92.4 Problem number 171

\[ \int \frac {1}{\coth ^{-1}(\tanh (a+b x))^2} \, dx \]

Optimal antiderivative \[ -\frac {1}{b \,\mathrm {arccoth}\left (\tanh \left (b x +a \right )\right )} \]

command

integrate(1/acoth(tanh(b*x+a))**2,x)

Sympy 1.10.1 under Python 3.10.4 output

\[ \begin {cases} - \frac {1}{b \operatorname {acoth}{\left (\tanh {\left (a + b x \right )} \right )}} & \text {for}\: b \neq 0 \\\frac {x}{\operatorname {acoth}^{2}{\left (\tanh {\left (a \right )} \right )}} & \text {otherwise} \end {cases} \]

Sympy 1.8 under Python 3.8.8 output

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