\[ \int \frac {x^3}{\tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx \]
Optimal antiderivative \[ -\frac {2 x^{3}}{3 b \arctanh \left (\tanh \left (b x +a \right )\right )^{\frac {3}{2}}}-\frac {32 \arctanh \left (\tanh \left (b x +a \right )\right )^{\frac {3}{2}}}{3 b^{4}}-\frac {4 x^{2}}{b^{2} \sqrt {\arctanh \left (\tanh \left (b x +a \right )\right )}}+\frac {16 x \sqrt {\arctanh \left (\tanh \left (b x +a \right )\right )}}{b^{3}} \]
command
integrate(x**3/atanh(tanh(b*x+a))**(5/2),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \begin {cases} - \frac {2 x^{3}}{3 b \operatorname {atanh}^{\frac {3}{2}}{\left (\tanh {\left (a + b x \right )} \right )}} - \frac {4 x^{2}}{b^{2} \sqrt {\operatorname {atanh}{\left (\tanh {\left (a + b x \right )} \right )}}} + \frac {16 x \sqrt {\operatorname {atanh}{\left (\tanh {\left (a + b x \right )} \right )}}}{b^{3}} - \frac {32 \operatorname {atanh}^{\frac {3}{2}}{\left (\tanh {\left (a + b x \right )} \right )}}{3 b^{4}} & \text {for}\: b \neq 0 \\\frac {x^{4}}{4 \operatorname {atanh}^{\frac {5}{2}}{\left (\tanh {\left (a \right )} \right )}} & \text {otherwise} \end {cases} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Exception raised: TypeError} \]________________________________________________________________________________________