\[ \int f^{a+b x^n} x^{-1-\frac {3 n}{2}} \, dx \]
Optimal antiderivative \[ -\frac {2 f^{a +b \,x^{n}} x^{-\frac {3 n}{2}}}{3 n}-\frac {4 b \,f^{a +b \,x^{n}} \ln \left (f \right ) x^{-\frac {n}{2}}}{3 n}+\frac {4 b^{\frac {3}{2}} f^{a} \erfi \left (x^{\frac {n}{2}} \sqrt {b}\, \sqrt {\ln \left (f \right )}\right ) \ln \left (f \right )^{\frac {3}{2}} \sqrt {\pi }}{3 n} \]
command
integrate(f**(a+b*x**n)*x**(-1-3/2*n),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \begin {cases} - \frac {4 b f^{a} f^{b x^{n}} x^{- \frac {n}{2}} \log {\left (f \right )}}{3 n} - \frac {2 f^{a} f^{b x^{n}} x^{- \frac {3 n}{2}}}{3 n} & \text {for}\: n \neq 0 \\f^{a + b} \log {\left (x \right )} & \text {otherwise} \end {cases} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________