2*c^3) + (a^2*CosIntegral(4*atan(a*x)))/(2*c^3) - (3*Unintegrable(1/(x^4*atan(a*x)), x))/(a*c^3) + (2*a*Unintegrable(1/(x^2*atan(a*x)), x))/c^3]
    @test_int [1/(x^4*(c + a^2*c*x^2)^3*atan(a*x)^2), x, 24, -(1/(a*c^3*x^4*atan(a*x))) + (2*a)/(c^3*x^2*atan(a*x)) - a^3/(c^3*(1 + a^2*x^2)^2*atan(a*x)) - (2*a^3)/(c^3*(1 + a^2*x^2)*atan(a*x)) - (3*a^3*SinIntegral(2*atan(a*x)))/c^3 - (a^3*SinIntegral(4*atan(a*x)))/(2*c^3) - (4*Unintegrable(1/(x^5*atan(a*x)), x))/(a*c^3) + (4*a*Unintegrable(1/(x^3*atan(a*x)), x))/c^3]

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

    #= ::Subsubsection::Closed:: =#
    #=q>0=#

    @test_int [(x*sqrt(c + a^2*c*x^2))/atan(a*x)^2, x, 0, Unintegrable((x*sqrt(c + a^2*c*x^2))/atan(a*x)^2, x)]
    @test_int [sqrt(c + a^2*c*x^2)/atan(a*x)^2, x, 0, Unintegrable(sqrt(c + a^2*c*x^2)/atan(a*x)^2, x)]
    @test_int [sqrt(c + a^2*c*x^2)/(x*atan(a*x)^2), x, 0, Unintegrable(sqrt(c + a^2*c*x^2)/(x*atan(a*x)^2), x)]

    @test_int [(x*(c + a^2*c*x^2)^(3/2))/atan(a*x)^2, x, 0, Unintegrable((x*(c + a^2*c*x^2)^(3/2))/atan(a*x)^2, x)]
    @test_int [(c + a^2*c*x^2)^(3/2)/atan(a*x)^2, x, 0, Unintegrable((c + a^2*c*x^2)^(3/2)/atan(a*x)^2, x)]
    @test_int [(c + a^2*c*x^2)^(3/2)/(x*atan(a*x)^2), x, 0, Unintegrable((c + a^2*c*x^2)^(3/2)/(x*atan(a*x)^2), x)]

    @test_int [(x*(c + a^2*c*x^2)^(5/2))/atan(a*x)^2, x, 0, Unintegrable((x*(c + a^2*c*x^2)^(5/2))/atan(a*x)^2, x)]
    @test_int [(c + a^2*c*x^2)^(5/2)/atan(a*x)^2, x, 0, Unintegrable((c + a^2*c*x^2)^(5/2)/atan(a*x)^2, x)]
    @test_int [(c + a^2*c*x^2)^(5/2)/(x*atan(a*x)^2), x, 0, Unintegrable((c + a^2*c*x^2)^(5/2)/(x*atan(a*x)^2), x)]

    #= ::Subsubsection::Closed:: =#
    #=q<0=#

    @test_int [x/(sqrt(c + a^2*c*x^2)*atan(a*x)^2), x, 0, Unintegrable(x/(sqrt(c + a^2*c*x^2)*atan(a*x)^2), x)]
    @test_int [1/(sqrt(c + a^2*c*x^2)*atan(a*x)^2), x, 0, Unintegrable(1/(sqrt(c + a^2*c*x^2)*atan(a*x)^2), x)]
    @test_int [1/(x*sqrt(c + a^2*c*x^2)*atan(a*x)^2), x, 1, -(sqrt(c + a^2*c*x^2)/(a*c*x*atan(a*x))) - Unintegrable(1/(x^2*sqrt(c + a^2*c*x^2)*atan(a*x)), x)/a]

    @test_int [x^3/((c + a^2*c*x^2)^(3/2)*atan(a*x)^2), x, 5, x/(a^3*c*sqrt(c + a^2*c*x^2)*atan(a*x)) - (sqrt(1 + a^2*x^2)*CosIntegral(atan(a*x)))/(a^4*c*sqrt(c + a^2*c*x^2)) + Unintegrable(x/(sqrt(c + a^2*c*x^2)*atan(a*x)^2), x)/(a^2*c)]
    @test_int [x^2/((c + a^2*c*x^2)^(3/2)*atan(a*x)^2), x, 5, 1/(a^3*c*sqrt(c + a^2*c*x^2)*atan(a*x)) + (sqrt(1 + a^2*x^2)*SinIntegral(atan(a*x)))/(a^3*c*sqrt(c + a^2*c*x^2)) + Unintegrable(1/(sqrt(c + a^2*c*x^2)*atan(a*x)^2), x)/(a^2*c)]
    @test_int [x/((c + a^2*c*x^2)^(3/2)*atan(a*x)^2), x, 4, -(x/(a*c*sqrt(c + a^2*c*x^2)*atan(a*x))) + (sqrt(1 + a^2*x^2)*CosIntegral(atan(a*x)))/(a^2*c*sqrt(c + a^2*c*x^2))]
    @test_int [1/((c + a^2*c*x^2)^(3/2)*atan(a*x)^2), x, 4, -(1/(a*c*sqrt(c + a^2*c*x^2)*atan(a*x))) - (sqrt(1 + a^2*x^2)*SinIntegral(atan(a*x)))/(a*c*sqrt(c + a^2*c*x^2))]
    @test_int [1/(x*(c + a^2*c*x^2)^(3/2)*atan(a*x)^2), x, 6, (a*x)/(c*sqrt(c + a^2*c*x^2)*atan(a*x)) - sqrt(c + a^2*c*x^2)/(a*c^2*x*atan(a*x)) - (sqrt(1 + a^2*x^2)*CosIntegral(atan(a*x)))/(c*sqrt(c + a^2*c*x^2)) - Unintegrable(1/(x^2*sqrt(c + a^2*c*x^2)*atan(a*x)), x)/(a*c)]
    @test_int [1/(x^2*(c + a^2*c*x^2)^(3/2)*atan(a*x)^2), x, 5, a/(c*sqrt(c + a^2*c*x^2)*atan(a*x)) + (a*sqrt(1 + a^2*x^2)*SinIntegral(atan(a*x)))/(c*sqrt(c + a^2*c*x^2)) + Unintegrable(1/(x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2), x)/c]
    @test_int [1/(x^3*(c + a^2*c*x^2)^(3/2)*atan(a*x)^2), x, 7, -((a^3*x)/(c*sqrt(c + a^2*c*x^2)*atan(a*x))) + (a*sqrt(c + a^2*c*x^2))/(c^2*x*atan(a*x)) + (a^2*sqrt(1 + a^2*x^2)*CosIntegral(atan(a*x)))/(c*sqrt(c + a^2*c*x^2)) + Unintegrable(1/(x^3*sqrt(c + a^2*c*x^2)*atan(a*x)^2), x)/c + (a*Unintegrable(1/(x^2*sqrt(c + a^2*c*x^2)*atan(a*x)), x))/c]
    @test_int [1/(x^4*(c + a^2*c*x^2)^(3/2)*atan(a*x)^2), x, 6, -(a^3/(c*sqrt(c + a^2*c*x^2)*atan(a*x))) - (a^3*sqrt(1 + a^2*x^2)*SinIntegral(atan(a*x)))/(c*sqrt(c + a^2*c*x^2)) + Unintegrable(1/(x^4*sqrt(c + a^2*c*x^2)*atan(a*x)^2), x)/c - (a^2*Unintegrable(1/(x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2), x))/c]

    @test_int [x^5/((c + a^2*c*x^2)^(5/2)*atan(a*x)^2), x, 13, x^3/(a^3*c*(c + a^2*c*x^2)^(3/2)*atan(a*x)) + x/(a^5*c^2*sqrt(c + a^2*c*x^2)*atan(a*x)) - (7*sqrt(1 + a^2*x^2)*CosIntegral(atan(a*x)))/(4*a^6*c^2*sqrt(c + a^2*c*x^2)) + (3*sqrt(1 + a^2*x^2)*CosIntegral(3*atan(a*x)))/(4*a^6*c^2*sqrt(c + a^2*c*x^2)) + Unintegrable(x/(sqrt(c + a^2*c*x^2)*atan(a*x)^2), x)/(a^4*c^2)]
    @test_int [x^4/((c + a^2*c*x^2)^(5/2)*atan(a*x)^2), x, 18, -(1/(a^5*c*(c + a^2*c*x^2)^(3/2)*atan(a*x))) + 2/(a^5*c^2*sqrt(c + a^2*c*x^2)*atan(a*x)) + (5*sqrt(1 + a^2*x^2)*SinIntegral(atan(a*x)))/(4*a^5*c^2*sqrt(c + a^2*c*x^2)) - (3*sqrt(1 + a^2*x^2)*SinIntegral(3*atan(a*x)))/(4*a^5*c^2*sqrt(c + a^2*c*x^2)) + Unintegrable(1/(sqrt(c + a^2*c*x^2)*atan(a*x)^2), x)/(a^4*c^2)]
    @test_int [x^3/((c + a^2*c*x^2)^(5/2)*atan(a*x)^2), x, 7, -(x^3/(a*c*(c + a^2*c*x^2)^(3/2)*atan(a*x))) + (3*sqrt(1 + a^2*x^2)*CosIntegral(atan(a*x)))/(4*a^4*c^2*sqrt(c + a^2*c*x^2)) - (3*sqrt(1 + a^2*x^2)*CosIntegral(3*atan(a*x)))/(4*a^4*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [x^2/((c + a^2*c*x^2)^(5/2)*atan(a*x)^2), x, 12, 1/(a^3*c*(c + a^2*c*x^2)^(3/2)*atan(a*x)) - 1/(a^3*c^2*sqrt(c + a^2*c*x^2)*atan(a*x)) - (sqrt(1 + a^2*x^2)*SinIntegral(atan(a*x)))/(4*a^3*c^2*sqrt(c + a^2*c*x^2)) + (3*sqrt(1 + a^2*x^2)*SinIntegral(3*atan(a*x)))/(4*a^3*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [x/((c + a^2*c*x^2)^(5/2)*atan(a*x)^2), x, 13, -(x/(a*c*(c + a^2*c*x^2)^(3/2)*atan(a*x))) + (sqrt(1 + a^2*x^2)*CosIntegral(atan(a*x)))/(4*a^2*c^2*sqrt(c + a^2*c*x^2)) + (3*sqrt(1 + a^2*x^2)*CosIntegral(3*atan(a*x)))/(4*a^2*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [1/((c + a^2*c*x^2)^(5/2)*atan(a*x)^2), x, 7, -(1/(a*c*(c + a^2*c*x^2)^(3/2)*atan(a*x))) - (3*sqrt(1 + a^2*x^2)*SinIntegral(atan(a*x)))/(4*a*c^2*sqrt(c + a^2*c*x^2)) - (3*sqrt(1 + a^2*x^2)*SinIntegral(3*atan(a*x)))/(4*a*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [1/(x*(c + a^2*c*x^2)^(5/2)*atan(a*x)^2), x, 20, (a*x)/(c*(c + a^2*c*x^2)^(3/2)*atan(a*x)) + (a*x)/(c^2*sqrt(c + a^2*c*x^2)*atan(a*x)) - sqrt(c + a^2*c*x^2)/(a*c^3*x*atan(a*x)) - (5*sqrt(1 + a^2*x^2)*CosIntegral(atan(a*x)))/(4*c^2*sqrt(c + a^2*c*x^2)) - (3*sqrt(1 + a^2*x^2)*CosIntegral(3*atan(a*x)))/(4*c^2*sqrt(c + a^2*c*x^2)) - Unintegrable(1/(x^2*sqrt(c + a^2*c*x^2)*atan(a*x)), x)/(a*c^2)]
    @test_int [1/(x^2*(c + a^2*c*x^2)^(5/2)*atan(a*x)^2), x, 13, a/(c*(c + a^2*c*x^2)^(3/2)*atan(a*x)) + a/(c^2*sqrt(c + a^2*c*x^2)*atan(a*x)) + (7*a*sqrt(1 + a^2*x^2)*SinIntegral(atan(a*x)))/(4*c^2*sqrt(c + a^2*c*x^2)) + (3*a*sqrt(1 + a^2*x^2)*SinIntegral(3*atan(a*x)))/(4*c^2*sqrt(c + a^2*c*x^2)) + Unintegrable(1/(x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2), x)/c^2]
    @test_int [1/(x^3*(c + a^2*c*x^2)^(5/2)*atan(a*x)^2), x, 28, -((a^3*x)/(c*(c + a^2*c*x^2)^(3/2)*atan(a*x))) - (2*a^3*x)/(c^2*sqrt(c + a^2*c*x^2)*atan(a*x)) + (2*a*sqrt(c + a^2*c*x^2))/(c^3*x*atan(a*x)) + (9*a^2*sqrt(1 + a^2*x^2)*CosIntegral(atan(a*x)))/(4*c^2*sqrt(c + a^2*c*x^2)) + (3*a^2*sqrt(1 + a^2*x^2)*CosIntegral(3*atan(a*x)))/(4*c^2*sqrt(c + a^2*c*x^2)) + Unintegrable(1/(x^3*sqrt(c + a^2*c*x^2)*atan(a*x)^2), x)/c^2 + (2*a*Unintegrable(1/(x^2*sqrt(c + a^2*c*x^2)*atan(a*x)), x))/c^2]
    @test_int [1/(x^4*(c + a^2*c*x^2)^(5/2)*atan(a*x)^2), x, 20, -(a^3/(c*(c + a^2*c*x^2)^(3/2)*atan(a*x))) - (2*a^3)/(c^2*sqrt(c + a^2*c*x^2)*atan(a*x)) - (11*a^3*sqrt(1 + a^2*x^2)*SinIntegral(atan(a*x)))/(4*c^2*sqrt(c + a^2*c*x^2)) - (3*a^3*sqrt(1 + a^2*x^2)*SinIntegral(3*atan(a*x)))/(4*c^2*sqrt(c + a^2*c*x^2)) + Unintegrable(1/(x^4*sqrt(c + a^2*c*x^2)*atan(a*x)^2), x)/c^2 - (2*a^2*Unintegrable(1/(x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2), x))/c^2]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(f*x)^(m/2)*(d+c^2*d*x^2)^q / (a+b*atan(c*x))^2=#

    @test_int [sqrt(f*x)/((d + c^2*d*x^2)^2*(a + b*atan(c*x))^2), x, 0, Unintegrable(sqrt(f*x)/((d + c^2*d*x^2)^2*(a + b*atan(c*x))^2), x)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d+c^2*d*x^2)^q / (a+b*atan(c*x))^2*with*m*symbolic=#

    @test_int [(x^m*(c + a^2*c*x^2)^3)/atan(a*x)^2, x, 0, Unintegrable((x^m*(c + a^2*c*x^2)^3)/atan(a*x)^2, x)]
    @test_int [(x^m*(c + a^2*c*x^2)^2)/atan(a*x)^2, x, 0, Unintegrable((x^m*(c + a^2*c*x^2)^2)/atan(a*x)^2, x)]
    @test_int [(x^m*(c + a^2*c*x^2))/atan(a*x)^2, x, 0, Unintegrable((x^m*(c + a^2*c*x^2))/atan(a*x)^2, x)]
    @test_int [x^m/((c + a^2*c*x^2)*atan(a*x)^2), x, 1, -(x^m/(a*c*atan(a*x))) + (m*Unintegrable(x^(-1 + m)/atan(a*x), x))/(a*c)]
    @test_int [x^m/((c + a^2*c*x^2)^2*atan(a*x)^2), x, 0, Unintegrable(x^m/((c + a^2*c*x^2)^2*atan(a*x)^2), x)]
    @test_int [x^m/((c + a^2*c*x^2)^3*atan(a*x)^2), x, 0, Unintegrable(x^m/((c + a^2*c*x^2)^3*atan(a*x)^2), x)]

    @test_int [(x^m*(c + a^2*c*x^2)^(5/2))/atan(a*x)^2, x, 0, Unintegrable((x^m*(c + a^2*c*x^2)^(5/2))/atan(a*x)^2, x)]
    @test_int [(x^m*(c + a^2*c*x^2)^(3/2))/atan(a*x)^2, x, 0, Unintegrable((x^m*(c + a^2*c*x^2)^(3/2))/atan(a*x)^2, x)]
    @test_int [(x^m*sqrt(c + a^2*c*x^2))/atan(a*x)^2, x, 0, Unintegrable((x^m*sqrt(c + a^2*c*x^2))/atan(a*x)^2, x)]
    @test_int [x^m/(sqrt(c + a^2*c*x^2)*atan(a*x)^2), x, 0, Unintegrable(x^m/(sqrt(c + a^2*c*x^2)*atan(a*x)^2), x)]
    @test_int [x^m/((c + a^2*c*x^2)^(3/2)*atan(a*x)^2), x, 0, Unintegrable(x^m/((c + a^2*c*x^2)^(3/2)*atan(a*x)^2), x)]
    @test_int [x^m/((c + a^2*c*x^2)^(5/2)*atan(a*x)^2), x, 0, Unintegrable(x^m/((c + a^2*c*x^2)^(5/2)*atan(a*x)^2), x)]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d+c^2*d*x^2)^q*(a+b*atan(c*x))^-3=#

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

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

    @test_int [(x*(c + a^2*c*x^2))/atan(a*x)^3, x, 0, Unintegrable((x*(c + a^2*c*x^2))/atan(a*x)^3, x)]
    @test_int [(c + a^2*c*x^2)/atan(a*x)^3, x, 0, Unintegrable((c + a^2*c*x^2)/atan(a*x)^3, x)]
    @test_int [(c + a^2*c*x^2)/(x*atan(a*x)^3), x, 0, Unintegrable((c + a^2*c*x^2)/(x*atan(a*x)^3), x)]

    @test_int [(x*(c + a^2*c*x^2)^2)/atan(a*x)^3, x, 0, Unintegrable((x*(c + a^2*c*x^2)^2)/atan(a*x)^3, x)]
    @test_int [(c + a^2*c*x^2)^2/atan(a*x)^3, x, 0, Unintegrable((c + a^2*c*x^2)^2/atan(a*x)^3, x)]
    @test_int [(c + a^2*c*x^2)^2/(x*atan(a*x)^3), x, 0, Unintegrable((c + a^2*c*x^2)^2/(x*atan(a*x)^3), x)]

    @test_int [(x*(c + a^2*c*x^2)^3)/atan(a*x)^3, x, 0, Unintegrable((x*(c + a^2*c*x^2)^3)/atan(a*x)^3, x)]
    @test_int [(c + a^2*c*x^2)^3/atan(a*x)^3, x, 0, Unintegrable((c + a^2*c*x^2)^3/atan(a*x)^3, x)]
    @test_int [(c + a^2*c*x^2)^3/(x*atan(a*x)^3), x, 0, Unintegrable((c + a^2*c*x^2)^3/(x*atan(a*x)^3), x)]

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

    @test_int [x^3/((c + a^2*c*x^2)*atan(a*x)^3), x, 1, -x^3/(2*a*c*atan(a*x)^2) + (3*Unintegrable(x^2/atan(a*x)^2, x))/(2*a*c)]
    @test_int [x^2/((c + a^2*c*x^2)*atan(a*x)^3), x, 1, -x^2/(2*a*c*atan(a*x)^2) + Unintegrable(x/atan(a*x)^2, x)/(a*c)]
    @test_int [x/((c + a^2*c*x^2)*atan(a*x)^3), x, 1, -x/(2*a*c*atan(a*x)^2) + Unintegrable(atan(a*x)^(-2), x)/(2*a*c)]
    @test_int [1/((c + a^2*c*x^2)*atan(a*x)^3), x, 1, -1/(2*a*c*atan(a*x)^2)]
    @test_int [1/(x*(c + a^2*c*x^2)*atan(a*x)^3), x, 1, -1/(2*a*c*x*atan(a*x)^2) - Unintegrable(1/(x^2*atan(a*x)^2), x)/(2*a*c)]
    @test_int [1/(x^2*(c + a^2*c*x^2)*atan(a*x)^3), x, 1, -1/(2*a*c*x^2*atan(a*x)^2) - Unintegrable(1/(x^3*atan(a*x)^2), x)/(a*c)]
    @test_int [1/(x^3*(c + a^2*c*x^2)*atan(a*x)^3), x, 1, -1/(2*a*c*x^3*atan(a*x)^2) - (3*Unintegrable(1/(x^4*atan(a*x)^2), x))/(2*a*c)]
    @test_int [1/(x^4*(c + a^2*c*x^2)*atan(a*x)^3), x, 1, -1/(2*a*c*x^4*atan(a*x)^2) - (2*Unintegrable(1/(x^5*atan(a*x)^2), x))/(a*c)]

    @test_int [x^3/((c + a^2*c*x^2)^2*atan(a*x)^3), x, 7, -x/(2*a^3*c^2*atan(a*x)^2) + x/(2*a^3*c^2*(1 + a^2*x^2)*atan(a*x)^2) + (1 - a^2*x^2)/(2*a^4*c^2*(1 + a^2*x^2)*atan(a*x)) + SinIntegral(2*atan(a*x))/(a^4*c^2) + Unintegrable(atan(a*x)^(-2), x)/(2*a^3*c^2)]
    @test_int [x^2/((c + a^2*c*x^2)^2*atan(a*x)^3), x, 10, -x^2/(2*a*c^2*(1 + a^2*x^2)*atan(a*x)^2) - x/(a^2*c^2*(1 + a^2*x^2)*atan(a*x)) + CosIntegral(2*atan(a*x))/(a^3*c^2)]
    @test_int [x/((c + a^2*c*x^2)^2*atan(a*x)^3), x, 5, -x/(2*a*c^2*(1 + a^2*x^2)*atan(a*x)^2) - (1 - a^2*x^2)/(2*a^2*c^2*(1 + a^2*x^2)*atan(a*x)) - SinIntegral(2*atan(a*x))/(a^2*c^2)]
    @test_int [1/((c + a^2*c*x^2)^2*atan(a*x)^3), x, 10, -1/(2*a*c^2*(1 + a^2*x^2)*atan(a*x)^2) + x/(c^2*(1 + a^2*x^2)*atan(a*x)) - CosIntegral(2*atan(a*x))/(a*c^2)]
    @test_int [1/(x*(c + a^2*c*x^2)^2*atan(a*x)^3), x, 7, -1/(2*a*c^2*x*atan(a*x)^2) + (a*x)/(2*c^2*(1 + a^2*x^2)*atan(a*x)^2) + (1 - a^2*x^2)/(2*c^2*(1 + a^2*x^2)*atan(a*x)) + SinIntegral(2*atan(a*x))/c^2 - Unintegrable(1/(x^2*atan(a*x)^2), x)/(2*a*c^2)]
    @test_int [1/(x^2*(c + a^2*c*x^2)^2*atan(a*x)^3), x, 12, -1/(2*a*c^2*x^2*atan(a*x)^2) + a/(2*c^2*(1 + a^2*x^2)*atan(a*x)^2) - (a^2*x)/(c^2*(1 + a^2*x^2)*atan(a*x)) + (a*CosIntegral(2*atan(a*x)))/c^2 - Unintegrable(1/(x^3*atan(a*x)^2), x)/(a*c^2)]
    @test_int [1/(x^3*(c + a^2*c*x^2)^2*atan(a*x)^3), x, 9, -1/(2*a*c^2*x^3*atan(a*x)^2) + a/(2*c^2*x*atan(a*x)^2) - (a^3*x)/(2*c^2*(1 + a^2*x^2)*atan(a*x)^2) - (a^2*(1 - a^2*x^2))/(2*c^2*(1 + a^2*x^2)*atan(a*x)) - (a^2*SinIntegral(2*atan(a*x)))/c^2 - (3*Unintegrable(1/(x^4*atan(a*x)^2), x))/(2*a*c^2) + (a*Unintegrable(1/(x^2*atan(a*x)^2), x))/(2*c^2)]
    @test_int [1/(x^4*(c + a^2*c*x^2)^2*atan(a*x)^3), x, 14, -1/(2*a*c^2*x^4*atan(a*x)^2) + a/(2*c^2*x^2*atan(a*x)^2) - a^3/(2*c^2*(1 + a^2*x^2)*atan(a*x)^2) + (a^4*x)/(c^2*(1 + a^2*x^2)*atan(a*x)) - (a^3*CosIntegral(2*atan(a*x)))/c^2 - (2*Unintegrable(1/(x^5*atan(a*x)^2), x))/(a*c^2) + (a*Unintegrable(1/(x^3*atan(a*x)^2), x))/c^2]

    @test_int [x^3/((c + a^2*c*x^2)^3*atan(a*x)^3), x, 25, x/(2*a^3*c^3*(1 + a^2*x^2)^2*atan(a*x)^2) - x/(2*a^3*c^3*(1 + a^2*x^2)*atan(a*x)^2) + 2/(a^4*c^3*(1 + a^2*x^2)^2*atan(a*x)) - 3/(2*a^4*c^3*(1 + a^2*x^2)*atan(a*x)) - (1 - a^2*x^2)/(2*a^4*c^3*(1 + a^2*x^2)*atan(a*x)) - SinIntegral(2*atan(a*x))/(2*a^4*c^3) + SinIntegral(4*atan(a*x))/(a^4*c^3)]
    @test_int [x^2/((c + a^2*c*x^2)^3*atan(a*x)^3), x, 22, 1/(2*a^3*c^3*(1 + a^2*x^2)^2*atan(a*x)^2) - 1/(2*a^3*c^3*(1 + a^2*x^2)*atan(a*x)^2) - (2*x)/(a^2*c^3*(1 + a^2*x^2)^2*atan(a*x)) + x/(a^2*c^3*(1 + a^2*x^2)*atan(a*x)) + CosIntegral(4*atan(a*x))/(a^3*c^3)]
    @test_int [x/((c + a^2*c*x^2)^3*atan(a*x)^3), x, 19, -x/(2*a*c^3*(1 + a^2*x^2)^2*atan(a*x)^2) - 2/(a^2*c^3*(1 + a^2*x^2)^2*atan(a*x)) + 3/(2*a^2*c^3*(1 + a^2*x^2)*atan(a*x)) - SinIntegral(2*atan(a*x))/(2*a^2*c^3) - SinIntegral(4*atan(a*x))/(a^2*c^3)]
    @test_int [1/((c + a^2*c*x^2)^3*atan(a*x)^3), x, 11, -1/(2*a*c^3*(1 + a^2*x^2)^2*atan(a*x)^2) + (2*x)/(c^3*(1 + a^2*x^2)^2*atan(a*x)) - CosIntegral(2*atan(a*x))/(a*c^3) - CosIntegral(4*atan(a*x))/(a*c^3)]
    @test_int [1/(x*(c + a^2*c*x^2)^3*atan(a*x)^3), x, 27, -1/(2*a*c^3*x*atan(a*x)^2) + (a*x)/(2*c^3*(1 + a^2*x^2)^2*atan(a*x)^2) + (a*x)/(2*c^3*(1 + a^2*x^2)*atan(a*x)^2) + 2/(c^3*(1 + a^2*x^2)^2*atan(a*x)) - 3/(2*c^3*(1 + a^2*x^2)*atan(a*x)) + (1 - a^2*x^2)/(2*c^3*(1 + a^2*x^2)*atan(a*x)) + (3*SinIntegral(2*atan(a*x)))/(2*c^3) + SinIntegral(4*atan(a*x))/c^3 - Unintegrable(1/(x^2*atan(a*x)^2), x)/(2*a*c^3)]
    @test_int [1/(x^2*(c + a^2*c*x^2)^3*atan(a*x)^3), x, 24, -1/(2*a*c^3*x^2*atan(a*x)^2) + a/(2*c^3*(1 + a^2*x^2)^2*atan(a*x)^2) + a/(2*c^3*(1 + a^2*x^2)*atan(a*x)^2) - (2*a^2*x)/(c^3*(1 + a^2*x^2)^2*atan(a*x)) - (a^2*x)/(c^3*(1 + a^2*x^2)*atan(a*x)) + (2*a*CosIntegral(2*atan(a*x)))/c^3 + (a*CosIntegral(4*atan(a*x)))/c^3 - Unintegrable(1/(x^3*atan(a*x)^2), x)/(a*c^3)]
    @test_int [1/(x^3*(c + a^2*c*x^2)^3*atan(a*x)^3), x, 37, -1/(2*a*c^3*x^3*atan(a*x)^2) + a/(c^3*x*atan(a*x)^2) - (a^3*x)/(2*c^3*(1 + a^2*x^2)^2*atan(a*x)^2) - (a^3*x)/(c^3*(1 + a^2*x^2)*atan(a*x)^2) - (2*a^2)/(c^3*(1 + a^2*x^2)^2*atan(a*x)) + (3*a^2)/(2*c^3*(1 + a^2*x^2)*atan(a*x)) - (a^2*(1 - a^2*x^2))/(c^3*(1 + a^2*x^2)*atan(a*x)) - (5*a^2*SinIntegral(2*atan(a*x)))/(2*c^3) - (a^2*SinIntegral(4*atan(a*x)))/c^3 - (3*Unintegrable(1/(x^4*atan(a*x)^2), x))/(2*a*c^3) + (a*Unintegrable(1/(x^2*atan(a*x)^2), x))/c^3]
    @test_int [1/(x^4*(c + a^2*c*x^2)^3*atan(a*x)^3), x, 39, -1/(2*a*c^3*x^4*atan(a*x)^2) + a/(c^3*x^2*atan(a*x)^2) - a^3/(2*c^3*(1 + a^2*x^2)^2*atan(a*x)^2) - a^3/(c^3*(1 + a^2*x^2)*atan(a*x)^2) + (2*a^4*x)/(c^3*(1 + a^2*x^2)^2*atan(a*x)) + (2*a^4*x)/(c^3*(1 + a^2*x^2)*atan(a*x)) - (3*a^3*CosIntegral(2*atan(a*x)))/c^3 - (a^3*CosIntegral(4*atan(a*x)))/c^3 - (2*Unintegrable(1/(x^5*atan(a*x)^2), x))/(a*c^3) + (2*a*Unintegrable(1/(x^3*atan(a*x)^2), x))/c^3]

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

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

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

    @test_int [(x*sqrt(c + a^2*c*x^2))/atan(a*x)^3, x, 0, Unintegrable((x*sqrt(c + a^2*c*x^2))/atan(a*x)^3, x)]
    @test_int [sqrt(c + a^2*c*x^2)/atan(a*x)^3, x, 0, Unintegrable(sqrt(c + a^2*c*x^2)/atan(a*x)^3, x)]
    @test_int [sqrt(c + a^2*c*x^2)/(x*atan(a*x)^3), x, 0, Unintegrable(sqrt(c + a^2*c*x^2)/(x*atan(a*x)^3), x)]

    @test_int [(x*(c + a^2*c*x^2)^(3/2))/atan(a*x)^3, x, 0, Unintegrable((x*(c + a^2*c*x^2)^(3/2))/atan(a*x)^3, x)]
    @test_int [(c + a^2*c*x^2)^(3/2)/atan(a*x)^3, x, 0, Unintegrable((c + a^2*c*x^2)^(3/2)/atan(a*x)^3, x)]
    @test_int [(c + a^2*c*x^2)^(3/2)/(x*atan(a*x)^3), x, 0, Unintegrable((c + a^2*c*x^2)^(3/2)/(x*atan(a*x)^3), x)]

    @test_int [(x*(c + a^2*c*x^2)^(5/2))/atan(a*x)^3, x, 0, Unintegrable((x*(c + a^2*c*x^2)^(5/2))/atan(a*x)^3, x)]
    @test_int [(c + a^2*c*x^2)^(5/2)/atan(a*x)^3, x, 0, Unintegrable((c + a^2*c*x^2)^(5/2)/atan(a*x)^3, x)]
    @test_int [(c + a^2*c*x^2)^(5/2)/(x*atan(a*x)^3), x, 0, Unintegrable((c + a^2*c*x^2)^(5/2)/(x*atan(a*x)^3), x)]

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

    @test_int [x/(sqrt(c + a^2*c*x^2)*atan(a*x)^3), x, 0, Unintegrable(x/(sqrt(c + a^2*c*x^2)*atan(a*x)^3), x)]
    @test_int [1/(sqrt(c + a^2*c*x^2)*atan(a*x)^3), x, 0, Unintegrable(1/(sqrt(c + a^2*c*x^2)*atan(a*x)^3), x)]
    @test_int [1/(x*sqrt(c + a^2*c*x^2)*atan(a*x)^3), x, 1, -(sqrt(c + a^2*c*x^2)/(2*a*c*x*atan(a*x)^2)) - Unintegrable(1/(x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2), x)/(2*a)]
    @test_int [1/(x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^3), x, 0, Unintegrable(1/(x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^3), x)]
    @test_int [1/(x^3*sqrt(c + a^2*c*x^2)*atan(a*x)^3), x, 0, Unintegrable(1/(x^3*sqrt(c + a^2*c*x^2)*atan(a*x)^3), x)]

    @test_int [x^3/((c + a^2*c*x^2)^(3/2)*atan(a*x)^3), x, 6, x/(2*a^3*c*sqrt(c + a^2*c*x^2)*atan(a*x)^2) + 1/(2*a^4*c*sqrt(c + a^2*c*x^2)*atan(a*x)) + (sqrt(1 + a^2*x^2)*SinIntegral(atan(a*x)))/(2*a^4*c*sqrt(c + a^2*c*x^2)) + Unintegrable(x/(sqrt(c + a^2*c*x^2)*atan(a*x)^3), x)/(a^2*c)]
    @test_int [x^2/((c + a^2*c*x^2)^(3/2)*atan(a*x)^3), x, 6, 1/(2*a^3*c*sqrt(c + a^2*c*x^2)*atan(a*x)^2) - x/(2*a^2*c*sqrt(c + a^2*c*x^2)*atan(a*x)) + (sqrt(1 + a^2*x^2)*CosIntegral(atan(a*x)))/(2*a^3*c*sqrt(c + a^2*c*x^2)) + Unintegrable(1/(sqrt(c + a^2*c*x^2)*atan(a*x)^3), x)/(a^2*c)]
    @test_int [x/((c + a^2*c*x^2)^(3/2)*atan(a*x)^3), x, 5, -(x/(2*a*c*sqrt(c + a^2*c*x^2)*atan(a*x)^2)) - 1/(2*a^2*c*sqrt(c + a^2*c*x^2)*atan(a*x)) - (sqrt(1 + a^2*x^2)*SinIntegral(atan(a*x)))/(2*a^2*c*sqrt(c + a^2*c*x^2))]
    @test_int [1/((c + a^2*c*x^2)^(3/2)*atan(a*x)^3), x, 5, -(1/(2*a*c*sqrt(c + a^2*c*x^2)*atan(a*x)^2)) + x/(2*c*sqrt(c + a^2*c*x^2)*atan(a*x)) - (sqrt(1 + a^2*x^2)*CosIntegral(atan(a*x)))/(2*a*c*sqrt(c + a^2*c*x^2))]
    @test_int [1/(x*(c + a^2*c*x^2)^(3/2)*atan(a*x)^3), x, 7, (a*x)/(2*c*sqrt(c + a^2*c*x^2)*atan(a*x)^2) - sqrt(c + a^2*c*x^2)/(2*a*c^2*x*atan(a*x)^2) + 1/(2*c*sqrt(c + a^2*c*x^2)*atan(a*x)) + (sqrt(1 + a^2*x^2)*SinIntegral(atan(a*x)))/(2*c*sqrt(c + a^2*c*x^2)) - Unintegrable(1/(x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2), x)/(2*a*c)]
    @test_int [1/(x^2*(c + a^2*c*x^2)^(3/2)*atan(a*x)^3), x, 6, a/(2*c*sqrt(c + a^2*c*x^2)*atan(a*x)^2) - (a^2*x)/(2*c*sqrt(c + a^2*c*x^2)*atan(a*x)) + (a*sqrt(1 + a^2*x^2)*CosIntegral(atan(a*x)))/(2*c*sqrt(c + a^2*c*x^2)) + Unintegrable(1/(x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^3), x)/c]
    @test_int [1/(x^3*(c + a^2*c*x^2)^(3/2)*atan(a*x)^3), x, 8, -((a^3*x)/(2*c*sqrt(c + a^2*c*x^2)*atan(a*x)^2)) + (a*sqrt(c + a^2*c*x^2))/(2*c^2*x*atan(a*x)^2) - a^2/(2*c*sqrt(c + a^2*c*x^2)*atan(a*x)) - (a^2*sqrt(1 + a^2*x^2)*SinIntegral(atan(a*x)))/(2*c*sqrt(c + a^2*c*x^2)) + Unintegrable(1/(x^3*sqrt(c + a^2*c*x^2)*atan(a*x)^3), x)/c + (a*Unintegrable(1/(x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2), x))/(2*c)]
    @test_int [1/(x^4*(c + a^2*c*x^2)^(3/2)*atan(a*x)^3), x, 7, -(a^3/(2*c*sqrt(c + a^2*c*x^2)*atan(a*x)^2)) + (a^4*x)/(2*c*sqrt(c + a^2*c*x^2)*atan(a*x)) - (a^3*sqrt(1 + a^2*x^2)*CosIntegral(atan(a*x)))/(2*c*sqrt(c + a^2*c*x^2)) + Unintegrable(1/(x^4*sqrt(c + a^2*c*x^2)*atan(a*x)^3), x)/c - (a^2*Unintegrable(1/(x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^3), x))/c]

    @test_int [x^5/((c + a^2*c*x^2)^(5/2)*atan(a*x)^3), x, 20, x^3/(2*a^3*c*(c + a^2*c*x^2)^(3/2)*atan(a*x)^2) + x/(2*a^5*c^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2) - 3/(2*a^6*c*(c + a^2*c*x^2)^(3/2)*atan(a*x)) + 2/(a^6*c^2*sqrt(c + a^2*c*x^2)*atan(a*x)) + (7*sqrt(1 + a^2*x^2)*SinIntegral(atan(a*x)))/(8*a^6*c^2*sqrt(c + a^2*c*x^2)) - (9*sqrt(1 + a^2*x^2)*SinIntegral(3*atan(a*x)))/(8*a^6*c^2*sqrt(c + a^2*c*x^2)) + Unintegrable(x/(sqrt(c + a^2*c*x^2)*atan(a*x)^3), x)/(a^4*c^2)]
    @test_int [x^4/((c + a^2*c*x^2)^(5/2)*atan(a*x)^3), x, 27, -(1/(2*a^5*c*(c + a^2*c*x^2)^(3/2)*atan(a*x)^2)) + 1/(a^5*c^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2) + (3*x)/(2*a^4*c*(c + a^2*c*x^2)^(3/2)*atan(a*x)) - x/(a^4*c^2*sqrt(c + a^2*c*x^2)*atan(a*x)) + (5*sqrt(1 + a^2*x^2)*CosIntegral(atan(a*x)))/(8*a^5*c^2*sqrt(c + a^2*c*x^2)) - (9*sqrt(1 + a^2*x^2)*CosIntegral(3*atan(a*x)))/(8*a^5*c^2*sqrt(c + a^2*c*x^2)) + Unintegrable(1/(sqrt(c + a^2*c*x^2)*atan(a*x)^3), x)/(a^4*c^2)]
    @test_int [x^3/((c + a^2*c*x^2)^(5/2)*atan(a*x)^3), x, 13, -(x^3/(2*a*c*(c + a^2*c*x^2)^(3/2)*atan(a*x)^2)) + 3/(2*a^4*c*(c + a^2*c*x^2)^(3/2)*atan(a*x)) - 3/(2*a^4*c^2*sqrt(c + a^2*c*x^2)*atan(a*x)) - (3*sqrt(1 + a^2*x^2)*SinIntegral(atan(a*x)))/(8*a^4*c^2*sqrt(c + a^2*c*x^2)) + (9*sqrt(1 + a^2*x^2)*SinIntegral(3*atan(a*x)))/(8*a^4*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [x^2/((c + a^2*c*x^2)^(5/2)*atan(a*x)^3), x, 20, 1/(2*a^3*c*(c + a^2*c*x^2)^(3/2)*atan(a*x)^2) - 1/(2*a^3*c^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2) - (3*x)/(2*a^2*c*(c + a^2*c*x^2)^(3/2)*atan(a*x)) + x/(2*a^2*c^2*sqrt(c + a^2*c*x^2)*atan(a*x)) - (sqrt(1 + a^2*x^2)*CosIntegral(atan(a*x)))/(8*a^3*c^2*sqrt(c + a^2*c*x^2)) + (9*sqrt(1 + a^2*x^2)*CosIntegral(3*atan(a*x)))/(8*a^3*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [x/((c + a^2*c*x^2)^(5/2)*atan(a*x)^3), x, 20, -(x/(2*a*c*(c + a^2*c*x^2)^(3/2)*atan(a*x)^2)) - 3/(2*a^2*c*(c + a^2*c*x^2)^(3/2)*atan(a*x)) + 1/(a^2*c^2*sqrt(c + a^2*c*x^2)*atan(a*x)) - (sqrt(1 + a^2*x^2)*SinIntegral(atan(a*x)))/(8*a^2*c^2*sqrt(c + a^2*c*x^2)) - (9*sqrt(1 + a^2*x^2)*SinIntegral(3*atan(a*x)))/(8*a^2*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [1/((c + a^2*c*x^2)^(5/2)*atan(a*x)^3), x, 14, -(1/(2*a*c*(c + a^2*c*x^2)^(3/2)*atan(a*x)^2)) + (3*x)/(2*c*(c + a^2*c*x^2)^(3/2)*atan(a*x)) - (3*sqrt(1 + a^2*x^2)*CosIntegral(atan(a*x)))/(8*a*c^2*sqrt(c + a^2*c*x^2)) - (9*sqrt(1 + a^2*x^2)*CosIntegral(3*atan(a*x)))/(8*a*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [1/(x*(c + a^2*c*x^2)^(5/2)*atan(a*x)^3), x, 28, (a*x)/(2*c*(c + a^2*c*x^2)^(3/2)*atan(a*x)^2) + (a*x)/(2*c^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2) - sqrt(c + a^2*c*x^2)/(2*a*c^3*x*atan(a*x)^2) + 3/(2*c*(c + a^2*c*x^2)^(3/2)*atan(a*x)) - 1/(2*c^2*sqrt(c + a^2*c*x^2)*atan(a*x)) + (5*sqrt(1 + a^2*x^2)*SinIntegral(atan(a*x)))/(8*c^2*sqrt(c + a^2*c*x^2)) + (9*sqrt(1 + a^2*x^2)*SinIntegral(3*atan(a*x)))/(8*c^2*sqrt(c + a^2*c*x^2)) - Unintegrable(1/(x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2), x)/(2*a*c^2)]
    @test_int [1/(x^2*(c + a^2*c*x^2)^(5/2)*atan(a*x)^3), x, 21, a/(2*c*(c + a^2*c*x^2)^(3/2)*atan(a*x)^2) + a/(2*c^2*sqrt(c + a^2*c*x^2)*atan(a*x)^2) - (3*a^2*x)/(2*c*(c + a^2*c*x^2)^(3/2)*atan(a*x)) - (a^2*x)/(2*c^2*sqrt(c + a^2*c*x^2)*atan(a*x)) + (7*a*sqrt(1 + a^2*x^2)*CosIntegral(atan(a*x)))/(8*c^2*sqrt(c + a^2*c*x^2)) + (9*a*sqrt(1 + a^2*x^2)*CosIntegral(3*atan(a*x)))/(8*c^2*sqrt(c + a^2*c*x^2)) + Unintegrable(1/(x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^3), x)/c^2]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x^2)^p / atan(a*x)^3*with*d=a^2*c*and*m*symbolic=#

    @test_int [(x^m*(c + a^2*c*x^2)^3)/atan(a*x)^3, x, 0, Unintegrable((x^m*(c + a^2*c*x^2)^3)/atan(a*x)^3, x)]
    @test_int [(x^m*(c + a^2*c*x^2)^2)/atan(a*x)^3, x, 0, Unintegrable((x^m*(c + a^2*c*x^2)^2)/atan(a*x)^3, x)]
    @test_int [(x^m*(c + a^2*c*x^2))/atan(a*x)^3, x, 0, Unintegrable((x^m*(c + a^2*c*x^2))/atan(a*x)^3, x)]
    @test_int [x^m/((c + a^2*c*x^2)*atan(a*x)^3), x, 1, -x^m/(2*a*c*atan(a*x)^2) + (m*Unintegrable(x^(-1 + m)/atan(a*x)^2, x))/(2*a*c)]
    @test_int [x^m/((c + a^2*c*x^2)^2*atan(a*x)^3), x, 0, Unintegrable(x^m/((c + a^2*c*x^2)^2*atan(a*x)^3), x)]
    @test_int [x^m/((c + a^2*c*x^2)^3*atan(a*x)^3), x, 0, Unintegrable(x^m/((c + a^2*c*x^2)^3*atan(a*x)^3), x)]

    @test_int [(x^m*(c + a^2*c*x^2)^(5/2))/atan(a*x)^3, x, 0, Unintegrable((x^m*(c + a^2*c*x^2)^(5/2))/atan(a*x)^3, x)]
    @test_int [(x^m*(c + a^2*c*x^2)^(3/2))/atan(a*x)^3, x, 0, Unintegrable((x^m*(c + a^2*c*x^2)^(3/2))/atan(a*x)^3, x)]
    @test_int [(x^m*sqrt(c + a^2*c*x^2))/atan(a*x)^3, x, 0, Unintegrable((x^m*sqrt(c + a^2*c*x^2))/atan(a*x)^3, x)]
    @test_int [x^m/(sqrt(c + a^2*c*x^2)*atan(a*x)^3), x, 0, Unintegrable(x^m/(sqrt(c + a^2*c*x^2)*atan(a*x)^3), x)]
    @test_int [x^m/((c + a^2*c*x^2)^(3/2)*atan(a*x)^3), x, 0, Unintegrable(x^m/((c + a^2*c*x^2)^(3/2)*atan(a*x)^3), x)]
    @test_int [x^m/((c + a^2*c*x^2)^(5/2)*atan(a*x)^3), x, 0, Unintegrable(x^m/((c + a^2*c*x^2)^(5/2)*atan(a*x)^3), x)]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d+c^2*d*x^2)^q*(a+b*atan(c*x))^(1/2)=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x^2)^p*atan(a*x)^(1/2)*with*d=a^2*c=#

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

    @test_int [x^m*(c + a^2*c*x^2)*sqrt(atan(a*x)), x, 0, Unintegrable(x^m*(c + a^2*c*x^2)*sqrt(atan(a*x)), x)]

    @test_int [x*(c + a^2*c*x^2)*sqrt(atan(a*x)), x, 1, (c*(1 + a^2*x^2)^2*sqrt(atan(a*x)))/(4*a^2) - Unintegrable((c + a^2*c*x^2)/sqrt(atan(a*x)), x)/(8*a)]
    @test_int [(c + a^2*c*x^2)*sqrt(atan(a*x)), x, 0, Unintegrable((c + a^2*c*x^2)*sqrt(atan(a*x)), x)]
    @test_int [((c + a^2*c*x^2)*sqrt(atan(a*x)))/x, x, 0, Unintegrable(((c + a^2*c*x^2)*sqrt(atan(a*x)))/x, x)]

    @test_int [x^m*(c + a^2*c*x^2)^2*sqrt(atan(a*x)), x, 0, Unintegrable(x^m*(c + a^2*c*x^2)^2*sqrt(atan(a*x)), x)]

    @test_int [x*(c + a^2*c*x^2)^2*sqrt(atan(a*x)), x, 1, (c^2*(1 + a^2*x^2)^3*sqrt(atan(a*x)))/(6*a^2) - Unintegrable((c + a^2*c*x^2)^2/sqrt(atan(a*x)), x)/(12*a)]
    @test_int [(c + a^2*c*x^2)^2*sqrt(atan(a*x)), x, 0, Unintegrable((c + a^2*c*x^2)^2*sqrt(atan(a*x)), x)]
    @test_int [((c + a^2*c*x^2)^2*sqrt(atan(a*x)))/x, x, 0, Unintegrable(((c + a^2*c*x^2)^2*sqrt(atan(a*x)))/x, x)]

    @test_int [x^m*(c + a^2*c*x^2)^3*sqrt(atan(a*x)), x, 0, Unintegrable(x^m*(c + a^2*c*x^2)^3*sqrt(atan(a*x)), x)]

    @test_int [x*(c + a^2*c*x^2)^3*sqrt(atan(a*x)), x, 1, (c^3*(1 + a^2*x^2)^4*sqrt(atan(a*x)))/(8*a^2) - Unintegrable((c + a^2*c*x^2)^3/sqrt(atan(a*x)), x)/(16*a)]
    @test_int [(c + a^2*c*x^2)^3*sqrt(atan(a*x)), x, 0, Unintegrable((c + a^2*c*x^2)^3*sqrt(atan(a*x)), x)]
    @test_int [((c + a^2*c*x^2)^3*sqrt(atan(a*x)))/x, x, 0, Unintegrable(((c + a^2*c*x^2)^3*sqrt(atan(a*x)))/x, x)]

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

    @test_int [(x^m*sqrt(atan(a*x)))/(c + a^2*c*x^2), x, 0, Unintegrable((x^m*sqrt(atan(a*x)))/(c + a^2*c*x^2), x)]

    @test_int [(x^3*sqrt(atan(a*x)))/(c + a^2*c*x^2), x, 2, -((2*x*atan(a*x)^(3/2))/(3*a^3*c)) + Unintegrable(x*sqrt(atan(a*x)), x)/(a^2*c) + (2*Unintegrable(atan(a*x)^(3/2), x))/(3*a^3*c)]
    @test_int [(x^2*sqrt(atan(a*x)))/(c + a^2*c*x^2), x, 2, (-2*atan(a*x)^(3/2))/(3*a^3*c) + Unintegrable(sqrt(atan(a*x)), x)/(a^2*c)]
    @test_int [(x*sqrt(atan(a*x)))/(c + a^2*c*x^2), x, 1, (2*x*atan(a*x)^(3/2))/(3*a*c) - (2*Unintegrable(atan(a*x)^(3/2), x))/(3*a*c)]
    @test_int [sqrt(atan(a*x))/(c + a^2*c*x^2), x, 1, (2*atan(a*x)^(3/2))/(3*a*c)]
    @test_int [sqrt(atan(a*x))/(x*(c + a^2*c*x^2)), x, 1, (((-2*im)/3)*atan(a*x)^(3/2))/c + (im*Unintegrable(sqrt(atan(a*x))/(x*(im + a*x)), x))/c]
    @test_int [sqrt(atan(a*x))/(x^2*(c + a^2*c*x^2)), x, 2, (-2*a*atan(a*x)^(3/2))/(3*c) + Unintegrable(sqrt(atan(a*x))/x^2, x)/c]
    @test_int [sqrt(atan(a*x))/(x^3*(c + a^2*c*x^2)), x, 2, (((2*im)/3)*a^2*atan(a*x)^(3/2))/c + Unintegrable(sqrt(atan(a*x))/x^3, x)/c - (im*a^2*Unintegrable(sqrt(atan(a*x))/(x*(im + a*x)), x))/c]
    @test_int [sqrt(atan(a*x))/(x^4*(c + a^2*c*x^2)), x, 3, (2*a^3*atan(a*x)^(3/2))/(3*c) + Unintegrable(sqrt(atan(a*x))/x^4, x)/c - (a^2*Unintegrable(sqrt(atan(a*x))/x^2, x))/c]

    @test_int [(x^m*sqrt(atan(a*x)))/(c + a^2*c*x^2)^2, x, 0, Unintegrable((x^m*sqrt(atan(a*x)))/(c + a^2*c*x^2)^2, x)]

    @test_int [(x^3*sqrt(atan(a*x)))/(c + a^2*c*x^2)^2, x, 0, Unintegrable((x^3*sqrt(atan(a*x)))/(c + a^2*c*x^2)^2, x)]
    @test_int [(x^2*sqrt(atan(a*x)))/(c + a^2*c*x^2)^2, x, 6, -((x*sqrt(atan(a*x)))/(2*a^2*c^2*(1 + a^2*x^2))) + atan(a*x)^(3/2)/(3*a^3*c^2) + (sqrt(pi)*FresnelS((2*sqrt(atan(a*x)))/sqrt(pi)))/(8*a^3*c^2)]
    @test_int [(x*sqrt(atan(a*x)))/(c + a^2*c*x^2)^2, x, 6, sqrt(atan(a*x))/(4*a^2*c^2) - sqrt(atan(a*x))/(2*a^2*c^2*(1 + a^2*x^2)) + (sqrt(pi)*FresnelC((2*sqrt(atan(a*x)))/sqrt(pi)))/(8*a^2*c^2)]
    @test_int [sqrt(atan(a*x))/(c + a^2*c*x^2)^2, x, 6, (x*sqrt(atan(a*x)))/(2*c^2*(1 + a^2*x^2)) + atan(a*x)^(3/2)/(3*a*c^2) - (sqrt(pi)*FresnelS((2*sqrt(atan(a*x)))/sqrt(pi)))/(8*a*c^2)]
    @test_int [sqrt(atan(a*x))/(x*(c + a^2*c*x^2)^2), x, 0, Unintegrable(sqrt(atan(a*x))/(x*(c + a^2*c*x^2)^2), x)]

    @test_int [(x^m*sqrt(atan(a*x)))/(c + a^2*c*x^2)^3, x, 0, Unintegrable((x^m*sqrt(atan(a*x)))/(c + a^2*c*x^2)^3, x)]

    @test_int [(x^5*sqrt(atan(a*x)))/(c + a^2*c*x^2)^3, x, 0, Unintegrable((x^5*sqrt(atan(a*x)))/(c + a^2*c*x^2)^3, x)]
    @test_int [(x^4*sqrt(atan(a*x)))/(c + a^2*c*x^2)^3, x, 9, atan(a*x)^(3/2)/(4*a^5*c^3) - (sqrt(pi/2)*FresnelS(2*sqrt(2/pi)*sqrt(atan(a*x))))/(64*a^5*c^3) + (sqrt(pi)*FresnelS((2*sqrt(atan(a*x)))/sqrt(pi)))/(8*a^5*c^3) - (sqrt(atan(a*x))*sin(2*atan(a*x)))/(4*a^5*c^3) + (sqrt(atan(a*x))*sin(4*atan(a*x)))/(32*a^5*c^3)]
    @test_int [(x^3*sqrt(atan(a*x)))/(c + a^2*c*x^2)^3, x, 8, -((3*sqrt(atan(a*x)))/(32*a^4*c^3)) + (x^4*sqrt(atan(a*x)))/(4*c^3*(1 + a^2*x^2)^2) - (sqrt(pi/2)*FresnelC(2*sqrt(2/pi)*sqrt(atan(a*x))))/(64*a^4*c^3) + (sqrt(pi)*FresnelC((2*sqrt(atan(a*x)))/sqrt(pi)))/(16*a^4*c^3)]
    @test_int [(x^2*sqrt(atan(a*x)))/(c + a^2*c*x^2)^3, x, 6, atan(a*x)^(3/2)/(12*a^3*c^3) + (sqrt(pi/2)*FresnelS(2*sqrt(2/pi)*sqrt(atan(a*x))))/(64*a^3*c^3) - (sqrt(atan(a*x))*sin(4*atan(a*x)))/(32*a^3*c^3)]
    @test_int [(x*sqrt(atan(a*x)))/(c + a^2*c*x^2)^3, x, 8, (3*sqrt(atan(a*x)))/(32*a^2*c^3) - sqrt(atan(a*x))/(4*a^2*c^3*(1 + a^2*x^2)^2) + (sqrt(pi/2)*FresnelC(2*sqrt(2/pi)*sqrt(atan(a*x))))/(64*a^2*c^3) + (sqrt(pi)*FresnelC((2*sqrt(atan(a*x)))/sqrt(pi)))/(16*a^2*c^3)]
    @test_int [sqrt(atan(a*x))/(c + a^2*c*x^2)^3, x, 9, atan(a*x)^(3/2)/(4*a*c^3) - (sqrt(pi/2)*FresnelS(2*sqrt(2/pi)*sqrt(atan(a*x))))/(64*a*c^3) - (sqrt(pi)*FresnelS((2*sqrt(atan(a*x)))/sqrt(pi)))/(8*a*c^3) + (sqrt(atan(a*x))*sin(2*atan(a*x)))/(4*a*c^3) + (sqrt(atan(a*x))*sin(4*atan(a*x)))/(32*a*c^3)]
    @test_int [sqrt(atan(a*x))/(x*(c + a^2*c*x^2)^3), x, 0, Unintegrable(sqrt(atan(a*x))/(x*(c + a^2*c*x^2)^3), x)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x^2)^(p/2)*atan(a*x)^(1/2)*with*d=a^2*c=#

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

    @test_int [x^m*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)), x, 0, Unintegrable(x^m*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)), x)]

    @test_int [x^2*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)), x, 0, Unintegrable(x^2*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)), x)]
    @test_int [x*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)), x, 1, ((c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x)))/(3*a^2*c) - Unintegrable(sqrt(c + a^2*c*x^2)/sqrt(atan(a*x)), x)/(6*a)]
    @test_int [sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)), x, 0, Unintegrable(sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)), x)]

    @test_int [x^m*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x)), x, 0, Unintegrable(x^m*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x)), x)]

    @test_int [x^2*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x)), x, 0, Unintegrable(x^2*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x)), x)]
    @test_int [x*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x)), x, 1, ((c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x)))/(5*a^2*c) - Unintegrable((c + a^2*c*x^2)^(3/2)/sqrt(atan(a*x)), x)/(10*a)]
    @test_int [(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x)), x, 0, Unintegrable((c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x)), x)]

    @test_int [x^m*(c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x)), x, 0, Unintegrable(x^m*(c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x)), x)]

    @test_int [x^2*(c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x)), x, 0, Unintegrable(x^2*(c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x)), x)]
    @test_int [x*(c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x)), x, 1, ((c + a^2*c*x^2)^(7/2)*sqrt(atan(a*x)))/(7*a^2*c) - Unintegrable((c + a^2*c*x^2)^(5/2)/sqrt(atan(a*x)), x)/(14*a)]
    @test_int [(c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x)), x, 0, Unintegrable((c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x)), x)]

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

    @test_int [(x^m*sqrt(atan(a*x)))/sqrt(c + a^2*c*x^2), x, 0, Unintegrable((x^m*sqrt(atan(a*x)))/sqrt(c + a^2*c*x^2), x)]

    @test_int [(x^3*sqrt(atan(a*x)))/sqrt(c + a^2*c*x^2), x, 2, -((2*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)))/(3*a^4*c)) + (x^2*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)))/(3*a^2*c) + Unintegrable(1/(sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))), x)/(3*a^3) - Unintegrable(x^2/(sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))), x)/(6*a)]
    @test_int [(x^2*sqrt(atan(a*x)))/sqrt(c + a^2*c*x^2), x, 1, (x*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)))/(2*a^2*c) - Unintegrable(x/(sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))), x)/(4*a) - Unintegrable(sqrt(atan(a*x))/sqrt(c + a^2*c*x^2), x)/(2*a^2)]
    @test_int [(x*sqrt(atan(a*x)))/sqrt(c + a^2*c*x^2), x, 1, (sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)))/(a^2*c) - Unintegrable(1/(sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))), x)/(2*a)]
    @test_int [sqrt(atan(a*x))/sqrt(c + a^2*c*x^2), x, 0, Unintegrable(sqrt(atan(a*x))/sqrt(c + a^2*c*x^2), x)]
    @test_int [sqrt(atan(a*x))/(x*sqrt(c + a^2*c*x^2)), x, 0, Unintegrable(sqrt(atan(a*x))/(x*sqrt(c + a^2*c*x^2)), x)]
    @test_int [sqrt(atan(a*x))/(x^2*sqrt(c + a^2*c*x^2)), x, 1, -((sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)))/(c*x)) + (a*Unintegrable(1/(x*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))), x))/2]
    @test_int [sqrt(atan(a*x))/(x^3*sqrt(c + a^2*c*x^2)), x, 1, -(sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)))/(2*c*x^2) + (a*Unintegrable(1/(x^2*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))), x))/4 - (a^2*Unintegrable(sqrt(atan(a*x))/(x*sqrt(c + a^2*c*x^2)), x))/2]
    @test_int [sqrt(atan(a*x))/(x^4*sqrt(c + a^2*c*x^2)), x, 2, -(sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)))/(3*c*x^3) + (2*a^2*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)))/(3*c*x) + (a*Unintegrable(1/(x^3*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))), x))/6 - (a^3*Unintegrable(1/(x*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))), x))/3]

    @test_int [(x^m*sqrt(atan(a*x)))/(c + a^2*c*x^2)^(3/2), x, 0, Unintegrable((x^m*sqrt(atan(a*x)))/(c + a^2*c*x^2)^(3/2), x)]

    @test_int [(x^3*sqrt(atan(a*x)))/(c + a^2*c*x^2)^(3/2), x, 0, Unintegrable((x^3*sqrt(atan(a*x)))/(c + a^2*c*x^2)^(3/2), x)]
    @test_int [(x^2*sqrt(atan(a*x)))/(c + a^2*c*x^2)^(3/2), x, 0, Unintegrable((x^2*sqrt(atan(a*x)))/(c + a^2*c*x^2)^(3/2), x)]
    @test_int [(x*sqrt(atan(a*x)))/(c + a^2*c*x^2)^(3/2), x, 5, -(sqrt(atan(a*x))/(a^2*c*sqrt(c + a^2*c*x^2))) + (sqrt(pi/2)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(2/pi)*sqrt(atan(a*x))))/(a^2*c*sqrt(c + a^2*c*x^2))]
    @test_int [sqrt(atan(a*x))/(c + a^2*c*x^2)^(3/2), x, 5, (x*sqrt(atan(a*x)))/(c*sqrt(c + a^2*c*x^2)) - (sqrt(pi/2)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(2/pi)*sqrt(atan(a*x))))/(a*c*sqrt(c + a^2*c*x^2))]
    @test_int [sqrt(atan(a*x))/(x*(c + a^2*c*x^2)^(3/2)), x, 0, Unintegrable(sqrt(atan(a*x))/(x*(c + a^2*c*x^2)^(3/2)), x)]
    @test_int [sqrt(atan(a*x))/(x^2*(c + a^2*c*x^2)^(3/2)), x, 0, Unintegrable(sqrt(atan(a*x))/(x^2*(c + a^2*c*x^2)^(3/2)), x)]

    @test_int [(x^m*sqrt(atan(a*x)))/(c + a^2*c*x^2)^(5/2), x, 0, Unintegrable((x^m*sqrt(atan(a*x)))/(c + a^2*c*x^2)^(5/2), x)]

    @test_int [(x^4*sqrt(atan(a*x)))/(c + a^2*c*x^2)^(5/2), x, 0, Unintegrable((x^4*sqrt(atan(a*x)))/(c + a^2*c*x^2)^(5/2), x)]
    @test_int [(x^3*sqrt(atan(a*x)))/(c + a^2*c*x^2)^(5/2), x, 10, -((3*sqrt(atan(a*x)))/(4*a^4*c^2*sqrt(c + a^2*c*x^2))) + (sqrt(1 + a^2*x^2)*sqrt(atan(a*x))*cos(3*atan(a*x)))/(12*a^4*c^2*sqrt(c + a^2*c*x^2)) + (3*sqrt(pi/2)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(2/pi)*sqrt(atan(a*x))))/(4*a^4*c^2*sqrt(c + a^2*c*x^2)) - (sqrt(pi/6)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(6/pi)*sqrt(atan(a*x))))/(12*a^4*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [(x^2*sqrt(atan(a*x)))/(c + a^2*c*x^2)^(5/2), x, 9, (x^3*sqrt(atan(a*x)))/(3*c*(c + a^2*c*x^2)^(3/2)) - (sqrt(pi/2)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(2/pi)*sqrt(atan(a*x))))/(4*a^3*c^2*sqrt(c + a^2*c*x^2)) + (sqrt(pi/6)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(6/pi)*sqrt(atan(a*x))))/(12*a^3*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [(x*sqrt(atan(a*x)))/(c + a^2*c*x^2)^(5/2), x, 9, -(sqrt(atan(a*x))/(3*a^2*c*(c + a^2*c*x^2)^(3/2))) + (sqrt(pi/2)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(2/pi)*sqrt(atan(a*x))))/(4*a^2*c^2*sqrt(c + a^2*c*x^2)) + (sqrt(pi/6)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(6/pi)*sqrt(atan(a*x))))/(12*a^2*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [sqrt(atan(a*x))/(c + a^2*c*x^2)^(5/2), x, 10, (3*x*sqrt(atan(a*x)))/(4*c^2*sqrt(c + a^2*c*x^2)) - (3*sqrt(pi/2)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(2/pi)*sqrt(atan(a*x))))/(4*a*c^2*sqrt(c + a^2*c*x^2)) - (sqrt(pi/6)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(6/pi)*sqrt(atan(a*x))))/(12*a*c^2*sqrt(c + a^2*c*x^2)) + (sqrt(1 + a^2*x^2)*sqrt(atan(a*x))*sin(3*atan(a*x)))/(12*a*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [sqrt(atan(a*x))/(x*(c + a^2*c*x^2)^(5/2)), x, 0, Unintegrable(sqrt(atan(a*x))/(x*(c + a^2*c*x^2)^(5/2)), x)]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d+c^2*d*x^2)^q*(a+b*atan(c*x))^(3/2)=#

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

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

    @test_int [x^m*(c + a^2*c*x^2)*atan(a*x)^(3/2), x, 0, Unintegrable(x^m*(c + a^2*c*x^2)*atan(a*x)^(3/2), x)]

    @test_int [x^2*(c + a^2*c*x^2)*atan(a*x)^(3/2), x, 0, Unintegrable(x^2*(c + a^2*c*x^2)*atan(a*x)^(3/2), x)]
    @test_int [x*(c + a^2*c*x^2)*atan(a*x)^(3/2), x, 1, (c*(1 + a^2*x^2)^2*atan(a*x)^(3/2))/(4*a^2) - (3*Unintegrable((c + a^2*c*x^2)*sqrt(atan(a*x)), x))/(8*a)]
    @test_int [(c + a^2*c*x^2)*atan(a*x)^(3/2), x, 1, -(c*(1 + a^2*x^2)*sqrt(atan(a*x)))/(4*a) + (c*x*(1 + a^2*x^2)*atan(a*x)^(3/2))/3 + (c*Unintegrable(1/sqrt(atan(a*x)), x))/8 + (2*c*Unintegrable(atan(a*x)^(3/2), x))/3]
    @test_int [((c + a^2*c*x^2)*atan(a*x)^(3/2))/x, x, 0, Unintegrable(((c + a^2*c*x^2)*atan(a*x)^(3/2))/x, x)]
    @test_int [((c + a^2*c*x^2)*atan(a*x)^(3/2))/x^2, x, 0, Unintegrable(((c + a^2*c*x^2)*atan(a*x)^(3/2))/x^2, x)]

    @test_int [x^m*(c + a^2*c*x^2)^2*atan(a*x)^(3/2), x, 0, Unintegrable(x^m*(c + a^2*c*x^2)^2*atan(a*x)^(3/2), x)]

    @test_int [x^2*(c + a^2*c*x^2)^2*atan(a*x)^(3/2), x, 0, Unintegrable(x^2*(c + a^2*c*x^2)^2*atan(a*x)^(3/2), x)]
    @test_int [x*(c + a^2*c*x^2)^2*atan(a*x)^(3/2), x, 1, (c^2*(1 + a^2*x^2)^3*atan(a*x)^(3/2))/(6*a^2) - Unintegrable((c + a^2*c*x^2)^2*sqrt(atan(a*x)), x)/(4*a)]
    @test_int [(c + a^2*c*x^2)^2*atan(a*x)^(3/2), x, 2, -(c^2*(1 + a^2*x^2)*sqrt(atan(a*x)))/(5*a) - (3*c^2*(1 + a^2*x^2)^2*sqrt(atan(a*x)))/(40*a) + (4*c^2*x*(1 + a^2*x^2)*atan(a*x)^(3/2))/15 + (c^2*x*(1 + a^2*x^2)^2*atan(a*x)^(3/2))/5 + (c^2*Unintegrable(1/sqrt(atan(a*x)), x))/10 + (3*c*Unintegrable((c + a^2*c*x^2)/sqrt(atan(a*x)), x))/80 + (8*c^2*Unintegrable(atan(a*x)^(3/2), x))/15]
    @test_int [((c + a^2*c*x^2)^2*atan(a*x)^(3/2))/x, x, 0, Unintegrable(((c + a^2*c*x^2)^2*atan(a*x)^(3/2))/x, x)]
    @test_int [((c + a^2*c*x^2)^2*atan(a*x)^(3/2))/x^2, x, 0, Unintegrable(((c + a^2*c*x^2)^2*atan(a*x)^(3/2))/x^2, x)]

    @test_int [x^m*(c + a^2*c*x^2)^3*atan(a*x)^(3/2), x, 0, Unintegrable(x^m*(c + a^2*c*x^2)^3*atan(a*x)^(3/2), x)]

    @test_int [x^2*(c + a^2*c*x^2)^3*atan(a*x)^(3/2), x, 0, Unintegrable(x^2*(c + a^2*c*x^2)^3*atan(a*x)^(3/2), x)]
    @test_int [x*(c + a^2*c*x^2)^3*atan(a*x)^(3/2), x, 1, (c^3*(1 + a^2*x^2)^4*atan(a*x)^(3/2))/(8*a^2) - (3*Unintegrable((c + a^2*c*x^2)^3*sqrt(atan(a*x)), x))/(16*a)]
    @test_int [(c + a^2*c*x^2)^3*atan(a*x)^(3/2), x, 3, (-6*c^3*(1 + a^2*x^2)*sqrt(atan(a*x)))/(35*a) - (9*c^3*(1 + a^2*x^2)^2*sqrt(atan(a*x)))/(140*a) - (c^3*(1 + a^2*x^2)^3*sqrt(atan(a*x)))/(28*a) + (8*c^3*x*(1 + a^2*x^2)*atan(a*x)^(3/2))/35 + (6*c^3*x*(1 + a^2*x^2)^2*atan(a*x)^(3/2))/35 + (c^3*x*(1 + a^2*x^2)^3*atan(a*x)^(3/2))/7 + (3*c^3*Unintegrable(1/sqrt(atan(a*x)), x))/35 + (9*c^2*Unintegrable((c + a^2*c*x^2)/sqrt(atan(a*x)), x))/280 + (c*Unintegrable((c + a^2*c*x^2)^2/sqrt(atan(a*x)), x))/56 + (16*c^3*Unintegrable(atan(a*x)^(3/2), x))/35]
    @test_int [((c + a^2*c*x^2)^3*atan(a*x)^(3/2))/x, x, 0, Unintegrable(((c + a^2*c*x^2)^3*atan(a*x)^(3/2))/x, x)]
    @test_int [((c + a^2*c*x^2)^3*atan(a*x)^(3/2))/x^2, x, 0, Unintegrable(((c + a^2*c*x^2)^3*atan(a*x)^(3/2))/x^2, x)]

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

    @test_int [(x^m*atan(a*x)^(3/2))/(c + a^2*c*x^2), x, 0, Unintegrable((x^m*atan(a*x)^(3/2))/(c + a^2*c*x^2), x)]

    @test_int [(x^3*atan(a*x)^(3/2))/(c + a^2*c*x^2), x, 2, -((2*x*atan(a*x)^(5/2))/(5*a^3*c)) + Unintegrable(x*atan(a*x)^(3/2), x)/(a^2*c) + (2*Unintegrable(atan(a*x)^(5/2), x))/(5*a^3*c)]
    @test_int [(x^2*atan(a*x)^(3/2))/(c + a^2*c*x^2), x, 2, (-2*atan(a*x)^(5/2))/(5*a^3*c) + Unintegrable(atan(a*x)^(3/2), x)/(a^2*c)]
    @test_int [(x*atan(a*x)^(3/2))/(c + a^2*c*x^2), x, 1, (2*x*atan(a*x)^(5/2))/(5*a*c) - (2*Unintegrable(atan(a*x)^(5/2), x))/(5*a*c)]
    @test_int [atan(a*x)^(3/2)/(c + a^2*c*x^2), x, 1, (2*atan(a*x)^(5/2))/(5*a*c)]
    @test_int [atan(a*x)^(3/2)/(x*(c + a^2*c*x^2)), x, 1, (((-2*im)/5)*atan(a*x)^(5/2))/c + (im*Unintegrable(atan(a*x)^(3/2)/(x*(im + a*x)), x))/c]
    @test_int [atan(a*x)^(3/2)/(x^2*(c + a^2*c*x^2)), x, 2, (-2*a*atan(a*x)^(5/2))/(5*c) + Unintegrable(atan(a*x)^(3/2)/x^2, x)/c]
    @test_int [atan(a*x)^(3/2)/(x^3*(c + a^2*c*x^2)), x, 2, (((2*im)/5)*a^2*atan(a*x)^(5/2))/c + Unintegrable(atan(a*x)^(3/2)/x^3, x)/c - (im*a^2*Unintegrable(atan(a*x)^(3/2)/(x*(im + a*x)), x))/c]
    @test_int [atan(a*x)^(3/2)/(x^4*(c + a^2*c*x^2)), x, 3, (2*a^3*atan(a*x)^(5/2))/(5*c) + Unintegrable(atan(a*x)^(3/2)/x^4, x)/c - (a^2*Unintegrable(atan(a*x)^(3/2)/x^2, x))/c]

    @test_int [(x^m*atan(a*x)^(3/2))/(c + a^2*c*x^2)^2, x, 0, Unintegrable((x^m*atan(a*x)^(3/2))/(c + a^2*c*x^2)^2, x)]

    @test_int [(x^3*atan(a*x)^(3/2))/(c + a^2*c*x^2)^2, x, 0, Unintegrable((x^3*atan(a*x)^(3/2))/(c + a^2*c*x^2)^2, x)]
    @test_int [(x^2*atan(a*x)^(3/2))/(c + a^2*c*x^2)^2, x, 7, (3*sqrt(atan(a*x)))/(16*a^3*c^2) - (3*sqrt(atan(a*x)))/(8*a^3*c^2*(1 + a^2*x^2)) - (x*atan(a*x)^(3/2))/(2*a^2*c^2*(1 + a^2*x^2)) + atan(a*x)^(5/2)/(5*a^3*c^2) + (3*sqrt(pi)*FresnelC((2*sqrt(atan(a*x)))/sqrt(pi)))/(32*a^3*c^2)]
    @test_int [(x*atan(a*x)^(3/2))/(c + a^2*c*x^2)^2, x, 7, (3*x*sqrt(atan(a*x)))/(8*a*c^2*(1 + a^2*x^2)) + atan(a*x)^(3/2)/(4*a^2*c^2) - atan(a*x)^(3/2)/(2*a^2*c^2*(1 + a^2*x^2)) - (3*sqrt(pi)*FresnelS((2*sqrt(atan(a*x)))/sqrt(pi)))/(32*a^2*c^2)]
    @test_int [atan(a*x)^(3/2)/(c + a^2*c*x^2)^2, x, 7, -((3*sqrt(atan(a*x)))/(16*a*c^2)) + (3*sqrt(atan(a*x)))/(8*a*c^2*(1 + a^2*x^2)) + (x*atan(a*x)^(3/2))/(2*c^2*(1 + a^2*x^2)) + atan(a*x)^(5/2)/(5*a*c^2) - (3*sqrt(pi)*FresnelC((2*sqrt(atan(a*x)))/sqrt(pi)))/(32*a*c^2)]
    @test_int [atan(a*x)^(3/2)/(x*(c + a^2*c*x^2)^2), x, 0, Unintegrable(atan(a*x)^(3/2)/(x*(c + a^2*c*x^2)^2), x)]

    @test_int [(x^m*atan(a*x)^(3/2))/(c + a^2*c*x^2)^3, x, 0, Unintegrable((x^m*atan(a*x)^(3/2))/(c + a^2*c*x^2)^3, x)]

    @test_int [(x^5*atan(a*x)^(3/2))/(c + a^2*c*x^2)^3, x, 0, Unintegrable((x^5*atan(a*x)^(3/2))/(c + a^2*c*x^2)^3, x)]
    @test_int [(x^4*atan(a*x)^(3/2))/(c + a^2*c*x^2)^3, x, 15, (27*sqrt(atan(a*x)))/(256*a^5*c^3) + (3*x^4*sqrt(atan(a*x)))/(32*a*c^3*(1 + a^2*x^2)^2) - (9*sqrt(atan(a*x)))/(32*a^5*c^3*(1 + a^2*x^2)) - (x^3*atan(a*x)^(3/2))/(4*a^2*c^3*(1 + a^2*x^2)^2) - (3*x*atan(a*x)^(3/2))/(8*a^4*c^3*(1 + a^2*x^2)) + (3*atan(a*x)^(5/2))/(20*a^5*c^3) - (3*sqrt(pi/2)*FresnelC(2*sqrt(2/pi)*sqrt(atan(a*x))))/(512*a^5*c^3) + (3*sqrt(pi)*FresnelC((2*sqrt(atan(a*x)))/sqrt(pi)))/(32*a^5*c^3)]
    @test_int [(x^3*atan(a*x)^(3/2))/(c + a^2*c*x^2)^3, x, 10, -((3*atan(a*x)^(3/2))/(32*a^4*c^3)) + (x^4*atan(a*x)^(3/2))/(4*c^3*(1 + a^2*x^2)^2) + (3*sqrt(pi/2)*FresnelS(2*sqrt(2/pi)*sqrt(atan(a*x))))/(512*a^4*c^3) - (3*sqrt(pi)*FresnelS((2*sqrt(atan(a*x)))/sqrt(pi)))/(64*a^4*c^3) + (3*sqrt(atan(a*x))*sin(2*atan(a*x)))/(32*a^4*c^3) - (3*sqrt(atan(a*x))*sin(4*atan(a*x)))/(256*a^4*c^3)]
    @test_int [(x^2*atan(a*x)^(3/2))/(c + a^2*c*x^2)^3, x, 7, atan(a*x)^(5/2)/(20*a^3*c^3) - (3*sqrt(atan(a*x))*cos(4*atan(a*x)))/(256*a^3*c^3) + (3*sqrt(pi/2)*FresnelC(2*sqrt(2/pi)*sqrt(atan(a*x))))/(512*a^3*c^3) - (atan(a*x)^(3/2)*sin(4*atan(a*x)))/(32*a^3*c^3)]
    @test_int [(x*atan(a*x)^(3/2))/(c + a^2*c*x^2)^3, x, 10, (3*atan(a*x)^(3/2))/(32*a^2*c^3) - atan(a*x)^(3/2)/(4*a^2*c^3*(1 + a^2*x^2)^2) - (3*sqrt(pi/2)*FresnelS(2*sqrt(2/pi)*sqrt(atan(a*x))))/(512*a^2*c^3) - (3*sqrt(pi)*FresnelS((2*sqrt(atan(a*x)))/sqrt(pi)))/(64*a^2*c^3) + (3*sqrt(atan(a*x))*sin(2*atan(a*x)))/(32*a^2*c^3) + (3*sqrt(atan(a*x))*sin(4*atan(a*x)))/(256*a^2*c^3)]
    @test_int [atan(a*x)^(3/2)/(c + a^2*c*x^2)^3, x, 15, -((45*sqrt(atan(a*x)))/(256*a*c^3)) + (3*sqrt(atan(a*x)))/(32*a*c^3*(1 + a^2*x^2)^2) + (9*sqrt(atan(a*x)))/(32*a*c^3*(1 + a^2*x^2)) + (x*atan(a*x)^(3/2))/(4*c^3*(1 + a^2*x^2)^2) + (3*x*atan(a*x)^(3/2))/(8*c^3*(1 + a^2*x^2)) + (3*atan(a*x)^(5/2))/(20*a*c^3) - (3*sqrt(pi/2)*FresnelC(2*sqrt(2/pi)*sqrt(atan(a*x))))/(512*a*c^3) - (3*sqrt(pi)*FresnelC((2*sqrt(atan(a*x)))/sqrt(pi)))/(32*a*c^3)]
    @test_int [atan(a*x)^(3/2)/(x*(c + a^2*c*x^2)^3), x, 0, Unintegrable(atan(a*x)^(3/2)/(x*(c + a^2*c*x^2)^3), x)]

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

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

    @test_int [x^m*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2), x, 0, Unintegrable(x^m*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2), x)]

    @test_int [x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2), x, 0, Unintegrable(x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2), x)]
    @test_int [x*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2), x, 1, ((c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2))/(3*a^2*c) - Unintegrable(sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)), x)/(2*a)]
    @test_int [sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2), x, 1, (-3*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)))/(4*a) + (x*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2))/2 + (3*c*Unintegrable(1/(sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))), x))/8 + (c*Unintegrable(atan(a*x)^(3/2)/sqrt(c + a^2*c*x^2), x))/2]
    @test_int [(sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2))/x, x, 0, Unintegrable((sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2))/x, x)]

    @test_int [x^m*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2), x, 0, Unintegrable(x^m*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2), x)]

    @test_int [x^2*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2), x, 0, Unintegrable(x^2*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2), x)]
    @test_int [x*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2), x, 1, ((c + a^2*c*x^2)^(5/2)*atan(a*x)^(3/2))/(5*a^2*c) - (3*Unintegrable((c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x)), x))/(10*a)]
    @test_int [(c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2), x, 2, (-9*c*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)))/(16*a) - ((c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x)))/(8*a) + (3*c*x*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2))/8 + (x*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2))/4 + (9*c^2*Unintegrable(1/(sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))), x))/32 + (c*Unintegrable(sqrt(c + a^2*c*x^2)/sqrt(atan(a*x)), x))/16 + (3*c^2*Unintegrable(atan(a*x)^(3/2)/sqrt(c + a^2*c*x^2), x))/8]
    @test_int [((c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2))/x, x, 0, Unintegrable(((c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2))/x, x)]

    @test_int [x^m*(c + a^2*c*x^2)^(5/2)*atan(a*x)^(3/2), x, 0, Unintegrable(x^m*(c + a^2*c*x^2)^(5/2)*atan(a*x)^(3/2), x)]

    @test_int [x^2*(c + a^2*c*x^2)^(5/2)*atan(a*x)^(3/2), x, 0, Unintegrable(x^2*(c + a^2*c*x^2)^(5/2)*atan(a*x)^(3/2), x)]
    @test_int [x*(c + a^2*c*x^2)^(5/2)*atan(a*x)^(3/2), x, 1, ((c + a^2*c*x^2)^(7/2)*atan(a*x)^(3/2))/(7*a^2*c) - (3*Unintegrable((c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x)), x))/(14*a)]
    @test_int [(c + a^2*c*x^2)^(5/2)*atan(a*x)^(3/2), x, 3, (-15*c^2*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)))/(32*a) - (5*c*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x)))/(48*a) - ((c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x)))/(20*a) + (5*c^2*x*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2))/16 + (5*c*x*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2))/24 + (x*(c + a^2*c*x^2)^(5/2)*atan(a*x)^(3/2))/6 + (15*c^3*Unintegrable(1/(sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))), x))/64 + (5*c^2*Unintegrable(sqrt(c + a^2*c*x^2)/sqrt(atan(a*x)), x))/96 + (c*Unintegrable((c + a^2*c*x^2)^(3/2)/sqrt(atan(a*x)), x))/40 + (5*c^3*Unintegrable(atan(a*x)^(3/2)/sqrt(c + a^2*c*x^2), x))/16]
    @test_int [((c + a^2*c*x^2)^(5/2)*atan(a*x)^(3/2))/x, x, 0, Unintegrable(((c + a^2*c*x^2)^(5/2)*atan(a*x)^(3/2))/x, x)]

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

    @test_int [(x^m*atan(a*x)^(3/2))/sqrt(c + a^2*c*x^2), x, 0, Unintegrable((x^m*atan(a*x)^(3/2))/sqrt(c + a^2*c*x^2), x)]

    @test_int [(x^3*atan(a*x)^(3/2))/sqrt(c + a^2*c*x^2), x, 3, -((x*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)))/(4*a^3*c)) - (2*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2))/(3*a^4*c) + (x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2))/(3*a^2*c) + Unintegrable(x/(sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))), x)/(8*a^2) + (5*Unintegrable(sqrt(atan(a*x))/sqrt(c + a^2*c*x^2), x))/(4*a^3)]
    @test_int [(x^2*atan(a*x)^(3/2))/sqrt(c + a^2*c*x^2), x, 2, -((3*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)))/(4*a^3*c)) + (x*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2))/(2*a^2*c) + (3*Unintegrable(1/(sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))), x))/(8*a^2) - Unintegrable(atan(a*x)^(3/2)/sqrt(c + a^2*c*x^2), x)/(2*a^2)]
    @test_int [(x*atan(a*x)^(3/2))/sqrt(c + a^2*c*x^2), x, 1, (sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2))/(a^2*c) - (3*Unintegrable(sqrt(atan(a*x))/sqrt(c + a^2*c*x^2), x))/(2*a)]
    @test_int [atan(a*x)^(3/2)/sqrt(c + a^2*c*x^2), x, 0, Unintegrable(atan(a*x)^(3/2)/sqrt(c + a^2*c*x^2), x)]
    @test_int [atan(a*x)^(3/2)/(x*sqrt(c + a^2*c*x^2)), x, 0, Unintegrable(atan(a*x)^(3/2)/(x*sqrt(c + a^2*c*x^2)), x)]
    @test_int [atan(a*x)^(3/2)/(x^2*sqrt(c + a^2*c*x^2)), x, 1, -((sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2))/(c*x)) + (3*a*Unintegrable(sqrt(atan(a*x))/(x*sqrt(c + a^2*c*x^2)), x))/2]
    @test_int [atan(a*x)^(3/2)/(x^3*sqrt(c + a^2*c*x^2)), x, 2, (-3*a*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)))/(4*c*x) - (sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2))/(2*c*x^2) + (3*a^2*Unintegrable(1/(x*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))), x))/8 - (a^2*Unintegrable(atan(a*x)^(3/2)/(x*sqrt(c + a^2*c*x^2)), x))/2]
    @test_int [atan(a*x)^(3/2)/(x^4*sqrt(c + a^2*c*x^2)), x, 3, -(a*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)))/(4*c*x^2) - (sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2))/(3*c*x^3) + (2*a^2*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2))/(3*c*x) + (a^2*Unintegrable(1/(x^2*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))), x))/8 - (5*a^3*Unintegrable(sqrt(atan(a*x))/(x*sqrt(c + a^2*c*x^2)), x))/4]

    @test_int [(x^m*atan(a*x)^(3/2))/(c + a^2*c*x^2)^(3/2), x, 0, Unintegrable((x^m*atan(a*x)^(3/2))/(c + a^2*c*x^2)^(3/2), x)]

    @test_int [(x^3*atan(a*x)^(3/2))/(c + a^2*c*x^2)^(3/2), x, 0, Unintegrable((x^3*atan(a*x)^(3/2))/(c + a^2*c*x^2)^(3/2), x)]
    @test_int [(x^2*atan(a*x)^(3/2))/(c + a^2*c*x^2)^(3/2), x, 0, Unintegrable((x^2*atan(a*x)^(3/2))/(c + a^2*c*x^2)^(3/2), x)]
    @test_int [(x*atan(a*x)^(3/2))/(c + a^2*c*x^2)^(3/2), x, 6, (3*x*sqrt(atan(a*x)))/(2*a*c*sqrt(c + a^2*c*x^2)) - atan(a*x)^(3/2)/(a^2*c*sqrt(c + a^2*c*x^2)) - (3*sqrt(pi/2)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(2/pi)*sqrt(atan(a*x))))/(2*a^2*c*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)^(3/2)/(c + a^2*c*x^2)^(3/2), x, 5, (3*sqrt(atan(a*x)))/(2*a*c*sqrt(c + a^2*c*x^2)) + (x*atan(a*x)^(3/2))/(c*sqrt(c + a^2*c*x^2)) - (3*sqrt(pi/2)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(2/pi)*sqrt(atan(a*x))))/(2*a*c*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)^(3/2)/(x*(c + a^2*c*x^2)^(3/2)), x, 0, Unintegrable(atan(a*x)^(3/2)/(x*(c + a^2*c*x^2)^(3/2)), x)]
    @test_int [atan(a*x)^(3/2)/(x^2*(c + a^2*c*x^2)^(3/2)), x, 0, Unintegrable(atan(a*x)^(3/2)/(x^2*(c + a^2*c*x^2)^(3/2)), x)]

    @test_int [(x^m*atan(a*x)^(3/2))/(c + a^2*c*x^2)^(5/2), x, 0, Unintegrable((x^m*atan(a*x)^(3/2))/(c + a^2*c*x^2)^(5/2), x)]

    @test_int [(x^5*atan(a*x)^(3/2))/(c + a^2*c*x^2)^(5/2), x, 0, Unintegrable((x^5*atan(a*x)^(3/2))/(c + a^2*c*x^2)^(5/2), x)]
    @test_int [(x^4*atan(a*x)^(3/2))/(c + a^2*c*x^2)^(5/2), x, 0, Unintegrable((x^4*atan(a*x)^(3/2))/(c + a^2*c*x^2)^(5/2), x)]
    @test_int [(x^3*atan(a*x)^(3/2))/(c + a^2*c*x^2)^(5/2), x, 15, (x^3*sqrt(atan(a*x)))/(6*a*c*(c + a^2*c*x^2)^(3/2)) + (x*sqrt(atan(a*x)))/(a^3*c^2*sqrt(c + a^2*c*x^2)) - (x^2*atan(a*x)^(3/2))/(3*a^2*c*(c + a^2*c*x^2)^(3/2)) - (2*atan(a*x)^(3/2))/(3*a^4*c^2*sqrt(c + a^2*c*x^2)) - (9*sqrt(pi/2)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(2/pi)*sqrt(atan(a*x))))/(8*a^4*c^2*sqrt(c + a^2*c*x^2)) + (sqrt(pi/6)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(6/pi)*sqrt(atan(a*x))))/(24*a^4*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [(x^2*atan(a*x)^(3/2))/(c + a^2*c*x^2)^(5/2), x, 11, (3*sqrt(atan(a*x)))/(8*a^3*c^2*sqrt(c + a^2*c*x^2)) + (x^3*atan(a*x)^(3/2))/(3*c*(c + a^2*c*x^2)^(3/2)) - (sqrt(1 + a^2*x^2)*sqrt(atan(a*x))*cos(3*atan(a*x)))/(24*a^3*c^2*sqrt(c + a^2*c*x^2)) - (3*sqrt(pi/2)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(2/pi)*sqrt(atan(a*x))))/(8*a^3*c^2*sqrt(c + a^2*c*x^2)) + (sqrt(pi/6)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(6/pi)*sqrt(atan(a*x))))/(24*a^3*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [(x*atan(a*x)^(3/2))/(c + a^2*c*x^2)^(5/2), x, 11, (3*x*sqrt(atan(a*x)))/(8*a*c^2*sqrt(c + a^2*c*x^2)) - atan(a*x)^(3/2)/(3*a^2*c*(c + a^2*c*x^2)^(3/2)) - (3*sqrt(pi/2)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(2/pi)*sqrt(atan(a*x))))/(8*a^2*c^2*sqrt(c + a^2*c*x^2)) - (sqrt(pi/6)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(6/pi)*sqrt(atan(a*x))))/(24*a^2*c^2*sqrt(c + a^2*c*x^2)) + (sqrt(1 + a^2*x^2)*sqrt(atan(a*x))*sin(3*atan(a*x)))/(24*a^2*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)^(3/2)/(c + a^2*c*x^2)^(5/2), x, 14, sqrt(atan(a*x))/(6*a*c*(c + a^2*c*x^2)^(3/2)) + sqrt(atan(a*x))/(a*c^2*sqrt(c + a^2*c*x^2)) + (x*atan(a*x)^(3/2))/(3*c*(c + a^2*c*x^2)^(3/2)) + (2*x*atan(a*x)^(3/2))/(3*c^2*sqrt(c + a^2*c*x^2)) - (9*sqrt(pi/2)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(2/pi)*sqrt(atan(a*x))))/(8*a*c^2*sqrt(c + a^2*c*x^2)) - (sqrt(pi/6)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(6/pi)*sqrt(atan(a*x))))/(24*a*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)^(3/2)/(x*(c + a^2*c*x^2)^(5/2)), x, 0, Unintegrable(atan(a*x)^(3/2)/(x*(c + a^2*c*x^2)^(5/2)), x)]
    @test_int [atan(a*x)^(3/2)/(x^2*(c + a^2*c*x^2)^(5/2)), x, 0, Unintegrable(atan(a*x)^(3/2)/(x^2*(c + a^2*c*x^2)^(5/2)), x)]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d+c^2*d*x^2)^q*(a+b*atan(c*x))^(5/2)=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x^2)^p*atan(a*x)^(5/2)*with*d=a^2*c=#

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

    @test_int [x^m*(c + a^2*c*x^2)*atan(a*x)^(5/2), x, 0, Unintegrable(x^m*(c + a^2*c*x^2)*atan(a*x)^(5/2), x)]

    @test_int [x^2*(c + a^2*c*x^2)*atan(a*x)^(5/2), x, 0, Unintegrable(x^2*(c + a^2*c*x^2)*atan(a*x)^(5/2), x)]
    @test_int [x*(c + a^2*c*x^2)*atan(a*x)^(5/2), x, 2, (5*c*(1 + a^2*x^2)*sqrt(atan(a*x)))/(32*a^2) - (5*c*x*(1 + a^2*x^2)*atan(a*x)^(3/2))/(24*a) + (c*(1 + a^2*x^2)^2*atan(a*x)^(5/2))/(4*a^2) - (5*c*Unintegrable(1/sqrt(atan(a*x)), x))/(64*a) - (5*c*Unintegrable(atan(a*x)^(3/2), x))/(12*a)]
    @test_int [(c + a^2*c*x^2)*atan(a*x)^(5/2), x, 1, (-5*c*(1 + a^2*x^2)*atan(a*x)^(3/2))/(12*a) + (c*x*(1 + a^2*x^2)*atan(a*x)^(5/2))/3 + (5*c*Unintegrable(sqrt(atan(a*x)), x))/8 + (2*c*Unintegrable(atan(a*x)^(5/2), x))/3]
    @test_int [((c + a^2*c*x^2)*atan(a*x)^(5/2))/x, x, 0, Unintegrable(((c + a^2*c*x^2)*atan(a*x)^(5/2))/x, x)]
    @test_int [((c + a^2*c*x^2)*atan(a*x)^(5/2))/x^2, x, 0, Unintegrable(((c + a^2*c*x^2)*atan(a*x)^(5/2))/x^2, x)]

    @test_int [x^m*(c + a^2*c*x^2)^2*atan(a*x)^(5/2), x, 0, Unintegrable(x^m*(c + a^2*c*x^2)^2*atan(a*x)^(5/2), x)]

    @test_int [x^2*(c + a^2*c*x^2)^2*atan(a*x)^(5/2), x, 0, Unintegrable(x^2*(c + a^2*c*x^2)^2*atan(a*x)^(5/2), x)]
    @test_int [x*(c + a^2*c*x^2)^2*atan(a*x)^(5/2), x, 3, (c^2*(1 + a^2*x^2)*sqrt(atan(a*x)))/(12*a^2) + (c^2*(1 + a^2*x^2)^2*sqrt(atan(a*x)))/(32*a^2) - (c^2*x*(1 + a^2*x^2)*atan(a*x)^(3/2))/(9*a) - (c^2*x*(1 + a^2*x^2)^2*atan(a*x)^(3/2))/(12*a) + (c^2*(1 + a^2*x^2)^3*atan(a*x)^(5/2))/(6*a^2) - (c^2*Unintegrable(1/sqrt(atan(a*x)), x))/(24*a) - (c*Unintegrable((c + a^2*c*x^2)/sqrt(atan(a*x)), x))/(64*a) - (2*c^2*Unintegrable(atan(a*x)^(3/2), x))/(9*a)]
    @test_int [(c + a^2*c*x^2)^2*atan(a*x)^(5/2), x, 2, -(c^2*(1 + a^2*x^2)*atan(a*x)^(3/2))/(3*a) - (c^2*(1 + a^2*x^2)^2*atan(a*x)^(3/2))/(8*a) + (4*c^2*x*(1 + a^2*x^2)*atan(a*x)^(5/2))/15 + (c^2*x*(1 + a^2*x^2)^2*atan(a*x)^(5/2))/5 + (c^2*Unintegrable(sqrt(atan(a*x)), x))/2 + (3*c*Unintegrable((c + a^2*c*x^2)*sqrt(atan(a*x)), x))/16 + (8*c^2*Unintegrable(atan(a*x)^(5/2), x))/15]
    @test_int [((c + a^2*c*x^2)^2*atan(a*x)^(5/2))/x, x, 0, Unintegrable(((c + a^2*c*x^2)^2*atan(a*x)^(5/2))/x, x)]
    @test_int [((c + a^2*c*x^2)^2*atan(a*x)^(5/2))/x^2, x, 0, Unintegrable(((c + a^2*c*x^2)^2*atan(a*x)^(5/2))/x^2, x)]

    @test_int [x^m*(c + a^2*c*x^2)^3*atan(a*x)^(5/2), x, 0, Unintegrable(x^m*(c + a^2*c*x^2)^3*atan(a*x)^(5/2), x)]

    @test_int [x^2*(c + a^2*c*x^2)^3*atan(a*x)^(5/2), x, 0, Unintegrable(x^2*(c + a^2*c*x^2)^3*atan(a*x)^(5/2), x)]
    @test_int [x*(c + a^2*c*x^2)^3*atan(a*x)^(5/2), x, 4, (3*c^3*(1 + a^2*x^2)*sqrt(atan(a*x)))/(56*a^2) + (9*c^3*(1 + a^2*x^2)^2*sqrt(atan(a*x)))/(448*a^2) + (5*c^3*(1 + a^2*x^2)^3*sqrt(atan(a*x)))/(448*a^2) - (c^3*x*(1 + a^2*x^2)*atan(a*x)^(3/2))/(14*a) - (3*c^3*x*(1 + a^2*x^2)^2*atan(a*x)^(3/2))/(56*a) - (5*c^3*x*(1 + a^2*x^2)^3*atan(a*x)^(3/2))/(112*a) + (c^3*(1 + a^2*x^2)^4*atan(a*x)^(5/2))/(8*a^2) - (3*c^3*Unintegrable(1/sqrt(atan(a*x)), x))/(112*a) - (9*c^2*Unintegrable((c + a^2*c*x^2)/sqrt(atan(a*x)), x))/(896*a) - (5*c*Unintegrable((c + a^2*c*x^2)^2/sqrt(atan(a*x)), x))/(896*a) - (c^3*Unintegrable(atan(a*x)^(3/2), x))/(7*a)]
    @test_int [(c + a^2*c*x^2)^3*atan(a*x)^(5/2), x, 3, (-2*c^3*(1 + a^2*x^2)*atan(a*x)^(3/2))/(7*a) - (3*c^3*(1 + a^2*x^2)^2*atan(a*x)^(3/2))/(28*a) - (5*c^3*(1 + a^2*x^2)^3*atan(a*x)^(3/2))/(84*a) + (8*c^3*x*(1 + a^2*x^2)*atan(a*x)^(5/2))/35 + (6*c^3*x*(1 + a^2*x^2)^2*atan(a*x)^(5/2))/35 + (c^3*x*(1 + a^2*x^2)^3*atan(a*x)^(5/2))/7 + (3*c^3*Unintegrable(sqrt(atan(a*x)), x))/7 + (9*c^2*Unintegrable((c + a^2*c*x^2)*sqrt(atan(a*x)), x))/56 + (5*c*Unintegrable((c + a^2*c*x^2)^2*sqrt(atan(a*x)), x))/56 + (16*c^3*Unintegrable(atan(a*x)^(5/2), x))/35]
    @test_int [((c + a^2*c*x^2)^3*atan(a*x)^(5/2))/x, x, 0, Unintegrable(((c + a^2*c*x^2)^3*atan(a*x)^(5/2))/x, x)]
    @test_int [((c + a^2*c*x^2)^3*atan(a*x)^(5/2))/x^2, x, 0, Unintegrable(((c + a^2*c*x^2)^3*atan(a*x)^(5/2))/x^2, x)]

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

    @test_int [(x^m*atan(a*x)^(5/2))/(c + a^2*c*x^2), x, 0, Unintegrable((x^m*atan(a*x)^(5/2))/(c + a^2*c*x^2), x)]

    @test_int [(x^3*atan(a*x)^(5/2))/(c + a^2*c*x^2), x, 2, -((2*x*atan(a*x)^(7/2))/(7*a^3*c)) + Unintegrable(x*atan(a*x)^(5/2), x)/(a^2*c) + (2*Unintegrable(atan(a*x)^(7/2), x))/(7*a^3*c)]
    @test_int [(x^2*atan(a*x)^(5/2))/(c + a^2*c*x^2), x, 2, (-2*atan(a*x)^(7/2))/(7*a^3*c) + Unintegrable(atan(a*x)^(5/2), x)/(a^2*c)]
    @test_int [(x*atan(a*x)^(5/2))/(c + a^2*c*x^2), x, 1, (2*x*atan(a*x)^(7/2))/(7*a*c) - (2*Unintegrable(atan(a*x)^(7/2), x))/(7*a*c)]
    @test_int [atan(a*x)^(5/2)/(c + a^2*c*x^2), x, 1, (2*atan(a*x)^(7/2))/(7*a*c)]
    @test_int [atan(a*x)^(5/2)/(x*(c + a^2*c*x^2)), x, 1, (((-2*im)/7)*atan(a*x)^(7/2))/c + (im*Unintegrable(atan(a*x)^(5/2)/(x*(im + a*x)), x))/c]
    @test_int [atan(a*x)^(5/2)/(x^2*(c + a^2*c*x^2)), x, 2, (-2*a*atan(a*x)^(7/2))/(7*c) + Unintegrable(atan(a*x)^(5/2)/x^2, x)/c]
    @test_int [atan(a*x)^(5/2)/(x^3*(c + a^2*c*x^2)), x, 2, (((2*im)/7)*a^2*atan(a*x)^(7/2))/c + Unintegrable(atan(a*x)^(5/2)/x^3, x)/c - (im*a^2*Unintegrable(atan(a*x)^(5/2)/(x*(im + a*x)), x))/c]
    @test_int [atan(a*x)^(5/2)/(x^4*(c + a^2*c*x^2)), x, 3, (2*a^3*atan(a*x)^(7/2))/(7*c) + Unintegrable(atan(a*x)^(5/2)/x^4, x)/c - (a^2*Unintegrable(atan(a*x)^(5/2)/x^2, x))/c]

    @test_int [(x^m*atan(a*x)^(5/2))/(c + a^2*c*x^2)^2, x, 0, Unintegrable((x^m*atan(a*x)^(5/2))/(c + a^2*c*x^2)^2, x)]

    @test_int [(x^3*atan(a*x)^(5/2))/(c + a^2*c*x^2)^2, x, 0, Unintegrable((x^3*atan(a*x)^(5/2))/(c + a^2*c*x^2)^2, x)]
    @test_int [(x^2*atan(a*x)^(5/2))/(c + a^2*c*x^2)^2, x, 8, (15*x*sqrt(atan(a*x)))/(32*a^2*c^2*(1 + a^2*x^2)) + (5*atan(a*x)^(3/2))/(16*a^3*c^2) - (5*atan(a*x)^(3/2))/(8*a^3*c^2*(1 + a^2*x^2)) - (x*atan(a*x)^(5/2))/(2*a^2*c^2*(1 + a^2*x^2)) + atan(a*x)^(7/2)/(7*a^3*c^2) - (15*sqrt(pi)*FresnelS((2*sqrt(atan(a*x)))/sqrt(pi)))/(128*a^3*c^2)]
    @test_int [(x*atan(a*x)^(5/2))/(c + a^2*c*x^2)^2, x, 8, -((15*sqrt(atan(a*x)))/(64*a^2*c^2)) + (15*sqrt(atan(a*x)))/(32*a^2*c^2*(1 + a^2*x^2)) + (5*x*atan(a*x)^(3/2))/(8*a*c^2*(1 + a^2*x^2)) + atan(a*x)^(5/2)/(4*a^2*c^2) - atan(a*x)^(5/2)/(2*a^2*c^2*(1 + a^2*x^2)) - (15*sqrt(pi)*FresnelC((2*sqrt(atan(a*x)))/sqrt(pi)))/(128*a^2*c^2)]
    @test_int [atan(a*x)^(5/2)/(c + a^2*c*x^2)^2, x, 8, -((15*x*sqrt(atan(a*x)))/(32*c^2*(1 + a^2*x^2))) - (5*atan(a*x)^(3/2))/(16*a*c^2) + (5*atan(a*x)^(3/2))/(8*a*c^2*(1 + a^2*x^2)) + (x*atan(a*x)^(5/2))/(2*c^2*(1 + a^2*x^2)) + atan(a*x)^(7/2)/(7*a*c^2) + (15*sqrt(pi)*FresnelS((2*sqrt(atan(a*x)))/sqrt(pi)))/(128*a*c^2)]
    @test_int [atan(a*x)^(5/2)/(x*(c + a^2*c*x^2)^2), x, 0, Unintegrable(atan(a*x)^(5/2)/(x*(c + a^2*c*x^2)^2), x)]

    @test_int [(x^m*atan(a*x)^(5/2))/(c + a^2*c*x^2)^3, x, 0, Unintegrable((x^m*atan(a*x)^(5/2))/(c + a^2*c*x^2)^3, x)]

    @test_int [(x^5*atan(a*x)^(5/2))/(c + a^2*c*x^2)^3, x, 0, Unintegrable((x^5*atan(a*x)^(5/2))/(c + a^2*c*x^2)^3, x)]
    @test_int [(x^4*atan(a*x)^(5/2))/(c + a^2*c*x^2)^3, x, 18, (45*x*sqrt(atan(a*x)))/(128*a^4*c^3*(1 + a^2*x^2)) + (45*atan(a*x)^(3/2))/(256*a^5*c^3) + (5*x^4*atan(a*x)^(3/2))/(32*a*c^3*(1 + a^2*x^2)^2) - (15*atan(a*x)^(3/2))/(32*a^5*c^3*(1 + a^2*x^2)) - (x^3*atan(a*x)^(5/2))/(4*a^2*c^3*(1 + a^2*x^2)^2) - (3*x*atan(a*x)^(5/2))/(8*a^4*c^3*(1 + a^2*x^2)) + (3*atan(a*x)^(7/2))/(28*a^5*c^3) + (15*sqrt(pi/2)*FresnelS(2*sqrt(2/pi)*sqrt(atan(a*x))))/(4096*a^5*c^3) - (15*sqrt(pi)*FresnelS((2*sqrt(atan(a*x)))/sqrt(pi)))/(128*a^5*c^3) + (15*sqrt(atan(a*x))*sin(2*atan(a*x)))/(256*a^5*c^3) - (15*sqrt(atan(a*x))*sin(4*atan(a*x)))/(2048*a^5*c^3)]
    @test_int [(x^3*atan(a*x)^(5/2))/(c + a^2*c*x^2)^3, x, 16, -((135*sqrt(atan(a*x)))/(2048*a^4*c^3)) - (15*x^4*sqrt(atan(a*x)))/(256*c^3*(1 + a^2*x^2)^2) + (45*sqrt(atan(a*x)))/(256*a^4*c^3*(1 + a^2*x^2)) + (5*x^3*atan(a*x)^(3/2))/(32*a*c^3*(1 + a^2*x^2)^2) + (15*x*atan(a*x)^(3/2))/(64*a^3*c^3*(1 + a^2*x^2)) - (3*atan(a*x)^(5/2))/(32*a^4*c^3) + (x^4*atan(a*x)^(5/2))/(4*c^3*(1 + a^2*x^2)^2) + (15*sqrt(pi/2)*FresnelC(2*sqrt(2/pi)*sqrt(atan(a*x))))/(4096*a^4*c^3) - (15*sqrt(pi)*FresnelC((2*sqrt(atan(a*x)))/sqrt(pi)))/(256*a^4*c^3)]
    @test_int [(x^2*atan(a*x)^(5/2))/(c + a^2*c*x^2)^3, x, 8, atan(a*x)^(7/2)/(28*a^3*c^3) - (5*atan(a*x)^(3/2)*cos(4*atan(a*x)))/(256*a^3*c^3) - (15*sqrt(pi/2)*FresnelS(2*sqrt(2/pi)*sqrt(atan(a*x))))/(4096*a^3*c^3) + (15*sqrt(atan(a*x))*sin(4*atan(a*x)))/(2048*a^3*c^3) - (atan(a*x)^(5/2)*sin(4*atan(a*x)))/(32*a^3*c^3)]
    @test_int [(x*atan(a*x)^(5/2))/(c + a^2*c*x^2)^3, x, 16, -((225*sqrt(atan(a*x)))/(2048*a^2*c^3)) + (15*sqrt(atan(a*x)))/(256*a^2*c^3*(1 + a^2*x^2)^2) + (45*sqrt(atan(a*x)))/(256*a^2*c^3*(1 + a^2*x^2)) + (5*x*atan(a*x)^(3/2))/(32*a*c^3*(1 + a^2*x^2)^2) + (15*x*atan(a*x)^(3/2))/(64*a*c^3*(1 + a^2*x^2)) + (3*atan(a*x)^(5/2))/(32*a^2*c^3) - atan(a*x)^(5/2)/(4*a^2*c^3*(1 + a^2*x^2)^2) - (15*sqrt(pi/2)*FresnelC(2*sqrt(2/pi)*sqrt(atan(a*x))))/(4096*a^2*c^3) - (15*sqrt(pi)*FresnelC((2*sqrt(atan(a*x)))/sqrt(pi)))/(256*a^2*c^3)]
    @test_int [atan(a*x)^(5/2)/(c + a^2*c*x^2)^3, x, 18, -((45*x*sqrt(atan(a*x)))/(128*c^3*(1 + a^2*x^2))) - (75*atan(a*x)^(3/2))/(256*a*c^3) + (5*atan(a*x)^(3/2))/(32*a*c^3*(1 + a^2*x^2)^2) + (15*atan(a*x)^(3/2))/(32*a*c^3*(1 + a^2*x^2)) + (x*atan(a*x)^(5/2))/(4*c^3*(1 + a^2*x^2)^2) + (3*x*atan(a*x)^(5/2))/(8*c^3*(1 + a^2*x^2)) + (3*atan(a*x)^(7/2))/(28*a*c^3) + (15*sqrt(pi/2)*FresnelS(2*sqrt(2/pi)*sqrt(atan(a*x))))/(4096*a*c^3) + (15*sqrt(pi)*FresnelS((2*sqrt(atan(a*x)))/sqrt(pi)))/(128*a*c^3) - (15*sqrt(atan(a*x))*sin(2*atan(a*x)))/(256*a*c^3) - (15*sqrt(atan(a*x))*sin(4*atan(a*x)))/(2048*a*c^3)]
    @test_int [atan(a*x)^(5/2)/(x*(c + a^2*c*x^2)^3), x, 0, Unintegrable(atan(a*x)^(5/2)/(x*(c + a^2*c*x^2)^3), x)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x^2)^(p/2)*atan(a*x)^(5/2)*with*d=a^2*c=#

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

    @test_int [x^m*sqrt(c + a^2*c*x^2)*atan(a*x)^(5/2), x, 0, Unintegrable(x^m*sqrt(c + a^2*c*x^2)*atan(a*x)^(5/2), x)]

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

    @test_int [x^m*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(5/2), x, 0, Unintegrable(x^m*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(5/2), x)]

    @test_int [x^2*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(5/2), x, 0, Unintegrable(x^2*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(5/2), x)]
    @test_int [x*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(5/2), x, 3, (9*c*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)))/(32*a^2) + ((c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x)))/(16*a^2) - (3*c*x*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2))/(16*a) - (x*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2))/(8*a) + ((c + a^2*c*x^2)^(5/2)*atan(a*x)^(5/2))/(5*a^2*c) - (9*c^2*Unintegrable(1/(sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))), x))/(64*a) - (c*Unintegrable(sqrt(c + a^2*c*x^2)/sqrt(atan(a*x)), x))/(32*a) - (3*c^2*Unintegrable(atan(a*x)^(3/2)/sqrt(c + a^2*c*x^2), x))/(16*a)]
    @test_int [(c + a^2*c*x^2)^(3/2)*atan(a*x)^(5/2), x, 2, (-15*c*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2))/(16*a) - (5*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2))/(24*a) + (3*c*x*sqrt(c + a^2*c*x^2)*atan(a*x)^(5/2))/8 + (x*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(5/2))/4 + (45*c^2*Unintegrable(sqrt(atan(a*x))/sqrt(c + a^2*c*x^2), x))/32 + (5*c*Unintegrable(sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)), x))/16 + (3*c^2*Unintegrable(atan(a*x)^(5/2)/sqrt(c + a^2*c*x^2), x))/8]
    @test_int [((c + a^2*c*x^2)^(3/2)*atan(a*x)^(5/2))/x, x, 0, Unintegrable(((c + a^2*c*x^2)^(3/2)*atan(a*x)^(5/2))/x, x)]

    @test_int [x^m*(c + a^2*c*x^2)^(5/2)*atan(a*x)^(5/2), x, 0, Unintegrable(x^m*(c + a^2*c*x^2)^(5/2)*atan(a*x)^(5/2), x)]

    @test_int [x^2*(c + a^2*c*x^2)^(5/2)*atan(a*x)^(5/2), x, 0, Unintegrable(x^2*(c + a^2*c*x^2)^(5/2)*atan(a*x)^(5/2), x)]
    @test_int [x*(c + a^2*c*x^2)^(5/2)*atan(a*x)^(5/2), x, 4, (75*c^2*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)))/(448*a^2) + (25*c*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x)))/(672*a^2) + ((c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x)))/(56*a^2) - (25*c^2*x*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2))/(224*a) - (25*c*x*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2))/(336*a) - (5*x*(c + a^2*c*x^2)^(5/2)*atan(a*x)^(3/2))/(84*a) + ((c + a^2*c*x^2)^(7/2)*atan(a*x)^(5/2))/(7*a^2*c) - (75*c^3*Unintegrable(1/(sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))), x))/(896*a) - (25*c^2*Unintegrable(sqrt(c + a^2*c*x^2)/sqrt(atan(a*x)), x))/(1344*a) - (c*Unintegrable((c + a^2*c*x^2)^(3/2)/sqrt(atan(a*x)), x))/(112*a) - (25*c^3*Unintegrable(atan(a*x)^(3/2)/sqrt(c + a^2*c*x^2), x))/(224*a)]
    @test_int [(c + a^2*c*x^2)^(5/2)*atan(a*x)^(5/2), x, 3, (-25*c^2*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2))/(32*a) - (25*c*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2))/(144*a) - ((c + a^2*c*x^2)^(5/2)*atan(a*x)^(3/2))/(12*a) + (5*c^2*x*sqrt(c + a^2*c*x^2)*atan(a*x)^(5/2))/16 + (5*c*x*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(5/2))/24 + (x*(c + a^2*c*x^2)^(5/2)*atan(a*x)^(5/2))/6 + (75*c^3*Unintegrable(sqrt(atan(a*x))/sqrt(c + a^2*c*x^2), x))/64 + (25*c^2*Unintegrable(sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)), x))/96 + (c*Unintegrable((c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x)), x))/8 + (5*c^3*Unintegrable(atan(a*x)^(5/2)/sqrt(c + a^2*c*x^2), x))/16]
    @test_int [((c + a^2*c*x^2)^(5/2)*atan(a*x)^(5/2))/x, x, 0, Unintegrable(((c + a^2*c*x^2)^(5/2)*atan(a*x)^(5/2))/x, x)]

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

    @test_int [(x^m*atan(a*x)^(5/2))/sqrt(c + a^2*c*x^2), x, 0, Unintegrable((x^m*atan(a*x)^(5/2))/sqrt(c + a^2*c*x^2), x)]

    @test_int [(x^3*atan(a*x)^(5/2))/sqrt(c + a^2*c*x^2), x, 4, (5*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)))/(8*a^4*c) - (5*x*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2))/(12*a^3*c) - (2*sqrt(c + a^2*c*x^2)*atan(a*x)^(5/2))/(3*a^4*c) + (x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^(5/2))/(3*a^2*c) - (5*Unintegrable(1/(sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))), x))/(16*a^3) + (25*Unintegrable(atan(a*x)^(3/2)/sqrt(c + a^2*c*x^2), x))/(12*a^3)]
    @test_int [(x^2*atan(a*x)^(5/2))/sqrt(c + a^2*c*x^2), x, 2, -((5*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2))/(4*a^3*c)) + (x*sqrt(c + a^2*c*x^2)*atan(a*x)^(5/2))/(2*a^2*c) + (15*Unintegrable(sqrt(atan(a*x))/sqrt(c + a^2*c*x^2), x))/(8*a^2) - Unintegrable(atan(a*x)^(5/2)/sqrt(c + a^2*c*x^2), x)/(2*a^2)]
    @test_int [(x*atan(a*x)^(5/2))/sqrt(c + a^2*c*x^2), x, 1, (sqrt(c + a^2*c*x^2)*atan(a*x)^(5/2))/(a^2*c) - (5*Unintegrable(atan(a*x)^(3/2)/sqrt(c + a^2*c*x^2), x))/(2*a)]
    @test_int [atan(a*x)^(5/2)/sqrt(c + a^2*c*x^2), x, 0, Unintegrable(atan(a*x)^(5/2)/sqrt(c + a^2*c*x^2), x)]
    @test_int [atan(a*x)^(5/2)/(x*sqrt(c + a^2*c*x^2)), x, 0, Unintegrable(atan(a*x)^(5/2)/(x*sqrt(c + a^2*c*x^2)), x)]
    @test_int [atan(a*x)^(5/2)/(x^2*sqrt(c + a^2*c*x^2)), x, 1, -((sqrt(c + a^2*c*x^2)*atan(a*x)^(5/2))/(c*x)) + (5*a*Unintegrable(atan(a*x)^(3/2)/(x*sqrt(c + a^2*c*x^2)), x))/2]
    @test_int [atan(a*x)^(5/2)/(x^3*sqrt(c + a^2*c*x^2)), x, 2, (-5*a*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2))/(4*c*x) - (sqrt(c + a^2*c*x^2)*atan(a*x)^(5/2))/(2*c*x^2) + (15*a^2*Unintegrable(sqrt(atan(a*x))/(x*sqrt(c + a^2*c*x^2)), x))/8 - (a^2*Unintegrable(atan(a*x)^(5/2)/(x*sqrt(c + a^2*c*x^2)), x))/2]
    @test_int [atan(a*x)^(5/2)/(x^4*sqrt(c + a^2*c*x^2)), x, 4, (-5*a^2*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)))/(8*c*x) - (5*a*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2))/(12*c*x^2) - (sqrt(c + a^2*c*x^2)*atan(a*x)^(5/2))/(3*c*x^3) + (2*a^2*sqrt(c + a^2*c*x^2)*atan(a*x)^(5/2))/(3*c*x) + (5*a^3*Unintegrable(1/(x*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))), x))/16 - (25*a^3*Unintegrable(atan(a*x)^(3/2)/(x*sqrt(c + a^2*c*x^2)), x))/12]

    @test_int [(x^m*atan(a*x)^(5/2))/(c + a^2*c*x^2)^(3/2), x, 0, Unintegrable((x^m*atan(a*x)^(5/2))/(c + a^2*c*x^2)^(3/2), x)]

    @test_int [(x^2*atan(a*x)^(5/2))/(c + a^2*c*x^2)^(3/2), x, 0, Unintegrable((x^2*atan(a*x)^(5/2))/(c + a^2*c*x^2)^(3/2), x)]
    @test_int [(x*atan(a*x)^(5/2))/(c + a^2*c*x^2)^(3/2), x, 6, (15*sqrt(atan(a*x)))/(4*a^2*c*sqrt(c + a^2*c*x^2)) + (5*x*atan(a*x)^(3/2))/(2*a*c*sqrt(c + a^2*c*x^2)) - atan(a*x)^(5/2)/(a^2*c*sqrt(c + a^2*c*x^2)) - (15*sqrt(pi/2)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(2/pi)*sqrt(atan(a*x))))/(4*a^2*c*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)^(5/2)/(c + a^2*c*x^2)^(3/2), x, 6, -((15*x*sqrt(atan(a*x)))/(4*c*sqrt(c + a^2*c*x^2))) + (5*atan(a*x)^(3/2))/(2*a*c*sqrt(c + a^2*c*x^2)) + (x*atan(a*x)^(5/2))/(c*sqrt(c + a^2*c*x^2)) + (15*sqrt(pi/2)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(2/pi)*sqrt(atan(a*x))))/(4*a*c*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)^(5/2)/(x*(c + a^2*c*x^2)^(3/2)), x, 0, Unintegrable(atan(a*x)^(5/2)/(x*(c + a^2*c*x^2)^(3/2)), x)]

    @test_int [(x^m*atan(a*x)^(5/2))/(c + a^2*c*x^2)^(5/2), x, 0, Unintegrable((x^m*atan(a*x)^(5/2))/(c + a^2*c*x^2)^(5/2), x)]

    @test_int [(x^4*atan(a*x)^(5/2))/(c + a^2*c*x^2)^(5/2), x, 0, Unintegrable((x^4*atan(a*x)^(5/2))/(c + a^2*c*x^2)^(5/2), x)]
    @test_int [(x^3*atan(a*x)^(5/2))/(c + a^2*c*x^2)^(5/2), x, 17, (45*sqrt(atan(a*x)))/(16*a^4*c^2*sqrt(c + a^2*c*x^2)) + (5*x^3*atan(a*x)^(3/2))/(18*a*c*(c + a^2*c*x^2)^(3/2)) + (5*x*atan(a*x)^(3/2))/(3*a^3*c^2*sqrt(c + a^2*c*x^2)) - (x^2*atan(a*x)^(5/2))/(3*a^2*c*(c + a^2*c*x^2)^(3/2)) - (2*atan(a*x)^(5/2))/(3*a^4*c^2*sqrt(c + a^2*c*x^2)) - (5*sqrt(1 + a^2*x^2)*sqrt(atan(a*x))*cos(3*atan(a*x)))/(144*a^4*c^2*sqrt(c + a^2*c*x^2)) - (45*sqrt(pi/2)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(2/pi)*sqrt(atan(a*x))))/(16*a^4*c^2*sqrt(c + a^2*c*x^2)) + (5*sqrt(pi/6)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(6/pi)*sqrt(atan(a*x))))/(144*a^4*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [(x^2*atan(a*x)^(5/2))/(c + a^2*c*x^2)^(5/2), x, 16, -((5*x^3*sqrt(atan(a*x)))/(36*c*(c + a^2*c*x^2)^(3/2))) - (5*x*sqrt(atan(a*x)))/(6*a^2*c^2*sqrt(c + a^2*c*x^2)) + (5*x^2*atan(a*x)^(3/2))/(18*a*c*(c + a^2*c*x^2)^(3/2)) + (5*atan(a*x)^(3/2))/(9*a^3*c^2*sqrt(c + a^2*c*x^2)) + (x^3*atan(a*x)^(5/2))/(3*c*(c + a^2*c*x^2)^(3/2)) + (15*sqrt(pi/2)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(2/pi)*sqrt(atan(a*x))))/(16*a^3*c^2*sqrt(c + a^2*c*x^2)) - (5*sqrt(pi/6)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(6/pi)*sqrt(atan(a*x))))/(144*a^3*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [(x*atan(a*x)^(5/2))/(c + a^2*c*x^2)^(5/2), x, 15, (5*sqrt(atan(a*x)))/(36*a^2*c*(c + a^2*c*x^2)^(3/2)) + (5*sqrt(atan(a*x)))/(6*a^2*c^2*sqrt(c + a^2*c*x^2)) + (5*x*atan(a*x)^(3/2))/(18*a*c*(c + a^2*c*x^2)^(3/2)) + (5*x*atan(a*x)^(3/2))/(9*a*c^2*sqrt(c + a^2*c*x^2)) - atan(a*x)^(5/2)/(3*a^2*c*(c + a^2*c*x^2)^(3/2)) - (15*sqrt(pi/2)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(2/pi)*sqrt(atan(a*x))))/(16*a^2*c^2*sqrt(c + a^2*c*x^2)) - (5*sqrt(pi/6)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(6/pi)*sqrt(atan(a*x))))/(144*a^2*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)^(5/2)/(c + a^2*c*x^2)^(5/2), x, 17, -((45*x*sqrt(atan(a*x)))/(16*c^2*sqrt(c + a^2*c*x^2))) + (5*atan(a*x)^(3/2))/(18*a*c*(c + a^2*c*x^2)^(3/2)) + (5*atan(a*x)^(3/2))/(3*a*c^2*sqrt(c + a^2*c*x^2)) + (x*atan(a*x)^(5/2))/(3*c*(c + a^2*c*x^2)^(3/2)) + (2*x*atan(a*x)^(5/2))/(3*c^2*sqrt(c + a^2*c*x^2)) + (45*sqrt(pi/2)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(2/pi)*sqrt(atan(a*x))))/(16*a*c^2*sqrt(c + a^2*c*x^2)) + (5*sqrt(pi/6)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(6/pi)*sqrt(atan(a*x))))/(144*a*c^2*sqrt(c + a^2*c*x^2)) - (5*sqrt(1 + a^2*x^2)*sqrt(atan(a*x))*sin(3*atan(a*x)))/(144*a*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [atan(a*x)^(5/2)/(x*(c + a^2*c*x^2)^(5/2)), x, 0, Unintegrable(atan(a*x)^(5/2)/(x*(c + a^2*c*x^2)^(5/2)), x)]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d+c^2*d*x^2)^q*(a+b*atan(c*x))^(-1/2)=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x^2)^p / atan(a*x)^(1/2)*with*d=a^2*c=#

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

    @test_int [(x^m*(c + a^2*c*x^2))/sqrt(atan(a*x)), x, 0, Unintegrable((x^m*(c + a^2*c*x^2))/sqrt(atan(a*x)), x)]

    @test_int [(x*(c + a^2*c*x^2))/sqrt(atan(a*x)), x, 0, Unintegrable((x*(c + a^2*c*x^2))/sqrt(atan(a*x)), x)]
    @test_int [(c + a^2*c*x^2)/sqrt(atan(a*x)), x, 0, Unintegrable((c + a^2*c*x^2)/sqrt(atan(a*x)), x)]
    @test_int [(c + a^2*c*x^2)/(x*sqrt(atan(a*x))), x, 0, Unintegrable((c + a^2*c*x^2)/(x*sqrt(atan(a*x))), x)]

    @test_int [(x^m*(c + a^2*c*x^2)^2)/sqrt(atan(a*x)), x, 0, Unintegrable((x^m*(c + a^2*c*x^2)^2)/sqrt(atan(a*x)), x)]

    @test_int [(x*(c + a^2*c*x^2)^2)/sqrt(atan(a*x)), x, 0, Unintegrable((x*(c + a^2*c*x^2)^2)/sqrt(atan(a*x)), x)]
    @test_int [(c + a^2*c*x^2)^2/sqrt(atan(a*x)), x, 0, Unintegrable((c + a^2*c*x^2)^2/sqrt(atan(a*x)), x)]
    @test_int [(c + a^2*c*x^2)^2/(x*sqrt(atan(a*x))), x, 0, Unintegrable((c + a^2*c*x^2)^2/(x*sqrt(atan(a*x))), x)]

    @test_int [(x^m*(c + a^2*c*x^2)^3)/sqrt(atan(a*x)), x, 0, Unintegrable((x^m*(c + a^2*c*x^2)^3)/sqrt(atan(a*x)), x)]

    @test_int [(x*(c + a^2*c*x^2)^3)/sqrt(atan(a*x)), x, 0, Unintegrable((x*(c + a^2*c*x^2)^3)/sqrt(atan(a*x)), x)]
    @test_int [(c + a^2*c*x^2)^3/sqrt(atan(a*x)), x, 0, Unintegrable((c + a^2*c*x^2)^3/sqrt(atan(a*x)), x)]
    @test_int [(c + a^2*c*x^2)^3/(x*sqrt(atan(a*x))), x, 0, Unintegrable((c + a^2*c*x^2)^3/(x*sqrt(atan(a*x))), x)]

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

    @test_int [x^m/((c + a^2*c*x^2)*sqrt(atan(a*x))), x, 0, Unintegrable(x^m/((c + a^2*c*x^2)*sqrt(atan(a*x))), x)]

    @test_int [x/((c + a^2*c*x^2)*sqrt(atan(a*x))), x, 1, (2*x*sqrt(atan(a*x)))/(a*c) - (2*Unintegrable(sqrt(atan(a*x)), x))/(a*c)]
    @test_int [1/((c + a^2*c*x^2)*sqrt(atan(a*x))), x, 1, (2*sqrt(atan(a*x)))/(a*c)]
    @test_int [1/(x*(c + a^2*c*x^2)*sqrt(atan(a*x))), x, 0, Unintegrable(1/(x*(c + a^2*c*x^2)*sqrt(atan(a*x))), x)]

    @test_int [x^m/((c + a^2*c*x^2)^2*sqrt(atan(a*x))), x, 0, Unintegrable(x^m/((c + a^2*c*x^2)^2*sqrt(atan(a*x))), x)]

    @test_int [x^3/((c + a^2*c*x^2)^2*sqrt(atan(a*x))), x, 0, Unintegrable(x^3/((c + a^2*c*x^2)^2*sqrt(atan(a*x))), x)]
    @test_int [x^2/((c + a^2*c*x^2)^2*sqrt(atan(a*x))), x, 5, sqrt(atan(a*x))/(a^3*c^2) - (sqrt(pi)*FresnelC((2*sqrt(atan(a*x)))/sqrt(pi)))/(2*a^3*c^2)]
    @test_int [x/((c + a^2*c*x^2)^2*sqrt(atan(a*x))), x, 5, (sqrt(pi)*FresnelS((2*sqrt(atan(a*x)))/sqrt(pi)))/(2*a^2*c^2)]
    @test_int [1/((c + a^2*c*x^2)^2*sqrt(atan(a*x))), x, 5, sqrt(atan(a*x))/(a*c^2) + (sqrt(pi)*FresnelC((2*sqrt(atan(a*x)))/sqrt(pi)))/(2*a*c^2)]
    @test_int [1/(x*(c + a^2*c*x^2)^2*sqrt(atan(a*x))), x, 0, Unintegrable(1/(x*(c + a^2*c*x^2)^2*sqrt(atan(a*x))), x)]

    @test_int [x^m/((c + a^2*c*x^2)^3*sqrt(atan(a*x))), x, 0, Unintegrable(x^m/((c + a^2*c*x^2)^3*sqrt(atan(a*x))), x)]

    @test_int [x^5/((c + a^2*c*x^2)^3*sqrt(atan(a*x))), x, 0, Unintegrable(x^5/((c + a^2*c*x^2)^3*sqrt(atan(a*x))), x)]
    @test_int [x^4/((c + a^2*c*x^2)^3*sqrt(atan(a*x))), x, 7, (3*sqrt(atan(a*x)))/(4*a^5*c^3) + (sqrt(pi/2)*FresnelC(2*sqrt(2/pi)*sqrt(atan(a*x))))/(8*a^5*c^3) - (sqrt(pi)*FresnelC((2*sqrt(atan(a*x)))/sqrt(pi)))/(2*a^5*c^3)]
    @test_int [x^3/((c + a^2*c*x^2)^3*sqrt(atan(a*x))), x, 7, -((sqrt(pi/2)*FresnelS(2*sqrt(2/pi)*sqrt(atan(a*x))))/(8*a^4*c^3)) + (sqrt(pi)*FresnelS((2*sqrt(atan(a*x)))/sqrt(pi)))/(4*a^4*c^3)]
    @test_int [x^2/((c + a^2*c*x^2)^3*sqrt(atan(a*x))), x, 5, sqrt(atan(a*x))/(4*a^3*c^3) - (sqrt(pi/2)*FresnelC(2*sqrt(2/pi)*sqrt(atan(a*x))))/(8*a^3*c^3)]
    @test_int [x/((c + a^2*c*x^2)^3*sqrt(atan(a*x))), x, 7, (sqrt(pi/2)*FresnelS(2*sqrt(2/pi)*sqrt(atan(a*x))))/(8*a^2*c^3) + (sqrt(pi)*FresnelS((2*sqrt(atan(a*x)))/sqrt(pi)))/(4*a^2*c^3)]
    @test_int [1/((c + a^2*c*x^2)^3*sqrt(atan(a*x))), x, 7, (3*sqrt(atan(a*x)))/(4*a*c^3) + (sqrt(pi/2)*FresnelC(2*sqrt(2/pi)*sqrt(atan(a*x))))/(8*a*c^3) + (sqrt(pi)*FresnelC((2*sqrt(atan(a*x)))/sqrt(pi)))/(2*a*c^3)]
    @test_int [1/(x*(c + a^2*c*x^2)^3*sqrt(atan(a*x))), x, 0, Unintegrable(1/(x*(c + a^2*c*x^2)^3*sqrt(atan(a*x))), x)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x^2)^(p/2) / atan(a*x)^(1/2)*with*d=a^2*c=#

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

    @test_int [(x^m*sqrt(c + a^2*c*x^2))/sqrt(atan(a*x)), x, 0, Unintegrable((x^m*sqrt(c + a^2*c*x^2))/sqrt(atan(a*x)), x)]

    @test_int [(x*sqrt(c + a^2*c*x^2))/sqrt(atan(a*x)), x, 0, Unintegrable((x*sqrt(c + a^2*c*x^2))/sqrt(atan(a*x)), x)]
    @test_int [sqrt(c + a^2*c*x^2)/sqrt(atan(a*x)), x, 0, Unintegrable(sqrt(c + a^2*c*x^2)/sqrt(atan(a*x)), x)]
    @test_int [sqrt(c + a^2*c*x^2)/(x*sqrt(atan(a*x))), x, 0, Unintegrable(sqrt(c + a^2*c*x^2)/(x*sqrt(atan(a*x))), x)]

    @test_int [(x^m*(c + a^2*c*x^2)^(3/2))/sqrt(atan(a*x)), x, 0, Unintegrable((x^m*(c + a^2*c*x^2)^(3/2))/sqrt(atan(a*x)), x)]

    @test_int [(x*(c + a^2*c*x^2)^(3/2))/sqrt(atan(a*x)), x, 0, Unintegrable((x*(c + a^2*c*x^2)^(3/2))/sqrt(atan(a*x)), x)]
    @test_int [(c + a^2*c*x^2)^(3/2)/sqrt(atan(a*x)), x, 0, Unintegrable((c + a^2*c*x^2)^(3/2)/sqrt(atan(a*x)), x)]
    @test_int [(c + a^2*c*x^2)^(3/2)/(x*sqrt(atan(a*x))), x, 0, Unintegrable((c + a^2*c*x^2)^(3/2)/(x*sqrt(atan(a*x))), x)]

    @test_int [(x^m*(c + a^2*c*x^2)^(5/2))/sqrt(atan(a*x)), x, 0, Unintegrable((x^m*(c + a^2*c*x^2)^(5/2))/sqrt(atan(a*x)), x)]

    @test_int [(x*(c + a^2*c*x^2)^(5/2))/sqrt(atan(a*x)), x, 0, Unintegrable((x*(c + a^2*c*x^2)^(5/2))/sqrt(atan(a*x)), x)]
    @test_int [(c + a^2*c*x^2)^(5/2)/sqrt(atan(a*x)), x, 0, Unintegrable((c + a^2*c*x^2)^(5/2)/sqrt(atan(a*x)), x)]
    @test_int [(c + a^2*c*x^2)^(5/2)/(x*sqrt(atan(a*x))), x, 0, Unintegrable((c + a^2*c*x^2)^(5/2)/(x*sqrt(atan(a*x))), x)]

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

    @test_int [x^m/(sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))), x, 0, Unintegrable(x^m/(sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))), x)]

    @test_int [x/(sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))), x, 0, Unintegrable(x/(sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))), x)]
    @test_int [1/(sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))), x, 0, Unintegrable(1/(sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))), x)]
    @test_int [1/(x*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))), x, 0, Unintegrable(1/(x*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))), x)]

    @test_int [x^m/((c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x, 0, Unintegrable(x^m/((c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x)]

    @test_int [x^2/((c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x, 0, Unintegrable(x^2/((c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x)]
    @test_int [x/((c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x, 4, (sqrt(2*pi)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(2/pi)*sqrt(atan(a*x))))/(a^2*c*sqrt(c + a^2*c*x^2))]
    @test_int [1/((c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x, 4, (sqrt(2*pi)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(2/pi)*sqrt(atan(a*x))))/(a*c*sqrt(c + a^2*c*x^2))]
    @test_int [1/(x*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x, 0, Unintegrable(1/(x*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x)]

    @test_int [x^m/((c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x))), x, 0, Unintegrable(x^m/((c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x))), x)]

    @test_int [x^4/((c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x))), x, 0, Unintegrable(x^4/((c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x))), x)]
    @test_int [x^3/((c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x))), x, 8, (3*sqrt(pi/2)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(2/pi)*sqrt(atan(a*x))))/(2*a^4*c^2*sqrt(c + a^2*c*x^2)) - (sqrt(pi/6)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(6/pi)*sqrt(atan(a*x))))/(2*a^4*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [x^2/((c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x))), x, 8, (sqrt(pi/2)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(2/pi)*sqrt(atan(a*x))))/(2*a^3*c^2*sqrt(c + a^2*c*x^2)) - (sqrt(pi/6)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(6/pi)*sqrt(atan(a*x))))/(2*a^3*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [x/((c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x))), x, 8, (sqrt(pi/2)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(2/pi)*sqrt(atan(a*x))))/(2*a^2*c^2*sqrt(c + a^2*c*x^2)) + (sqrt(pi/6)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(6/pi)*sqrt(atan(a*x))))/(2*a^2*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [1/((c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x))), x, 8, (3*sqrt(pi/2)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(2/pi)*sqrt(atan(a*x))))/(2*a*c^2*sqrt(c + a^2*c*x^2)) + (sqrt(pi/6)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(6/pi)*sqrt(atan(a*x))))/(2*a*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [1/(x*(c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x))), x, 0, Unintegrable(1/(x*(c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x))), x)]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d+c^2*d*x^2)^q*(a+b*atan(c*x))^(-3/2)=#

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

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

    @test_int [(x^m*(c + a^2*c*x^2))/atan(a*x)^(3/2), x, 0, Unintegrable((x^m*(c + a^2*c*x^2))/atan(a*x)^(3/2), x)]

    @test_int [(x*(c + a^2*c*x^2))/atan(a*x)^(3/2), x, 0, Unintegrable((x*(c + a^2*c*x^2))/atan(a*x)^(3/2), x)]
    @test_int [(c + a^2*c*x^2)/atan(a*x)^(3/2), x, 0, Unintegrable((c + a^2*c*x^2)/atan(a*x)^(3/2), x)]
    @test_int [(c + a^2*c*x^2)/(x*atan(a*x)^(3/2)), x, 0, Unintegrable((c + a^2*c*x^2)/(x*atan(a*x)^(3/2)), x)]

    @test_int [(x^m*(c + a^2*c*x^2)^2)/atan(a*x)^(3/2), x, 0, Unintegrable((x^m*(c + a^2*c*x^2)^2)/atan(a*x)^(3/2), x)]

    @test_int [(x*(c + a^2*c*x^2)^2)/atan(a*x)^(3/2), x, 0, Unintegrable((x*(c + a^2*c*x^2)^2)/atan(a*x)^(3/2), x)]
    @test_int [(c + a^2*c*x^2)^2/atan(a*x)^(3/2), x, 0, Unintegrable((c + a^2*c*x^2)^2/atan(a*x)^(3/2), x)]
    @test_int [(c + a^2*c*x^2)^2/(x*atan(a*x)^(3/2)), x, 0, Unintegrable((c + a^2*c*x^2)^2/(x*atan(a*x)^(3/2)), x)]

    @test_int [(x^m*(c + a^2*c*x^2)^3)/atan(a*x)^(3/2), x, 0, Unintegrable((x^m*(c + a^2*c*x^2)^3)/atan(a*x)^(3/2), x)]

    @test_int [(x*(c + a^2*c*x^2)^3)/atan(a*x)^(3/2), x, 0, Unintegrable((x*(c + a^2*c*x^2)^3)/atan(a*x)^(3/2), x)]
    @test_int [(c + a^2*c*x^2)^3/atan(a*x)^(3/2), x, 0, Unintegrable((c + a^2*c*x^2)^3/atan(a*x)^(3/2), x)]
    @test_int [(c + a^2*c*x^2)^3/(x*atan(a*x)^(3/2)), x, 0, Unintegrable((c + a^2*c*x^2)^3/(x*atan(a*x)^(3/2)), x)]

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

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

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

    @test_int [x^m/((c + a^2*c*x^2)^2*atan(a*x)^(3/2)), x, 0, Unintegrable(x^m/((c + a^2*c*x^2)^2*atan(a*x)^(3/2)), x)]

    @test_int [x^4/((c + a^2*c*x^2)^2*atan(a*x)^(3/2)), x, 1, -((2*x^4)/(a*c^2*(1 + a^2*x^2)*sqrt(atan(a*x)))) + (8*Unintegrable(x^3/((c + a^2*c*x^2)^2*sqrt(atan(a*x))), x))/a + 4*a*Unintegrable(x^5/((c + a^2*c*x^2)^2*sqrt(atan(a*x))), x)]
    @test_int [x^3/((c + a^2*c*x^2)^2*atan(a*x)^(3/2)), x, 6, -((2*x^3)/(a*c^2*(1 + a^2*x^2)*sqrt(atan(a*x)))) + (6*sqrt(atan(a*x)))/(a^4*c^2) - (3*sqrt(pi)*FresnelC((2*sqrt(atan(a*x)))/sqrt(pi)))/(a^4*c^2) + 2*a*Unintegrable(x^4/((c + a^2*c*x^2)^2*sqrt(atan(a*x))), x)]
    @test_int [x^2/((c + a^2*c*x^2)^2*atan(a*x)^(3/2)), x, 6, -((2*x^2)/(a*c^2*(1 + a^2*x^2)*sqrt(atan(a*x)))) + (2*sqrt(pi)*FresnelS((2*sqrt(atan(a*x)))/sqrt(pi)))/(a^3*c^2)]
    @test_int [x/((c + a^2*c*x^2)^2*atan(a*x)^(3/2)), x, 7, -((2*x)/(a*c^2*(1 + a^2*x^2)*sqrt(atan(a*x)))) + (4*sqrt(atan(a*x)))/(a^2*c^2) - (8*sqrt(atan(a*x)))/(a^2*c^2*(1 + a^2*x^2)) + (4*(1 - a^2*x^2)*sqrt(atan(a*x)))/(a^2*c^2*(1 + a^2*x^2)) + (2*sqrt(pi)*FresnelC((2*sqrt(atan(a*x)))/sqrt(pi)))/(a^2*c^2)]
    @test_int [1/((c + a^2*c*x^2)^2*atan(a*x)^(3/2)), x, 6, -(2/(a*c^2*(1 + a^2*x^2)*sqrt(atan(a*x)))) - (2*sqrt(pi)*FresnelS((2*sqrt(atan(a*x)))/sqrt(pi)))/(a*c^2)]
    @test_int [1/(x*(c + a^2*c*x^2)^2*atan(a*x)^(3/2)), x, 6, -(2/(a*c^2*x*(1 + a^2*x^2)*sqrt(atan(a*x)))) - (6*sqrt(atan(a*x)))/c^2 - (3*sqrt(pi)*FresnelC((2*sqrt(atan(a*x)))/sqrt(pi)))/c^2 - (2*Unintegrable(1/(x^2*(c + a^2*c*x^2)^2*sqrt(atan(a*x))), x))/a]
    @test_int [1/(x^2*(c + a^2*c*x^2)^2*atan(a*x)^(3/2)), x, 1, -2/(a*c^2*x^2*(1 + a^2*x^2)*sqrt(atan(a*x))) - (4*Unintegrable(1/(x^3*(c + a^2*c*x^2)^2*sqrt(atan(a*x))), x))/a - 8*a*Unintegrable(1/(x*(c + a^2*c*x^2)^2*sqrt(atan(a*x))), x)]
    @test_int [1/(x^3*(c + a^2*c*x^2)^2*atan(a*x)^(3/2)), x, 1, -2/(a*c^2*x^3*(1 + a^2*x^2)*sqrt(atan(a*x))) - (6*Unintegrable(1/(x^4*(c + a^2*c*x^2)^2*sqrt(atan(a*x))), x))/a - 10*a*Unintegrable(1/(x^2*(c + a^2*c*x^2)^2*sqrt(atan(a*x))), x)]
    @test_int [1/(x^4*(c + a^2*c*x^2)^2*atan(a*x)^(3/2)), x, 1, -2/(a*c^2*x^4*(1 + a^2*x^2)*sqrt(atan(a*x))) - (8*Unintegrable(1/(x^5*(c + a^2*c*x^2)^2*sqrt(atan(a*x))), x))/a - 12*a*Unintegrable(1/(x^3*(c + a^2*c*x^2)^2*sqrt(atan(a*x))), x)]

    @test_int [x^m/((c + a^2*c*x^2)^3*atan(a*x)^(3/2)), x, 0, Unintegrable(x^m/((c + a^2*c*x^2)^3*atan(a*x)^(3/2)), x)]

    @test_int [x^3/((c + a^2*c*x^2)^3*atan(a*x)^(3/2)), x, 13, -((2*x^3)/(a*c^3*(1 + a^2*x^2)^2*sqrt(atan(a*x)))) - (sqrt(pi/2)*FresnelC(2*sqrt(2/pi)*sqrt(atan(a*x))))/(a^4*c^3) + (sqrt(pi)*FresnelC((2*sqrt(atan(a*x)))/sqrt(pi)))/(a^4*c^3)]
    @test_int [x^2/((c + a^2*c*x^2)^3*atan(a*x)^(3/2)), x, 15, -((2*x^2)/(a*c^3*(1 + a^2*x^2)^2*sqrt(atan(a*x)))) + (sqrt(pi/2)*FresnelS(2*sqrt(2/pi)*sqrt(atan(a*x))))/(a^3*c^3)]
    @test_int [x/((c + a^2*c*x^2)^3*atan(a*x)^(3/2)), x, 13, -((2*x)/(a*c^3*(1 + a^2*x^2)^2*sqrt(atan(a*x)))) + (sqrt(pi/2)*FresnelC(2*sqrt(2/pi)*sqrt(atan(a*x))))/(a^2*c^3) + (sqrt(pi)*FresnelC((2*sqrt(atan(a*x)))/sqrt(pi)))/(a^2*c^3)]
    @test_int [1/((c + a^2*c*x^2)^3*atan(a*x)^(3/2)), x, 8, -(2/(a*c^3*(1 + a^2*x^2)^2*sqrt(atan(a*x)))) - (sqrt(pi/2)*FresnelS(2*sqrt(2/pi)*sqrt(atan(a*x))))/(a*c^3) - (2*sqrt(pi)*FresnelS((2*sqrt(atan(a*x)))/sqrt(pi)))/(a*c^3)]
    @test_int [1/(x*(c + a^2*c*x^2)^3*atan(a*x)^(3/2)), x, 8, -(2/(a*c^3*x*(1 + a^2*x^2)^2*sqrt(atan(a*x)))) - (15*sqrt(atan(a*x)))/(2*c^3) - (5*sqrt(pi/2)*FresnelC(2*sqrt(2/pi)*sqrt(atan(a*x))))/(4*c^3) - (5*sqrt(pi)*FresnelC((2*sqrt(atan(a*x)))/sqrt(pi)))/c^3 - (2*Unintegrable(1/(x^2*(c + a^2*c*x^2)^3*sqrt(atan(a*x))), x))/a]
    @test_int [1/(x^2*(c + a^2*c*x^2)^3*atan(a*x)^(3/2)), x, 1, -2/(a*c^3*x^2*(1 + a^2*x^2)^2*sqrt(atan(a*x))) - (4*Unintegrable(1/(x^3*(c + a^2*c*x^2)^3*sqrt(atan(a*x))), x))/a - 12*a*Unintegrable(1/(x*(c + a^2*c*x^2)^3*sqrt(atan(a*x))), x)]
    @test_int [1/(x^3*(c + a^2*c*x^2)^3*atan(a*x)^(3/2)), x, 1, -2/(a*c^3*x^3*(1 + a^2*x^2)^2*sqrt(atan(a*x))) - (6*Unintegrable(1/(x^4*(c + a^2*c*x^2)^3*sqrt(atan(a*x))), x))/a - 14*a*Unintegrable(1/(x^2*(c + a^2*c*x^2)^3*sqrt(atan(a*x))), x)]
    @test_int [1/(x^4*(c + a^2*c*x^2)^3*atan(a*x)^(3/2)), x, 1, -2/(a*c^3*x^4*(1 + a^2*x^2)^2*sqrt(atan(a*x))) - (8*Unintegrable(1/(x^5*(c + a^2*c*x^2)^3*sqrt(atan(a*x))), x))/a - 16*a*Unintegrable(1/(x^3*(c + a^2*c*x^2)^3*sqrt(atan(a*x))), x)]

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

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

    @test_int [(x^m*sqrt(c + a^2*c*x^2))/atan(a*x)^(3/2), x, 0, Unintegrable((x^m*sqrt(c + a^2*c*x^2))/atan(a*x)^(3/2), x)]

    @test_int [(x*sqrt(c + a^2*c*x^2))/atan(a*x)^(3/2), x, 0, Unintegrable((x*sqrt(c + a^2*c*x^2))/atan(a*x)^(3/2), x)]
    @test_int [sqrt(c + a^2*c*x^2)/atan(a*x)^(3/2), x, 0, Unintegrable(sqrt(c + a^2*c*x^2)/atan(a*x)^(3/2), x)]
    @test_int [sqrt(c + a^2*c*x^2)/(x*atan(a*x)^(3/2)), x, 0, Unintegrable(sqrt(c + a^2*c*x^2)/(x*atan(a*x)^(3/2)), x)]

    @test_int [(x^m*(c + a^2*c*x^2)^(3/2))/atan(a*x)^(3/2), x, 0, Unintegrable((x^m*(c + a^2*c*x^2)^(3/2))/atan(a*x)^(3/2), x)]

    @test_int [(x*(c + a^2*c*x^2)^(3/2))/atan(a*x)^(3/2), x, 0, Unintegrable((x*(c + a^2*c*x^2)^(3/2))/atan(a*x)^(3/2), x)]
    @test_int [(c + a^2*c*x^2)^(3/2)/atan(a*x)^(3/2), x, 0, Unintegrable((c + a^2*c*x^2)^(3/2)/atan(a*x)^(3/2), x)]
    @test_int [(c + a^2*c*x^2)^(3/2)/(x*atan(a*x)^(3/2)), x, 0, Unintegrable((c + a^2*c*x^2)^(3/2)/(x*atan(a*x)^(3/2)), x)]

    @test_int [(x^m*(c + a^2*c*x^2)^(5/2))/atan(a*x)^(3/2), x, 0, Unintegrable((x^m*(c + a^2*c*x^2)^(5/2))/atan(a*x)^(3/2), x)]

    @test_int [(x*(c + a^2*c*x^2)^(5/2))/atan(a*x)^(3/2), x, 0, Unintegrable((x*(c + a^2*c*x^2)^(5/2))/atan(a*x)^(3/2), x)]
    @test_int [(c + a^2*c*x^2)^(5/2)/atan(a*x)^(3/2), x, 0, Unintegrable((c + a^2*c*x^2)^(5/2)/atan(a*x)^(3/2), x)]
    @test_int [(c + a^2*c*x^2)^(5/2)/(x*atan(a*x)^(3/2)), x, 0, Unintegrable((c + a^2*c*x^2)^(5/2)/(x*atan(a*x)^(3/2)), x)]

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

    @test_int [x^m/(sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2)), x, 0, Unintegrable(x^m/(sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2)), x)]

    @test_int [x/(sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2)), x, 0, Unintegrable(x/(sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2)), x)]
    @test_int [1/(sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2)), x, 0, Unintegrable(1/(sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2)), x)]
    @test_int [1/(x*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2)), x, 1, -((2*sqrt(c + a^2*c*x^2))/(a*c*x*sqrt(atan(a*x)))) - (2*Unintegrable(1/(x^2*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))), x))/a]
    @test_int [1/(x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2)), x, 0, Unintegrable(1/(x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2)), x)]

    @test_int [x^m/((c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2)), x, 0, Unintegrable(x^m/((c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2)), x)]

    @test_int [x^3/((c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2)), x, 1, (-2*x^3)/(a*c*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))) + (6*Unintegrable(x^2/((c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x))/a + 4*a*Unintegrable(x^4/((c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x)]
    @test_int [x^2/((c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2)), x, 5, -((2*x^2)/(a*c*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)))) + (4*sqrt(2*pi)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(2/pi)*sqrt(atan(a*x))))/(a^3*c*sqrt(c + a^2*c*x^2)) + 2*a*Unintegrable(x^3/((c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x)]
    @test_int [x/((c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2)), x, 5, -((2*x)/(a*c*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)))) + (2*sqrt(2*pi)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(2/pi)*sqrt(atan(a*x))))/(a^2*c*sqrt(c + a^2*c*x^2))]
    @test_int [1/((c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2)), x, 5, -(2/(a*c*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)))) - (2*sqrt(2*pi)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(2/pi)*sqrt(atan(a*x))))/(a*c*sqrt(c + a^2*c*x^2))]
    @test_int [1/(x*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2)), x, 5, -(2/(a*c*x*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x)))) - (4*sqrt(2*pi)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(2/pi)*sqrt(atan(a*x))))/(c*sqrt(c + a^2*c*x^2)) - (2*Unintegrable(1/(x^2*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x))/a]
    @test_int [1/(x^2*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2)), x, 1, -2/(a*c*x^2*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))) - (4*Unintegrable(1/(x^3*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x))/a - 6*a*Unintegrable(1/(x*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x)]
    @test_int [1/(x^3*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2)), x, 1, -2/(a*c*x^3*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))) - (6*Unintegrable(1/(x^4*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x))/a - 8*a*Unintegrable(1/(x^2*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x)]
    @test_int [1/(x^4*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2)), x, 1, -2/(a*c*x^4*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))) - (8*Unintegrable(1/(x^5*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x))/a - 10*a*Unintegrable(1/(x^3*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x)]

    @test_int [x^m/((c + a^2*c*x^2)^(5/2)*atan(a*x)^(3/2)), x, 0, Unintegrable(x^m/((c + a^2*c*x^2)^(5/2)*atan(a*x)^(3/2)), x)]

    @test_int [x^3/((c + a^2*c*x^2)^(5/2)*atan(a*x)^(3/2)), x, 9, -((2*x^3)/(a*c*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x)))) + (3*sqrt(pi/2)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(2/pi)*sqrt(atan(a*x))))/(a^4*c^2*sqrt(c + a^2*c*x^2)) - (sqrt((3*pi)/2)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(6/pi)*sqrt(atan(a*x))))/(a^4*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [x^2/((c + a^2*c*x^2)^(5/2)*atan(a*x)^(3/2)), x, 17, -((2*x^2)/(a*c*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x)))) - (3*sqrt(pi/2)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(2/pi)*sqrt(atan(a*x))))/(a^3*c^2*sqrt(c + a^2*c*x^2)) + (sqrt(2*pi)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(2/pi)*sqrt(atan(a*x))))/(a^3*c^2*sqrt(c + a^2*c*x^2)) + (sqrt(pi/6)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(6/pi)*sqrt(atan(a*x))))/(a^3*c^2*sqrt(c + a^2*c*x^2)) + (sqrt((2*pi)/3)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(6/pi)*sqrt(atan(a*x))))/(a^3*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [x/((c + a^2*c*x^2)^(5/2)*atan(a*x)^(3/2)), x, 17, -((2*x)/(a*c*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x)))) + (3*sqrt(pi/2)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(2/pi)*sqrt(atan(a*x))))/(a^2*c^2*sqrt(c + a^2*c*x^2)) - (sqrt(2*pi)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(2/pi)*sqrt(atan(a*x))))/(a^2*c^2*sqrt(c + a^2*c*x^2)) + (sqrt(pi/6)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(6/pi)*sqrt(atan(a*x))))/(a^2*c^2*sqrt(c + a^2*c*x^2)) + (sqrt((2*pi)/3)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(6/pi)*sqrt(atan(a*x))))/(a^2*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [1/((c + a^2*c*x^2)^(5/2)*atan(a*x)^(3/2)), x, 9, -(2/(a*c*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x)))) - (3*sqrt(pi/2)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(2/pi)*sqrt(atan(a*x))))/(a*c^2*sqrt(c + a^2*c*x^2)) - (sqrt((3*pi)/2)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(6/pi)*sqrt(atan(a*x))))/(a*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [1/(x*(c + a^2*c*x^2)^(5/2)*atan(a*x)^(3/2)), x, 9, -(2/(a*c*x*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x)))) - (6*sqrt(2*pi)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(2/pi)*sqrt(atan(a*x))))/(c^2*sqrt(c + a^2*c*x^2)) - (2*sqrt((2*pi)/3)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(6/pi)*sqrt(atan(a*x))))/(c^2*sqrt(c + a^2*c*x^2)) - (2*Unintegrable(1/(x^2*(c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x))), x))/a]
    @test_int [1/(x^2*(c + a^2*c*x^2)^(5/2)*atan(a*x)^(3/2)), x, 1, -2/(a*c*x^2*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))) - (4*Unintegrable(1/(x^3*(c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x))), x))/a - 10*a*Unintegrable(1/(x*(c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x))), x)]
    @test_int [1/(x^3*(c + a^2*c*x^2)^(5/2)*atan(a*x)^(3/2)), x, 1, -2/(a*c*x^3*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))) - (6*Unintegrable(1/(x^4*(c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x))), x))/a - 12*a*Unintegrable(1/(x^2*(c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x))), x)]
    @test_int [1/(x^4*(c + a^2*c*x^2)^(5/2)*atan(a*x)^(3/2)), x, 1, -2/(a*c*x^4*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))) - (8*Unintegrable(1/(x^5*(c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x))), x))/a - 14*a*Unintegrable(1/(x^3*(c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x))), x)]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d+c^2*d*x^2)^q*(a+b*atan(c*x))^(-5/2)=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x^2)^p / atan(a*x)^(5/2)*with*d=a^2*c=#

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

    @test_int [(x^m*(c + a^2*c*x^2))/atan(a*x)^(5/2), x, 0, Unintegrable((x^m*(c + a^2*c*x^2))/atan(a*x)^(5/2), x)]

    @test_int [(x*(c + a^2*c*x^2))/atan(a*x)^(5/2), x, 0, Unintegrable((x*(c + a^2*c*x^2))/atan(a*x)^(5/2), x)]
    @test_int [(c + a^2*c*x^2)/atan(a*x)^(5/2), x, 0, Unintegrable((c + a^2*c*x^2)/atan(a*x)^(5/2), x)]
    @test_int [(c + a^2*c*x^2)/(x*atan(a*x)^(5/2)), x, 0, Unintegrable((c + a^2*c*x^2)/(x*atan(a*x)^(5/2)), x)]

    @test_int [(x^m*(c + a^2*c*x^2)^2)/atan(a*x)^(5/2), x, 0, Unintegrable((x^m*(c + a^2*c*x^2)^2)/atan(a*x)^(5/2), x)]

    @test_int [(x*(c + a^2*c*x^2)^2)/atan(a*x)^(5/2), x, 0, Unintegrable((x*(c + a^2*c*x^2)^2)/atan(a*x)^(5/2), x)]
    @test_int [(c + a^2*c*x^2)^2/atan(a*x)^(5/2), x, 0, Unintegrable((c + a^2*c*x^2)^2/atan(a*x)^(5/2), x)]
    @test_int [(c + a^2*c*x^2)^2/(x*atan(a*x)^(5/2)), x, 0, Unintegrable((c + a^2*c*x^2)^2/(x*atan(a*x)^(5/2)), x)]

    @test_int [(x^m*(c + a^2*c*x^2)^3)/atan(a*x)^(5/2), x, 0, Unintegrable((x^m*(c + a^2*c*x^2)^3)/atan(a*x)^(5/2), x)]

    @test_int [(x*(c + a^2*c*x^2)^3)/atan(a*x)^(5/2), x, 0, Unintegrable((x*(c + a^2*c*x^2)^3)/atan(a*x)^(5/2), x)]
    @test_int [(c + a^2*c*x^2)^3/atan(a*x)^(5/2), x, 0, Unintegrable((c + a^2*c*x^2)^3/atan(a*x)^(5/2), x)]
    @test_int [(c + a^2*c*x^2)^3/(x*atan(a*x)^(5/2)), x, 0, Unintegrable((c + a^2*c*x^2)^3/(x*atan(a*x)^(5/2)), x)]

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

    @test_int [x^m/((c + a^2*c*x^2)*atan(a*x)^(5/2)), x, 1, (-2*x^m)/(3*a*c*atan(a*x)^(3/2)) + (2*m*Unintegrable(x^(-1 + m)/atan(a*x)^(3/2), x))/(3*a*c)]

    @test_int [x/((c + a^2*c*x^2)*atan(a*x)^(5/2)), x, 1, (-2*x)/(3*a*c*atan(a*x)^(3/2)) + (2*Unintegrable(atan(a*x)^(-3/2), x))/(3*a*c)]
    @test_int [1/((c + a^2*c*x^2)*atan(a*x)^(5/2)), x, 1, -2/(3*a*c*atan(a*x)^(3/2))]
    @test_int [1/(x*(c + a^2*c*x^2)*atan(a*x)^(5/2)), x, 1, -2/(3*a*c*x*atan(a*x)^(3/2)) - (2*Unintegrable(1/(x^2*atan(a*x)^(3/2)), x))/(3*a*c)]

    @test_int [x^m/((c + a^2*c*x^2)^2*atan(a*x)^(5/2)), x, 0, Unintegrable(x^m/((c + a^2*c*x^2)^2*atan(a*x)^(5/2)), x)]

    @test_int [x^3/((c + a^2*c*x^2)^2*atan(a*x)^(5/2)), x, 8, -((2*x^3)/(3*a*c^2*(1 + a^2*x^2)*atan(a*x)^(3/2))) - (4*x^2)/(a^2*c^2*(1 + a^2*x^2)*sqrt(atan(a*x))) - (4*x^4)/(3*c^2*(1 + a^2*x^2)*sqrt(atan(a*x))) + (4*sqrt(pi)*FresnelS((2*sqrt(atan(a*x)))/sqrt(pi)))/(a^4*c^2) + (16/3)*Unintegrable(x^3/((c + a^2*c*x^2)^2*sqrt(atan(a*x))), x) + (8/3)*a^2*Unintegrable(x^5/((c + a^2*c*x^2)^2*sqrt(atan(a*x))), x)]
    @test_int [x^2/((c + a^2*c*x^2)^2*atan(a*x)^(5/2)), x, 8, -((2*x^2)/(3*a*c^2*(1 + a^2*x^2)*atan(a*x)^(3/2))) - (8*x)/(3*a^2*c^2*(1 + a^2*x^2)*sqrt(atan(a*x))) + (16*sqrt(atan(a*x)))/(3*a^3*c^2) - (32*sqrt(atan(a*x)))/(3*a^3*c^2*(1 + a^2*x^2)) + (16*(1 - a^2*x^2)*sqrt(atan(a*x)))/(3*a^3*c^2*(1 + a^2*x^2)) + (8*sqrt(pi)*FresnelC((2*sqrt(atan(a*x)))/sqrt(pi)))/(3*a^3*c^2)]
    @test_int [x/((c + a^2*c*x^2)^2*atan(a*x)^(5/2)), x, 6, -((2*x)/(3*a*c^2*(1 + a^2*x^2)*atan(a*x)^(3/2))) - (4*(1 - a^2*x^2))/(3*a^2*c^2*(1 + a^2*x^2)*sqrt(atan(a*x))) - (8*sqrt(pi)*FresnelS((2*sqrt(atan(a*x)))/sqrt(pi)))/(3*a^2*c^2)]
    @test_int [1/((c + a^2*c*x^2)^2*atan(a*x)^(5/2)), x, 8, -(2/(3*a*c^2*(1 + a^2*x^2)*atan(a*x)^(3/2))) + (8*x)/(3*c^2*(1 + a^2*x^2)*sqrt(atan(a*x))) - (16*sqrt(atan(a*x)))/(3*a*c^2) + (32*sqrt(atan(a*x)))/(3*a*c^2*(1 + a^2*x^2)) - (16*(1 - a^2*x^2)*sqrt(atan(a*x)))/(3*a*c^2*(1 + a^2*x^2)) - (8*sqrt(pi)*FresnelC((2*sqrt(atan(a*x)))/sqrt(pi)))/(3*a*c^2)]
    @test_int [1/(x*(c + a^2*c*x^2)^2*atan(a*x)^(5/2)), x, 8, -(2/(3*a*c^2*x*(1 + a^2*x^2)*atan(a*x)^(3/2))) + 4/(c^2*(1 + a^2*x^2)*sqrt(atan(a*x))) + 4/(3*a^2*c^2*x^2*(1 + a^2*x^2)*sqrt(atan(a*x))) + (4*sqrt(pi)*FresnelS((2*sqrt(atan(a*x)))/sqrt(pi)))/c^2 + (8*Unintegrable(1/(x^3*(c + a^2*c*x^2)^2*sqrt(atan(a*x))), x))/(3*a^2) + (16/3)*Unintegrable(1/(x*(c + a^2*c*x^2)^2*sqrt(atan(a*x))), x)]
    @test_int [1/(x^2*(c + a^2*c*x^2)^2*atan(a*x)^(5/2)), x, 8, -(2/(3*a*c^2*x^2*(1 + a^2*x^2)*atan(a*x)^(3/2))) + 8/(3*a^2*c^2*x^3*(1 + a^2*x^2)*sqrt(atan(a*x))) + 16/(3*c^2*x*(1 + a^2*x^2)*sqrt(atan(a*x))) + (16*a*sqrt(atan(a*x)))/c^2 + (8*a*sqrt(pi)*FresnelC((2*sqrt(atan(a*x)))/sqrt(pi)))/c^2 + (8*Unintegrable(1/(x^4*(c + a^2*c*x^2)^2*sqrt(atan(a*x))), x))/a^2 + (56/3)*Unintegrable(1/(x^2*(c + a^2*c*x^2)^2*sqrt(atan(a*x))), x)]
    @test_int [1/(x^3*(c + a^2*c*x^2)^2*atan(a*x)^(5/2)), x, 3, -2/(3*a*c^2*x^3*(1 + a^2*x^2)*atan(a*x)^(3/2)) + 4/(a^2*c^2*x^4*(1 + a^2*x^2)*sqrt(atan(a*x))) + 20/(3*c^2*x^2*(1 + a^2*x^2)*sqrt(atan(a*x))) + (16*Unintegrable(1/(x^5*(c + a^2*c*x^2)^2*sqrt(atan(a*x))), x))/a^2 + (112*Unintegrable(1/(x^3*(c + a^2*c*x^2)^2*sqrt(atan(a*x))), x))/3 + (80*a^2*Unintegrable(1/(x*(c + a^2*c*x^2)^2*sqrt(atan(a*x))), x))/3]
    @test_int [1/(x^4*(c + a^2*c*x^2)^2*atan(a*x)^(5/2)), x, 3, -2/(3*a*c^2*x^4*(1 + a^2*x^2)*atan(a*x)^(3/2)) + 16/(3*a^2*c^2*x^5*(1 + a^2*x^2)*sqrt(atan(a*x))) + 8/(c^2*x^3*(1 + a^2*x^2)*sqrt(atan(a*x))) + (80*Unintegrable(1/(x^6*(c + a^2*c*x^2)^2*sqrt(atan(a*x))), x))/(3*a^2) + (184*Unintegrable(1/(x^4*(c + a^2*c*x^2)^2*sqrt(atan(a*x))), x))/3 + 40*a^2*Unintegrable(1/(x^2*(c + a^2*c*x^2)^2*sqrt(atan(a*x))), x)]

    @test_int [x^m/((c + a^2*c*x^2)^3*atan(a*x)^(5/2)), x, 0, Unintegrable(x^m/((c + a^2*c*x^2)^3*atan(a*x)^(5/2)), x)]

    @test_int [x^3/((c + a^2*c*x^2)^3*atan(a*x)^(5/2)), x, 24, -((2*x^3)/(3*a*c^3*(1 + a^2*x^2)^2*atan(a*x)^(3/2))) - (4*x^2)/(a^2*c^3*(1 + a^2*x^2)^2*sqrt(atan(a*x))) + (4*x^4)/(3*c^3*(1 + a^2*x^2)^2*sqrt(atan(a*x))) + (4*sqrt(2*pi)*FresnelS(2*sqrt(2/pi)*sqrt(atan(a*x))))/(3*a^4*c^3) - (4*sqrt(pi)*FresnelS((2*sqrt(atan(a*x)))/sqrt(pi)))/(3*a^4*c^3)]
    @test_int [x^2/((c + a^2*c*x^2)^3*atan(a*x)^(5/2)), x, 27, -((2*x^2)/(3*a*c^3*(1 + a^2*x^2)^2*atan(a*x)^(3/2))) - (8*x)/(3*a^2*c^3*(1 + a^2*x^2)^2*sqrt(atan(a*x))) + (8*x^3)/(3*c^3*(1 + a^2*x^2)^2*sqrt(atan(a*x))) + (4*sqrt(2*pi)*FresnelC(2*sqrt(2/pi)*sqrt(atan(a*x))))/(3*a^3*c^3)]
    @test_int [x/((c + a^2*c*x^2)^3*atan(a*x)^(5/2)), x, 24, -((2*x)/(3*a*c^3*(1 + a^2*x^2)^2*atan(a*x)^(3/2))) - 4/(3*a^2*c^3*(1 + a^2*x^2)^2*sqrt(atan(a*x))) + (4*x^2)/(c^3*(1 + a^2*x^2)^2*sqrt(atan(a*x))) - (4*sqrt(2*pi)*FresnelS(2*sqrt(2/pi)*sqrt(atan(a*x))))/(3*a^2*c^3) - (4*sqrt(pi)*FresnelS((2*sqrt(atan(a*x)))/sqrt(pi)))/(3*a^2*c^3)]
    @test_int [1/((c + a^2*c*x^2)^3*atan(a*x)^(5/2)), x, 14, -(2/(3*a*c^3*(1 + a^2*x^2)^2*atan(a*x)^(3/2))) + (16*x)/(3*c^3*(1 + a^2*x^2)^2*sqrt(atan(a*x))) - (4*sqrt(2*pi)*FresnelC(2*sqrt(2/pi)*sqrt(atan(a*x))))/(3*a*c^3) - (8*sqrt(pi)*FresnelC((2*sqrt(atan(a*x)))/sqrt(pi)))/(3*a*c^3)]
    @test_int [1/(x*(c + a^2*c*x^2)^3*atan(a*x)^(5/2)), x, 10, -(2/(3*a*c^3*x*(1 + a^2*x^2)^2*atan(a*x)^(3/2))) + 20/(3*c^3*(1 + a^2*x^2)^2*sqrt(atan(a*x))) + 4/(3*a^2*c^3*x^2*(1 + a^2*x^2)^2*sqrt(atan(a*x))) + (5*sqrt(2*pi)*FresnelS(2*sqrt(2/pi)*sqrt(atan(a*x))))/(3*c^3) + (20*sqrt(pi)*FresnelS((2*sqrt(atan(a*x)))/sqrt(pi)))/(3*c^3) + (8*Unintegrable(1/(x^3*(c + a^2*c*x^2)^3*sqrt(atan(a*x))), x))/(3*a^2) + 8*Unintegrable(1/(x*(c + a^2*c*x^2)^3*sqrt(atan(a*x))), x)]
    @test_int [1/(x^2*(c + a^2*c*x^2)^3*atan(a*x)^(5/2)), x, 10, -(2/(3*a*c^3*x^2*(1 + a^2*x^2)^2*atan(a*x)^(3/2))) + 8/(3*a^2*c^3*x^3*(1 + a^2*x^2)^2*sqrt(atan(a*x))) + 8/(c^3*x*(1 + a^2*x^2)^2*sqrt(atan(a*x))) + (30*a*sqrt(atan(a*x)))/c^3 + (5*a*sqrt(pi/2)*FresnelC(2*sqrt(2/pi)*sqrt(atan(a*x))))/c^3 + (20*a*sqrt(pi)*FresnelC((2*sqrt(atan(a*x)))/sqrt(pi)))/c^3 + (8*Unintegrable(1/(x^4*(c + a^2*c*x^2)^3*sqrt(atan(a*x))), x))/a^2 + (80/3)*Unintegrable(1/(x^2*(c + a^2*c*x^2)^3*sqrt(atan(a*x))), x)]
    @test_int [1/(x^3*(c + a^2*c*x^2)^3*atan(a*x)^(5/2)), x, 3, -2/(3*a*c^3*x^3*(1 + a^2*x^2)^2*atan(a*x)^(3/2)) + 4/(a^2*c^3*x^4*(1 + a^2*x^2)^2*sqrt(atan(a*x))) + 28/(3*c^3*x^2*(1 + a^2*x^2)^2*sqrt(atan(a*x))) + (16*Unintegrable(1/(x^5*(c + a^2*c*x^2)^3*sqrt(atan(a*x))), x))/a^2 + (152*Unintegrable(1/(x^3*(c + a^2*c*x^2)^3*sqrt(atan(a*x))), x))/3 + 56*a^2*Unintegrable(1/(x*(c + a^2*c*x^2)^3*sqrt(atan(a*x))), x)]
    @test_int [1/(x^4*(c + a^2*c*x^2)^3*atan(a*x)^(5/2)), x, 3, -2/(3*a*c^3*x^4*(1 + a^2*x^2)^2*atan(a*x)^(3/2)) + 16/(3*a^2*c^3*x^5*(1 + a^2*x^2)^2*sqrt(atan(a*x))) + 32/(3*c^3*x^3*(1 + a^2*x^2)^2*sqrt(atan(a*x))) + (80*Unintegrable(1/(x^6*(c + a^2*c*x^2)^3*sqrt(atan(a*x))), x))/(3*a^2) + 80*Unintegrable(1/(x^4*(c + a^2*c*x^2)^3*sqrt(atan(a*x))), x) + (224*a^2*Unintegrable(1/(x^2*(c + a^2*c*x^2)^3*sqrt(atan(a*x))), x))/3]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x^2)^(p/2) / atan(a*x)^(5/2)*with*d=a^2*c=#

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

    @test_int [(x^m*sqrt(c + a^2*c*x^2))/atan(a*x)^(5/2), x, 0, Unintegrable((x^m*sqrt(c + a^2*c*x^2))/atan(a*x)^(5/2), x)]

    @test_int [(x*sqrt(c + a^2*c*x^2))/atan(a*x)^(5/2), x, 0, Unintegrable((x*sqrt(c + a^2*c*x^2))/atan(a*x)^(5/2), x)]
    @test_int [sqrt(c + a^2*c*x^2)/atan(a*x)^(5/2), x, 0, Unintegrable(sqrt(c + a^2*c*x^2)/atan(a*x)^(5/2), x)]
    @test_int [sqrt(c + a^2*c*x^2)/(x*atan(a*x)^(5/2)), x, 0, Unintegrable(sqrt(c + a^2*c*x^2)/(x*atan(a*x)^(5/2)), x)]

    @test_int [(x^m*(c + a^2*c*x^2)^(3/2))/atan(a*x)^(5/2), x, 0, Unintegrable((x^m*(c + a^2*c*x^2)^(3/2))/atan(a*x)^(5/2), x)]

    @test_int [(x*(c + a^2*c*x^2)^(3/2))/atan(a*x)^(5/2), x, 0, Unintegrable((x*(c + a^2*c*x^2)^(3/2))/atan(a*x)^(5/2), x)]
    @test_int [(c + a^2*c*x^2)^(3/2)/atan(a*x)^(5/2), x, 0, Unintegrable((c + a^2*c*x^2)^(3/2)/atan(a*x)^(5/2), x)]
    @test_int [(c + a^2*c*x^2)^(3/2)/(x*atan(a*x)^(5/2)), x, 0, Unintegrable((c + a^2*c*x^2)^(3/2)/(x*atan(a*x)^(5/2)), x)]

    @test_int [(x^m*(c + a^2*c*x^2)^(5/2))/atan(a*x)^(5/2), x, 0, Unintegrable((x^m*(c + a^2*c*x^2)^(5/2))/atan(a*x)^(5/2), x)]

    @test_int [(x*(c + a^2*c*x^2)^(5/2))/atan(a*x)^(5/2), x, 0, Unintegrable((x*(c + a^2*c*x^2)^(5/2))/atan(a*x)^(5/2), x)]
    @test_int [(c + a^2*c*x^2)^(5/2)/atan(a*x)^(5/2), x, 0, Unintegrable((c + a^2*c*x^2)^(5/2)/atan(a*x)^(5/2), x)]
    @test_int [(c + a^2*c*x^2)^(5/2)/(x*atan(a*x)^(5/2)), x, 0, Unintegrable((c + a^2*c*x^2)^(5/2)/(x*atan(a*x)^(5/2)), x)]

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

    @test_int [x^m/(sqrt(c + a^2*c*x^2)*atan(a*x)^(5/2)), x, 0, Unintegrable(x^m/(sqrt(c + a^2*c*x^2)*atan(a*x)^(5/2)), x)]

    @test_int [x/(sqrt(c + a^2*c*x^2)*atan(a*x)^(5/2)), x, 0, Unintegrable(x/(sqrt(c + a^2*c*x^2)*atan(a*x)^(5/2)), x)]
    @test_int [1/(sqrt(c + a^2*c*x^2)*atan(a*x)^(5/2)), x, 0, Unintegrable(1/(sqrt(c + a^2*c*x^2)*atan(a*x)^(5/2)), x)]
    @test_int [1/(x*sqrt(c + a^2*c*x^2)*atan(a*x)^(5/2)), x, 1, -((2*sqrt(c + a^2*c*x^2))/(3*a*c*x*atan(a*x)^(3/2))) - (2*Unintegrable(1/(x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2)), x))/(3*a)]
    @test_int [1/(x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^(5/2)), x, 0, Unintegrable(1/(x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^(5/2)), x)]

    @test_int [x^m/((c + a^2*c*x^2)^(3/2)*atan(a*x)^(5/2)), x, 0, Unintegrable(x^m/((c + a^2*c*x^2)^(3/2)*atan(a*x)^(5/2)), x)]

    @test_int [x^3/((c + a^2*c*x^2)^(3/2)*atan(a*x)^(5/2)), x, 7, -((2*x^3)/(3*a*c*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2))) - (4*x^2)/(a^2*c*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))) - (8*x^4)/(3*c*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))) + (8*sqrt(2*pi)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(2/pi)*sqrt(atan(a*x))))/(a^4*c*sqrt(c + a^2*c*x^2)) + (44/3)*Unintegrable(x^3/((c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x) + 8*a^2*Unintegrable(x^5/((c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x)]
    @test_int [x^2/((c + a^2*c*x^2)^(3/2)*atan(a*x)^(5/2)), x, 7, -((2*x^2)/(3*a*c*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2))) - (8*x)/(3*a^2*c*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))) - (4*x^3)/(3*c*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))) + (8*sqrt(2*pi)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(2/pi)*sqrt(atan(a*x))))/(3*a^3*c*sqrt(c + a^2*c*x^2)) + 4*Unintegrable(x^2/((c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x) + (8/3)*a^2*Unintegrable(x^4/((c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x)]
    @test_int [x/((c + a^2*c*x^2)^(3/2)*atan(a*x)^(5/2)), x, 6, -((2*x)/(3*a*c*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2))) - 4/(3*a^2*c*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))) - (4*sqrt(2*pi)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(2/pi)*sqrt(atan(a*x))))/(3*a^2*c*sqrt(c + a^2*c*x^2))]
    @test_int [1/((c + a^2*c*x^2)^(3/2)*atan(a*x)^(5/2)), x, 6, -(2/(3*a*c*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2))) + (4*x)/(3*c*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))) - (4*sqrt(2*pi)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(2/pi)*sqrt(atan(a*x))))/(3*a*c*sqrt(c + a^2*c*x^2))]
    @test_int [1/(x*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(5/2)), x, 7, -(2/(3*a*c*x*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2))) + 8/(3*c*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))) + 4/(3*a^2*c*x^2*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))) + (8*sqrt(2*pi)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(2/pi)*sqrt(atan(a*x))))/(3*c*sqrt(c + a^2*c*x^2)) + (8*Unintegrable(1/(x^3*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x))/(3*a^2) + 4*Unintegrable(1/(x*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x)]
    @test_int [1/(x^2*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(5/2)), x, 7, -(2/(3*a*c*x^2*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2))) + 8/(3*a^2*c*x^3*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))) + 4/(c*x*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))) + (8*a*sqrt(2*pi)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(2/pi)*sqrt(atan(a*x))))/(c*sqrt(c + a^2*c*x^2)) + (8*Unintegrable(1/(x^4*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x))/a^2 + (44/3)*Unintegrable(1/(x^2*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x)]
    @test_int [1/(x^3*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(5/2)), x, 3, -2/(3*a*c*x^3*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2)) + 4/(a^2*c*x^4*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))) + 16/(3*c*x^2*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))) + (16*Unintegrable(1/(x^5*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x))/a^2 + (92*Unintegrable(1/(x^3*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x))/3 + 16*a^2*Unintegrable(1/(x*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x)]
    @test_int [1/(x^4*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(5/2)), x, 3, -2/(3*a*c*x^4*sqrt(c + a^2*c*x^2)*atan(a*x)^(3/2)) + 16/(3*a^2*c*x^5*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))) + 20/(3*c*x^3*sqrt(c + a^2*c*x^2)*sqrt(atan(a*x))) + (80*Unintegrable(1/(x^6*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x))/(3*a^2) + 52*Unintegrable(1/(x^4*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x) + (80*a^2*Unintegrable(1/(x^2*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))), x))/3]

    @test_int [x^m/((c + a^2*c*x^2)^(5/2)*atan(a*x)^(5/2)), x, 0, Unintegrable(x^m/((c + a^2*c*x^2)^(5/2)*atan(a*x)^(5/2)), x)]

    @test_int [x^3/((c + a^2*c*x^2)^(5/2)*atan(a*x)^(5/2)), x, 18, -((2*x^3)/(3*a*c*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2))) - (4*x^2)/(a^2*c*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))) - (sqrt(2*pi)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(2/pi)*sqrt(atan(a*x))))/(a^4*c^2*sqrt(c + a^2*c*x^2)) + (sqrt(6*pi)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(6/pi)*sqrt(atan(a*x))))/(a^4*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [x^2/((c + a^2*c*x^2)^(5/2)*atan(a*x)^(5/2)), x, 27, -((2*x^2)/(3*a*c*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2))) - (8*x)/(3*a^2*c*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))) + (4*x^3)/(3*c*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))) - (sqrt(2*pi)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(2/pi)*sqrt(atan(a*x))))/(3*a^3*c^2*sqrt(c + a^2*c*x^2)) + (sqrt(6*pi)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(6/pi)*sqrt(atan(a*x))))/(a^3*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [x/((c + a^2*c*x^2)^(5/2)*atan(a*x)^(5/2)), x, 27, -((2*x)/(3*a*c*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2))) - 4/(3*a^2*c*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))) + (8*x^2)/(3*c*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))) - (sqrt(2*pi)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(2/pi)*sqrt(atan(a*x))))/(3*a^2*c^2*sqrt(c + a^2*c*x^2)) - (sqrt(6*pi)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(6/pi)*sqrt(atan(a*x))))/(a^2*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [1/((c + a^2*c*x^2)^(5/2)*atan(a*x)^(5/2)), x, 18, -(2/(3*a*c*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2))) + (4*x)/(c*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))) - (sqrt(2*pi)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(2/pi)*sqrt(atan(a*x))))/(a*c^2*sqrt(c + a^2*c*x^2)) - (sqrt(6*pi)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(6/pi)*sqrt(atan(a*x))))/(a*c^2*sqrt(c + a^2*c*x^2))]
    @test_int [1/(x*(c + a^2*c*x^2)^(5/2)*atan(a*x)^(5/2)), x, 11, -(2/(3*a*c*x*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2))) + 16/(3*c*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))) + 4/(3*a^2*c*x^2*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))) + (4*sqrt(2*pi)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(2/pi)*sqrt(atan(a*x))))/(c^2*sqrt(c + a^2*c*x^2)) + (4*sqrt((2*pi)/3)*sqrt(1 + a^2*x^2)*FresnelS(sqrt(6/pi)*sqrt(atan(a*x))))/(c^2*sqrt(c + a^2*c*x^2)) + (8*Unintegrable(1/(x^3*(c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x))), x))/(3*a^2) + (20/3)*Unintegrable(1/(x*(c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x))), x)]
    @test_int [1/(x^2*(c + a^2*c*x^2)^(5/2)*atan(a*x)^(5/2)), x, 11, -(2/(3*a*c*x^2*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2))) + 8/(3*a^2*c*x^3*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))) + 20/(3*c*x*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))) + (20*a*sqrt(2*pi)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(2/pi)*sqrt(atan(a*x))))/(c^2*sqrt(c + a^2*c*x^2)) + (20*a*sqrt((2*pi)/3)*sqrt(1 + a^2*x^2)*FresnelC(sqrt(6/pi)*sqrt(atan(a*x))))/(3*c^2*sqrt(c + a^2*c*x^2)) + (8*Unintegrable(1/(x^4*(c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x))), x))/a^2 + (68/3)*Unintegrable(1/(x^2*(c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x))), x)]
    @test_int [1/(x^3*(c + a^2*c*x^2)^(5/2)*atan(a*x)^(5/2)), x, 3, -2/(3*a*c*x^3*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2)) + 4/(a^2*c*x^4*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))) + 8/(c*x^2*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))) + (16*Unintegrable(1/(x^5*(c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x))), x))/a^2 + 44*Unintegrable(1/(x^3*(c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x))), x) + 40*a^2*Unintegrable(1/(x*(c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x))), x)]
    @test_int [1/(x^4*(c + a^2*c*x^2)^(5/2)*atan(a*x)^(5/2)), x, 3, -2/(3*a*c*x^4*(c + a^2*c*x^2)^(3/2)*atan(a*x)^(3/2)) + 16/(3*a^2*c*x^5*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))) + 28/(3*c*x^3*(c + a^2*c*x^2)^(3/2)*sqrt(atan(a*x))) + (80*Unintegrable(1/(x^6*(c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x))), x))/(3*a^2) + (212*Unintegrable(1/(x^4*(c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x))), x))/3 + 56*a^2*Unintegrable(1/(x^2*(c + a^2*c*x^2)^(5/2)*sqrt(atan(a*x))), x)]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d+c^2*d*x^2)^q*(a+b*atan(c*x))^p*with*p*symbolic=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d+c^2*d*x^2)^q*(a+b*atan(c*x))^p*with*p*symbolic=#

    @test_int [x^1*atan(a*x)^n/(c + a^2*c*x^2), x, 1, (x*atan(a*x)^(1 + n))/(a*c*(1 + n)) - Unintegrable(atan(a*x)^(1 + n), x)/(a*c*(1 + n))]
    @test_int [x^0*atan(a*x)^n/(c + a^2*c*x^2), x, 1, atan(a*x)^(1 + n)/(a*c*(1 + n))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d+c^2*d*x^2)^q*(a+b*atan(c*x))^p*with*p*and*q*symbolic=#

    @test_int [(f*x)^m*(d + c^2*d*x^2)^q*(a + b*atan(c*x))^p, x, 0, Unintegrable((f*x)^m*(d + c^2*d*x^2)^q*(a + b*atan(c*x))^p, x)]

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

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d+e*x^2)^p*(a+b*atan(c*x))^1=#

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

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

    @test_int [x^3*(a + b*atan(c*x))*(d + e*x^2), x, 5, (b*(3*c^2*d - 2*e)*x)/(12*c^5) - (b*(3*c^2*d - 2*e)*x^3)/(36*c^3) - (b*e*x^5)/(30*c) - (b*(3*c^2*d - 2*e)*atan(c*x))/(12*c^6) + (1/4)*d*x^4*(a + b*atan(c*x)) + (1/6)*e*x^6*(a + b*atan(c*x))]
    @test_int [x^2*(a + b*atan(c*x))*(d + e*x^2), x, 4, -((b*(5*c^2*d - 3*e)*x^2)/(30*c^3)) - (b*e*x^4)/(20*c) + (1/3)*d*x^3*(a + b*atan(c*x)) + (1/5)*e*x^5*(a + b*atan(c*x)) + (b*(5*c^2*d - 3*e)*log(1 + c^2*x^2))/(30*c^5)]
    @test_int [x^1*(a + b*atan(c*x))*(d + e*x^2), x, 4, -((b*(2*c^2*d - e)*x)/(4*c^3)) - (b*e*x^3)/(12*c) - (b*(c^2*d - e)^2*atan(c*x))/(4*c^4*e) + ((d + e*x^2)^2*(a + b*atan(c*x)))/(4*e)]
    @test_int [x^0*(a + b*atan(c*x))*(d + e*x^2), x, 5, -((b*e*x^2)/(6*c)) + d*x*(a + b*atan(c*x)) + (1/3)*e*x^3*(a + b*atan(c*x)) - (b*(3*c^2*d - e)*log(1 + c^2*x^2))/(6*c^3)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)/x^1, x, 8, -((b*e*x)/(2*c)) + (b*e*atan(c*x))/(2*c^2) + (1/2)*e*x^2*(a + b*atan(c*x)) + a*d*log(x) + (1/2)*im*b*d*PolyLog(2, (-im)*c*x) - (1/2)*im*b*d*PolyLog(2, im*c*x)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)/x^2, x, 4, -((d*(a + b*atan(c*x)))/x) + e*x*(a + b*atan(c*x)) + b*c*d*log(x) - (b*(c^2*d + e)*log(1 + c^2*x^2))/(2*c)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)/x^3, x, 8, -((b*c*d)/(2*x)) - (1/2)*b*c^2*d*atan(c*x) - (d*(a + b*atan(c*x)))/(2*x^2) + a*e*log(x) + (1/2)*im*b*e*PolyLog(2, (-im)*c*x) - (1/2)*im*b*e*PolyLog(2, im*c*x)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)/x^4, x, 5, -((b*c*d)/(6*x^2)) - (d*(a + b*atan(c*x)))/(3*x^3) - (e*(a + b*atan(c*x)))/x - (1/3)*b*c*(c^2*d - 3*e)*log(x) + (1/6)*b*c*(c^2*d - 3*e)*log(1 + c^2*x^2)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)/x^5, x, 5, -((b*c*d)/(12*x^3)) + (b*c*(c^2*d - 2*e))/(4*x) + (1/4)*b*c^2*(c^2*d - 2*e)*atan(c*x) - (d*(a + b*atan(c*x)))/(4*x^4) - (e*(a + b*atan(c*x)))/(2*x^2)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)/x^6, x, 5, -((b*c*d)/(20*x^4)) + (b*c*(3*c^2*d - 5*e))/(30*x^2) - (d*(a + b*atan(c*x)))/(5*x^5) - (e*(a + b*atan(c*x)))/(3*x^3) + (1/15)*b*c^3*(3*c^2*d - 5*e)*log(x) - (1/30)*b*c^3*(3*c^2*d - 5*e)*log(1 + c^2*x^2)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)/x^7, x, 6, -((b*c*d)/(30*x^5)) + (b*c*(2*c^2*d - 3*e))/(36*x^3) - (b*c^3*(2*c^2*d - 3*e))/(12*x) - (1/12)*b*c^4*(2*c^2*d - 3*e)*atan(c*x) - (d*(a + b*atan(c*x)))/(6*x^6) - (e*(a + b*atan(c*x)))/(4*x^4)]

    @test_int [x^3*(a + b*atan(c*x))*(d + e*x^2)^2, x, 4, (b*(6*c^4*d^2 - 8*c^2*d*e + 3*e^2)*x)/(24*c^7) - (b*(6*c^4*d^2 - 8*c^2*d*e + 3*e^2)*x^3)/(72*c^5) - (b*(8*c^2*d - 3*e)*e*x^5)/(120*c^3) - (b*e^2*x^7)/(56*c) - (b*(6*c^4*d^2 - 8*c^2*d*e + 3*e^2)*atan(c*x))/(24*c^8) + (1/4)*d^2*x^4*(a + b*atan(c*x)) + (1/3)*d*e*x^6*(a + b*atan(c*x)) + (1/8)*e^2*x^8*(a + b*atan(c*x))]
    @test_int [x^2*(a + b*atan(c*x))*(d + e*x^2)^2, x, 5, -((b*(35*c^4*d^2 - 42*c^2*d*e + 15*e^2)*x^2)/(210*c^5)) - (b*(14*c^2*d - 5*e)*e*x^4)/(140*c^3) - (b*e^2*x^6)/(42*c) + (1/3)*d^2*x^3*(a + b*atan(c*x)) + (2/5)*d*e*x^5*(a + b*atan(c*x)) + (1/7)*e^2*x^7*(a + b*atan(c*x)) + (b*(35*c^4*d^2 - 42*c^2*d*e + 15*e^2)*log(1 + c^2*x^2))/(210*c^7)]
    @test_int [x^1*(a + b*atan(c*x))*(d + e*x^2)^2, x, 4, -((b*(3*c^4*d^2 - 3*c^2*d*e + e^2)*x)/(6*c^5)) - (b*(3*c^2*d - e)*e*x^3)/(18*c^3) - (b*e^2*x^5)/(30*c) - (b*(c^2*d - e)^3*atan(c*x))/(6*c^6*e) + ((d + e*x^2)^3*(a + b*atan(c*x)))/(6*e)]
    @test_int [x^0*(a + b*atan(c*x))*(d + e*x^2)^2, x, 5, -((b*(10*c^2*d - 3*e)*e*x^2)/(30*c^3)) - (b*e^2*x^4)/(20*c) + d^2*x*(a + b*atan(c*x)) + (2/3)*d*e*x^3*(a + b*atan(c*x)) + (1/5)*e^2*x^5*(a + b*atan(c*x)) - (b*(15*c^4*d^2 - 10*c^2*d*e + 3*e^2)*log(1 + c^2*x^2))/(30*c^5)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^2/x^1, x, 12, -((b*d*e*x)/c) + (b*e^2*x)/(4*c^3) - (b*e^2*x^3)/(12*c) + (b*d*e*atan(c*x))/c^2 - (b*e^2*atan(c*x))/(4*c^4) + d*e*x^2*(a + b*atan(c*x)) + (1/4)*e^2*x^4*(a + b*atan(c*x)) + a*d^2*log(x) + (1/2)*im*b*d^2*PolyLog(2, (-im)*c*x) - (1/2)*im*b*d^2*PolyLog(2, im*c*x)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^2/x^2, x, 4, -((b*e^2*x^2)/(6*c)) - (d^2*(a + b*atan(c*x)))/x + 2*d*e*x*(a + b*atan(c*x)) + (1/3)*e^2*x^3*(a + b*atan(c*x)) + b*c*d^2*log(x) - (b*(3*c^4*d^2 + 6*c^2*d*e - e^2)*log(1 + c^2*x^2))/(6*c^3)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^2/x^3, x, 11, -((b*c*d^2)/(2*x)) - (b*e^2*x)/(2*c) - (1/2)*b*c^2*d^2*atan(c*x) + (b*e^2*atan(c*x))/(2*c^2) - (d^2*(a + b*atan(c*x)))/(2*x^2) + (1/2)*e^2*x^2*(a + b*atan(c*x)) + 2*a*d*e*log(x) + im*b*d*e*PolyLog(2, (-im)*c*x) - im*b*d*e*PolyLog(2, im*c*x)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^2/x^4, x, 5, -((b*c*d^2)/(6*x^2)) - (d^2*(a + b*atan(c*x)))/(3*x^3) - (2*d*e*(a + b*atan(c*x)))/x + e^2*x*(a + b*atan(c*x)) - (1/3)*b*c*d*(c^2*d - 6*e)*log(x) + (b*(c^4*d^2 - 6*c^2*d*e - 3*e^2)*log(1 + c^2*x^2))/(6*c)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^2/x^5, x, 12, -((b*c*d^2)/(12*x^3)) + (b*c^3*d^2)/(4*x) - (b*c*d*e)/x + (1/4)*b*c^4*d^2*atan(c*x) - b*c^2*d*e*atan(c*x) - (d^2*(a + b*atan(c*x)))/(4*x^4) - (d*e*(a + b*atan(c*x)))/x^2 + a*e^2*log(x) + (1/2)*im*b*e^2*PolyLog(2, (-im)*c*x) - (1/2)*im*b*e^2*PolyLog(2, im*c*x)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^2/x^6, x, 5, -((b*c*d^2)/(20*x^4)) + (b*c*d*(3*c^2*d - 10*e))/(30*x^2) - (d^2*(a + b*atan(c*x)))/(5*x^5) - (2*d*e*(a + b*atan(c*x)))/(3*x^3) - (e^2*(a + b*atan(c*x)))/x + (1/15)*b*c*(3*c^4*d^2 - 10*c^2*d*e + 15*e^2)*log(x) - (1/30)*b*c*(3*c^4*d^2 - 10*c^2*d*e + 15*e^2)*log(1 + c^2*x^2)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^2/x^7, x, 5, -((b*c*d^2)/(30*x^5)) + (b*c*d*(c^2*d - 3*e))/(18*x^3) - (b*c*(c^4*d^2 - 3*c^2*d*e + 3*e^2))/(6*x) - (b*(c^2*d - e)^3*atan(c*x))/(6*d) - ((d + e*x^2)^3*(a + b*atan(c*x)))/(6*d*x^6)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^2/x^8, x, 5, -((b*c*d^2)/(42*x^6)) + (b*c*d*(5*c^2*d - 14*e))/(140*x^4) - (b*c*(15*c^4*d^2 - 42*c^2*d*e + 35*e^2))/(210*x^2) - (d^2*(a + b*atan(c*x)))/(7*x^7) - (2*d*e*(a + b*atan(c*x)))/(5*x^5) - (e^2*(a + b*atan(c*x)))/(3*x^3) - (1/105)*b*c^3*(15*c^4*d^2 - 42*c^2*d*e + 35*e^2)*log(x) + (1/210)*b*c^3*(15*c^4*d^2 - 42*c^2*d*e + 35*e^2)*log(1 + c^2*x^2)]

    @test_int [x^3*(a + b*atan(c*x))*(d + e*x^2)^3, x, -8, (b*(10*c^6*d^3 - 20*c^4*d^2*e + 15*c^2*d*e^2 - 4*e^3)*x)/(40*c^9) - (b*(10*c^6*d^3 - 20*c^4*d^2*e + 15*c^2*d*e^2 - 4*e^3)*x^3)/(120*c^7) - (b*e*(20*c^4*d^2 - 15*c^2*d*e + 4*e^2)*x^5)/(200*c^5) - (b*(15*c^2*d - 4*e)*e^2*x^7)/(280*c^3) - (b*e^3*x^9)/(90*c) + (b*(c^2*d - e)^4*(c^2*d + 4*e)*atan(c*x))/(40*c^10*e^2) - (d*(d + e*x^2)^4*(a + b*atan(c*x)))/(8*e^2) + ((d + e*x^2)^5*(a + b*atan(c*x)))/(10*e^2)]
    @test_int [x^2*(a + b*atan(c*x))*(d + e*x^2)^3, x, 5, -((b*(105*c^6*d^3 - 189*c^4*d^2*e + 135*c^2*d*e^2 - 35*e^3)*x^2)/(630*c^7)) - (b*e*(189*c^4*d^2 - 135*c^2*d*e + 35*e^2)*x^4)/(1260*c^5) - (b*(27*c^2*d - 7*e)*e^2*x^6)/(378*c^3) - (b*e^3*x^8)/(72*c) + (1/3)*d^3*x^3*(a + b*atan(c*x)) + (3/5)*d^2*e*x^5*(a + b*atan(c*x)) + (3/7)*d*e^2*x^7*(a + b*atan(c*x)) + (1/9)*e^3*x^9*(a + b*atan(c*x)) + (b*(105*c^6*d^3 - 189*c^4*d^2*e + 135*c^2*d*e^2 - 35*e^3)*log(1 + c^2*x^2))/(630*c^9)]
    @test_int [x^1*(a + b*atan(c*x))*(d + e*x^2)^3, x, 4, -((b*(2*c^2*d - e)*(2*c^4*d^2 - 2*c^2*d*e + e^2)*x)/(8*c^7)) - (b*e*(6*c^4*d^2 - 4*c^2*d*e + e^2)*x^3)/(24*c^5) - (b*(4*c^2*d - e)*e^2*x^5)/(40*c^3) - (b*e^3*x^7)/(56*c) - (b*(c^2*d - e)^4*atan(c*x))/(8*c^8*e) + ((d + e*x^2)^4*(a + b*atan(c*x)))/(8*e)]
    @test_int [x^0*(a + b*atan(c*x))*(d + e*x^2)^3, x, 4, -((b*e*(35*c^4*d^2 - 21*c^2*d*e + 5*e^2)*x^2)/(70*c^5)) - (b*(21*c^2*d - 5*e)*e^2*x^4)/(140*c^3) - (b*e^3*x^6)/(42*c) + d^3*x*(a + b*atan(c*x)) + d^2*e*x^3*(a + b*atan(c*x)) + (3/5)*d*e^2*x^5*(a + b*atan(c*x)) + (1/7)*e^3*x^7*(a + b*atan(c*x)) - (b*(35*c^6*d^3 - 35*c^4*d^2*e + 21*c^2*d*e^2 - 5*e^3)*log(1 + c^2*x^2))/(70*c^7)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^3/x^1, x, 16, -((3*b*d^2*e*x)/(2*c)) + (3*b*d*e^2*x)/(4*c^3) - (b*e^3*x)/(6*c^5) - (b*d*e^2*x^3)/(4*c) + (b*e^3*x^3)/(18*c^3) - (b*e^3*x^5)/(30*c) + (3*b*d^2*e*atan(c*x))/(2*c^2) - (3*b*d*e^2*atan(c*x))/(4*c^4) + (b*e^3*atan(c*x))/(6*c^6) + (3/2)*d^2*e*x^2*(a + b*atan(c*x)) + (3/4)*d*e^2*x^4*(a + b*atan(c*x)) + (1/6)*e^3*x^6*(a + b*atan(c*x)) + a*d^3*log(x) + (1/2)*im*b*d^3*PolyLog(2, (-im)*c*x) - (1/2)*im*b*d^3*PolyLog(2, im*c*x)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^3/x^2, x, 4, -((b*(5*c^2*d - e)*e^2*x^2)/(10*c^3)) - (b*e^3*x^4)/(20*c) - (d^3*(a + b*atan(c*x)))/x + 3*d^2*e*x*(a + b*atan(c*x)) + d*e^2*x^3*(a + b*atan(c*x)) + (1/5)*e^3*x^5*(a + b*atan(c*x)) + b*c*d^3*log(x) - (b*(5*c^6*d^3 + 15*c^4*d^2*e - 5*c^2*d*e^2 + e^3)*log(1 + c^2*x^2))/(10*c^5)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^3/x^3, x, 15, -((b*c*d^3)/(2*x)) - (3*b*d*e^2*x)/(2*c) + (b*e^3*x)/(4*c^3) - (b*e^3*x^3)/(12*c) - (1/2)*b*c^2*d^3*atan(c*x) + (3*b*d*e^2*atan(c*x))/(2*c^2) - (b*e^3*atan(c*x))/(4*c^4) - (d^3*(a + b*atan(c*x)))/(2*x^2) + (3/2)*d*e^2*x^2*(a + b*atan(c*x)) + (1/4)*e^3*x^4*(a + b*atan(c*x)) + 3*a*d^2*e*log(x) + (3/2)*im*b*d^2*e*PolyLog(2, (-im)*c*x) - (3/2)*im*b*d^2*e*PolyLog(2, im*c*x)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^3/x^4, x, 5, -((b*c*d^3)/(6*x^2)) - (b*e^3*x^2)/(6*c) - (d^3*(a + b*atan(c*x)))/(3*x^3) - (3*d^2*e*(a + b*atan(c*x)))/x + 3*d*e^2*x*(a + b*atan(c*x)) + (1/3)*e^3*x^3*(a + b*atan(c*x)) - (1/3)*b*c*d^2*(c^2*d - 9*e)*log(x) + (b*(c^2*d + e)*(c^4*d^2 - 10*c^2*d*e + e^2)*log(1 + c^2*x^2))/(6*c^3)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^3/x^5, x, 15, -((b*c*d^3)/(12*x^3)) + (b*c^3*d^3)/(4*x) - (3*b*c*d^2*e)/(2*x) - (b*e^3*x)/(2*c) + (1/4)*b*c^4*d^3*atan(c*x) - (3/2)*b*c^2*d^2*e*atan(c*x) + (b*e^3*atan(c*x))/(2*c^2) - (d^3*(a + b*atan(c*x)))/(4*x^4) - (3*d^2*e*(a + b*atan(c*x)))/(2*x^2) + (1/2)*e^3*x^2*(a + b*atan(c*x)) + 3*a*d*e^2*log(x) + (3/2)*im*b*d*e^2*PolyLog(2, (-im)*c*x) - (3/2)*im*b*d*e^2*PolyLog(2, im*c*x)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^3/x^6, x, 5, -((b*c*d^3)/(20*x^4)) + (b*c*d^2*(c^2*d - 5*e))/(10*x^2) - (d^3*(a + b*atan(c*x)))/(5*x^5) - (d^2*e*(a + b*atan(c*x)))/x^3 - (3*d*e^2*(a + b*atan(c*x)))/x + e^3*x*(a + b*atan(c*x)) + (1/5)*b*c*d*(c^4*d^2 - 5*c^2*d*e + 15*e^2)*log(x) - (b*(c^6*d^3 - 5*c^4*d^2*e + 15*c^2*d*e^2 + 5*e^3)*log(1 + c^2*x^2))/(10*c)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^3/x^7, x, 17, -((b*c*d^3)/(30*x^5)) + (b*c^3*d^3)/(18*x^3) - (b*c*d^2*e)/(4*x^3) - (b*c^5*d^3)/(6*x) + (3*b*c^3*d^2*e)/(4*x) - (3*b*c*d*e^2)/(2*x) - (1/6)*b*c^6*d^3*atan(c*x) + (3/4)*b*c^4*d^2*e*atan(c*x) - (3/2)*b*c^2*d*e^2*atan(c*x) - (d^3*(a + b*atan(c*x)))/(6*x^6) - (3*d^2*e*(a + b*atan(c*x)))/(4*x^4) - (3*d*e^2*(a + b*atan(c*x)))/(2*x^2) + a*e^3*log(x) + (1/2)*im*b*e^3*PolyLog(2, (-im)*c*x) - (1/2)*im*b*e^3*PolyLog(2, im*c*x)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^3/x^8, x, 5, -((b*c*d^3)/(42*x^6)) + (b*c*d^2*(5*c^2*d - 21*e))/(140*x^4) - (b*c*d*(5*c^4*d^2 - 21*c^2*d*e + 35*e^2))/(70*x^2) - (d^3*(a + b*atan(c*x)))/(7*x^7) - (3*d^2*e*(a + b*atan(c*x)))/(5*x^5) - (d*e^2*(a + b*atan(c*x)))/x^3 - (e^3*(a + b*atan(c*x)))/x - (1/35)*b*c*(5*c^6*d^3 - 21*c^4*d^2*e + 35*c^2*d*e^2 - 35*e^3)*log(x) + (1/70)*b*c*(5*c^6*d^3 - 21*c^4*d^2*e + 35*c^2*d*e^2 - 35*e^3)*log(1 + c^2*x^2)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^3/x^9, x, 5, -((b*c*d^3)/(56*x^7)) + (b*c*d^2*(c^2*d - 4*e))/(40*x^5) - (b*c*d*(c^4*d^2 - 4*c^2*d*e + 6*e^2))/(24*x^3) + (b*c*(c^2*d - 2*e)*(c^4*d^2 - 2*c^2*d*e + 2*e^2))/(8*x) + (b*(c^2*d - e)^4*atan(c*x))/(8*d) - ((d + e*x^2)^4*(a + b*atan(c*x)))/(8*d*x^8)]

    @test_int [atan(a*x)*(c + d*x^2)^4, x, 4, -((d*(420*a^6*c^3 - 378*a^4*c^2*d + 180*a^2*c*d^2 - 35*d^3)*x^2)/(630*a^7)) - (d^2*(378*a^4*c^2 - 180*a^2*c*d + 35*d^2)*x^4)/(1260*a^5) - ((36*a^2*c - 7*d)*d^3*x^6)/(378*a^3) - (d^4*x^8)/(72*a) + c^4*x*atan(a*x) + (4/3)*c^3*d*x^3*atan(a*x) + (6/5)*c^2*d^2*x^5*atan(a*x) + (4/7)*c*d^3*x^7*atan(a*x) + (1/9)*d^4*x^9*atan(a*x) - ((315*a^8*c^4 - 420*a^6*c^3*d + 378*a^4*c^2*d^2 - 180*a^2*c*d^3 + 35*d^4)*log(1 + a^2*x^2))/(630*a^9)]

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

    @test_int [x^3*(a + b*atan(c*x))/(d + e*x^2), x, 14, -((b*x)/(2*c*e)) + (b*atan(c*x))/(2*c^2*e) + (x^2*(a + b*atan(c*x)))/(2*e) + (d*(a + b*atan(c*x))*log(2/(1 - im*c*x)))/e^2 - (d*(a + b*atan(c*x))*log((2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*e^2) - (d*(a + b*atan(c*x))*log((2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*e^2) - (im*b*d*PolyLog(2, 1 - 2/(1 - im*c*x)))/(2*e^2) + (im*b*d*PolyLog(2, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*e^2) + (im*b*d*PolyLog(2, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*e^2)]
    @test_int [x^1*(a + b*atan(c*x))/(d + e*x^2), x, 10, -(((a + b*atan(c*x))*log(2/(1 - im*c*x)))/e) + ((a + b*atan(c*x))*log((2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*e) + ((a + b*atan(c*x))*log((2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*e) + (im*b*PolyLog(2, 1 - 2/(1 - im*c*x)))/(2*e) - (im*b*PolyLog(2, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*e) - (im*b*PolyLog(2, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*e)]
    @test_int [(a + b*atan(c*x))/(x^1*(d + e*x^2)), x, 15, (a*log(x))/d + ((a + b*atan(c*x))*log(2/(1 - im*c*x)))/d - ((a + b*atan(c*x))*log((2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*d) - ((a + b*atan(c*x))*log((2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*d) + (im*b*PolyLog(2, (-im)*c*x))/(2*d) - (im*b*PolyLog(2, im*c*x))/(2*d) - (im*b*PolyLog(2, 1 - 2/(1 - im*c*x)))/(2*d) + (im*b*PolyLog(2, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*d) + (im*b*PolyLog(2, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*d)]
    @test_int [(a + b*atan(c*x))/(x^3*(d + e*x^2)), x, 19, -((b*c)/(2*d*x)) - (b*c^2*atan(c*x))/(2*d) - (a + b*atan(c*x))/(2*d*x^2) - (a*e*log(x))/d^2 - (e*(a + b*atan(c*x))*log(2/(1 - im*c*x)))/d^2 + (e*(a + b*atan(c*x))*log((2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*d^2) + (e*(a + b*atan(c*x))*log((2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*d^2) - (im*b*e*PolyLog(2, (-im)*c*x))/(2*d^2) + (im*b*e*PolyLog(2, im*c*x))/(2*d^2) + (im*b*e*PolyLog(2, 1 - 2/(1 - im*c*x)))/(2*d^2) - (im*b*e*PolyLog(2, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*d^2) - (im*b*e*PolyLog(2, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*d^2)]

    @test_int [x^2*(a + b*atan(c*x))/(d + e*x^2), x, 23, (a*x)/e + (b*x*atan(c*x))/e - (a*sqrt(d)*atan((sqrt(e)*x)/sqrt(d)))/e^(3/2) - (im*b*sqrt(-d)*log(1 + im*c*x)*log((c*(sqrt(-d) - sqrt(e)*x))/(c*sqrt(-d) - im*sqrt(e))))/(4*e^(3/2)) + (im*b*sqrt(-d)*log(1 - im*c*x)*log((c*(sqrt(-d) - sqrt(e)*x))/(c*sqrt(-d) + im*sqrt(e))))/(4*e^(3/2)) - (im*b*sqrt(-d)*log(1 - im*c*x)*log((c*(sqrt(-d) + sqrt(e)*x))/(c*sqrt(-d) - im*sqrt(e))))/(4*e^(3/2)) + (im*b*sqrt(-d)*log(1 + im*c*x)*log((c*(sqrt(-d) + sqrt(e)*x))/(c*sqrt(-d) + im*sqrt(e))))/(4*e^(3/2)) - (b*log(1 + c^2*x^2))/(2*c*e) + (im*b*sqrt(-d)*PolyLog(2, (sqrt(e)*(im - c*x))/(c*sqrt(-d) + im*sqrt(e))))/(4*e^(3/2)) - (im*b*sqrt(-d)*PolyLog(2, (sqrt(e)*(1 - im*c*x))/(im*c*sqrt(-d) + sqrt(e))))/(4*e^(3/2)) - (im*b*sqrt(-d)*PolyLog(2, (sqrt(e)*(1 + im*c*x))/(im*c*sqrt(-d) + sqrt(e))))/(4*e^(3/2)) + (im*b*sqrt(-d)*PolyLog(2, (sqrt(e)*(im + c*x))/(c*sqrt(-d) + im*sqrt(e))))/(4*e^(3/2))]
    @test_int [x^0*(a + b*atan(c*x))/(d + e*x^2), x, 19, (a*atan((sqrt(e)*x)/sqrt(d)))/(sqrt(d)*sqrt(e)) - (im*b*log(1 + im*c*x)*log((c*(sqrt(-d) - sqrt(e)*x))/(c*sqrt(-d) - im*sqrt(e))))/(4*sqrt(-d)*sqrt(e)) + (im*b*log(1 - im*c*x)*log((c*(sqrt(-d) - sqrt(e)*x))/(c*sqrt(-d) + im*sqrt(e))))/(4*sqrt(-d)*sqrt(e)) - (im*b*log(1 - im*c*x)*log((c*(sqrt(-d) + sqrt(e)*x))/(c*sqrt(-d) - im*sqrt(e))))/(4*sqrt(-d)*sqrt(e)) + (im*b*log(1 + im*c*x)*log((c*(sqrt(-d) + sqrt(e)*x))/(c*sqrt(-d) + im*sqrt(e))))/(4*sqrt(-d)*sqrt(e)) + (im*b*PolyLog(2, (sqrt(e)*(im - c*x))/(c*sqrt(-d) + im*sqrt(e))))/(4*sqrt(-d)*sqrt(e)) - (im*b*PolyLog(2, (sqrt(e)*(1 - im*c*x))/(im*c*sqrt(-d) + sqrt(e))))/(4*sqrt(-d)*sqrt(e)) - (im*b*PolyLog(2, (sqrt(e)*(1 + im*c*x))/(im*c*sqrt(-d) + sqrt(e))))/(4*sqrt(-d)*sqrt(e)) + (im*b*PolyLog(2, (sqrt(e)*(im + c*x))/(c*sqrt(-d) + im*sqrt(e))))/(4*sqrt(-d)*sqrt(e))]
    @test_int [(a + b*atan(c*x))/(x^2*(d + e*x^2)), x, 25, -((a + b*atan(c*x))/(d*x)) - (a*sqrt(e)*atan((sqrt(e)*x)/sqrt(d)))/d^(3/2) + (b*c*log(x))/d - (im*b*sqrt(e)*log(1 + im*c*x)*log((c*(sqrt(-d) - sqrt(e)*x))/(c*sqrt(-d) - im*sqrt(e))))/(4*(-d)^(3/2)) + (im*b*sqrt(e)*log(1 - im*c*x)*log((c*(sqrt(-d) - sqrt(e)*x))/(c*sqrt(-d) + im*sqrt(e))))/(4*(-d)^(3/2)) - (im*b*sqrt(e)*log(1 - im*c*x)*log((c*(sqrt(-d) + sqrt(e)*x))/(c*sqrt(-d) - im*sqrt(e))))/(4*(-d)^(3/2)) + (im*b*sqrt(e)*log(1 + im*c*x)*log((c*(sqrt(-d) + sqrt(e)*x))/(c*sqrt(-d) + im*sqrt(e))))/(4*(-d)^(3/2)) - (b*c*log(1 + c^2*x^2))/(2*d) + (im*b*sqrt(e)*PolyLog(2, (sqrt(e)*(im - c*x))/(c*sqrt(-d) + im*sqrt(e))))/(4*(-d)^(3/2)) - (im*b*sqrt(e)*PolyLog(2, (sqrt(e)*(1 - im*c*x))/(im*c*sqrt(-d) + sqrt(e))))/(4*(-d)^(3/2)) - (im*b*sqrt(e)*PolyLog(2, (sqrt(e)*(1 + im*c*x))/(im*c*sqrt(-d) + sqrt(e))))/(4*(-d)^(3/2)) + (im*b*sqrt(e)*PolyLog(2, (sqrt(e)*(im + c*x))/(c*sqrt(-d) + im*sqrt(e))))/(4*(-d)^(3/2))]

    @test_int [x^3*(a + b*atan(c*x))/(d + e*x^2)^2, x, 16, -((b*c^2*d*atan(c*x))/(2*(c^2*d - e)*e^2)) + (d*(a + b*atan(c*x)))/(2*e^2*(d + e*x^2)) + (b*c*sqrt(d)*atan((sqrt(e)*x)/sqrt(d)))/(2*(c^2*d - e)*e^(3/2)) - ((a + b*atan(c*x))*log(2/(1 - im*c*x)))/e^2 + ((a + b*atan(c*x))*log((2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*e^2) + ((a + b*atan(c*x))*log((2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*e^2) + (im*b*PolyLog(2, 1 - 2/(1 - im*c*x)))/(2*e^2) - (im*b*PolyLog(2, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*e^2) - (im*b*PolyLog(2, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*e^2)]
    @test_int [x^1*(a + b*atan(c*x))/(d + e*x^2)^2, x, 4, (b*c^2*atan(c*x))/(2*(c^2*d - e)*e) - (a + b*atan(c*x))/(2*e*(d + e*x^2)) - (b*c*atan((sqrt(e)*x)/sqrt(d)))/(2*sqrt(d)*(c^2*d - e)*sqrt(e))]
    @test_int [(a + b*atan(c*x))/(x^1*(d + e*x^2)^2), x, 19, -((b*c^2*atan(c*x))/(2*d*(c^2*d - e))) + (a + b*atan(c*x))/(2*d*(d + e*x^2)) + (b*c*sqrt(e)*atan((sqrt(e)*x)/sqrt(d)))/(2*d^(3/2)*(c^2*d - e)) + (a*log(x))/d^2 + ((a + b*atan(c*x))*log(2/(1 - im*c*x)))/d^2 - ((a + b*atan(c*x))*log((2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*d^2) - ((a + b*atan(c*x))*log((2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*d^2) + (im*b*PolyLog(2, (-im)*c*x))/(2*d^2) - (im*b*PolyLog(2, im*c*x))/(2*d^2) - (im*b*PolyLog(2, 1 - 2/(1 - im*c*x)))/(2*d^2) + (im*b*PolyLog(2, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*d^2) + (im*b*PolyLog(2, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*d^2)]
    @test_int [(a + b*atan(c*x))/(x^3*(d + e*x^2)^2), x, 22, -((b*c)/(2*d^2*x)) - (b*c^2*atan(c*x))/(2*d^2) + (b*c^2*e*atan(c*x))/(2*d^2*(c^2*d - e)) - (a + b*atan(c*x))/(2*d^2*x^2) - (e*(a + b*atan(c*x)))/(2*d^2*(d + e*x^2)) - (b*c*e^(3/2)*atan((sqrt(e)*x)/sqrt(d)))/(2*d^(5/2)*(c^2*d - e)) - (2*a*e*log(x))/d^3 - (2*e*(a + b*atan(c*x))*log(2/(1 - im*c*x)))/d^3 + (e*(a + b*atan(c*x))*log((2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/d^3 + (e*(a + b*atan(c*x))*log((2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/d^3 - (im*b*e*PolyLog(2, (-im)*c*x))/d^3 + (im*b*e*PolyLog(2, im*c*x))/d^3 + (im*b*e*PolyLog(2, 1 - 2/(1 - im*c*x)))/d^3 - (im*b*e*PolyLog(2, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*d^3) - (im*b*e*PolyLog(2, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*d^3)]

    @test_int [x^2*(a + b*atan(c*x))/(d + e*x^2)^2, x, 45, -((x*(a + b*atan(c*x)))/(2*e*(d + e*x^2))) + (a*atan((sqrt(e)*x)/sqrt(d)))/(sqrt(d)*e^(3/2)) - ((a + b*atan(c*x))*atan((sqrt(e)*x)/sqrt(d)))/(2*sqrt(d)*e^(3/2)) - (im*b*log(1 + im*c*x)*log((c*(sqrt(-d) - sqrt(e)*x))/(c*sqrt(-d) - im*sqrt(e))))/(4*sqrt(-d)*e^(3/2)) + (im*b*log(1 - im*c*x)*log((c*(sqrt(-d) - sqrt(e)*x))/(c*sqrt(-d) + im*sqrt(e))))/(4*sqrt(-d)*e^(3/2)) - (im*b*log(1 - im*c*x)*log((c*(sqrt(-d) + sqrt(e)*x))/(c*sqrt(-d) - im*sqrt(e))))/(4*sqrt(-d)*e^(3/2)) + (im*b*log(1 + im*c*x)*log((c*(sqrt(-d) + sqrt(e)*x))/(c*sqrt(-d) + im*sqrt(e))))/(4*sqrt(-d)*e^(3/2)) - (im*b*c*log((sqrt(e)*(1 - sqrt(-c^2)*x))/(im*sqrt(-c^2)*sqrt(d) + sqrt(e)))*log(1 - (im*sqrt(e)*x)/sqrt(d)))/(8*sqrt(-c^2)*sqrt(d)*e^(3/2)) + (im*b*c*log(-((sqrt(e)*(1 + sqrt(-c^2)*x))/(im*sqrt(-c^2)*sqrt(d) - sqrt(e))))*log(1 - (im*sqrt(e)*x)/sqrt(d)))/(8*sqrt(-c^2)*sqrt(d)*e^(3/2)) + (im*b*c*log(-((sqrt(e)*(1 - sqrt(-c^2)*x))/(im*sqrt(-c^2)*sqrt(d) - sqrt(e))))*log(1 + (im*sqrt(e)*x)/sqrt(d)))/(8*sqrt(-c^2)*sqrt(d)*e^(3/2)) - (im*b*c*log((sqrt(e)*(1 + sqrt(-c^2)*x))/(im*sqrt(-c^2)*sqrt(d) + sqrt(e)))*log(1 + (im*sqrt(e)*x)/sqrt(d)))/(8*sqrt(-c^2)*sqrt(d)*e^(3/2)) + (b*c*log(1 + c^2*x^2))/(4*(c^2*d - e)*e) - (b*c*log(d + e*x^2))/(4*(c^2*d - e)*e) + (im*b*PolyLog(2, (sqrt(e)*(im - c*x))/(c*sqrt(-d) + im*sqrt(e))))/(4*sqrt(-d)*e^(3/2)) - (im*b*PolyLog(2, (sqrt(e)*(1 - im*c*x))/(im*c*sqrt(-d) + sqrt(e))))/(4*sqrt(-d)*e^(3/2)) - (im*b*PolyLog(2, (sqrt(e)*(1 + im*c*x))/(im*c*sqrt(-d) + sqrt(e))))/(4*sqrt(-d)*e^(3/2)) + (im*b*PolyLog(2, (sqrt(e)*(im + c*x))/(c*sqrt(-d) + im*sqrt(e))))/(4*sqrt(-d)*e^(3/2)) - (im*b*c*PolyLog(2, (sqrt(-c^2)*(sqrt(d) - im*sqrt(e)*x))/(sqrt(-c^2)*sqrt(d) - im*sqrt(e))))/(8*sqrt(-c^2)*sqrt(d)*e^(3/2)) + (im*b*c*PolyLog(2, (sqrt(-c^2)*(sqrt(d) - im*sqrt(e)*x))/(sqrt(-c^2)*sqrt(d) + im*sqrt(e))))/(8*sqrt(-c^2)*sqrt(d)*e^(3/2)) - (im*b*c*PolyLog(2, (sqrt(-c^2)*(sqrt(d) + im*sqrt(e)*x))/(sqrt(-c^2)*sqrt(d) - im*sqrt(e))))/(8*sqrt(-c^2)*sqrt(d)*e^(3/2)) + (im*b*c*PolyLog(2, (sqrt(-c^2)*(sqrt(d) + im*sqrt(e)*x))/(sqrt(-c^2)*sqrt(d) + im*sqrt(e))))/(8*sqrt(-c^2)*sqrt(d)*e^(3/2))]
    @test_int [x^0*(a + b*atan(c*x))/(d + e*x^2)^2, x, 24, (x*(a + b*atan(c*x)))/(2*d*(d + e*x^2)) + ((a + b*atan(c*x))*atan((sqrt(e)*x)/sqrt(d)))/(2*d^(3/2)*sqrt(e)) + (im*b*c*log((sqrt(e)*(1 - sqrt(-c^2)*x))/(im*sqrt(-c^2)*sqrt(d) + sqrt(e)))*log(1 - (im*sqrt(e)*x)/sqrt(d)))/(8*sqrt(-c^2)*d^(3/2)*sqrt(e)) - (im*b*c*log(-((sqrt(e)*(1 + sqrt(-c^2)*x))/(im*sqrt(-c^2)*sqrt(d) - sqrt(e))))*log(1 - (im*sqrt(e)*x)/sqrt(d)))/(8*sqrt(-c^2)*d^(3/2)*sqrt(e)) - (im*b*c*log(-((sqrt(e)*(1 - sqrt(-c^2)*x))/(im*sqrt(-c^2)*sqrt(d) - sqrt(e))))*log(1 + (im*sqrt(e)*x)/sqrt(d)))/(8*sqrt(-c^2)*d^(3/2)*sqrt(e)) + (im*b*c*log((sqrt(e)*(1 + sqrt(-c^2)*x))/(im*sqrt(-c^2)*sqrt(d) + sqrt(e)))*log(1 + (im*sqrt(e)*x)/sqrt(d)))/(8*sqrt(-c^2)*d^(3/2)*sqrt(e)) - (b*c*log(1 + c^2*x^2))/(4*d*(c^2*d - e)) + (b*c*log(d + e*x^2))/(4*d*(c^2*d - e)) + (im*b*c*PolyLog(2, (sqrt(-c^2)*(sqrt(d) - im*sqrt(e)*x))/(sqrt(-c^2)*sqrt(d) - im*sqrt(e))))/(8*sqrt(-c^2)*d^(3/2)*sqrt(e)) - (im*b*c*PolyLog(2, (sqrt(-c^2)*(sqrt(d) - im*sqrt(e)*x))/(sqrt(-c^2)*sqrt(d) + im*sqrt(e))))/(8*sqrt(-c^2)*d^(3/2)*sqrt(e)) + (im*b*c*PolyLog(2, (sqrt(-c^2)*(sqrt(d) + im*sqrt(e)*x))/(sqrt(-c^2)*sqrt(d) - im*sqrt(e))))/(8*sqrt(-c^2)*d^(3/2)*sqrt(e)) - (im*b*c*PolyLog(2, (sqrt(-c^2)*(sqrt(d) + im*sqrt(e)*x))/(sqrt(-c^2)*sqrt(d) + im*sqrt(e))))/(8*sqrt(-c^2)*d^(3/2)*sqrt(e))]
    @test_int [(a + b*atan(c*x))/(x^2*(d + e*x^2)^2), x, 50, -((a + b*atan(c*x))/(d^2*x)) - (e*x*(a + b*atan(c*x)))/(2*d^2*(d + e*x^2)) - (a*sqrt(e)*atan((sqrt(e)*x)/sqrt(d)))/d^(5/2) - (sqrt(e)*(a + b*atan(c*x))*atan((sqrt(e)*x)/sqrt(d)))/(2*d^(5/2)) + (b*c*log(x))/d^2 + (im*b*sqrt(e)*log(1 + im*c*x)*log((c*(sqrt(-d) - sqrt(e)*x))/(c*sqrt(-d) - im*sqrt(e))))/(4*(-d)^(5/2)) - (im*b*sqrt(e)*log(1 - im*c*x)*log((c*(sqrt(-d) - sqrt(e)*x))/(c*sqrt(-d) + im*sqrt(e))))/(4*(-d)^(5/2)) + (im*b*sqrt(e)*log(1 - im*c*x)*log((c*(sqrt(-d) + sqrt(e)*x))/(c*sqrt(-d) - im*sqrt(e))))/(4*(-d)^(5/2)) - (im*b*sqrt(e)*log(1 + im*c*x)*log((c*(sqrt(-d) + sqrt(e)*x))/(c*sqrt(-d) + im*sqrt(e))))/(4*(-d)^(5/2)) - (im*b*c*sqrt(e)*log((sqrt(e)*(1 - sqrt(-c^2)*x))/(im*sqrt(-c^2)*sqrt(d) + sqrt(e)))*log(1 - (im*sqrt(e)*x)/sqrt(d)))/(8*sqrt(-c^2)*d^(5/2)) + (im*b*c*sqrt(e)*log(-((sqrt(e)*(1 + sqrt(-c^2)*x))/(im*sqrt(-c^2)*sqrt(d) - sqrt(e))))*log(1 - (im*sqrt(e)*x)/sqrt(d)))/(8*sqrt(-c^2)*d^(5/2)) + (im*b*c*sqrt(e)*log(-((sqrt(e)*(1 - sqrt(-c^2)*x))/(im*sqrt(-c^2)*sqrt(d) - sqrt(e))))*log(1 + (im*sqrt(e)*x)/sqrt(d)))/(8*sqrt(-c^2)*d^(5/2)) - (im*b*c*sqrt(e)*log((sqrt(e)*(1 + sqrt(-c^2)*x))/(im*sqrt(-c^2)*sqrt(d) + sqrt(e)))*log(1 + (im*sqrt(e)*x)/sqrt(d)))/(8*sqrt(-c^2)*d^(5/2)) - (b*c*log(1 + c^2*x^2))/(2*d^2) + (b*c*e*log(1 + c^2*x^2))/(4*d^2*(c^2*d - e)) - (b*c*e*log(d + e*x^2))/(4*d^2*(c^2*d - e)) - (im*b*sqrt(e)*PolyLog(2, (sqrt(e)*(im - c*x))/(c*sqrt(-d) + im*sqrt(e))))/(4*(-d)^(5/2)) + (im*b*sqrt(e)*PolyLog(2, (sqrt(e)*(1 - im*c*x))/(im*c*sqrt(-d) + sqrt(e))))/(4*(-d)^(5/2)) + (im*b*sqrt(e)*PolyLog(2, (sqrt(e)*(1 + im*c*x))/(im*c*sqrt(-d) + sqrt(e))))/(4*(-d)^(5/2)) - (im*b*sqrt(e)*PolyLog(2, (sqrt(e)*(im + c*x))/(c*sqrt(-d) + im*sqrt(e))))/(4*(-d)^(5/2)) - (im*b*c*sqrt(e)*PolyLog(2, (sqrt(-c^2)*(sqrt(d) - im*sqrt(e)*x))/(sqrt(-c^2)*sqrt(d) - im*sqrt(e))))/(8*sqrt(-c^2)*d^(5/2)) + (im*b*c*sqrt(e)*PolyLog(2, (sqrt(-c^2)*(sqrt(d) - im*sqrt(e)*x))/(sqrt(-c^2)*sqrt(d) + im*sqrt(e))))/(8*sqrt(-c^2)*d^(5/2)) - (im*b*c*sqrt(e)*PolyLog(2, (sqrt(-c^2)*(sqrt(d) + im*sqrt(e)*x))/(sqrt(-c^2)*sqrt(d) - im*sqrt(e))))/(8*sqrt(-c^2)*d^(5/2)) + (im*b*c*sqrt(e)*PolyLog(2, (sqrt(-c^2)*(sqrt(d) + im*sqrt(e)*x))/(sqrt(-c^2)*sqrt(d) + im*sqrt(e))))/(8*sqrt(-c^2)*d^(5/2))]

    @test_int [x^5*(a + b*atan(c*x))/(d + e*x^2)^3, x, 21, -((b*c*d*x)/(8*(c^2*d - e)*e^2*(d + e*x^2))) + (b*c^4*d^2*atan(c*x))/(4*(c^2*d - e)^2*e^3) - (b*c^2*d*atan(c*x))/((c^2*d - e)*e^3) - (d^2*(a + b*atan(c*x)))/(4*e^3*(d + e*x^2)^2) + (d*(a + b*atan(c*x)))/(e^3*(d + e*x^2)) + (b*c*sqrt(d)*atan((sqrt(e)*x)/sqrt(d)))/((c^2*d - e)*e^(5/2)) - (b*c*sqrt(d)*(3*c^2*d - e)*atan((sqrt(e)*x)/sqrt(d)))/(8*(c^2*d - e)^2*e^(5/2)) - ((a + b*atan(c*x))*log(2/(1 - im*c*x)))/e^3 + ((a + b*atan(c*x))*log((2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*e^3) + ((a + b*atan(c*x))*log((2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*e^3) + (im*b*PolyLog(2, 1 - 2/(1 - im*c*x)))/(2*e^3) - (im*b*PolyLog(2, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*e^3) - (im*b*PolyLog(2, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*e^3)]
    @test_int [x^3*(a + b*atan(c*x))/(d + e*x^2)^3, x, 6, (b*c*x)/(8*(c^2*d - e)*e*(d + e*x^2)) - (b*atan(c*x))/(4*d*(c^2*d - e)^2) + (x^4*(a + b*atan(c*x)))/(4*d*(d + e*x^2)^2) - (b*c*(c^2*d - 3*e)*atan((sqrt(e)*x)/sqrt(d)))/(8*sqrt(d)*(c^2*d - e)^2*e^(3/2))]
    @test_int [x^1*(a + b*atan(c*x))/(d + e*x^2)^3, x, 5, -((b*c*x)/(8*d*(c^2*d - e)*(d + e*x^2))) + (b*c^4*atan(c*x))/(4*(c^2*d - e)^2*e) - (a + b*atan(c*x))/(4*e*(d + e*x^2)^2) - (b*c*(3*c^2*d - e)*atan((sqrt(e)*x)/sqrt(d)))/(8*d^(3/2)*(c^2*d - e)^2*sqrt(e))]
    @test_int [(a + b*atan(c*x))/(x^1*(d + e*x^2)^3), x, 24, (b*c*e*x)/(8*d^2*(c^2*d - e)*(d + e*x^2)) - (b*c^4*atan(c*x))/(4*d*(c^2*d - e)^2) - (b*c^2*atan(c*x))/(2*d^2*(c^2*d - e)) + (a + b*atan(c*x))/(4*d*(d + e*x^2)^2) + (a + b*atan(c*x))/(2*d^2*(d + e*x^2)) + (b*c*sqrt(e)*atan((sqrt(e)*x)/sqrt(d)))/(2*d^(5/2)*(c^2*d - e)) + (b*c*(3*c^2*d - e)*sqrt(e)*atan((sqrt(e)*x)/sqrt(d)))/(8*d^(5/2)*(c^2*d - e)^2) + (a*log(x))/d^3 + ((a + b*atan(c*x))*log(2/(1 - im*c*x)))/d^3 - ((a + b*atan(c*x))*log((2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*d^3) - ((a + b*atan(c*x))*log((2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*d^3) + (im*b*PolyLog(2, (-im)*c*x))/(2*d^3) - (im*b*PolyLog(2, im*c*x))/(2*d^3) - (im*b*PolyLog(2, 1 - 2/(1 - im*c*x)))/(2*d^3) + (im*b*PolyLog(2, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*d^3) + (im*b*PolyLog(2, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*d^3)]
    @test_int [(a + b*atan(c*x))/(x^3*(d + e*x^2)^3), x, 27, -((b*c)/(2*d^3*x)) - (b*c*e^2*x)/(8*d^3*(c^2*d - e)*(d + e*x^2)) - (b*c^2*atan(c*x))/(2*d^3) + (b*c^4*e*atan(c*x))/(4*d^2*(c^2*d - e)^2) + (b*c^2*e*atan(c*x))/(d^3*(c^2*d - e)) - (a + b*atan(c*x))/(2*d^3*x^2) - (e*(a + b*atan(c*x)))/(4*d^2*(d + e*x^2)^2) - (e*(a + b*atan(c*x)))/(d^3*(d + e*x^2)) - (b*c*e^(3/2)*atan((sqrt(e)*x)/sqrt(d)))/(d^(7/2)*(c^2*d - e)) - (b*c*(3*c^2*d - e)*e^(3/2)*atan((sqrt(e)*x)/sqrt(d)))/(8*d^(7/2)*(c^2*d - e)^2) - (3*a*e*log(x))/d^4 - (3*e*(a + b*atan(c*x))*log(2/(1 - im*c*x)))/d^4 + (3*e*(a + b*atan(c*x))*log((2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*d^4) + (3*e*(a + b*atan(c*x))*log((2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*d^4) - (3*im*b*e*PolyLog(2, (-im)*c*x))/(2*d^4) + (3*im*b*e*PolyLog(2, im*c*x))/(2*d^4) + (3*im*b*e*PolyLog(2, 1 - 2/(1 - im*c*x)))/(2*d^4) - (3*im*b*e*PolyLog(2, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*d^4) - (3*im*b*e*PolyLog(2, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*d^4)]

    @test_int [x^2*(a + b*atan(c*x))/(d + e*x^2)^3, x, 49, (b*c)/(8*(c^2*d - e)*e*(d + e*x^2)) - (x*(a + b*atan(c*x)))/(4*e*(d + e*x^2)^2) + (x*(a + b*atan(c*x)))/(8*d*e*(d + e*x^2)) + ((a + b*atan(c*x))*atan((sqrt(e)*x)/sqrt(d)))/(8*d^(3/2)*e^(3/2)) + (im*b*c*log((sqrt(e)*(1 - sqrt(-c^2)*x))/(im*sqrt(-c^2)*sqrt(d) + sqrt(e)))*log(1 - (im*sqrt(e)*x)/sqrt(d)))/(32*sqrt(-c^2)*d^(3/2)*e^(3/2)) - (im*b*c*log(-((sqrt(e)*(1 + sqrt(-c^2)*x))/(im*sqrt(-c^2)*sqrt(d) - sqrt(e))))*log(1 - (im*sqrt(e)*x)/sqrt(d)))/(32*sqrt(-c^2)*d^(3/2)*e^(3/2)) - (im*b*c*log(-((sqrt(e)*(1 - sqrt(-c^2)*x))/(im*sqrt(-c^2)*sqrt(d) - sqrt(e))))*log(1 + (im*sqrt(e)*x)/sqrt(d)))/(32*sqrt(-c^2)*d^(3/2)*e^(3/2)) + (im*b*c*log((sqrt(e)*(1 + sqrt(-c^2)*x))/(im*sqrt(-c^2)*sqrt(d) + sqrt(e)))*log(1 + (im*sqrt(e)*x)/sqrt(d)))/(32*sqrt(-c^2)*d^(3/2)*e^(3/2)) + (b*c*(5*c^2*d - 3*e)*log(1 + c^2*x^2))/(16*d*(c^2*d - e)^2*e) - (b*c*log(1 + c^2*x^2))/(4*d*(c^2*d - e)*e) - (b*c*(5*c^2*d - 3*e)*log(d + e*x^2))/(16*d*(c^2*d - e)^2*e) + (b*c*log(d + e*x^2))/(4*d*(c^2*d - e)*e) + (im*b*c*PolyLog(2, (sqrt(-c^2)*(sqrt(d) - im*sqrt(e)*x))/(sqrt(-c^2)*sqrt(d) - im*sqrt(e))))/(32*sqrt(-c^2)*d^(3/2)*e^(3/2)) - (im*b*c*PolyLog(2, (sqrt(-c^2)*(sqrt(d) - im*sqrt(e)*x))/(sqrt(-c^2)*sqrt(d) + im*sqrt(e))))/(32*sqrt(-c^2)*d^(3/2)*e^(3/2)) + (im*b*c*PolyLog(2, (sqrt(-c^2)*(sqrt(d) + im*sqrt(e)*x))/(sqrt(-c^2)*sqrt(d) - im*sqrt(e))))/(32*sqrt(-c^2)*d^(3/2)*e^(3/2)) - (im*b*c*PolyLog(2, (sqrt(-c^2)*(sqrt(d) + im*sqrt(e)*x))/(sqrt(-c^2)*sqrt(d) + im*sqrt(e))))/(32*sqrt(-c^2)*d^(3/2)*e^(3/2))]
    @test_int [x^0*(a + b*atan(c*x))/(d + e*x^2)^3, x, 23, -((b*c)/(8*d*(c^2*d - e)*(d + e*x^2))) + (x*(a + b*atan(c*x)))/(4*d*(d + e*x^2)^2) + (3*x*(a + b*atan(c*x)))/(8*d^2*(d + e*x^2)) + (3*(a + b*atan(c*x))*atan((sqrt(e)*x)/sqrt(d)))/(8*d^(5/2)*sqrt(e)) + (3*im*b*c*log((sqrt(e)*(1 - sqrt(-c^2)*x))/(im*sqrt(-c^2)*sqrt(d) + sqrt(e)))*log(1 - (im*sqrt(e)*x)/sqrt(d)))/(32*sqrt(-c^2)*d^(5/2)*sqrt(e)) - (3*im*b*c*log(-((sqrt(e)*(1 + sqrt(-c^2)*x))/(im*sqrt(-c^2)*sqrt(d) - sqrt(e))))*log(1 - (im*sqrt(e)*x)/sqrt(d)))/(32*sqrt(-c^2)*d^(5/2)*sqrt(e)) - (3*im*b*c*log(-((sqrt(e)*(1 - sqrt(-c^2)*x))/(im*sqrt(-c^2)*sqrt(d) - sqrt(e))))*log(1 + (im*sqrt(e)*x)/sqrt(d)))/(32*sqrt(-c^2)*d^(5/2)*sqrt(e)) + (3*im*b*c*log((sqrt(e)*(1 + sqrt(-c^2)*x))/(im*sqrt(-c^2)*sqrt(d) + sqrt(e)))*log(1 + (im*sqrt(e)*x)/sqrt(d)))/(32*sqrt(-c^2)*d^(5/2)*sqrt(e)) - (b*c*(5*c^2*d - 3*e)*log(1 + c^2*x^2))/(16*d^2*(c^2*d - e)^2) + (b*c*(5*c^2*d - 3*e)*log(d + e*x^2))/(16*d^2*(c^2*d - e)^2) + (3*im*b*c*PolyLog(2, (sqrt(-c^2)*(sqrt(d) - im*sqrt(e)*x))/(sqrt(-c^2)*sqrt(d) - im*sqrt(e))))/(32*sqrt(-c^2)*d^(5/2)*sqrt(e)) - (3*im*b*c*PolyLog(2, (sqrt(-c^2)*(sqrt(d) - im*sqrt(e)*x))/(sqrt(-c^2)*sqrt(d) + im*sqrt(e))))/(32*sqrt(-c^2)*d^(5/2)*sqrt(e)) + (3*im*b*c*PolyLog(2, (sqrt(-c^2)*(sqrt(d) + im*sqrt(e)*x))/(sqrt(-c^2)*sqrt(d) - im*sqrt(e))))/(32*sqrt(-c^2)*d^(5/2)*sqrt(e)) - (3*im*b*c*PolyLog(2, (sqrt(-c^2)*(sqrt(d) + im*sqrt(e)*x))/(sqrt(-c^2)*sqrt(d) + im*sqrt(e))))/(32*sqrt(-c^2)*d^(5/2)*sqrt(e))]
    @test_int [(a + b*atan(c*x))/(x^2*(d + e*x^2)^3), x, 73, (b*c*e)/(8*d^2*(c^2*d - e)*(d + e*x^2)) - (a + b*atan(c*x))/(d^3*x) - (e*x*(a + b*atan(c*x)))/(4*d^2*(d + e*x^2)^2) - (7*e*x*(a + b*atan(c*x)))/(8*d^3*(d + e*x^2)) - (a*sqrt(e)*atan((sqrt(e)*x)/sqrt(d)))/d^(7/2) - (7*sqrt(e)*(a + b*atan(c*x))*atan((sqrt(e)*x)/sqrt(d)))/(8*d^(7/2)) + (b*c*log(x))/d^3 - (im*b*sqrt(e)*log(1 + im*c*x)*log((c*(sqrt(-d) - sqrt(e)*x))/(c*sqrt(-d) - im*sqrt(e))))/(4*(-d)^(7/2)) + (im*b*sqrt(e)*log(1 - im*c*x)*log((c*(sqrt(-d) - sqrt(e)*x))/(c*sqrt(-d) + im*sqrt(e))))/(4*(-d)^(7/2)) - (im*b*sqrt(e)*log(1 - im*c*x)*log((c*(sqrt(-d) + sqrt(e)*x))/(c*sqrt(-d) - im*sqrt(e))))/(4*(-d)^(7/2)) + (im*b*sqrt(e)*log(1 + im*c*x)*log((c*(sqrt(-d) + sqrt(e)*x))/(c*sqrt(-d) + im*sqrt(e))))/(4*(-d)^(7/2)) - (7*im*b*c*sqrt(e)*log((sqrt(e)*(1 - sqrt(-c^2)*x))/(im*sqrt(-c^2)*sqrt(d) + sqrt(e)))*log(1 - (im*sqrt(e)*x)/sqrt(d)))/(32*sqrt(-c^2)*d^(7/2)) + (7*im*b*c*sqrt(e)*log(-((sqrt(e)*(1 + sqrt(-c^2)*x))/(im*sqrt(-c^2)*sqrt(d) - sqrt(e))))*log(1 - (im*sqrt(e)*x)/sqrt(d)))/(32*sqrt(-c^2)*d^(7/2)) + (7*im*b*c*sqrt(e)*log(-((sqrt(e)*(1 - sqrt(-c^2)*x))/(im*sqrt(-c^2)*sqrt(d) - sqrt(e))))*log(1 + (im*sqrt(e)*x)/sqrt(d)))/(32*sqrt(-c^2)*d^(7/2)) - (7*im*b*c*sqrt(e)*log((sqrt(e)*(1 + sqrt(-c^2)*x))/(im*sqrt(-c^2)*sqrt(d) + sqrt(e)))*log(1 + (im*sqrt(e)*x)/sqrt(d)))/(32*sqrt(-c^2)*d^(7/2)) - (b*c*log(1 + c^2*x^2))/(2*d^3) + (b*c*(5*c^2*d - 3*e)*e*log(1 + c^2*x^2))/(16*d^3*(c^2*d - e)^2) + (b*c*e*log(1 + c^2*x^2))/(4*d^3*(c^2*d - e)) - (b*c*(5*c^2*d - 3*e)*e*log(d + e*x^2))/(16*d^3*(c^2*d - e)^2) - (b*c*e*log(d + e*x^2))/(4*d^3*(c^2*d - e)) + (im*b*sqrt(e)*PolyLog(2, (sqrt(e)*(im - c*x))/(c*sqrt(-d) + im*sqrt(e))))/(4*(-d)^(7/2)) - (im*b*sqrt(e)*PolyLog(2, (sqrt(e)*(1 - im*c*x))/(im*c*sqrt(-d) + sqrt(e))))/(4*(-d)^(7/2)) - (im*b*sqrt(e)*PolyLog(2, (sqrt(e)*(1 + im*c*x))/(im*c*sqrt(-d) + sqrt(e))))/(4*(-d)^(7/2)) + (im*b*sqrt(e)*PolyLog(2, (sqrt(e)*(im + c*x))/(c*sqrt(-d) + im*sqrt(e))))/(4*(-d)^(7/2)) - (7*im*b*c*sqrt(e)*PolyLog(2, (sqrt(-c^2)*(sqrt(d) - im*sqrt(e)*x))/(sqrt(-c^2)*sqrt(d) - im*sqrt(e))))/(32*sqrt(-c^2)*d^(7/2)) + (7*im*b*c*sqrt(e)*PolyLog(2, (sqrt(-c^2)*(sqrt(d) - im*sqrt(e)*x))/(sqrt(-c^2)*sqrt(d) + im*sqrt(e))))/(32*sqrt(-c^2)*d^(7/2)) - (7*im*b*c*sqrt(e)*PolyLog(2, (sqrt(-c^2)*(sqrt(d) + im*sqrt(e)*x))/(sqrt(-c^2)*sqrt(d) - im*sqrt(e))))/(32*sqrt(-c^2)*d^(7/2)) + (7*im*b*c*sqrt(e)*PolyLog(2, (sqrt(-c^2)*(sqrt(d) + im*sqrt(e)*x))/(sqrt(-c^2)*sqrt(d) + im*sqrt(e))))/(32*sqrt(-c^2)*d^(7/2))]

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

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

    @test_int [x^3*(a + b*atan(c*x))*(d + e*x^2)^(1/2), x, If(13>=8, 9, 10), If(13>=8, -((b*(c^2*d - 12*e)*x*sqrt(d + e*x^2))/(120*c^3*e)) - (b*x*(d + e*x^2)^(3/2))/(20*c*e) - (d*(d + e*x^2)^(3/2)*(a + b*atan(c*x)))/(3*e^2) + ((d + e*x^2)^(5/2)*(a + b*atan(c*x)))/(5*e^2) + (b*(c^2*d - e)^(3/2)*(2*c^2*d + 3*e)*atan((sqrt(c^2*d - e)*x)/sqrt(d + e*x^2)))/(15*c^5*e^2) + (b*(15*c^4*d^2 + 20*c^2*d*e - 24*e^2)*atanh((sqrt(e)*x)/sqrt(d + e*x^2)))/(120*c^5*e^(3/2)), -((b*(c^2*d - 12*e)*x*sqrt(d + e*x^2))/(120*c^3*e)) - (b*x*(d + e*x^2)^(3/2))/(20*c*e) - (d*(d + e*x^2)^(3/2)*(a + b*atan(c*x)))/(3*e^2) + ((d + e*x^2)^(5/2)*(a + b*atan(c*x)))/(5*e^2) + (b*(c^2*d - e)^(3/2)*(2*c^2*d + 3*e)*atan((sqrt(c^2*d - e)*x)/sqrt(d + e*x^2)))/(15*c^5*e^2) + (b*(15*c^4*d^2 + 20*c^2*d*e - 24*e^2)*atanh((sqrt(e)*x)/sqrt(d + e*x^2)))/(120*c^5*e^(3/2)))]
    @test_int [x^2*(a + b*atan(c*x))*(d + e*x^2)^(1/2), x, 5, (a*d*x*sqrt(d + e*x^2))/(8*e) + (1/4)*a*x^3*sqrt(d + e*x^2) - (a*d^2*atanh((sqrt(e)*x)/sqrt(d + e*x^2)))/(8*e^(3/2)) + b*Unintegrable(x^2*sqrt(d + e*x^2)*atan(c*x), x)]
    @test_int [x^1*(a + b*atan(c*x))*(d + e*x^2)^(1/2), x, 7, -((b*x*sqrt(d + e*x^2))/(6*c)) + ((d + e*x^2)^(3/2)*(a + b*atan(c*x)))/(3*e) - (b*(c^2*d - e)^(3/2)*atan((sqrt(c^2*d - e)*x)/sqrt(d + e*x^2)))/(3*c^3*e) - (b*(3*c^2*d - 2*e)*atanh((sqrt(e)*x)/sqrt(d + e*x^2)))/(6*c^3*sqrt(e))]
    @test_int [x^0*(a + b*atan(c*x))*(d + e*x^2)^(1/2), x, 0, Unintegrable(sqrt(d + e*x^2)*(a + b*atan(c*x)), x)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^(1/2)/x^1, x, 5, a*sqrt(d + e*x^2) - a*sqrt(d)*atanh(sqrt(d + e*x^2)/sqrt(d)) + b*Unintegrable((sqrt(d + e*x^2)*atan(c*x))/x, x)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^(1/2)/x^2, x, 4, -((a*sqrt(d + e*x^2))/x) + a*sqrt(e)*atanh((sqrt(e)*x)/sqrt(d + e*x^2)) + b*Unintegrable((sqrt(d + e*x^2)*atan(c*x))/x^2, x)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^(1/2)/x^3, x, 5, -((a*sqrt(d + e*x^2))/(2*x^2)) - (a*e*atanh(sqrt(d + e*x^2)/sqrt(d)))/(2*sqrt(d)) + b*Unintegrable((sqrt(d + e*x^2)*atan(c*x))/x^3, x)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^(1/2)/x^4, x, 9, -((b*c*sqrt(d + e*x^2))/(6*x^2)) - ((d + e*x^2)^(3/2)*(a + b*atan(c*x)))/(3*d*x^3) + (b*c*(2*c^2*d - 3*e)*atanh(sqrt(d + e*x^2)/sqrt(d)))/(6*sqrt(d)) - (b*(c^2*d - e)^(3/2)*atanh((c*sqrt(d + e*x^2))/sqrt(c^2*d - e)))/(3*d)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^(1/2)/x^5, x, 6, -((a*sqrt(d + e*x^2))/(4*x^4)) - (a*e*sqrt(d + e*x^2))/(8*d*x^2) + (a*e^2*atanh(sqrt(d + e*x^2)/sqrt(d)))/(8*d^(3/2)) + b*Unintegrable((sqrt(d + e*x^2)*atan(c*x))/x^5, x)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^(1/2)/x^6, x, If(13>=8, 10, 21), If(13>=8, (b*c*(12*c^2*d - e)*sqrt(d + e*x^2))/(120*d*x^2) - (b*c*(d + e*x^2)^(3/2))/(20*d*x^4) - ((d + e*x^2)^(3/2)*(a + b*atan(c*x)))/(5*d*x^5) + (2*e*(d + e*x^2)^(3/2)*(a + b*atan(c*x)))/(15*d^2*x^3) - (b*c*(24*c^4*d^2 - 20*c^2*d*e - 15*e^2)*atanh(sqrt(d + e*x^2)/sqrt(d)))/(120*d^(3/2)) + (b*(c^2*d - e)^(3/2)*(3*c^2*d + 2*e)*atanh((c*sqrt(d + e*x^2))/sqrt(c^2*d - e)))/(15*d^2), -((b*c*sqrt(d + e*x^2))/(20*x^4)) + (b*c*(3*c^2*d - e)*sqrt(d + e*x^2))/(30*d*x^2) - (b*c*e*sqrt(d + e*x^2))/(40*d*x^2) - ((d + e*x^2)^(3/2)*(a + b*atan(c*x)))/(5*d*x^5) + (2*e*(d + e*x^2)^(3/2)*(a + b*atan(c*x)))/(15*d^2*x^3) + (b*c*(3*c^2*d - e)*e*atanh(sqrt(d + e*x^2)/sqrt(d)))/(30*d^(3/2)) + (b*c*e^2*atanh(sqrt(d + e*x^2)/sqrt(d)))/(40*d^(3/2)) - (b*c*(c^2*d - e)*(3*c^2*d + 2*e)*atanh(sqrt(d + e*x^2)/sqrt(d)))/(15*d^(3/2)) + (b*(c^2*d - e)^(3/2)*(3*c^2*d + 2*e)*atanh((c*sqrt(d + e*x^2))/sqrt(c^2*d - e)))/(15*d^2))]

    @test_int [x^3*(a + b*atan(c*x))*(d + e*x^2)^(3/2), x, 10, (b*(3*c^4*d^2 + 54*c^2*d*e - 40*e^2)*x*sqrt(d + e*x^2))/(560*c^5*e) - (b*(13*c^2*d - 30*e)*x*(d + e*x^2)^(3/2))/(840*c^3*e) - (b*x*(d + e*x^2)^(5/2))/(42*c*e) - (d*(d + e*x^2)^(5/2)*(a + b*atan(c*x)))/(5*e^2) + ((d + e*x^2)^(7/2)*(a + b*atan(c*x)))/(7*e^2) + (b*(c^2*d - e)^(5/2)*(2*c^2*d + 5*e)*atan((sqrt(c^2*d - e)*x)/sqrt(d + e*x^2)))/(35*c^7*e^2) + (b*(35*c^6*d^3 + 70*c^4*d^2*e - 168*c^2*d*e^2 + 80*e^3)*atanh((sqrt(e)*x)/sqrt(d + e*x^2)))/(560*c^7*e^(3/2))]
    @test_int [x^2*(a + b*atan(c*x))*(d + e*x^2)^(3/2), x, 6, (a*d^2*x*sqrt(d + e*x^2))/(16*e) + (1/8)*a*d*x^3*sqrt(d + e*x^2) + (1/6)*a*x^3*(d + e*x^2)^(3/2) - (a*d^3*atanh((sqrt(e)*x)/sqrt(d + e*x^2)))/(16*e^(3/2)) + b*Unintegrable(x^2*(d + e*x^2)^(3/2)*atan(c*x), x)]
    @test_int [x^1*(a + b*atan(c*x))*(d + e*x^2)^(3/2), x, 8, -((b*(7*c^2*d - 4*e)*x*sqrt(d + e*x^2))/(40*c^3)) - (b*x*(d + e*x^2)^(3/2))/(20*c) + ((d + e*x^2)^(5/2)*(a + b*atan(c*x)))/(5*e) - (b*(c^2*d - e)^(5/2)*atan((sqrt(c^2*d - e)*x)/sqrt(d + e*x^2)))/(5*c^5*e) - (b*(15*c^4*d^2 - 20*c^2*d*e + 8*e^2)*atanh((sqrt(e)*x)/sqrt(d + e*x^2)))/(40*c^5*sqrt(e))]
    @test_int [x^0*(a + b*atan(c*x))*(d + e*x^2)^(3/2), x, 0, Unintegrable((d + e*x^2)^(3/2)*(a + b*atan(c*x)), x)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^(3/2)/x^1, x, 6, a*d*sqrt(d + e*x^2) + (1/3)*a*(d + e*x^2)^(3/2) - a*d^(3/2)*atanh(sqrt(d + e*x^2)/sqrt(d)) + b*Unintegrable(((d + e*x^2)^(3/2)*atan(c*x))/x, x)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^(3/2)/x^2, x, 5, (3/2)*a*e*x*sqrt(d + e*x^2) - (a*(d + e*x^2)^(3/2))/x + (3/2)*a*d*sqrt(e)*atanh((sqrt(e)*x)/sqrt(d + e*x^2)) + b*Unintegrable(((d + e*x^2)^(3/2)*atan(c*x))/x^2, x)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^(3/2)/x^3, x, 6, (3/2)*a*e*sqrt(d + e*x^2) - (a*(d + e*x^2)^(3/2))/(2*x^2) - (3/2)*a*sqrt(d)*e*atanh(sqrt(d + e*x^2)/sqrt(d)) + b*Unintegrable(((d + e*x^2)^(3/2)*atan(c*x))/x^3, x)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^(3/2)/x^4, x, 5, -((a*e*sqrt(d + e*x^2))/x) - (a*(d + e*x^2)^(3/2))/(3*x^3) + a*e^(3/2)*atanh((sqrt(e)*x)/sqrt(d + e*x^2)) + b*Unintegrable(((d + e*x^2)^(3/2)*atan(c*x))/x^4, x)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^(3/2)/x^5, x, 6, -((3*a*e*sqrt(d + e*x^2))/(8*x^2)) - (a*(d + e*x^2)^(3/2))/(4*x^4) - (3*a*e^2*atanh(sqrt(d + e*x^2)/sqrt(d)))/(8*sqrt(d)) + b*Unintegrable(((d + e*x^2)^(3/2)*atan(c*x))/x^5, x)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^(3/2)/x^6, x, 10, (b*c*(4*c^2*d - 7*e)*sqrt(d + e*x^2))/(40*x^2) - (b*c*(d + e*x^2)^(3/2))/(20*x^4) - ((d + e*x^2)^(5/2)*(a + b*atan(c*x)))/(5*d*x^5) - (b*c*(8*c^4*d^2 - 20*c^2*d*e + 15*e^2)*atanh(sqrt(d + e*x^2)/sqrt(d)))/(40*sqrt(d)) + (b*(c^2*d - e)^(5/2)*atanh((c*sqrt(d + e*x^2))/sqrt(c^2*d - e)))/(5*d)]

    @test_int [x^3*(a + b*atan(c*x))*(d + e*x^2)^(5/2), x, 11, (b*(59*c^6*d^3 + 712*c^4*d^2*e - 1104*c^2*d*e^2 + 448*e^3)*x*sqrt(d + e*x^2))/(8064*c^7*e) - (b*(69*c^4*d^2 - 520*c^2*d*e + 336*e^2)*x*(d + e*x^2)^(3/2))/(12096*c^5*e) - (b*(33*c^2*d - 56*e)*x*(d + e*x^2)^(5/2))/(3024*c^3*e) - (b*x*(d + e*x^2)^(7/2))/(72*c*e) - (d*(d + e*x^2)^(7/2)*(a + b*atan(c*x)))/(7*e^2) + ((d + e*x^2)^(9/2)*(a + b*atan(c*x)))/(9*e^2) + (b*(c^2*d - e)^(7/2)*(2*c^2*d + 7*e)*atan((sqrt(c^2*d - e)*x)/sqrt(d + e*x^2)))/(63*c^9*e^2) + (b*(315*c^8*d^4 + 840*c^6*d^3*e - 3024*c^4*d^2*e^2 + 2880*c^2*d*e^3 - 896*e^4)*atanh((sqrt(e)*x)/sqrt(d + e*x^2)))/(8064*c^9*e^(3/2))]
    @test_int [x^2*(a + b*atan(c*x))*(d + e*x^2)^(5/2), x, 7, (5*a*d^3*x*sqrt(d + e*x^2))/(128*e) + (5/64)*a*d^2*x^3*sqrt(d + e*x^2) + (5/48)*a*d*x^3*(d + e*x^2)^(3/2) + (1/8)*a*x^3*(d + e*x^2)^(5/2) - (5*a*d^4*atanh((sqrt(e)*x)/sqrt(d + e*x^2)))/(128*e^(3/2)) + b*Unintegrable(x^2*(d + e*x^2)^(5/2)*atan(c*x), x)]
    @test_int [x^1*(a + b*atan(c*x))*(d + e*x^2)^(5/2), x, 9, -((b*(19*c^4*d^2 - 22*c^2*d*e + 8*e^2)*x*sqrt(d + e*x^2))/(112*c^5)) - (b*(11*c^2*d - 6*e)*x*(d + e*x^2)^(3/2))/(168*c^3) - (b*x*(d + e*x^2)^(5/2))/(42*c) + ((d + e*x^2)^(7/2)*(a + b*atan(c*x)))/(7*e) - (b*(c^2*d - e)^(7/2)*atan((sqrt(c^2*d - e)*x)/sqrt(d + e*x^2)))/(7*c^7*e) - (b*(35*c^6*d^3 - 70*c^4*d^2*e + 56*c^2*d*e^2 - 16*e^3)*atanh((sqrt(e)*x)/sqrt(d + e*x^2)))/(112*c^7*sqrt(e))]
    @test_int [x^0*(a + b*atan(c*x))*(d + e*x^2)^(5/2), x, 0, Unintegrable((d + e*x^2)^(5/2)*(a + b*atan(c*x)), x)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^(5/2)/x^1, x, 7, a*d^2*sqrt(d + e*x^2) + (1/3)*a*d*(d + e*x^2)^(3/2) + (1/5)*a*(d + e*x^2)^(5/2) - a*d^(5/2)*atanh(sqrt(d + e*x^2)/sqrt(d)) + b*Unintegrable(((d + e*x^2)^(5/2)*atan(c*x))/x, x)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^(5/2)/x^2, x, 6, (15/8)*a*d*e*x*sqrt(d + e*x^2) + (5/4)*a*e*x*(d + e*x^2)^(3/2) - (a*(d + e*x^2)^(5/2))/x + (15/8)*a*d^2*sqrt(e)*atanh((sqrt(e)*x)/sqrt(d + e*x^2)) + b*Unintegrable(((d + e*x^2)^(5/2)*atan(c*x))/x^2, x)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^(5/2)/x^3, x, 7, (5/2)*a*d*e*sqrt(d + e*x^2) + (5/6)*a*e*(d + e*x^2)^(3/2) - (a*(d + e*x^2)^(5/2))/(2*x^2) - (5/2)*a*d^(3/2)*e*atanh(sqrt(d + e*x^2)/sqrt(d)) + b*Unintegrable(((d + e*x^2)^(5/2)*atan(c*x))/x^3, x)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^(5/2)/x^4, x, 6, (5/2)*a*e^2*x*sqrt(d + e*x^2) - (5*a*e*(d + e*x^2)^(3/2))/(3*x) - (a*(d + e*x^2)^(5/2))/(3*x^3) + (5/2)*a*d*e^(3/2)*atanh((sqrt(e)*x)/sqrt(d + e*x^2)) + b*Unintegrable(((d + e*x^2)^(5/2)*atan(c*x))/x^4, x)]

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

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

    @test_int [x^3*(a + b*atan(c*x))/(d + e*x^2)^(3/2), x, 7, (d*(a + b*atan(c*x)))/(e^2*sqrt(d + e*x^2)) + (sqrt(d + e*x^2)*(a + b*atan(c*x)))/e^2 - (b*(2*c^2*d - e)*atan((sqrt(c^2*d - e)*x)/sqrt(d + e*x^2)))/(c*sqrt(c^2*d - e)*e^2) - (b*atanh((sqrt(e)*x)/sqrt(d + e*x^2)))/(c*e^(3/2))]
    @test_int [x^2*(a + b*atan(c*x))/(d + e*x^2)^(3/2), x, 4, -((a*x)/(e*sqrt(d + e*x^2))) + (a*atanh((sqrt(e)*x)/sqrt(d + e*x^2)))/e^(3/2) + b*Unintegrable((x^2*atan(c*x))/(d + e*x^2)^(3/2), x)]
    @test_int [x^1*(a + b*atan(c*x))/(d + e*x^2)^(3/2), x, 3, -((a + b*atan(c*x))/(e*sqrt(d + e*x^2))) + (b*c*atan((sqrt(c^2*d - e)*x)/sqrt(d + e*x^2)))/(sqrt(c^2*d - e)*e)]
    @test_int [x^0*(a + b*atan(c*x))/(d + e*x^2)^(3/2), x, 5, (x*(a + b*atan(c*x)))/(d*sqrt(d + e*x^2)) + (b*atanh((c*sqrt(d + e*x^2))/sqrt(c^2*d - e)))/(d*sqrt(c^2*d - e))]
    @test_int [(a + b*atan(c*x))/(x^1*(d + e*x^2)^(3/2)), x, 5, a/(d*sqrt(d + e*x^2)) - (a*atanh(sqrt(d + e*x^2)/sqrt(d)))/d^(3/2) + b*Unintegrable(atan(c*x)/(x*(d + e*x^2)^(3/2)), x)]
    @test_int [(a + b*atan(c*x))/(x^2*(d + e*x^2)^(3/2)), x, 8, -((a + b*atan(c*x))/(d*x*sqrt(d + e*x^2))) - (2*e*x*(a + b*atan(c*x)))/(d^2*sqrt(d + e*x^2)) - (b*c*atanh(sqrt(d + e*x^2)/sqrt(d)))/d^(3/2) + (b*(c^2*d - 2*e)*atanh((c*sqrt(d + e*x^2))/sqrt(c^2*d - e)))/(d^2*sqrt(c^2*d - e))]
    @test_int [(a + b*atan(c*x))/(x^3*(d + e*x^2)^(3/2)), x, 6, -((3*a*e)/(2*d^2*sqrt(d + e*x^2))) - a/(2*d*x^2*sqrt(d + e*x^2)) + (3*a*e*atanh(sqrt(d + e*x^2)/sqrt(d)))/(2*d^(5/2)) + b*Unintegrable(atan(c*x)/(x^3*(d + e*x^2)^(3/2)), x)]
    @test_int [(a + b*atan(c*x))/(x^4*(d + e*x^2)^(3/2)), x, 14, -((b*c*sqrt(d + e*x^2))/(6*d^2*x^2)) - (a + b*atan(c*x))/(3*d*x^3*sqrt(d + e*x^2)) + (4*e*(a + b*atan(c*x)))/(3*d^2*x*sqrt(d + e*x^2)) + (8*e^2*x*(a + b*atan(c*x)))/(3*d^3*sqrt(d + e*x^2)) + (b*c*e*atanh(sqrt(d + e*x^2)/sqrt(d)))/(6*d^(5/2)) + (b*c*(c^2*d + 4*e)*atanh(sqrt(d + e*x^2)/sqrt(d)))/(3*d^(5/2)) - (b*(c^4*d^2 + 4*c^2*d*e - 8*e^2)*atanh((c*sqrt(d + e*x^2))/sqrt(c^2*d - e)))/(3*d^3*sqrt(c^2*d - e))]

    @test_int [x^4*(a + b*atan(c*x))/(d + e*x^2)^(5/2), x, 5, -((a*x^3)/(3*e*(d + e*x^2)^(3/2))) - (a*x)/(e^2*sqrt(d + e*x^2)) + (a*atanh((sqrt(e)*x)/sqrt(d + e*x^2)))/e^(5/2) + b*Unintegrable((x^4*atan(c*x))/(d + e*x^2)^(5/2), x)]
    @test_int [x^3*(a + b*atan(c*x))/(d + e*x^2)^(5/2), x, 6, (b*c*x)/(3*(c^2*d - e)*e*sqrt(d + e*x^2)) + (d*(a + b*atan(c*x)))/(3*e^2*(d + e*x^2)^(3/2)) - (a + b*atan(c*x))/(e^2*sqrt(d + e*x^2)) + (b*c*(2*c^2*d - 3*e)*atan((sqrt(c^2*d - e)*x)/sqrt(d + e*x^2)))/(3*(c^2*d - e)^(3/2)*e^2)]
    @test_int [x^2*(a + b*atan(c*x))/(d + e*x^2)^(5/2), x, 5, (b*c)/(3*(c^2*d - e)*e*sqrt(d + e*x^2)) + (x^3*(a + b*atan(c*x)))/(3*d*(d + e*x^2)^(3/2)) - (b*atanh((c*sqrt(d + e*x^2))/sqrt(c^2*d - e)))/(3*d*(c^2*d - e)^(3/2))]
    @test_int [x^1*(a + b*atan(c*x))/(d + e*x^2)^(5/2), x, 4, -((b*c*x)/(3*d*(c^2*d - e)*sqrt(d + e*x^2))) - (a + b*atan(c*x))/(3*e*(d + e*x^2)^(3/2)) + (b*c^3*atan((sqrt(c^2*d - e)*x)/sqrt(d + e*x^2)))/(3*(c^2*d - e)^(3/2)*e)]
    @test_int [x^0*(a + b*atan(c*x))/(d + e*x^2)^(5/2), x, 7, -((b*c)/(3*d*(c^2*d - e)*sqrt(d + e*x^2))) + (x*(a + b*atan(c*x)))/(3*d*(d + e*x^2)^(3/2)) + (2*x*(a + b*atan(c*x)))/(3*d^2*sqrt(d + e*x^2)) + (b*(3*c^2*d - 2*e)*atanh((c*sqrt(d + e*x^2))/sqrt(c^2*d - e)))/(3*d^2*(c^2*d - e)^(3/2))]
    @test_int [(a + b*atan(c*x))/(x^1*(d + e*x^2)^(5/2)), x, 6, a/(3*d*(d + e*x^2)^(3/2)) + a/(d^2*sqrt(d + e*x^2)) - (a*atanh(sqrt(d + e*x^2)/sqrt(d)))/d^(5/2) + b*Unintegrable(atan(c*x)/(x*(d + e*x^2)^(5/2)), x)]
    @test_int [(a + b*atan(c*x))/(x^2*(d + e*x^2)^(5/2)), x, 13, (b*c)/(d^2*sqrt(d + e*x^2)) - (8*b*e)/(3*c*d^3*sqrt(d + e*x^2)) - (b*(3*c^4*d^2 - 12*c^2*d*e + 8*e^2))/(3*c*d^3*(c^2*d - e)*sqrt(d + e*x^2)) - (a + b*atan(c*x))/(d*x*(d + e*x^2)^(3/2)) - (4*e*x*(a + b*atan(c*x)))/(3*d^2*(d + e*x^2)^(3/2)) - (8*e*x*(a + b*atan(c*x)))/(3*d^3*sqrt(d + e*x^2)) - (b*c*atanh(sqrt(d + e*x^2)/sqrt(d)))/d^(5/2) + (b*(3*c^4*d^2 - 12*c^2*d*e + 8*e^2)*atanh((c*sqrt(d + e*x^2))/sqrt(c^2*d - e)))/(3*d^3*(c^2*d - e)^(3/2))]
    @test_int [(a + b*atan(c*x))/(x^3*(d + e*x^2)^(5/2)), x, 7, -((5*a*e)/(6*d^2*(d + e*x^2)^(3/2))) - a/(2*d*x^2*(d + e*x^2)^(3/2)) - (5*a*e)/(2*d^3*sqrt(d + e*x^2)) + (5*a*e*atanh(sqrt(d + e*x^2)/sqrt(d)))/(2*d^(7/2)) + b*Unintegrable(atan(c*x)/(x^3*(d + e*x^2)^(5/2)), x)]
    @test_int [(a + b*atan(c*x))/(x^4*(d + e*x^2)^(5/2)), x, 18, -((b*c*e)/(2*d^3*sqrt(d + e*x^2))) + (16*b*e^2)/(3*c*d^4*sqrt(d + e*x^2)) - (b*c*(c^2*d + 6*e))/(3*d^3*sqrt(d + e*x^2)) + (b*(c^2*d - 2*e)*(c^4*d^2 + 8*c^2*d*e - 8*e^2))/(3*c*d^4*(c^2*d - e)*sqrt(d + e*x^2)) - (b*c)/(6*d^2*x^2*sqrt(d + e*x^2)) - (a + b*atan(c*x))/(3*d*x^3*(d + e*x^2)^(3/2)) + (2*e*(a + b*atan(c*x)))/(d^2*x*(d + e*x^2)^(3/2)) + (8*e^2*x*(a + b*atan(c*x)))/(3*d^3*(d + e*x^2)^(3/2)) + (16*e^2*x*(a + b*atan(c*x)))/(3*d^4*sqrt(d + e*x^2)) + (b*c*e*atanh(sqrt(d + e*x^2)/sqrt(d)))/(2*d^(7/2)) + (b*c*(c^2*d + 6*e)*atanh(sqrt(d + e*x^2)/sqrt(d)))/(3*d^(7/2)) - (b*(c^2*d - 2*e)*(c^4*d^2 + 8*c^2*d*e - 8*e^2)*atanh((c*sqrt(d + e*x^2))/sqrt(c^2*d - e)))/(3*d^4*(c^2*d - e)^(3/2))]

    @test_int [atan(a*x)/(c + d*x^2)^(7/2), x, 8, -(a/(15*c*(a^2*c - d)*(c + d*x^2)^(3/2))) - (a*(7*a^2*c - 4*d))/(15*c^2*(a^2*c - d)^2*sqrt(c + d*x^2)) + (x*atan(a*x))/(5*c*(c + d*x^2)^(5/2)) + (4*x*atan(a*x))/(15*c^2*(c + d*x^2)^(3/2)) + (8*x*atan(a*x))/(15*c^3*sqrt(c + d*x^2)) + ((15*a^4*c^2 - 20*a^2*c*d + 8*d^2)*atanh((a*sqrt(c + d*x^2))/sqrt(a^2*c - d)))/(15*c^3*(a^2*c - d)^(5/2))]

    @test_int [atan(a*x)/(c + d*x^2)^(9/2), x, 8, -(a/(35*c*(a^2*c - d)*(c + d*x^2)^(5/2))) - (a*(11*a^2*c - 6*d))/(105*c^2*(a^2*c - d)^2*(c + d*x^2)^(3/2)) - (a*(19*a^4*c^2 - 22*a^2*c*d + 8*d^2))/(35*c^3*(a^2*c - d)^3*sqrt(c + d*x^2)) + (x*atan(a*x))/(7*c*(c + d*x^2)^(7/2)) + (6*x*atan(a*x))/(35*c^2*(c + d*x^2)^(5/2)) + (8*x*atan(a*x))/(35*c^3*(c + d*x^2)^(3/2)) + (16*x*atan(a*x))/(35*c^4*sqrt(c + d*x^2)) + ((35*a^6*c^3 - 70*a^4*c^2*d + 56*a^2*c*d^2 - 16*d^3)*atanh((a*sqrt(c + d*x^2))/sqrt(a^2*c - d)))/(35*c^4*(a^2*c - d)^(7/2))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(d+e*x^2)^p*(a+b*atan(c*x))*with*m*symbolic=#

    @test_int [x^m*(a + b*atan(c*x))*(d + e*x^2)^3, x, 4, If(13>=8, -((b*e*(e^2*(15 + 8*m + m^2) - 3*c^2*d*e*(21 + 10*m + m^2) + 3*c^4*d^2*(35 + 12*m + m^2))*x^(2 + m))/(c^5*(2 + m)*(3 + m)*(5 + m)*(7 + m))) + (b*e^2*(e*(5 + m) - 3*c^2*d*(7 + m))*x^(4 + m))/(c^3*(4 + m)*(5 + m)*(7 + m)) - (b*e^3*x^(6 + m))/(c*(6 + m)*(7 + m)) + (d^3*x^(1 + m)*(a + b*atan(c*x)))/(1 + m) + (3*d^2*e*x^(3 + m)*(a + b*atan(c*x)))/(3 + m) + (3*d*e^2*x^(5 + m)*(a + b*atan(c*x)))/(5 + m) + (e^3*x^(7 + m)*(a + b*atan(c*x)))/(7 + m) + (b*(e^3*(15 + 23*m + 9*m^2 + m^3) - 3*c^2*d*e^2*(21 + 31*m + 11*m^2 + m^3) + 3*c^4*d^2*e*(35 + 47*m + 13*m^2 + m^3) - c^6*d^3*(105 + 71*m + 15*m^2 + m^3))*x^(2 + m)*HypergeometricFunctions._₂F₁(1, (2 + m)/2, (4 + m)/2, (-c^2)*x^2))/(c^5*(1 + m)*(2 + m)*(3 + m)*(5 + m)*(7 + m)), -((b*e*(e^2*(15 + 8*m + m^2) - 3*c^2*d*e*(21 + 10*m + m^2) + 3*c^4*d^2*(35 + 12*m + m^2))*x^(2 + m))/(c^5*(2 + m)*(7 + m)*(15 + 8*m + m^2))) + (b*e^2*(e*(5 + m) - 3*c^2*d*(7 + m))*x^(4 + m))/(c^3*(4 + m)*(5 + m)*(7 + m)) - (b*e^3*x^(6 + m))/(c*(6 + m)*(7 + m)) + (d^3*x^(1 + m)*(a + b*atan(c*x)))/(1 + m) + (3*d^2*e*x^(3 + m)*(a + b*atan(c*x)))/(3 + m) + (3*d*e^2*x^(5 + m)*(a + b*atan(c*x)))/(5 + m) + (e^3*x^(7 + m)*(a + b*atan(c*x)))/(7 + m) + (b*(e^3*(15 + 23*m + 9*m^2 + m^3) - 3*c^2*d*e^2*(21 + 31*m + 11*m^2 + m^3) + 3*c^4*d^2*e*(35 + 47*m + 13*m^2 + m^3) - c^6*d^3*(105 + 71*m + 15*m^2 + m^3))*x^(2 + m)*HypergeometricFunctions._₂F₁(1, (2 + m)/2, (4 + m)/2, (-c^2)*x^2))/(c^5*(35 + 12*m + m^2)*(6 + 11*m + 6*m^2 + m^3)))]
    @test_int [x^m*(a + b*atan(c*x))*(d + e*x^2)^2, x, 4, If(13>=8, (b*e*(e*(3 + m) - 2*c^2*d*(5 + m))*x^(2 + m))/(c^3*(2 + m)*(3 + m)*(5 + m)) - (b*e^2*x^(4 + m))/(c*(4 + m)*(5 + m)) + (d^2*x^(1 + m)*(a + b*atan(c*x)))/(1 + m) + (2*d*e*x^(3 + m)*(a + b*atan(c*x)))/(3 + m) + (e^2*x^(5 + m)*(a + b*atan(c*x)))/(5 + m) - (b*(e^2*(3 + 4*m + m^2) - 2*c^2*d*e*(5 + 6*m + m^2) + c^4*d^2*(15 + 8*m + m^2))*x^(2 + m)*HypergeometricFunctions._₂F₁(1, (2 + m)/2, (4 + m)/2, (-c^2)*x^2))/(c^3*(1 + m)*(2 + m)*(3 + m)*(5 + m)), (b*e*(e*(3 + m) - 2*c^2*d*(5 + m))*x^(2 + m))/(c^3*(5 + m)*(6 + 5*m + m^2)) - (b*e^2*x^(4 + m))/(c*(4 + m)*(5 + m)) + (d^2*x^(1 + m)*(a + b*atan(c*x)))/(1 + m) + (2*d*e*x^(3 + m)*(a + b*atan(c*x)))/(3 + m) + (e^2*x^(5 + m)*(a + b*atan(c*x)))/(5 + m) - (b*(e^2*(3 + 4*m + m^2) - 2*c^2*d*e*(5 + 6*m + m^2) + c^4*d^2*(15 + 8*m + m^2))*x^(2 + m)*HypergeometricFunctions._₂F₁(1, (2 + m)/2, (4 + m)/2, (-c^2)*x^2))/(c^3*(2 + 3*m + m^2)*(15 + 8*m + m^2)))]
    @test_int [x^m*(a + b*atan(c*x))*(d + e*x^2)^1, x, 3, -((b*e*x^(2 + m))/(c*(6 + 5*m + m^2))) + (d*x^(1 + m)*(a + b*atan(c*x)))/(1 + m) + (e*x^(3 + m)*(a + b*atan(c*x)))/(3 + m) - (b*((c^2*d)/(1 + m) - e/(3 + m))*x^(2 + m)*HypergeometricFunctions._₂F₁(1, (2 + m)/2, (4 + m)/2, (-c^2)*x^2))/(c*(2 + m))]
    @test_int [x^m*(a + b*atan(c*x))/(d + e*x^2)^1, x, 2, (a*x^(1 + m)*HypergeometricFunctions._₂F₁(1, (1 + m)/2, (3 + m)/2, -((e*x^2)/d)))/(d*(1 + m)) + b*Unintegrable((x^m*atan(c*x))/(d + e*x^2), x)]
    @test_int [x^m*(a + b*atan(c*x))/(d + e*x^2)^2, x, 2, (a*x^(1 + m)*HypergeometricFunctions._₂F₁(2, (1 + m)/2, (3 + m)/2, -((e*x^2)/d)))/(d^2*(1 + m)) + b*Unintegrable((x^m*atan(c*x))/(d + e*x^2)^2, x)]

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

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(d+e*x^2)^p*(a+b*atan(c*x))*with*p*symbolic=#

    @test_int [x^m*(a + b*atan(c*x))*(d + e*x^2)^p, x, 3, (a*x^(1 + m)*(d + e*x^2)^(1 + p)*HypergeometricFunctions._₂F₁(1, (1/2)*(3 + m + 2*p), (3 + m)/2, -((e*x^2)/d)))/(d*(1 + m)) + b*Unintegrable(x^m*(d + e*x^2)^p*atan(c*x), x), (a*x^(1 + m)*(d + e*x^2)^p*HypergeometricFunctions._₂F₁((1 + m)/2, -p, (3 + m)/2, -((e*x^2)/d)))/((1 + (e*x^2)/d)^p*(1 + m)) + b*Unintegrable(x^m*(d + e*x^2)^p*atan(c*x), x)]

    @test_int [(a + b*atan(c*x))*(d + e*x^2)^p/x^(2*p + 2), x, 3, -((a*x^(-1 - 2*p)*(d + e*x^2)^(1 + p)*HypergeometricFunctions._₂F₁(1/2, 1, (1/2)*(1 - 2*p), -((e*x^2)/d)))/(d*(1 + 2*p))) + b*Unintegrable(x^(-2 - 2*p)*(d + e*x^2)^p*atan(c*x), x), -((a*x^(-1 - 2*p)*(d + e*x^2)^p*HypergeometricFunctions._₂F₁((1/2)*(-1 - 2*p), -p, (1/2)*(1 - 2*p), -((e*x^2)/d)))/((1 + (e*x^2)/d)^p*(1 + 2*p))) + b*Unintegrable(x^(-2 - 2*p)*(d + e*x^2)^p*atan(c*x), x)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^p/x^(2*p + 3), x, 4, -((b*c*x^(-1 - 2*p)*(d + e*x^2)^p*AppellF1((1/2)*(-1 - 2*p), 1, -1 - p, (1/2)*(1 - 2*p), (-c^2)*x^2, -((e*x^2)/d)))/((1 + (e*x^2)/d)^p*(2*(1 + 3*p + 2*p^2)))) - ((d + e*x^2)^(1 + p)*(a + b*atan(c*x)))/(x^(2*(1 + p))*(2*d*(1 + p)))]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^p/x^(2*p + 4), x, 3, -((a*x^(-3 - 2*p)*(d + e*x^2)^(1 + p)*HypergeometricFunctions._₂F₁(-(1/2), 1, (1/2)*(-1 - 2*p), -((e*x^2)/d)))/(d*(3 + 2*p))) + b*Unintegrable(x^(-4 - 2*p)*(d + e*x^2)^p*atan(c*x), x), -((a*x^(-3 - 2*p)*(d + e*x^2)^p*HypergeometricFunctions._₂F₁((1/2)*(-3 - 2*p), -p, (1/2)*(-1 - 2*p), -((e*x^2)/d)))/((1 + (e*x^2)/d)^p*(3 + 2*p))) + b*Unintegrable(x^(-4 - 2*p)*(d + e*x^2)^p*atan(c*x), x)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^p/x^(2*p + 5), x, 8, If(13>=8, -((b*(e + c^2*d*(1 + p))*x^(-3 - 2*p)*(d + e*x^2)^p*AppellF1((1/2)*(-3 - 2*p), 1, -1 - p, (1/2)*(-1 - 2*p), (-c^2)*x^2, -((e*x^2)/d)))/((1 + (e*x^2)/d)^p*(2*c*d*(1 + p)*(2 + p)*(3 + 2*p)))) + (e*(d + e*x^2)^(1 + p)*(a + b*atan(c*x)))/(x^(2*(1 + p))*(2*d^2*(1 + p)*(2 + p))) - ((d + e*x^2)^(1 + p)*(a + b*atan(c*x)))/(x^(2*(2 + p))*(2*d*(2 + p))) + (b*e*x^(-3 - 2*p)*(d + e*x^2)^p*HypergeometricFunctions._₂F₁((1/2)*(-3 - 2*p), -1 - p, (1/2)*(-1 - 2*p), -((e*x^2)/d)))/((1 + (e*x^2)/d)^p*(2*c*d*(6 + 13*p + 9*p^2 + 2*p^3))), -((b*(e + c^2*d*(1 + p))*x^(-3 - 2*p)*(d + e*x^2)^p*AppellF1((1/2)*(-3 - 2*p), 1, -1 - p, (1/2)*(-1 - 2*p), (-c^2)*x^2, -((e*x^2)/d)))/((1 + (e*x^2)/d)^p*(2*c*d*(3 + 2*p)*(2 + 3*p + p^2)))) + (e*(d + e*x^2)^(1 + p)*(a + b*atan(c*x)))/(x^(2*(1 + p))*(2*d^2*(1 + p)*(2 + p))) - ((d + e*x^2)^(1 + p)*(a + b*atan(c*x)))/(x^(2*(2 + p))*(2*d*(2 + p))) + (b*e*x^(-3 - 2*p)*(d + e*x^2)^p*HypergeometricFunctions._₂F₁((1/2)*(-3 - 2*p), -1 - p, (1/2)*(-1 - 2*p), -((e*x^2)/d)))/((1 + (e*x^2)/d)^p*(2*c*d*(6 + 13*p + 9*p^2 + 2*p^3))))]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^p/x^(2*p + 6), x, 3, -((a*x^(-5 - 2*p)*(d + e*x^2)^(1 + p)*HypergeometricFunctions._₂F₁(-(3/2), 1, (1/2)*(-3 - 2*p), -((e*x^2)/d)))/(d*(5 + 2*p))) + b*Unintegrable(x^(-6 - 2*p)*(d + e*x^2)^p*atan(c*x), x), -((a*x^(-5 - 2*p)*(d + e*x^2)^p*HypergeometricFunctions._₂F₁((1/2)*(-5 - 2*p), -p, (1/2)*(-3 - 2*p), -((e*x^2)/d)))/((1 + (e*x^2)/d)^p*(5 + 2*p))) + b*Unintegrable(x^(-6 - 2*p)*(d + e*x^2)^p*atan(c*x), x)]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^p/x^(2*p + 7), x, 10, If(13>=8, -((b*(2*e^2 + 2*c^2*d*e*(1 + p) + c^4*d^2*(2 + 3*p + p^2))*x^(-5 - 2*p)*(d + e*x^2)^p*AppellF1((1/2)*(-5 - 2*p), 1, -1 - p, (1/2)*(-3 - 2*p), (-c^2)*x^2, -((e*x^2)/d)))/((1 + (e*x^2)/d)^p*(2*c^3*d^2*(1 + p)*(2 + p)*(3 + p)*(5 + 2*p)))) - (e^2*(d + e*x^2)^(1 + p)*(a + b*atan(c*x)))/(x^(2*(1 + p))*(d^3*(1 + p)*(2 + p)*(3 + p))) + (e*(d + e*x^2)^(1 + p)*(a + b*atan(c*x)))/(x^(2*(2 + p))*(d^2*(2 + p)*(3 + p))) - ((d + e*x^2)^(1 + p)*(a + b*atan(c*x)))/(x^(2*(3 + p))*(2*d*(3 + p))) + (b*e*(e + c^2*d*(1 + p))*x^(-5 - 2*p)*(d + e*x^2)^p*HypergeometricFunctions._₂F₁((1/2)*(-5 - 2*p), -1 - p, (1/2)*(-3 - 2*p), -((e*x^2)/d)))/((1 + (e*x^2)/d)^p*(c^3*d^2*(1 + p)*(2 + p)*(3 + p)*(5 + 2*p))) - (b*e^2*x^(-3 - 2*p)*(d + e*x^2)^p*HypergeometricFunctions._₂F₁((1/2)*(-3 - 2*p), -1 - p, (1/2)*(-1 - 2*p), -((e*x^2)/d)))/((1 + (e*x^2)/d)^p*(c*d^2*(1 + p)*(2 + p)*(3 + p)*(3 + 2*p))), -((b*(2*e^2 + 2*c^2*d*e*(1 + p) + c^4*d^2*(2 + 3*p + p^2))*x^(-5 - 2*p)*(d + e*x^2)^p*AppellF1((1/2)*(-5 - 2*p), 1, -1 - p, (1/2)*(-3 - 2*p), (-c^2)*x^2, -((e*x^2)/d)))/((1 + (e*x^2)/d)^p*(2*c^3*d^2*(3 + p)*(5 + 2*p)*(2 + 3*p + p^2)))) - (e^2*(d + e*x^2)^(1 + p)*(a + b*atan(c*x)))/(x^(2*(1 + p))*(d^3*(2 + p)*(3 + 4*p + p^2))) + (e*(d + e*x^2)^(1 + p)*(a + b*atan(c*x)))/(x^(2*(2 + p))*(d^2*(2 + p)*(3 + p))) - ((d + e*x^2)^(1 + p)*(a + b*atan(c*x)))/(x^(2*(3 + p))*(2*d*(3 + p))) + (b*e*(e + c^2*d*(1 + p))*x^(-5 - 2*p)*(d + e*x^2)^p*HypergeometricFunctions._₂F₁((1/2)*(-5 - 2*p), -1 - p, (1/2)*(-3 - 2*p), -((e*x^2)/d)))/((1 + (e*x^2)/d)^p*(c^3*d^2*(3 + p)*(5 + 2*p)*(2 + 3*p + p^2))) - (b*e^2*x^(-3 - 2*p)*(d + e*x^2)^p*HypergeometricFunctions._₂F₁((1/2)*(-3 - 2*p), -1 - p, (1/2)*(-1 - 2*p), -((e*x^2)/d)))/((1 + (e*x^2)/d)^p*(c*d^2*(2 + 3*p + p^2)*(9 + 9*p + 2*p^2))))]
    @test_int [(a + b*atan(c*x))*(d + e*x^2)^p/x^(2*p + 8), x, 3, -((a*x^(-7 - 2*p)*(d + e*x^2)^(1 + p)*HypergeometricFunctions._₂F₁(-(5/2), 1, (1/2)*(-5 - 2*p), -((e*x^2)/d)))/(d*(7 + 2*p))) + b*Unintegrable(x^(-8 - 2*p)*(d + e*x^2)^p*atan(c*x), x), -((a*x^(-7 - 2*p)*(d + e*x^2)^p*HypergeometricFunctions._₂F₁((1/2)*(-7 - 2*p), -p, (1/2)*(-5 - 2*p), -((e*x^2)/d)))/((1 + (e*x^2)/d)^p*(7 + 2*p))) + b*Unintegrable(x^(-8 - 2*p)*(d + e*x^2)^p*atan(c*x), x)]

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

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

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

    @test_int [x^3*(d + e*x^2)*(a + b*atan(c*x))^2, x, 29, (a*b*d*x)/(2*c^3) - (a*b*e*x)/(3*c^5) + (b^2*d*x^2)/(12*c^2) - (4*b^2*e*x^2)/(45*c^4) + (b^2*e*x^4)/(60*c^2) + (b^2*d*x*atan(c*x))/(2*c^3) - (b^2*e*x*atan(c*x))/(3*c^5) - (b*d*x^3*(a + b*atan(c*x)))/(6*c) + (b*e*x^3*(a + b*atan(c*x)))/(9*c^3) - (b*e*x^5*(a + b*atan(c*x)))/(15*c) - (d*(a + b*atan(c*x))^2)/(4*c^4) + (e*(a + b*atan(c*x))^2)/(6*c^6) + (1/4)*d*x^4*(a + b*atan(c*x))^2 + (1/6)*e*x^6*(a + b*atan(c*x))^2 - (b^2*d*log(1 + c^2*x^2))/(3*c^4) + (23*b^2*e*log(1 + c^2*x^2))/(90*c^6)]
    @test_int [x^2*(d + e*x^2)*(a + b*atan(c*x))^2, x, 25, (b^2*d*x)/(3*c^2) - (3*b^2*e*x)/(10*c^4) + (b^2*e*x^3)/(30*c^2) - (b^2*d*atan(c*x))/(3*c^3) + (3*b^2*e*atan(c*x))/(10*c^5) - (b*d*x^2*(a + b*atan(c*x)))/(3*c) + (b*e*x^2*(a + b*atan(c*x)))/(5*c^3) - (b*e*x^4*(a + b*atan(c*x)))/(10*c) - (im*d*(a + b*atan(c*x))^2)/(3*c^3) + (im*e*(a + b*atan(c*x))^2)/(5*c^5) + (1/3)*d*x^3*(a + b*atan(c*x))^2 + (1/5)*e*x^5*(a + b*atan(c*x))^2 - (2*b*d*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(3*c^3) + (2*b*e*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(5*c^5) - (im*b^2*d*PolyLog(2, 1 - 2/(1 + im*c*x)))/(3*c^3) + (im*b^2*e*PolyLog(2, 1 - 2/(1 + im*c*x)))/(5*c^5)]
    @test_int [x^1*(d + e*x^2)*(a + b*atan(c*x))^2, x, 19, -((a*b*d*x)/c) + (a*b*e*x)/(2*c^3) + (b^2*e*x^2)/(12*c^2) - (b^2*d*x*atan(c*x))/c + (b^2*e*x*atan(c*x))/(2*c^3) - (b*e*x^3*(a + b*atan(c*x)))/(6*c) + (d*(a + b*atan(c*x))^2)/(2*c^2) - (e*(a + b*atan(c*x))^2)/(4*c^4) + (1/2)*d*x^2*(a + b*atan(c*x))^2 + (1/4)*e*x^4*(a + b*atan(c*x))^2 + (b^2*d*log(1 + c^2*x^2))/(2*c^2) - (b^2*e*log(1 + c^2*x^2))/(3*c^4)]
    @test_int [x^0*(d + e*x^2)*(a + b*atan(c*x))^2, x, 16, (b^2*e*x)/(3*c^2) - (b^2*e*atan(c*x))/(3*c^3) - (b*e*x^2*(a + b*atan(c*x)))/(3*c) + (im*d*(a + b*atan(c*x))^2)/c - (im*e*(a + b*atan(c*x))^2)/(3*c^3) + d*x*(a + b*atan(c*x))^2 + (1/3)*e*x^3*(a + b*atan(c*x))^2 + (2*b*d*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/c - (2*b*e*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(3*c^3) + (im*b^2*d*PolyLog(2, 1 - 2/(1 + im*c*x)))/c - (im*b^2*e*PolyLog(2, 1 - 2/(1 + im*c*x)))/(3*c^3)]
    @test_int [(d + e*x^2)*(a + b*atan(c*x))^2/x^1, x, 14, -((a*b*e*x)/c) - (b^2*e*x*atan(c*x))/c + (e*(a + b*atan(c*x))^2)/(2*c^2) + (1/2)*e*x^2*(a + b*atan(c*x))^2 + 2*d*(a + b*atan(c*x))^2*atanh(1 - 2/(1 + im*c*x)) + (b^2*e*log(1 + c^2*x^2))/(2*c^2) - im*b*d*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)) + im*b*d*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 + im*c*x)) - (1/2)*b^2*d*PolyLog(3, 1 - 2/(1 + im*c*x)) + (1/2)*b^2*d*PolyLog(3, -1 + 2/(1 + im*c*x))]
    @test_int [(d + e*x^2)*(a + b*atan(c*x))^2/x^2, x, 11, (-im)*c*d*(a + b*atan(c*x))^2 + (im*e*(a + b*atan(c*x))^2)/c - (d*(a + b*atan(c*x))^2)/x + e*x*(a + b*atan(c*x))^2 + (2*b*e*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/c + 2*b*c*d*(a + b*atan(c*x))*log(2 - 2/(1 - im*c*x)) - im*b^2*c*d*PolyLog(2, -1 + 2/(1 - im*c*x)) + (im*b^2*e*PolyLog(2, 1 - 2/(1 + im*c*x)))/c]
    @test_int [(d + e*x^2)*(a + b*atan(c*x))^2/x^3, x, 16, -((b*c*d*(a + b*atan(c*x)))/x) - (1/2)*c^2*d*(a + b*atan(c*x))^2 - (d*(a + b*atan(c*x))^2)/(2*x^2) + 2*e*(a + b*atan(c*x))^2*atanh(1 - 2/(1 + im*c*x)) + b^2*c^2*d*log(x) - (1/2)*b^2*c^2*d*log(1 + c^2*x^2) - im*b*e*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)) + im*b*e*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 + im*c*x)) - (1/2)*b^2*e*PolyLog(3, 1 - 2/(1 + im*c*x)) + (1/2)*b^2*e*PolyLog(3, -1 + 2/(1 + im*c*x))]

    @test_int [x^3*(d + e*x^2)^2*(a + b*atan(c*x))^2, x, 50, (a*b*d^2*x)/(2*c^3) - (2*a*b*d*e*x)/(3*c^5) + (a*b*e^2*x)/(4*c^7) + (b^2*d^2*x^2)/(12*c^2) - (8*b^2*d*e*x^2)/(45*c^4) + (71*b^2*e^2*x^2)/(840*c^6) + (b^2*d*e*x^4)/(30*c^2) - (3*b^2*e^2*x^4)/(140*c^4) + (b^2*e^2*x^6)/(168*c^2) + (b^2*d^2*x*atan(c*x))/(2*c^3) - (2*b^2*d*e*x*atan(c*x))/(3*c^5) + (b^2*e^2*x*atan(c*x))/(4*c^7) - (b*d^2*x^3*(a + b*atan(c*x)))/(6*c) + (2*b*d*e*x^3*(a + b*atan(c*x)))/(9*c^3) - (b*e^2*x^3*(a + b*atan(c*x)))/(12*c^5) - (2*b*d*e*x^5*(a + b*atan(c*x)))/(15*c) + (b*e^2*x^5*(a + b*atan(c*x)))/(20*c^3) - (b*e^2*x^7*(a + b*atan(c*x)))/(28*c) - (d^2*(a + b*atan(c*x))^2)/(4*c^4) + (d*e*(a + b*atan(c*x))^2)/(3*c^6) - (e^2*(a + b*atan(c*x))^2)/(8*c^8) + (1/4)*d^2*x^4*(a + b*atan(c*x))^2 + (1/3)*d*e*x^6*(a + b*atan(c*x))^2 + (1/8)*e^2*x^8*(a + b*atan(c*x))^2 - (b^2*d^2*log(1 + c^2*x^2))/(3*c^4) + (23*b^2*d*e*log(1 + c^2*x^2))/(45*c^6) - (22*b^2*e^2*log(1 + c^2*x^2))/(105*c^8)]
    @test_int [x^2*(d + e*x^2)^2*(a + b*atan(c*x))^2, x, 44, (b^2*d^2*x)/(3*c^2) - (3*b^2*d*e*x)/(5*c^4) + (11*b^2*e^2*x)/(42*c^6) + (b^2*d*e*x^3)/(15*c^2) - (5*b^2*e^2*x^3)/(126*c^4) + (b^2*e^2*x^5)/(105*c^2) - (b^2*d^2*atan(c*x))/(3*c^3) + (3*b^2*d*e*atan(c*x))/(5*c^5) - (11*b^2*e^2*atan(c*x))/(42*c^7) - (b*d^2*x^2*(a + b*atan(c*x)))/(3*c) + (2*b*d*e*x^2*(a + b*atan(c*x)))/(5*c^3) - (b*e^2*x^2*(a + b*atan(c*x)))/(7*c^5) - (b*d*e*x^4*(a + b*atan(c*x)))/(5*c) + (b*e^2*x^4*(a + b*atan(c*x)))/(14*c^3) - (b*e^2*x^6*(a + b*atan(c*x)))/(21*c) - (im*d^2*(a + b*atan(c*x))^2)/(3*c^3) + (2*im*d*e*(a + b*atan(c*x))^2)/(5*c^5) - (im*e^2*(a + b*atan(c*x))^2)/(7*c^7) + (1/3)*d^2*x^3*(a + b*atan(c*x))^2 + (2/5)*d*e*x^5*(a + b*atan(c*x))^2 + (1/7)*e^2*x^7*(a + b*atan(c*x))^2 - (2*b*d^2*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(3*c^3) + (4*b*d*e*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(5*c^5) - (2*b*e^2*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(7*c^7) - (im*b^2*d^2*PolyLog(2, 1 - 2/(1 + im*c*x)))/(3*c^3) + (2*im*b^2*d*e*PolyLog(2, 1 - 2/(1 + im*c*x)))/(5*c^5) - (im*b^2*e^2*PolyLog(2, 1 - 2/(1 + im*c*x)))/(7*c^7)]
    @test_int [x^1*(d + e*x^2)^2*(a + b*atan(c*x))^2, x, 35, -((a*b*d^2*x)/c) + (a*b*d*e*x)/c^3 - (a*b*e^2*x)/(3*c^5) + (b^2*d*e*x^2)/(6*c^2) - (4*b^2*e^2*x^2)/(45*c^4) + (b^2*e^2*x^4)/(60*c^2) - (b^2*d^2*x*atan(c*x))/c + (b^2*d*e*x*atan(c*x))/c^3 - (b^2*e^2*x*atan(c*x))/(3*c^5) - (b*d*e*x^3*(a + b*atan(c*x)))/(3*c) + (b*e^2*x^3*(a + b*atan(c*x)))/(9*c^3) - (b*e^2*x^5*(a + b*atan(c*x)))/(15*c) + (d^2*(a + b*atan(c*x))^2)/(2*c^2) - (d*e*(a + b*atan(c*x))^2)/(2*c^4) + (e^2*(a + b*atan(c*x))^2)/(6*c^6) + (1/2)*d^2*x^2*(a + b*atan(c*x))^2 + (1/2)*d*e*x^4*(a + b*atan(c*x))^2 + (1/6)*e^2*x^6*(a + b*atan(c*x))^2 + (b^2*d^2*log(1 + c^2*x^2))/(2*c^2) - (2*b^2*d*e*log(1 + c^2*x^2))/(3*c^4) + (23*b^2*e^2*log(1 + c^2*x^2))/(90*c^6)]
    @test_int [x^0*(d + e*x^2)^2*(a + b*atan(c*x))^2, x, 30, (2*b^2*d*e*x)/(3*c^2) - (3*b^2*e^2*x)/(10*c^4) + (b^2*e^2*x^3)/(30*c^2) - (2*b^2*d*e*atan(c*x))/(3*c^3) + (3*b^2*e^2*atan(c*x))/(10*c^5) - (2*b*d*e*x^2*(a + b*atan(c*x)))/(3*c) + (b*e^2*x^2*(a + b*atan(c*x)))/(5*c^3) - (b*e^2*x^4*(a + b*atan(c*x)))/(10*c) + (im*d^2*(a + b*atan(c*x))^2)/c - (2*im*d*e*(a + b*atan(c*x))^2)/(3*c^3) + (im*e^2*(a + b*atan(c*x))^2)/(5*c^5) + d^2*x*(a + b*atan(c*x))^2 + (2/3)*d*e*x^3*(a + b*atan(c*x))^2 + (1/5)*e^2*x^5*(a + b*atan(c*x))^2 + (2*b*d^2*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/c - (4*b*d*e*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(3*c^3) + (2*b*e^2*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(5*c^5) + (im*b^2*d^2*PolyLog(2, 1 - 2/(1 + im*c*x)))/c - (2*im*b^2*d*e*PolyLog(2, 1 - 2/(1 + im*c*x)))/(3*c^3) + (im*b^2*e^2*PolyLog(2, 1 - 2/(1 + im*c*x)))/(5*c^5)]
    @test_int [(d + e*x^2)^2*(a + b*atan(c*x))^2/x^1, x, 25, -((2*a*b*d*e*x)/c) + (a*b*e^2*x)/(2*c^3) + (b^2*e^2*x^2)/(12*c^2) - (2*b^2*d*e*x*atan(c*x))/c + (b^2*e^2*x*atan(c*x))/(2*c^3) - (b*e^2*x^3*(a + b*atan(c*x)))/(6*c) + (d*e*(a + b*atan(c*x))^2)/c^2 - (e^2*(a + b*atan(c*x))^2)/(4*c^4) + d*e*x^2*(a + b*atan(c*x))^2 + (1/4)*e^2*x^4*(a + b*atan(c*x))^2 + 2*d^2*(a + b*atan(c*x))^2*atanh(1 - 2/(1 + im*c*x)) + (b^2*d*e*log(1 + c^2*x^2))/c^2 - (b^2*e^2*log(1 + c^2*x^2))/(3*c^4) - im*b*d^2*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)) + im*b*d^2*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 + im*c*x)) - (1/2)*b^2*d^2*PolyLog(3, 1 - 2/(1 + im*c*x)) + (1/2)*b^2*d^2*PolyLog(3, -1 + 2/(1 + im*c*x))]
    @test_int [(d + e*x^2)^2*(a + b*atan(c*x))^2/x^2, x, 20, (b^2*e^2*x)/(3*c^2) - (b^2*e^2*atan(c*x))/(3*c^3) - (b*e^2*x^2*(a + b*atan(c*x)))/(3*c) - im*c*d^2*(a + b*atan(c*x))^2 + (2*im*d*e*(a + b*atan(c*x))^2)/c - (im*e^2*(a + b*atan(c*x))^2)/(3*c^3) - (d^2*(a + b*atan(c*x))^2)/x + 2*d*e*x*(a + b*atan(c*x))^2 + (1/3)*e^2*x^3*(a + b*atan(c*x))^2 + (4*b*d*e*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/c - (2*b*e^2*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(3*c^3) + 2*b*c*d^2*(a + b*atan(c*x))*log(2 - 2/(1 - im*c*x)) - im*b^2*c*d^2*PolyLog(2, -1 + 2/(1 - im*c*x)) + (2*im*b^2*d*e*PolyLog(2, 1 - 2/(1 + im*c*x)))/c - (im*b^2*e^2*PolyLog(2, 1 - 2/(1 + im*c*x)))/(3*c^3)]
    @test_int [(d + e*x^2)^2*(a + b*atan(c*x))^2/x^3, x, 22, -((a*b*e^2*x)/c) - (b^2*e^2*x*atan(c*x))/c - (b*c*d^2*(a + b*atan(c*x)))/x - (1/2)*c^2*d^2*(a + b*atan(c*x))^2 + (e^2*(a + b*atan(c*x))^2)/(2*c^2) - (d^2*(a + b*atan(c*x))^2)/(2*x^2) + (1/2)*e^2*x^2*(a + b*atan(c*x))^2 + 4*d*e*(a + b*atan(c*x))^2*atanh(1 - 2/(1 + im*c*x)) + b^2*c^2*d^2*log(x) - (1/2)*b^2*c^2*d^2*log(1 + c^2*x^2) + (b^2*e^2*log(1 + c^2*x^2))/(2*c^2) - 2*im*b*d*e*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)) + 2*im*b*d*e*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 + im*c*x)) - b^2*d*e*PolyLog(3, 1 - 2/(1 + im*c*x)) + b^2*d*e*PolyLog(3, -1 + 2/(1 + im*c*x))]

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

    @test_int [x^3*(a + b*atan(c*x))^2/(d + e*x^2), x, 11, -((a*b*x)/(c*e)) - (b^2*x*atan(c*x))/(c*e) + (a + b*atan(c*x))^2/(2*c^2*e) + (x^2*(a + b*atan(c*x))^2)/(2*e) + (d*(a + b*atan(c*x))^2*log(2/(1 - im*c*x)))/e^2 - (d*(a + b*atan(c*x))^2*log((2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*e^2) - (d*(a + b*atan(c*x))^2*log((2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*e^2) + (b^2*log(1 + c^2*x^2))/(2*c^2*e) - (im*b*d*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 - im*c*x)))/e^2 + (im*b*d*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*e^2) + (im*b*d*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*e^2) + (b^2*d*PolyLog(3, 1 - 2/(1 - im*c*x)))/(2*e^2) - (b^2*d*PolyLog(3, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*e^2) - (b^2*d*PolyLog(3, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*e^2)]
    @test_int [x^2*(a + b*atan(c*x))^2/(d + e*x^2), x, 10, (im*(a + b*atan(c*x))^2)/(c*e) + (x*(a + b*atan(c*x))^2)/e + (2*b*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(c*e) + (sqrt(-d)*(a + b*atan(c*x))^2*log((2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*e^(3/2)) - (sqrt(-d)*(a + b*atan(c*x))^2*log((2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*e^(3/2)) + (im*b^2*PolyLog(2, 1 - 2/(1 + im*c*x)))/(c*e) - (im*b*sqrt(-d)*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*e^(3/2)) + (im*b*sqrt(-d)*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*e^(3/2)) + (b^2*sqrt(-d)*PolyLog(3, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*e^(3/2)) - (b^2*sqrt(-d)*PolyLog(3, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*e^(3/2))]
    @test_int [x^1*(a + b*atan(c*x))^2/(d + e*x^2), x, 4, -(((a + b*atan(c*x))^2*log(2/(1 - im*c*x)))/e) + ((a + b*atan(c*x))^2*log((2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*e) + ((a + b*atan(c*x))^2*log((2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*e) + (im*b*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 - im*c*x)))/e - (im*b*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*e) - (im*b*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*e) - (b^2*PolyLog(3, 1 - 2/(1 - im*c*x)))/(2*e) + (b^2*PolyLog(3, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*e) + (b^2*PolyLog(3, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*e)]
    @test_int [x^0*(a + b*atan(c*x))^2/(d + e*x^2), x, 4, ((a + b*atan(c*x))^2*log((2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*sqrt(-d)*sqrt(e)) - ((a + b*atan(c*x))^2*log((2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*sqrt(-d)*sqrt(e)) - (im*b*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*sqrt(-d)*sqrt(e)) + (im*b*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*sqrt(-d)*sqrt(e)) + (b^2*PolyLog(3, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*sqrt(-d)*sqrt(e)) - (b^2*PolyLog(3, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*sqrt(-d)*sqrt(e))]
    @test_int [(a + b*atan(c*x))^2/(x^1*(d + e*x^2)), x, 12, (2*(a + b*atan(c*x))^2*atanh(1 - 2/(1 + im*c*x)))/d + ((a + b*atan(c*x))^2*log(2/(1 - im*c*x)))/d - ((a + b*atan(c*x))^2*log((2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*d) - ((a + b*atan(c*x))^2*log((2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*d) - (im*b*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 - im*c*x)))/d - (im*b*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)))/d + (im*b*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 + im*c*x)))/d + (im*b*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*d) + (im*b*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*d) + (b^2*PolyLog(3, 1 - 2/(1 - im*c*x)))/(2*d) - (b^2*PolyLog(3, 1 - 2/(1 + im*c*x)))/(2*d) + (b^2*PolyLog(3, -1 + 2/(1 + im*c*x)))/(2*d) - (b^2*PolyLog(3, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*d) - (b^2*PolyLog(3, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*d)]
    @test_int [(a + b*atan(c*x))^2/(x^2*(d + e*x^2)), x, 9, -((im*c*(a + b*atan(c*x))^2)/d) - (a + b*atan(c*x))^2/(d*x) + (sqrt(e)*(a + b*atan(c*x))^2*log((2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*(-d)^(3/2)) - (sqrt(e)*(a + b*atan(c*x))^2*log((2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*(-d)^(3/2)) + (2*b*c*(a + b*atan(c*x))*log(2 - 2/(1 - im*c*x)))/d - (im*b^2*c*PolyLog(2, -1 + 2/(1 - im*c*x)))/d - (im*b*sqrt(e)*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*(-d)^(3/2)) + (im*b*sqrt(e)*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*(-d)^(3/2)) + (b^2*sqrt(e)*PolyLog(3, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*(-d)^(3/2)) - (b^2*sqrt(e)*PolyLog(3, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*(-d)^(3/2))]
    @test_int [(a + b*atan(c*x))^2/(x^3*(d + e*x^2)), x, 21, -((b*c*(a + b*atan(c*x)))/(d*x)) - (c^2*(a + b*atan(c*x))^2)/(2*d) - (a + b*atan(c*x))^2/(2*d*x^2) - (2*e*(a + b*atan(c*x))^2*atanh(1 - 2/(1 + im*c*x)))/d^2 + (b^2*c^2*log(x))/d - (e*(a + b*atan(c*x))^2*log(2/(1 - im*c*x)))/d^2 + (e*(a + b*atan(c*x))^2*log((2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*d^2) + (e*(a + b*atan(c*x))^2*log((2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*d^2) - (b^2*c^2*log(1 + c^2*x^2))/(2*d) + (im*b*e*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 - im*c*x)))/d^2 + (im*b*e*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)))/d^2 - (im*b*e*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 + im*c*x)))/d^2 - (im*b*e*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*d^2) - (im*b*e*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*d^2) - (b^2*e*PolyLog(3, 1 - 2/(1 - im*c*x)))/(2*d^2) + (b^2*e*PolyLog(3, 1 - 2/(1 + im*c*x)))/(2*d^2) - (b^2*e*PolyLog(3, -1 + 2/(1 + im*c*x)))/(2*d^2) + (b^2*e*PolyLog(3, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*d^2) + (b^2*e*PolyLog(3, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*d^2)]

    @test_int [x^3*(a + b*atan(c*x))^2/(d + e*x^2)^2, x, 33, -((c^2*d*(a + b*atan(c*x))^2)/(2*(c^2*d - e)*e^2)) + (a + b*atan(c*x))^2/(4*e^2*(1 - (sqrt(e)*x)/sqrt(-d))) + (a + b*atan(c*x))^2/(4*e^2*(1 + (sqrt(e)*x)/sqrt(-d))) - ((a + b*atan(c*x))^2*log(2/(1 - im*c*x)))/e^2 - (b*c*sqrt(-d)*(a + b*atan(c*x))*log((2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*(c^2*d - e)*e^(3/2)) + ((a + b*atan(c*x))^2*log((2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*e^2) + (b*c*sqrt(-d)*(a + b*atan(c*x))*log((2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*(c^2*d - e)*e^(3/2)) + ((a + b*atan(c*x))^2*log((2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*e^2) + (im*b*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 - im*c*x)))/e^2 + (im*b^2*c*sqrt(-d)*PolyLog(2, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*(c^2*d - e)*e^(3/2)) - (im*b*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*e^2) - (im*b^2*c*sqrt(-d)*PolyLog(2, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*(c^2*d - e)*e^(3/2)) - (im*b*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*e^2) - (b^2*PolyLog(3, 1 - 2/(1 - im*c*x)))/(2*e^2) + (b^2*PolyLog(3, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*e^2) + (b^2*PolyLog(3, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*e^2)]
    @test_int [x^2*(a + b*atan(c*x))^2/(d + e*x^2)^2, x, 38, -((im*c*(a + b*atan(c*x))^2)/(2*(c^2*d - e)*e)) + (a + b*atan(c*x))^2/(4*e^(3/2)*(sqrt(-d) - sqrt(e)*x)) - (a + b*atan(c*x))^2/(4*e^(3/2)*(sqrt(-d) + sqrt(e)*x)) + (b*c*(a + b*atan(c*x))*log(2/(1 - im*c*x)))/((c^2*d - e)*e) - (b*c*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/((c^2*d - e)*e) - (b*c*(a + b*atan(c*x))*log((2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*(c^2*d - e)*e) + ((a + b*atan(c*x))^2*log((2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*sqrt(-d)*e^(3/2)) - (b*c*(a + b*atan(c*x))*log((2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*(c^2*d - e)*e) - ((a + b*atan(c*x))^2*log((2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*sqrt(-d)*e^(3/2)) - (im*b^2*c*PolyLog(2, 1 - 2/(1 - im*c*x)))/(2*(c^2*d - e)*e) - (im*b^2*c*PolyLog(2, 1 - 2/(1 + im*c*x)))/(2*(c^2*d - e)*e) + (im*b^2*c*PolyLog(2, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*(c^2*d - e)*e) - (im*b*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*sqrt(-d)*e^(3/2)) + (im*b^2*c*PolyLog(2, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*(c^2*d - e)*e) + (im*b*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*sqrt(-d)*e^(3/2)) + (b^2*PolyLog(3, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(8*sqrt(-d)*e^(3/2)) - (b^2*PolyLog(3, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(8*sqrt(-d)*e^(3/2))]
    @test_int [x^1*(a + b*atan(c*x))^2/(d + e*x^2)^2, x, 27, (c^2*(a + b*atan(c*x))^2)/(2*(c^2*d - e)*e) - (a + b*atan(c*x))^2/(4*d*e*(1 - (sqrt(e)*x)/sqrt(-d))) - (a + b*atan(c*x))^2/(4*d*e*(1 + (sqrt(e)*x)/sqrt(-d))) - (b*c*(a + b*atan(c*x))*log((2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*sqrt(-d)*(c^2*d - e)*sqrt(e)) + (b*c*(a + b*atan(c*x))*log((2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*sqrt(-d)*(c^2*d - e)*sqrt(e)) + (im*b^2*c*PolyLog(2, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*sqrt(-d)*(c^2*d - e)*sqrt(e)) - (im*b^2*c*PolyLog(2, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*sqrt(-d)*(c^2*d - e)*sqrt(e))]
    @test_int [x^0*(a + b*atan(c*x))^2/(d + e*x^2)^2, x, 32, (im*c*(a + b*atan(c*x))^2)/(2*d*(c^2*d - e)) - (a + b*atan(c*x))^2/(4*d*sqrt(e)*(sqrt(-d) - sqrt(e)*x)) + (a + b*atan(c*x))^2/(4*d*sqrt(e)*(sqrt(-d) + sqrt(e)*x)) - (b*c*(a + b*atan(c*x))*log(2/(1 - im*c*x)))/(d*(c^2*d - e)) + (b*c*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(d*(c^2*d - e)) + (b*c*(a + b*atan(c*x))*log((2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*d*(c^2*d - e)) - ((a + b*atan(c*x))^2*log((2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*(-d)^(3/2)*sqrt(e)) + (b*c*(a + b*atan(c*x))*log((2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*d*(c^2*d - e)) + ((a + b*atan(c*x))^2*log((2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*(-d)^(3/2)*sqrt(e)) + (im*b^2*c*PolyLog(2, 1 - 2/(1 - im*c*x)))/(2*d*(c^2*d - e)) + (im*b^2*c*PolyLog(2, 1 - 2/(1 + im*c*x)))/(2*d*(c^2*d - e)) - (im*b^2*c*PolyLog(2, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*d*(c^2*d - e)) + (im*b*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*(-d)^(3/2)*sqrt(e)) - (im*b^2*c*PolyLog(2, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*d*(c^2*d - e)) - (im*b*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*(-d)^(3/2)*sqrt(e)) - (b^2*PolyLog(3, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(8*(-d)^(3/2)*sqrt(e)) + (b^2*PolyLog(3, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(8*(-d)^(3/2)*sqrt(e))]
    @test_int [(a + b*atan(c*x))^2/(x^1*(d + e*x^2)^2), x, 39, -((c^2*(a + b*atan(c*x))^2)/(2*d*(c^2*d - e))) + (a + b*atan(c*x))^2/(4*d^2*(1 - (sqrt(e)*x)/sqrt(-d))) + (a + b*atan(c*x))^2/(4*d^2*(1 + (sqrt(e)*x)/sqrt(-d))) + (2*(a + b*atan(c*x))^2*atanh(1 - 2/(1 + im*c*x)))/d^2 + ((a + b*atan(c*x))^2*log(2/(1 - im*c*x)))/d^2 - (b*c*sqrt(e)*(a + b*atan(c*x))*log((2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*(-d)^(3/2)*(c^2*d - e)) - ((a + b*atan(c*x))^2*log((2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*d^2) + (b*c*sqrt(e)*(a + b*atan(c*x))*log((2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*(-d)^(3/2)*(c^2*d - e)) - ((a + b*atan(c*x))^2*log((2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*d^2) - (im*b*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 - im*c*x)))/d^2 - (im*b*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)))/d^2 + (im*b*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 + im*c*x)))/d^2 + (im*b^2*c*sqrt(e)*PolyLog(2, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*(-d)^(3/2)*(c^2*d - e)) + (im*b*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*d^2) - (im*b^2*c*sqrt(e)*PolyLog(2, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*(-d)^(3/2)*(c^2*d - e)) + (im*b*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*d^2) + (b^2*PolyLog(3, 1 - 2/(1 - im*c*x)))/(2*d^2) - (b^2*PolyLog(3, 1 - 2/(1 + im*c*x)))/(2*d^2) + (b^2*PolyLog(3, -1 + 2/(1 + im*c*x)))/(2*d^2) - (b^2*PolyLog(3, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*d^2) - (b^2*PolyLog(3, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*d^2)]
    @test_int [(a + b*atan(c*x))^2/(x^2*(d + e*x^2)^2), x, 42, -((im*c*(a + b*atan(c*x))^2)/d^2) - (im*c*e*(a + b*atan(c*x))^2)/(2*d^2*(c^2*d - e)) - (a + b*atan(c*x))^2/(d^2*x) + (sqrt(e)*(a + b*atan(c*x))^2)/(4*d^2*(sqrt(-d) - sqrt(e)*x)) - (sqrt(e)*(a + b*atan(c*x))^2)/(4*d^2*(sqrt(-d) + sqrt(e)*x)) + (b*c*e*(a + b*atan(c*x))*log(2/(1 - im*c*x)))/(d^2*(c^2*d - e)) - (b*c*e*(a + b*atan(c*x))*log(2/(1 + im*c*x)))/(d^2*(c^2*d - e)) - (b*c*e*(a + b*atan(c*x))*log((2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*d^2*(c^2*d - e)) - (3*sqrt(e)*(a + b*atan(c*x))^2*log((2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*(-d)^(5/2)) - (b*c*e*(a + b*atan(c*x))*log((2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*d^2*(c^2*d - e)) + (3*sqrt(e)*(a + b*atan(c*x))^2*log((2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*(-d)^(5/2)) + (2*b*c*(a + b*atan(c*x))*log(2 - 2/(1 - im*c*x)))/d^2 - (im*b^2*c*e*PolyLog(2, 1 - 2/(1 - im*c*x)))/(2*d^2*(c^2*d - e)) - (im*b^2*c*PolyLog(2, -1 + 2/(1 - im*c*x)))/d^2 - (im*b^2*c*e*PolyLog(2, 1 - 2/(1 + im*c*x)))/(2*d^2*(c^2*d - e)) + (im*b^2*c*e*PolyLog(2, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*d^2*(c^2*d - e)) + (3*im*b*sqrt(e)*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*(-d)^(5/2)) + (im*b^2*c*e*PolyLog(2, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*d^2*(c^2*d - e)) - (3*im*b*sqrt(e)*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*(-d)^(5/2)) - (3*b^2*sqrt(e)*PolyLog(3, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(8*(-d)^(5/2)) + (3*b^2*sqrt(e)*PolyLog(3, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(8*(-d)^(5/2))]
    @test_int [(a + b*atan(c*x))^2/(x^3*(d + e*x^2)^2), x, 47, -((b*c*(a + b*atan(c*x)))/(d^2*x)) - (c^2*(a + b*atan(c*x))^2)/(2*d^2) + (c^2*e*(a + b*atan(c*x))^2)/(2*d^2*(c^2*d - e)) - (a + b*atan(c*x))^2/(2*d^2*x^2) - (e*(a + b*atan(c*x))^2)/(4*d^3*(1 - (sqrt(e)*x)/sqrt(-d))) - (e*(a + b*atan(c*x))^2)/(4*d^3*(1 + (sqrt(e)*x)/sqrt(-d))) - (4*e*(a + b*atan(c*x))^2*atanh(1 - 2/(1 + im*c*x)))/d^3 + (b^2*c^2*log(x))/d^2 - (2*e*(a + b*atan(c*x))^2*log(2/(1 - im*c*x)))/d^3 - (b*c*e^(3/2)*(a + b*atan(c*x))*log((2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*(-d)^(5/2)*(c^2*d - e)) + (e*(a + b*atan(c*x))^2*log((2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/d^3 + (b*c*e^(3/2)*(a + b*atan(c*x))*log((2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*(-d)^(5/2)*(c^2*d - e)) + (e*(a + b*atan(c*x))^2*log((2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/d^3 - (b^2*c^2*log(1 + c^2*x^2))/(2*d^2) + (2*im*b*e*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 - im*c*x)))/d^3 + (2*im*b*e*(a + b*atan(c*x))*PolyLog(2, 1 - 2/(1 + im*c*x)))/d^3 - (2*im*b*e*(a + b*atan(c*x))*PolyLog(2, -1 + 2/(1 + im*c*x)))/d^3 + (im*b^2*c*e^(3/2)*PolyLog(2, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(4*(-d)^(5/2)*(c^2*d - e)) - (im*b*e*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/d^3 - (im*b^2*c*e^(3/2)*PolyLog(2, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(4*(-d)^(5/2)*(c^2*d - e)) - (im*b*e*(a + b*atan(c*x))*PolyLog(2, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/d^3 - (b^2*e*PolyLog(3, 1 - 2/(1 - im*c*x)))/d^3 + (b^2*e*PolyLog(3, 1 - 2/(1 + im*c*x)))/d^3 - (b^2*e*PolyLog(3, -1 + 2/(1 + im*c*x)))/d^3 + (b^2*e*PolyLog(3, 1 - (2*c*(sqrt(-d) - sqrt(e)*x))/((c*sqrt(-d) - im*sqrt(e))*(1 - im*c*x))))/(2*d^3) + (b^2*e*PolyLog(3, 1 - (2*c*(sqrt(-d) + sqrt(e)*x))/((c*sqrt(-d) + im*sqrt(e))*(1 - im*c*x))))/(2*d^3)]

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

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

    @test_int [x^4*atan(x)*log(1 + x^2), x, 24, -((77*x^2)/300) + (9*x^4)/200 - (2/5)*x*atan(x) + (2/15)*x^3*atan(x) - (2/25)*x^5*atan(x) + atan(x)^2/5 + (137/300)*log(1 + x^2) + (1/10)*x^2*log(1 + x^2) - (1/20)*x^4*log(1 + x^2) + (1/5)*x^5*atan(x)*log(1 + x^2) - (1/20)*log(1 + x^2)^2]
    @test_int [x^3*atan(x)*log(1 + x^2), x, 14, -((25*x)/24) + (7*x^3)/72 + (25*atan(x))/24 + (1/4)*x^2*atan(x) - (1/8)*x^4*atan(x) + (1/4)*x*log(1 + x^2) - (1/12)*x^3*log(1 + x^2) - (1/4)*atan(x)*log(1 + x^2) + (1/4)*x^4*atan(x)*log(1 + x^2)]
    @test_int [x^2*atan(x)*log(1 + x^2), x, 19, (5*x^2)/18 + (2/3)*x*atan(x) - (2/9)*x^3*atan(x) - atan(x)^2/3 - (11/18)*log(1 + x^2) - (1/6)*x^2*log(1 + x^2) + (1/3)*x^3*atan(x)*log(1 + x^2) + (1/12)*log(1 + x^2)^2]
    @test_int [x^1*atan(x)*log(1 + x^2), x, 7, (3*x)/2 - (3*atan(x))/2 - (1/2)*x^2*atan(x) - (1/2)*x*log(1 + x^2) + (1/2)*(1 + x^2)*atan(x)*log(1 + x^2)]
    @test_int [x^0*atan(x)*log(1 + x^2), x, 8, -2*x*atan(x) + atan(x)^2 + log(1 + x^2) + x*atan(x)*log(1 + x^2) - (1/4)*log(1 + x^2)^2]
    @test_int [atan(x)*log(1 + x^2)/x^1, x, 12, (-(1/2))*im*log(1 + im*x)^2*log((-im)*x) + (1/2)*im*log(1 - im*x)^2*log(im*x) + im*log(1 - im*x)*PolyLog(2, 1 - im*x) - im*log(1 + im*x)*PolyLog(2, 1 + im*x) - (1/2)*im*(log(1 - im*x) + log(1 + im*x) - log(1 + x^2))*PolyLog(2, (-im)*x) + (1/2)*im*(log(1 - im*x) + log(1 + im*x) - log(1 + x^2))*PolyLog(2, im*x) - im*PolyLog(3, 1 - im*x) + im*PolyLog(3, 1 + im*x)]
    @test_int [atan(x)*log(1 + x^2)/x^2, x, 8, atan(x)^2 - (atan(x)*log(1 + x^2))/x - (1/4)*log(1 + x^2)^2 - (1/2)*PolyLog(2, -x^2)]
    @test_int [atan(x)*log(1 + x^2)/x^3, x, 6, atan(x) - log(1 + x^2)/(2*x) - (1/2)*atan(x)*log(1 + x^2) - (atan(x)*log(1 + x^2))/(2*x^2) + (1/2)*im*PolyLog(2, (-im)*x) - (1/2)*im*PolyLog(2, im*x)]
    @test_int [atan(x)*log(1 + x^2)/x^4, x, 18, -((2*atan(x))/(3*x)) - atan(x)^2/3 + log(x) - (1/2)*log(1 + x^2) - log(1 + x^2)/(6*x^2) - (atan(x)*log(1 + x^2))/(3*x^3) + (1/12)*log(1 + x^2)^2 + (1/6)*PolyLog(2, -x^2)]
    @test_int [atan(x)*log(1 + x^2)/x^5, x, 12, -(5/(12*x)) - (11*atan(x))/12 - atan(x)/(4*x^2) - log(1 + x^2)/(12*x^3) + log(1 + x^2)/(4*x) + (1/4)*atan(x)*log(1 + x^2) - (atan(x)*log(1 + x^2))/(4*x^4) - (1/4)*im*PolyLog(2, (-im)*x) + (1/4)*im*PolyLog(2, im*x)]
    @test_int [atan(x)*log(1 + x^2)/x^6, x, 26, -(7/(60*x^2)) - (2*atan(x))/(15*x^3) + (2*atan(x))/(5*x) + atan(x)^2/5 - (5*log(x))/6 + (5/12)*log(1 + x^2) - log(1 + x^2)/(20*x^4) + log(1 + x^2)/(10*x^2) - (atan(x)*log(1 + x^2))/(5*x^5) - (1/20)*log(1 + x^2)^2 - (1/10)*PolyLog(2, -x^2)]

    @test_int [x^4*(a + b*atan(c*x))*(d + e*log(1 + c^2*x^2)), x, 26, -((2*a*e*x)/(5*c^4)) - (77*b*e*x^2)/(300*c^3) + (2*a*e*x^3)/(15*c^2) + (9*b*e*x^4)/(200*c) - (2/25)*a*e*x^5 + (2*a*e*atan(c*x))/(5*c^5) - (2*b*e*x*atan(c*x))/(5*c^4) + (2*b*e*x^3*atan(c*x))/(15*c^2) - (2/25)*b*e*x^5*atan(c*x) + (b*e*atan(c*x)^2)/(5*c^5) + (137*b*e*log(1 + c^2*x^2))/(300*c^5) + (b*e*log(1 + c^2*x^2)^2)/(20*c^5) + (b*x^2*(d + e*log(1 + c^2*x^2)))/(10*c^3) - (b*x^4*(d + e*log(1 + c^2*x^2)))/(20*c) + (1/5)*x^5*(a + b*atan(c*x))*(d + e*log(1 + c^2*x^2)) - (b*log(1 + c^2*x^2)*(d + e*log(1 + c^2*x^2)))/(10*c^5)]
    @test_int [x^3*(a + b*atan(c*x))*(d + e*log(1 + c^2*x^2)), x, 14, (b*(2*d - 3*e)*x)/(8*c^3) - (2*b*e*x)/(3*c^3) - (b*(2*d - e)*x^3)/(24*c) + (b*e*x^3)/(18*c) - (b*(2*d - 3*e)*atan(c*x))/(8*c^4) + (2*b*e*atan(c*x))/(3*c^4) + (e*x^2*(a + b*atan(c*x)))/(4*c^2) - (1/8)*e*x^4*(a + b*atan(c*x)) + (b*e*x*log(1 + c^2*x^2))/(4*c^3) - (b*e*x^3*log(1 + c^2*x^2))/(12*c) - (e*(a + b*atan(c*x))*log(1 + c^2*x^2))/(4*c^4) + (1/4)*x^4*(a + b*atan(c*x))*(d + e*log(1 + c^2*x^2))]
    @test_int [x^2*(a + b*atan(c*x))*(d + e*log(1 + c^2*x^2)), x, 21, (2*a*e*x)/(3*c^2) + (5*b*e*x^2)/(18*c) - (2/9)*a*e*x^3 - (2*a*e*atan(c*x))/(3*c^3) + (2*b*e*x*atan(c*x))/(3*c^2) - (2/9)*b*e*x^3*atan(c*x) - (b*e*atan(c*x)^2)/(3*c^3) - (11*b*e*log(1 + c^2*x^2))/(18*c^3) - (b*e*log(1 + c^2*x^2)^2)/(12*c^3) - (b*x^2*(d + e*log(1 + c^2*x^2)))/(6*c) + (1/3)*x^3*(a + b*atan(c*x))*(d + e*log(1 + c^2*x^2)) + (b*log(1 + c^2*x^2)*(d + e*log(1 + c^2*x^2)))/(6*c^3)]
    @test_int [x^1*(a + b*atan(c*x))*(d + e*log(1 + c^2*x^2)), x, 7, -((b*(d - e)*x)/(2*c)) + (b*e*x)/c + (b*(d - e)*atan(c*x))/(2*c^2) - (b*e*atan(c*x))/c^2 + (1/2)*d*x^2*(a + b*atan(c*x)) - (1/2)*e*x^2*(a + b*atan(c*x)) - (b*e*x*log(1 + c^2*x^2))/(2*c) + (e*(1 + c^2*x^2)*(a + b*atan(c*x))*log(1 + c^2*x^2))/(2*c^2)]
    @test_int [x^0*(a + b*atan(c*x))*(d + e*log(1 + c^2*x^2)), x, 9, -2*a*e*x - 2*b*e*x*atan(c*x) + (e*(a + b*atan(c*x))^2)/(b*c) + (b*e*log(1 + c^2*x^2))/c + x*(a + b*atan(c*x))*(d + e*log(1 + c^2*x^2)) - (b*(d + e*log(1 + c^2*x^2))^2)/(4*c*e)]
    @test_int [(a + b*atan(c*x))*(d + e*log(1 + c^2*x^2))/x^1, x, 18, a*d*log(x) + (1/2)*im*b*e*log(im*c*x)*log(1 - im*c*x)^2 - (1/2)*im*b*e*log((-im)*c*x)*log(1 + im*c*x)^2 + (1/2)*im*b*d*PolyLog(2, (-im)*c*x) - (1/2)*im*b*e*(log(1 - im*c*x) + log(1 + im*c*x) - log(1 + c^2*x^2))*PolyLog(2, (-im)*c*x) - (1/2)*im*b*d*PolyLog(2, im*c*x) + (1/2)*im*b*e*(log(1 - im*c*x) + log(1 + im*c*x) - log(1 + c^2*x^2))*PolyLog(2, im*c*x) - (1/2)*a*e*PolyLog(2, (-c^2)*x^2) + im*b*e*log(1 - im*c*x)*PolyLog(2, 1 - im*c*x) - im*b*e*log(1 + im*c*x)*PolyLog(2, 1 + im*c*x) - im*b*e*PolyLog(3, 1 - im*c*x) + im*b*e*PolyLog(3, 1 + im*c*x)]
    @test_int [(a + b*atan(c*x))*(d + e*log(1 + c^2*x^2))/x^2, x, 6, (c*e*(a + b*atan(c*x))^2)/b - ((a + b*atan(c*x))*(d + e*log(1 + c^2*x^2)))/x + (1/2)*b*c*(d + e*log(1 + c^2*x^2))*log(1 - 1/(1 + c^2*x^2)) - (1/2)*b*c*e*PolyLog(2, 1/(1 + c^2*x^2))]
    @test_int [(a + b*atan(c*x))*(d + e*log(1 + c^2*x^2))/x^3, x, 10, b*c^2*e*atan(c*x) + a*c^2*e*log(x) - (1/2)*a*c^2*e*log(1 + c^2*x^2) - (b*c*(d + e*log(1 + c^2*x^2)))/(2*x) - (1/2)*b*c^2*atan(c*x)*(d + e*log(1 + c^2*x^2)) - ((a + b*atan(c*x))*(d + e*log(1 + c^2*x^2)))/(2*x^2) + (1/2)*im*b*c^2*e*PolyLog(2, (-im)*c*x) - (1/2)*im*b*c^2*e*PolyLog(2, im*c*x)]
    @test_int [(a + b*atan(c*x))*(d + e*log(1 + c^2*x^2))/x^4, x, 15, -((2*c^2*e*(a + b*atan(c*x)))/(3*x)) - (c^3*e*(a + b*atan(c*x))^2)/(3*b) + b*c^3*e*log(x) - (1/3)*b*c^3*e*log(1 + c^2*x^2) - (b*c*(1 + c^2*x^2)*(d + e*log(1 + c^2*x^2)))/(6*x^2) - ((a + b*atan(c*x))*(d + e*log(1 + c^2*x^2)))/(3*x^3) - (1/6)*b*c^3*(d + e*log(1 + c^2*x^2))*log(1 - 1/(1 + c^2*x^2)) + (1/6)*b*c^3*e*PolyLog(2, 1/(1 + c^2*x^2))]
    @test_int [(a + b*atan(c*x))*(d + e*log(1 + c^2*x^2))/x^5, x, 15, -((a*c^2*e)/(4*x^2)) - (5*b*c^3*e)/(12*x) - (11/12)*b*c^4*e*atan(c*x) - (b*c^2*e*atan(c*x))/(4*x^2) - (1/2)*a*c^4*e*log(x) + (1/4)*a*c^4*e*log(1 + c^2*x^2) - (b*c*(d + e*log(1 + c^2*x^2)))/(12*x^3) + (b*c^3*(d + e*log(1 + c^2*x^2)))/(4*x) + (1/4)*b*c^4*atan(c*x)*(d + e*log(1 + c^2*x^2)) - ((a + b*atan(c*x))*(d + e*log(1 + c^2*x^2)))/(4*x^4) - (1/4)*im*b*c^4*e*PolyLog(2, (-im)*c*x) + (1/4)*im*b*c^4*e*PolyLog(2, im*c*x)]
    @test_int [(a + b*atan(c*x))*(d + e*log(1 + c^2*x^2))/x^6, x, 24, -((7*b*c^3*e)/(60*x^2)) - (2*c^2*e*(a + b*atan(c*x)))/(15*x^3) + (2*c^4*e*(a + b*atan(c*x)))/(5*x) + (c^5*e*(a + b*atan(c*x))^2)/(5*b) - (5/6)*b*c^5*e*log(x) + (19/60)*b*c^5*e*log(1 + c^2*x^2) - (b*c*(d + e*log(1 + c^2*x^2)))/(20*x^4) + (b*c^3*(1 + c^2*x^2)*(d + e*log(1 + c^2*x^2)))/(10*x^2) - ((a + b*atan(c*x))*(d + e*log(1 + c^2*x^2)))/(5*x^5) + (1/10)*b*c^5*(d + e*log(1 + c^2*x^2))*log(1 - 1/(1 + c^2*x^2)) - (1/10)*b*c^5*e*PolyLog(2, 1/(1 + c^2*x^2))]

    @test_int [x^1*(a + b*atan(c*x))*(d + e*log(f + g*x^2)), x, 21, -((b*(d - e)*x)/(2*c)) + (b*e*x)/c + (b*(d - e)*atan(c*x))/(2*c^2) + (1/2)*d*x^2*(a + b*atan(c*x)) - (1/2)*e*x^2*(a + b*atan(c*x)) - (b*e*sqrt(f)*atan((sqrt(g)*x)/sqrt(f)))/(c*sqrt(g)) - (b*e*(c^2*f - g)*atan(c*x)*log(2/(1 - im*c*x)))/(c^2*g) + (b*e*(c^2*f - g)*atan(c*x)*log((2*c*(sqrt(-f) - sqrt(g)*x))/((c*sqrt(-f) - im*sqrt(g))*(1 - im*c*x))))/(2*c^2*g) + (b*e*(c^2*f - g)*atan(c*x)*log((2*c*(sqrt(-f) + sqrt(g)*x))/((c*sqrt(-f) + im*sqrt(g))*(1 - im*c*x))))/(2*c^2*g) - (b*e*x*log(f + g*x^2))/(2*c) - (b*e*(c^2*f - g)*atan(c*x)*log(f + g*x^2))/(2*c^2*g) + (e*(f + g*x^2)*(a + b*atan(c*x))*log(f + g*x^2))/(2*g) + (im*b*e*(c^2*f - g)*PolyLog(2, 1 - 2/(1 - im*c*x)))/(2*c^2*g) - (im*b*e*(c^2*f - g)*PolyLog(2, 1 - (2*c*(sqrt(-f) - sqrt(g)*x))/((c*sqrt(-f) - im*sqrt(g))*(1 - im*c*x))))/(4*c^2*g) - (im*b*e*(c^2*f - g)*PolyLog(2, 1 - (2*c*(sqrt(-f) + sqrt(g)*x))/((c*sqrt(-f) + im*sqrt(g))*(1 - im*c*x))))/(4*c^2*g)]
    @test_int [x^0*(a + b*atan(c*x))*(d + e*log(f + g*x^2)), x, 28, -2*a*e*x - 2*b*e*x*atan(c*x) + (2*a*e*sqrt(f)*atan((sqrt(g)*x)/sqrt(f)))/sqrt(g) + (im*b*e*sqrt(-f)*log(1 + im*c*x)*log((c*(sqrt(-f) - sqrt(g)*x))/(c*sqrt(-f) - im*sqrt(g))))/(2*sqrt(g)) - (im*b*e*sqrt(-f)*log(1 - im*c*x)*log((c*(sqrt(-f) - sqrt(g)*x))/(c*sqrt(-f) + im*sqrt(g))))/(2*sqrt(g)) + (im*b*e*sqrt(-f)*log(1 - im*c*x)*log((c*(sqrt(-f) + sqrt(g)*x))/(c*sqrt(-f) - im*sqrt(g))))/(2*sqrt(g)) - (im*b*e*sqrt(-f)*log(1 + im*c*x)*log((c*(sqrt(-f) + sqrt(g)*x))/(c*sqrt(-f) + im*sqrt(g))))/(2*sqrt(g)) + (b*e*log(1 + c^2*x^2))/c + x*(a + b*atan(c*x))*(d + e*log(f + g*x^2)) - (b*log(-((g*(1 + c^2*x^2))/(c^2*f - g)))*(d + e*log(f + g*x^2)))/(2*c) - (im*b*e*sqrt(-f)*PolyLog(2, (sqrt(g)*(im - c*x))/(c*sqrt(-f) + im*sqrt(g))))/(2*sqrt(g)) + (im*b*e*sqrt(-f)*PolyLog(2, (sqrt(g)*(1 - im*c*x))/(im*c*sqrt(-f) + sqrt(g))))/(2*sqrt(g)) + (im*b*e*sqrt(-f)*PolyLog(2, (sqrt(g)*(1 + im*c*x))/(im*c*sqrt(-f) + sqrt(g))))/(2*sqrt(g)) - (im*b*e*sqrt(-f)*PolyLog(2, (sqrt(g)*(im + c*x))/(c*sqrt(-f) + im*sqrt(g))))/(2*sqrt(g)) - (b*e*PolyLog(2, (c^2*(f + g*x^2))/(c^2*f - g)))/(2*c)]
    @test_int [(a + b*atan(c*x))*(d + e*log(f + g*x^2))/x^1, x, 8, b*e*CannotIntegrate((atan(c*x)*log(f + g*x^2))/x, x) + a*d*log(x) + (1/2)*a*e*log(-((g*x^2)/f))*log(f + g*x^2) + (1/2)*im*b*d*PolyLog(2, (-im)*c*x) - (1/2)*im*b*d*PolyLog(2, im*c*x) + (1/2)*a*e*PolyLog(2, 1 + (g*x^2)/f)]
    @test_int [(a + b*atan(c*x))*(d + e*log(f + g*x^2))/x^2, x, 28, (2*a*e*sqrt(g)*atan((sqrt(g)*x)/sqrt(f)))/sqrt(f) - (im*b*e*sqrt(g)*log(1 + im*c*x)*log((c*(sqrt(-f) - sqrt(g)*x))/(c*sqrt(-f) - im*sqrt(g))))/(2*sqrt(-f)) + (im*b*e*sqrt(g)*log(1 - im*c*x)*log((c*(sqrt(-f) - sqrt(g)*x))/(c*sqrt(-f) + im*sqrt(g))))/(2*sqrt(-f)) - (im*b*e*sqrt(g)*log(1 - im*c*x)*log((c*(sqrt(-f) + sqrt(g)*x))/(c*sqrt(-f) - im*sqrt(g))))/(2*sqrt(-f)) + (im*b*e*sqrt(g)*log(1 + im*c*x)*log((c*(sqrt(-f) + sqrt(g)*x))/(c*sqrt(-f) + im*sqrt(g))))/(2*sqrt(-f)) - ((a + b*atan(c*x))*(d + e*log(f + g*x^2)))/x + (1/2)*b*c*log(-((g*x^2)/f))*(d + e*log(f + g*x^2)) - (1/2)*b*c*log(-((g*(1 + c^2*x^2))/(c^2*f - g)))*(d + e*log(f + g*x^2)) + (im*b*e*sqrt(g)*PolyLog(2, (sqrt(g)*(im - c*x))/(c*sqrt(-f) + im*sqrt(g))))/(2*sqrt(-f)) - (im*b*e*sqrt(g)*PolyLog(2, (sqrt(g)*(1 - im*c*x))/(im*c*sqrt(-f) + sqrt(g))))/(2*sqrt(-f)) - (im*b*e*sqrt(g)*PolyLog(2, (sqrt(g)*(1 + im*c*x))/(im*c*sqrt(-f) + sqrt(g))))/(2*sqrt(-f)) + (im*b*e*sqrt(g)*PolyLog(2, (sqrt(g)*(im + c*x))/(c*sqrt(-f) + im*sqrt(g))))/(2*sqrt(-f)) - (1/2)*b*c*e*PolyLog(2, (c^2*(f + g*x^2))/(c^2*f - g)) + (1/2)*b*c*e*PolyLog(2, 1 + (g*x^2)/f)]
    @test_int [(a + b*atan(c*x))*(d + e*log(f + g*x^2))/x^3, x, 22, (b*c*e*sqrt(g)*atan((sqrt(g)*x)/sqrt(f)))/sqrt(f) + (a*e*g*log(x))/f - (b*e*(c^2*f - g)*atan(c*x)*log(2/(1 - im*c*x)))/f + (b*e*(c^2*f - g)*atan(c*x)*log((2*c*(sqrt(-f) - sqrt(g)*x))/((c*sqrt(-f) - im*sqrt(g))*(1 - im*c*x))))/(2*f) + (b*e*(c^2*f - g)*atan(c*x)*log((2*c*(sqrt(-f) + sqrt(g)*x))/((c*sqrt(-f) + im*sqrt(g))*(1 - im*c*x))))/(2*f) - (a*e*g*log(f + g*x^2))/(2*f) - (b*c*(d + e*log(f + g*x^2)))/(2*x) - (1/2)*b*c^2*atan(c*x)*(d + e*log(f + g*x^2)) - ((a + b*atan(c*x))*(d + e*log(f + g*x^2)))/(2*x^2) + (im*b*e*g*PolyLog(2, (-im)*c*x))/(2*f) - (im*b*e*g*PolyLog(2, im*c*x))/(2*f) + (im*b*e*(c^2*f - g)*PolyLog(2, 1 - 2/(1 - im*c*x)))/(2*f) - (im*b*e*(c^2*f - g)*PolyLog(2, 1 - (2*c*(sqrt(-f) - sqrt(g)*x))/((c*sqrt(-f) - im*sqrt(g))*(1 - im*c*x))))/(4*f) - (im*b*e*(c^2*f - g)*PolyLog(2, 1 - (2*c*(sqrt(-f) + sqrt(g)*x))/((c*sqrt(-f) + im*sqrt(g))*(1 - im*c*x))))/(4*f)]
    end

max_stars_repo_path: test/5 Inverse trig functions/5.3 Inverse tangent/5.3.4 u (a+b arctan(c x))^p.jl