\[ \int \frac {\coth ^{-1}(\tanh (a+b x))^3}{x^5} \, dx \]
Optimal antiderivative \[ \frac {\mathrm {arccoth}\left (\tanh \left (b x +a \right )\right )^{4}}{4 x^{4} \left (b x -\mathrm {arccoth}\left (\tanh \left (b x +a \right )\right )\right )} \]
command
integrate(arccoth(tanh(b*x+a))^3/x^5,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {32 \, b^{3} x^{3} + 24 i \, \pi b^{2} x^{2} + 48 \, a b^{2} x^{2} - 8 \, \pi ^{2} b x + 32 i \, \pi a b x + 32 \, a^{2} b x - i \, \pi ^{3} - 6 \, \pi ^{2} a + 12 i \, \pi a^{2} + 8 \, a^{3}}{32 \, x^{4}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {\operatorname {arcoth}\left (\tanh \left (b x + a\right )\right )^{3}}{x^{5}}\,{d x} \]________________________________________________________________________________________