\[ \int x^{5/2} \tanh ^{-1}(\tanh (a+b x)) \, dx \]
Optimal antiderivative \[ -\frac {4 b \,x^{\frac {9}{2}}}{63}+\frac {2 x^{\frac {7}{2}} \arctanh \left (\tanh \left (b x +a \right )\right )}{7} \]
command
integrate(x**(5/2)*atanh(tanh(b*x+a)),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ - \frac {4 b x^{\frac {9}{2}}}{63} + \frac {2 x^{\frac {7}{2}} \operatorname {atanh}{\left (\tanh {\left (a + b x \right )} \right )}}{7} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________