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