\[ \int \frac {1}{\coth ^{-1}(\tanh (a+b x))^3} \, dx \]
Optimal antiderivative \[ -\frac {1}{2 b \mathrm {arccoth}\left (\tanh \left (b x +a \right )\right )^{2}} \]
command
integrate(1/arccoth(tanh(b*x+a))^3,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {2 i}{4 i \, b^{3} x^{2} - 4 \, \pi b^{2} x + 8 i \, a b^{2} x - i \, \pi ^{2} b - 4 \, \pi a b + 4 i \, a^{2} b} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {1}{\operatorname {arcoth}\left (\tanh \left (b x + a\right )\right )^{3}}\,{d x} \]________________________________________________________________________________________