\[ \int \frac {x^2}{\coth ^{-1}(\tanh (a+b x))^2} \, dx \]
Optimal antiderivative \[ \frac {2 x}{b^{2}}-\frac {x^{2}}{b \,\mathrm {arccoth}\left (\tanh \left (b x +a \right )\right )}+\frac {2 \left (b x -\mathrm {arccoth}\left (\tanh \left (b x +a \right )\right )\right ) \ln \left (\mathrm {arccoth}\left (\tanh \left (b x +a \right )\right )\right )}{b^{3}} \]
command
integrate(x^2/arccoth(tanh(b*x+a))^2,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {\pi ^{2} - 4 i \, \pi a - 4 \, a^{2}}{2 \, {\left (2 \, b^{4} x + i \, \pi b^{3} + 2 \, a b^{3}\right )}} + \frac {x}{b^{2}} - \frac {{\left (i \, \pi + 2 \, a\right )} \log \left (i \, \pi + 2 \, b x + 2 \, a\right )}{b^{3}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {x^{2}}{\operatorname {arcoth}\left (\tanh \left (b x + a\right )\right )^{2}}\,{d x} \]________________________________________________________________________________________