\[ \int x^{-1+n} \left (a+b x^n\right )^{16} \, dx \]
Optimal antiderivative \[ \frac {\left (a +b \,x^{n}\right )^{17}}{17 b n} \]
command
integrate(x**(-1+n)*(a+b*x**n)**16,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \begin {cases} \frac {a^{16} x^{n}}{n} + \frac {8 a^{15} b x^{2 n}}{n} + \frac {40 a^{14} b^{2} x^{3 n}}{n} + \frac {140 a^{13} b^{3} x^{4 n}}{n} + \frac {364 a^{12} b^{4} x^{5 n}}{n} + \frac {728 a^{11} b^{5} x^{6 n}}{n} + \frac {1144 a^{10} b^{6} x^{7 n}}{n} + \frac {1430 a^{9} b^{7} x^{8 n}}{n} + \frac {1430 a^{8} b^{8} x^{9 n}}{n} + \frac {1144 a^{7} b^{9} x^{10 n}}{n} + \frac {728 a^{6} b^{10} x^{11 n}}{n} + \frac {364 a^{5} b^{11} x^{12 n}}{n} + \frac {140 a^{4} b^{12} x^{13 n}}{n} + \frac {40 a^{3} b^{13} x^{14 n}}{n} + \frac {8 a^{2} b^{14} x^{15 n}}{n} + \frac {a b^{15} x^{16 n}}{n} + \frac {b^{16} x^{17 n}}{17 n} & \text {for}\: n \neq 0 \\\left (a + b\right )^{16} \log {\left (x \right )} & \text {otherwise} \end {cases} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________