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