Optimal. Leaf size=374 \[ -\frac {(d e-c f) \left (\left (c^2+3\right ) f^2-2 c d e f+d^2 e^2\right ) \left (a+b \tanh ^{-1}(c+d x)\right )^2}{3 d^3 f}+\frac {\left (\left (3 c^2+1\right ) f^2-6 c d e f+3 d^2 e^2\right ) \left (a+b \tanh ^{-1}(c+d x)\right )^2}{3 d^3}-\frac {2 b \left (\left (3 c^2+1\right ) f^2-6 c d e f+3 d^2 e^2\right ) \log \left (\frac {2}{-c-d x+1}\right ) \left (a+b \tanh ^{-1}(c+d x)\right )}{3 d^3}+\frac {b f^2 (c+d x)^2 \left (a+b \tanh ^{-1}(c+d x)\right )}{3 d^3}+\frac {2 a b f x (d e-c f)}{d^2}+\frac {(e+f x)^3 \left (a+b \tanh ^{-1}(c+d x)\right )^2}{3 f}-\frac {b^2 \left (\left (3 c^2+1\right ) f^2-6 c d e f+3 d^2 e^2\right ) \text {Li}_2\left (-\frac {c+d x+1}{-c-d x+1}\right )}{3 d^3}+\frac {b^2 f (d e-c f) \log \left (1-(c+d x)^2\right )}{d^3}+\frac {2 b^2 f (c+d x) (d e-c f) \tanh ^{-1}(c+d x)}{d^3}-\frac {b^2 f^2 \tanh ^{-1}(c+d x)}{3 d^3}+\frac {b^2 f^2 x}{3 d^2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.64, antiderivative size = 374, normalized size of antiderivative = 1.00, number of steps used = 16, number of rules used = 13, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.650, Rules used = {6111, 5928, 5910, 260, 5916, 321, 206, 6048, 5948, 5984, 5918, 2402, 2315} \[ -\frac {b^2 \left (\left (3 c^2+1\right ) f^2-6 c d e f+3 d^2 e^2\right ) \text {PolyLog}\left (2,-\frac {c+d x+1}{-c-d x+1}\right )}{3 d^3}-\frac {(d e-c f) \left (\left (c^2+3\right ) f^2-2 c d e f+d^2 e^2\right ) \left (a+b \tanh ^{-1}(c+d x)\right )^2}{3 d^3 f}+\frac {\left (\left (3 c^2+1\right ) f^2-6 c d e f+3 d^2 e^2\right ) \left (a+b \tanh ^{-1}(c+d x)\right )^2}{3 d^3}-\frac {2 b \left (\left (3 c^2+1\right ) f^2-6 c d e f+3 d^2 e^2\right ) \log \left (\frac {2}{-c-d x+1}\right ) \left (a+b \tanh ^{-1}(c+d x)\right )}{3 d^3}+\frac {2 a b f x (d e-c f)}{d^2}+\frac {b f^2 (c+d x)^2 \left (a+b \tanh ^{-1}(c+d x)\right )}{3 d^3}+\frac {(e+f x)^3 \left (a+b \tanh ^{-1}(c+d x)\right )^2}{3 f}+\frac {b^2 f (d e-c f) \log \left (1-(c+d x)^2\right )}{d^3}+\frac {2 b^2 f (c+d x) (d e-c f) \tanh ^{-1}(c+d x)}{d^3}-\frac {b^2 f^2 \tanh ^{-1}(c+d x)}{3 d^3}+\frac {b^2 f^2 x}{3 d^2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 206
Rule 260
Rule 321
Rule 2315
Rule 2402
Rule 5910
Rule 5916
Rule 5918
Rule 5928
Rule 5948
Rule 5984
Rule 6048
Rule 6111
Rubi steps
\begin {align*} \int (e+f x)^2 \left (a+b \tanh ^{-1}(c+d x)\right )^2 \, dx &=\frac {\operatorname {Subst}\left (\int \left (\frac {d e-c f}{d}+\frac {f x}{d}\right )^2 \left (a+b \tanh ^{-1}(x)\right )^2 \, dx,x,c+d x\right )}{d}\\ &=\frac {(e+f x)^3 \left (a+b \tanh ^{-1}(c+d x)\right )^2}{3 f}-\frac {(2 b) \operatorname {Subst}\left (\int \left (-\frac {3 f^2 (d e-c f) \left (a+b \tanh ^{-1}(x)\right )}{d^3}-\frac {f^3 x \left (a+b \tanh ^{-1}(x)\right )}{d^3}+\frac {\left ((d e-c f) \left (d^2 e^2-2 c d e f+3 f^2+c^2 f^2\right )+f \left (3 d^2 e^2-6 c d e f+\left (1+3 c^2\right ) f^2\right ) x\right ) \left (a+b \tanh ^{-1}(x)\right )}{d^3 \left (1-x^2\right )}\right ) \, dx,x,c+d x\right )}{3 f}\\ &=\frac {(e+f x)^3 \left (a+b \tanh ^{-1}(c+d x)\right )^2}{3 f}-\frac {(2 b) \operatorname {Subst}\left (\int \frac {\left ((d e-c f) \left (d^2 e^2-2 c d e f+3 f^2+c^2 f^2\right )+f \left (3 d^2 e^2-6 c d e f+\left (1+3 c^2\right ) f^2\right ) x\right ) \left (a+b \tanh ^{-1}(x)\right )}{1-x^2} \, dx,x,c+d x\right )}{3 d^3 f}+\frac {\left (2 b f^2\right ) \operatorname {Subst}\left (\int x \left (a+b \tanh ^{-1}(x)\right ) \, dx,x,c+d x\right )}{3 d^3}+\frac {(2 b f (d e-c f)) \operatorname {Subst}\left (\int \left (a+b \tanh ^{-1}(x)\right ) \, dx,x,c+d x\right )}{d^3}\\ &=\frac {2 a b f (d e-c f) x}{d^2}+\frac {b f^2 (c+d x)^2 \left (a+b \tanh ^{-1}(c+d x)\right )}{3 d^3}+\frac {(e+f x)^3 \left (a+b \tanh ^{-1}(c+d x)\right )^2}{3 f}-\frac {(2 b) \operatorname {Subst}\left (\int \left (\frac {(d e-c f) \left (d^2 e^2-2 c d e f+\left (3+c^2\right ) f^2\right ) \left (a+b \tanh ^{-1}(x)\right )}{1-x^2}+\frac {f \left (3 d^2 e^2-6 c d e f+\left (1+3 c^2\right ) f^2\right ) x \left (a+b \tanh ^{-1}(x)\right )}{1-x^2}\right ) \, dx,x,c+d x\right )}{3 d^3 f}-\frac {\left (b^2 f^2\right ) \operatorname {Subst}\left (\int \frac {x^2}{1-x^2} \, dx,x,c+d x\right )}{3 d^3}+\frac {\left (2 b^2 f (d e-c f)\right ) \operatorname {Subst}\left (\int \tanh ^{-1}(x) \, dx,x,c+d x\right )}{d^3}\\ &=\frac {b^2 f^2 x}{3 d^2}+\frac {2 a b f (d e-c f) x}{d^2}+\frac {2 b^2 f (d e-c f) (c+d x) \tanh ^{-1}(c+d x)}{d^3}+\frac {b f^2 (c+d x)^2 \left (a+b \tanh ^{-1}(c+d x)\right )}{3 d^3}+\frac {(e+f x)^3 \left (a+b \tanh ^{-1}(c+d x)\right )^2}{3 f}-\frac {\left (b^2 f^2\right ) \operatorname {Subst}\left (\int \frac {1}{1-x^2} \, dx,x,c+d x\right )}{3 d^3}-\frac {\left (2 b^2 f (d e-c f)\right ) \operatorname {Subst}\left (\int \frac {x}{1-x^2} \, dx,x,c+d x\right )}{d^3}-\frac {\left (2 b (d e-c f) \left (d^2 e^2-2 c d e f+\left (3+c^2\right ) f^2\right )\right ) \operatorname {Subst}\left (\int \frac {a+b \tanh ^{-1}(x)}{1-x^2} \, dx,x,c+d x\right )}{3 d^3 f}-\frac {\left (2 b \left (3 d^2 e^2-6 c d e f+\left (1+3 c^2\right ) f^2\right )\right ) \operatorname {Subst}\left (\int \frac {x \left (a+b \tanh ^{-1}(x)\right )}{1-x^2} \, dx,x,c+d x\right )}{3 d^3}\\ &=\frac {b^2 f^2 x}{3 d^2}+\frac {2 a b f (d e-c f) x}{d^2}-\frac {b^2 f^2 \tanh ^{-1}(c+d x)}{3 d^3}+\frac {2 b^2 f (d e-c f) (c+d x) \tanh ^{-1}(c+d x)}{d^3}+\frac {b f^2 (c+d x)^2 \left (a+b \tanh ^{-1}(c+d x)\right )}{3 d^3}-\frac {(d e-c f) \left (d^2 e^2-2 c d e f+\left (3+c^2\right ) f^2\right ) \left (a+b \tanh ^{-1}(c+d x)\right )^2}{3 d^3 f}+\frac {\left (3 d^2 e^2-6 c d e f+\left (1+3 c^2\right ) f^2\right ) \left (a+b \tanh ^{-1}(c+d x)\right )^2}{3 d^3}+\frac {(e+f x)^3 \left (a+b \tanh ^{-1}(c+d x)\right )^2}{3 f}+\frac {b^2 f (d e-c f) \log \left (1-(c+d x)^2\right )}{d^3}-\frac {\left (2 b \left (3 d^2 e^2-6 c d e f+\left (1+3 c^2\right ) f^2\right )\right ) \operatorname {Subst}\left (\int \frac {a+b \tanh ^{-1}(x)}{1-x} \, dx,x,c+d x\right )}{3 d^3}\\ &=\frac {b^2 f^2 x}{3 d^2}+\frac {2 a b f (d e-c f) x}{d^2}-\frac {b^2 f^2 \tanh ^{-1}(c+d x)}{3 d^3}+\frac {2 b^2 f (d e-c f) (c+d x) \tanh ^{-1}(c+d x)}{d^3}+\frac {b f^2 (c+d x)^2 \left (a+b \tanh ^{-1}(c+d x)\right )}{3 d^3}-\frac {(d e-c f) \left (d^2 e^2-2 c d e f+\left (3+c^2\right ) f^2\right ) \left (a+b \tanh ^{-1}(c+d x)\right )^2}{3 d^3 f}+\frac {\left (3 d^2 e^2-6 c d e f+\left (1+3 c^2\right ) f^2\right ) \left (a+b \tanh ^{-1}(c+d x)\right )^2}{3 d^3}+\frac {(e+f x)^3 \left (a+b \tanh ^{-1}(c+d x)\right )^2}{3 f}-\frac {2 b \left (3 d^2 e^2-6 c d e f+\left (1+3 c^2\right ) f^2\right ) \left (a+b \tanh ^{-1}(c+d x)\right ) \log \left (\frac {2}{1-c-d x}\right )}{3 d^3}+\frac {b^2 f (d e-c f) \log \left (1-(c+d x)^2\right )}{d^3}+\frac {\left (2 b^2 \left (3 d^2 e^2-6 c d e f+\left (1+3 c^2\right ) f^2\right )\right ) \operatorname {Subst}\left (\int \frac {\log \left (\frac {2}{1-x}\right )}{1-x^2} \, dx,x,c+d x\right )}{3 d^3}\\ &=\frac {b^2 f^2 x}{3 d^2}+\frac {2 a b f (d e-c f) x}{d^2}-\frac {b^2 f^2 \tanh ^{-1}(c+d x)}{3 d^3}+\frac {2 b^2 f (d e-c f) (c+d x) \tanh ^{-1}(c+d x)}{d^3}+\frac {b f^2 (c+d x)^2 \left (a+b \tanh ^{-1}(c+d x)\right )}{3 d^3}-\frac {(d e-c f) \left (d^2 e^2-2 c d e f+\left (3+c^2\right ) f^2\right ) \left (a+b \tanh ^{-1}(c+d x)\right )^2}{3 d^3 f}+\frac {\left (3 d^2 e^2-6 c d e f+\left (1+3 c^2\right ) f^2\right ) \left (a+b \tanh ^{-1}(c+d x)\right )^2}{3 d^3}+\frac {(e+f x)^3 \left (a+b \tanh ^{-1}(c+d x)\right )^2}{3 f}-\frac {2 b \left (3 d^2 e^2-6 c d e f+\left (1+3 c^2\right ) f^2\right ) \left (a+b \tanh ^{-1}(c+d x)\right ) \log \left (\frac {2}{1-c-d x}\right )}{3 d^3}+\frac {b^2 f (d e-c f) \log \left (1-(c+d x)^2\right )}{d^3}-\frac {\left (2 b^2 \left (3 d^2 e^2-6 c d e f+\left (1+3 c^2\right ) f^2\right )\right ) \operatorname {Subst}\left (\int \frac {\log (2 x)}{1-2 x} \, dx,x,\frac {1}{1-c-d x}\right )}{3 d^3}\\ &=\frac {b^2 f^2 x}{3 d^2}+\frac {2 a b f (d e-c f) x}{d^2}-\frac {b^2 f^2 \tanh ^{-1}(c+d x)}{3 d^3}+\frac {2 b^2 f (d e-c f) (c+d x) \tanh ^{-1}(c+d x)}{d^3}+\frac {b f^2 (c+d x)^2 \left (a+b \tanh ^{-1}(c+d x)\right )}{3 d^3}-\frac {(d e-c f) \left (d^2 e^2-2 c d e f+\left (3+c^2\right ) f^2\right ) \left (a+b \tanh ^{-1}(c+d x)\right )^2}{3 d^3 f}+\frac {\left (3 d^2 e^2-6 c d e f+\left (1+3 c^2\right ) f^2\right ) \left (a+b \tanh ^{-1}(c+d x)\right )^2}{3 d^3}+\frac {(e+f x)^3 \left (a+b \tanh ^{-1}(c+d x)\right )^2}{3 f}-\frac {2 b \left (3 d^2 e^2-6 c d e f+\left (1+3 c^2\right ) f^2\right ) \left (a+b \tanh ^{-1}(c+d x)\right ) \log \left (\frac {2}{1-c-d x}\right )}{3 d^3}+\frac {b^2 f (d e-c f) \log \left (1-(c+d x)^2\right )}{d^3}-\frac {b^2 \left (3 d^2 e^2-6 c d e f+\left (1+3 c^2\right ) f^2\right ) \text {Li}_2\left (1-\frac {2}{1-c-d x}\right )}{3 d^3}\\ \end {align*}
________________________________________________________________________________________
Mathematica [B] time = 3.81, size = 795, normalized size = 2.13 \[ \frac {1}{3} a^2 f^2 x^3+a^2 e f x^2+a^2 e^2 x+\frac {1}{3} a b \left (2 x \left (3 e^2+3 f x e+f^2 x^2\right ) \tanh ^{-1}(c+d x)+\frac {d f x (6 d e-4 c f+d f x)-(c-1) \left (3 d^2 e^2-3 (c-1) d f e+(c-1)^2 f^2\right ) \log (-c-d x+1)+(c+1) \left (3 d^2 e^2-3 (c+1) d f e+(c+1)^2 f^2\right ) \log (c+d x+1)}{d^3}\right )+\frac {b^2 e^2 \left (\tanh ^{-1}(c+d x) \left ((c+d x-1) \tanh ^{-1}(c+d x)-2 \log \left (1+e^{-2 \tanh ^{-1}(c+d x)}\right )\right )+\text {Li}_2\left (-e^{-2 \tanh ^{-1}(c+d x)}\right )\right )}{d}+\frac {b^2 e f \left (\left (-c^2+2 c+d^2 x^2-1\right ) \tanh ^{-1}(c+d x)^2+2 \left (2 \log \left (1+e^{-2 \tanh ^{-1}(c+d x)}\right ) c+c+d x\right ) \tanh ^{-1}(c+d x)-2 \log \left (\frac {1}{\sqrt {1-(c+d x)^2}}\right )-2 c \text {Li}_2\left (-e^{-2 \tanh ^{-1}(c+d x)}\right )\right )}{d^2}-\frac {b^2 f^2 \left (1-(c+d x)^2\right )^{3/2} \left (-\frac {3 (c+d x) \tanh ^{-1}(c+d x)^2 c^2}{\sqrt {1-(c+d x)^2}}+3 \tanh ^{-1}(c+d x)^2 \cosh \left (3 \tanh ^{-1}(c+d x)\right ) c^2+6 \tanh ^{-1}(c+d x) \cosh \left (3 \tanh ^{-1}(c+d x)\right ) \log \left (1+e^{-2 \tanh ^{-1}(c+d x)}\right ) c^2-3 \tanh ^{-1}(c+d x)^2 \sinh \left (3 \tanh ^{-1}(c+d x)\right ) c^2+\frac {6 (c+d x) \tanh ^{-1}(c+d x) c}{\sqrt {1-(c+d x)^2}}-6 \cosh \left (3 \tanh ^{-1}(c+d x)\right ) \log \left (\frac {1}{\sqrt {1-(c+d x)^2}}\right ) c+6 \tanh ^{-1}(c+d x) \sinh \left (3 \tanh ^{-1}(c+d x)\right ) c+\frac {3 (c+d x) \tanh ^{-1}(c+d x)^2}{\sqrt {1-(c+d x)^2}}+\tanh ^{-1}(c+d x)^2 \cosh \left (3 \tanh ^{-1}(c+d x)\right )+2 \tanh ^{-1}(c+d x) \cosh \left (3 \tanh ^{-1}(c+d x)\right ) \log \left (1+e^{-2 \tanh ^{-1}(c+d x)}\right )+\frac {3 \left (3 c^2-4 c+1\right ) \tanh ^{-1}(c+d x)^2+2 \left (\left (9 c^2+3\right ) \log \left (1+e^{-2 \tanh ^{-1}(c+d x)}\right )+2\right ) \tanh ^{-1}(c+d x)-18 c \log \left (\frac {1}{\sqrt {1-(c+d x)^2}}\right )}{\sqrt {1-(c+d x)^2}}-\frac {4 \left (3 c^2+1\right ) \text {Li}_2\left (-e^{-2 \tanh ^{-1}(c+d x)}\right )}{\left (1-(c+d x)^2\right )^{3/2}}-\tanh ^{-1}(c+d x)^2 \sinh \left (3 \tanh ^{-1}(c+d x)\right )-\sinh \left (3 \tanh ^{-1}(c+d x)\right )-\frac {c+d x}{\sqrt {1-(c+d x)^2}}\right )}{12 d^3} \]
Warning: Unable to verify antiderivative.
[In]
[Out]
________________________________________________________________________________________
fricas [F] time = 0.57, size = 0, normalized size = 0.00 \[ {\rm integral}\left (a^{2} f^{2} x^{2} + 2 \, a^{2} e f x + a^{2} e^{2} + {\left (b^{2} f^{2} x^{2} + 2 \, b^{2} e f x + b^{2} e^{2}\right )} \operatorname {artanh}\left (d x + c\right )^{2} + 2 \, {\left (a b f^{2} x^{2} + 2 \, a b e f x + a b e^{2}\right )} \operatorname {artanh}\left (d x + c\right ), x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [B] time = 0.07, size = 2694, normalized size = 7.20 \[ \text {Expression too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 0.62, size = 806, normalized size = 2.16 \[ \frac {1}{3} \, a^{2} f^{2} x^{3} + a^{2} e f x^{2} + {\left (2 \, x^{2} \operatorname {artanh}\left (d x + c\right ) + d {\left (\frac {2 \, x}{d^{2}} - \frac {{\left (c^{2} + 2 \, c + 1\right )} \log \left (d x + c + 1\right )}{d^{3}} + \frac {{\left (c^{2} - 2 \, c + 1\right )} \log \left (d x + c - 1\right )}{d^{3}}\right )}\right )} a b e f + \frac {1}{3} \, {\left (2 \, x^{3} \operatorname {artanh}\left (d x + c\right ) + d {\left (\frac {d x^{2} - 4 \, c x}{d^{3}} + \frac {{\left (c^{3} + 3 \, c^{2} + 3 \, c + 1\right )} \log \left (d x + c + 1\right )}{d^{4}} - \frac {{\left (c^{3} - 3 \, c^{2} + 3 \, c - 1\right )} \log \left (d x + c - 1\right )}{d^{4}}\right )}\right )} a b f^{2} + a^{2} e^{2} x + \frac {{\left (2 \, {\left (d x + c\right )} \operatorname {artanh}\left (d x + c\right ) + \log \left (-{\left (d x + c\right )}^{2} + 1\right )\right )} a b e^{2}}{d} + \frac {{\left (3 \, d^{2} e^{2} - 6 \, c d e f + 3 \, c^{2} f^{2} + f^{2}\right )} {\left (\log \left (d x + c + 1\right ) \log \left (-\frac {1}{2} \, d x - \frac {1}{2} \, c + \frac {1}{2}\right ) + {\rm Li}_2\left (\frac {1}{2} \, d x + \frac {1}{2} \, c + \frac {1}{2}\right )\right )} b^{2}}{3 \, d^{3}} - \frac {{\left (5 \, c^{2} f^{2} - 6 \, d e f - 6 \, {\left (d e f - f^{2}\right )} c + f^{2}\right )} b^{2} \log \left (d x + c + 1\right )}{6 \, d^{3}} + \frac {{\left (5 \, c^{2} f^{2} + 6 \, d e f - 6 \, {\left (d e f + f^{2}\right )} c + f^{2}\right )} b^{2} \log \left (d x + c - 1\right )}{6 \, d^{3}} + \frac {4 \, b^{2} d f^{2} x + {\left (b^{2} d^{3} f^{2} x^{3} + 3 \, b^{2} d^{3} e f x^{2} + 3 \, b^{2} d^{3} e^{2} x + {\left (c^{3} f^{2} + 3 \, d^{2} e^{2} - 3 \, {\left (d e f - f^{2}\right )} c^{2} - 3 \, d e f + 3 \, {\left (d^{2} e^{2} - 2 \, d e f + f^{2}\right )} c + f^{2}\right )} b^{2}\right )} \log \left (d x + c + 1\right )^{2} + {\left (b^{2} d^{3} f^{2} x^{3} + 3 \, b^{2} d^{3} e f x^{2} + 3 \, b^{2} d^{3} e^{2} x + {\left (c^{3} f^{2} - 3 \, d^{2} e^{2} - 3 \, {\left (d e f + f^{2}\right )} c^{2} - 3 \, d e f + 3 \, {\left (d^{2} e^{2} + 2 \, d e f + f^{2}\right )} c - f^{2}\right )} b^{2}\right )} \log \left (-d x - c + 1\right )^{2} + 2 \, {\left (b^{2} d^{2} f^{2} x^{2} + 2 \, {\left (3 \, d^{2} e f - 2 \, c d f^{2}\right )} b^{2} x\right )} \log \left (d x + c + 1\right ) - 2 \, {\left (b^{2} d^{2} f^{2} x^{2} + 2 \, {\left (3 \, d^{2} e f - 2 \, c d f^{2}\right )} b^{2} x + {\left (b^{2} d^{3} f^{2} x^{3} + 3 \, b^{2} d^{3} e f x^{2} + 3 \, b^{2} d^{3} e^{2} x + {\left (c^{3} f^{2} + 3 \, d^{2} e^{2} - 3 \, {\left (d e f - f^{2}\right )} c^{2} - 3 \, d e f + 3 \, {\left (d^{2} e^{2} - 2 \, d e f + f^{2}\right )} c + f^{2}\right )} b^{2}\right )} \log \left (d x + c + 1\right )\right )} \log \left (-d x - c + 1\right )}{12 \, d^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.00 \[ \int {\left (e+f\,x\right )}^2\,{\left (a+b\,\mathrm {atanh}\left (c+d\,x\right )\right )}^2 \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \left (a + b \operatorname {atanh}{\left (c + d x \right )}\right )^{2} \left (e + f x\right )^{2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________