\[ \int f^{a+b x^n} x^{-1+\frac {3 n}{2}} \, dx \]
Optimal antiderivative \[ \frac {f^{a +b \,x^{n}} x^{\frac {n}{2}}}{b n \ln \left (f \right )}-\frac {f^{a} \erfi \left (x^{\frac {n}{2}} \sqrt {b}\, \sqrt {\ln \left (f \right )}\right ) \sqrt {\pi }}{2 b^{\frac {3}{2}} n \ln \left (f \right )^{\frac {3}{2}}} \]
command
integrate(f**(a+b*x**n)*x**(-1+3/2*n),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \begin {cases} - \frac {4 b f^{a} f^{b x^{n}} x^{\frac {5 n}{2}} \log {\left (f \right )}}{15 n} + \frac {2 f^{a} f^{b x^{n}} x^{\frac {3 n}{2}}}{3 n} & \text {for}\: n \neq 0 \\f^{a + b} \log {\left (x \right )} & \text {otherwise} \end {cases} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________