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