\[ \int x^{-1+n} (a+b x)^{-n} \, dx \]
Optimal antiderivative \[ \frac {x^{n} \left (1+\frac {b x}{a}\right )^{n} \hypergeom \left (\left [n , n\right ], \left [1+n \right ], -\frac {b x}{a}\right ) \left (b x +a \right )^{-n}}{n} \]
command
integrate(x**(-1+n)/((b*x+a)**n),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \frac {a^{- n} x^{n} \Gamma \left (n\right ) {{}_{2}F_{1}\left (\begin {matrix} n, n \\ n + 1 \end {matrix}\middle | {\frac {b x e^{i \pi }}{a}} \right )}}{\Gamma \left (n + 1\right )} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________