92.2 Problem number 162

\[ \int \frac {1}{\coth ^{-1}(\tanh (a+b x))} \, dx \]

Optimal antiderivative \[ \frac {\ln \left (\mathrm {arccoth}\left (\tanh \left (b x +a \right )\right )\right )}{b} \]

command

integrate(1/acoth(tanh(b*x+a)),x)

Sympy 1.10.1 under Python 3.10.4 output

\[ \begin {cases} \frac {\log {\left (\operatorname {acoth}{\left (\tanh {\left (a + b x \right )} \right )} \right )}}{b} & \text {for}\: b \neq 0 \\\frac {x}{\operatorname {acoth}{\left (\tanh {\left (a \right )} \right )}} & \text {otherwise} \end {cases} \]

Sympy 1.8 under Python 3.8.8 output

\[ \text {Exception raised: TypeError} \]________________________________________________________________________________________