\[ \int \left (a x^m+b x^{1+6 m}\right )^5 \, dx \]
Optimal antiderivative \[ \frac {\left (a +b \,x^{1+5 m}\right )^{6}}{6 b \left (1+5 m \right )} \]
command
integrate((a*x**m+b*x**(1+6*m))**5,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \begin {cases} \frac {6 a^{5} x x^{5 m}}{30 m + 6} + \frac {15 a^{4} b x^{2} x^{10 m}}{30 m + 6} + \frac {20 a^{3} b^{2} x^{3} x^{15 m}}{30 m + 6} + \frac {15 a^{2} b^{3} x^{4} x^{20 m}}{30 m + 6} + \frac {6 a b^{4} x^{5} x^{25 m}}{30 m + 6} + \frac {b^{5} x^{6} x^{30 m}}{30 m + 6} & \text {for}\: m \neq - \frac {1}{5} \\a^{5} \log {\left (x \right )} + 5 a^{4} b \log {\left (x \right )} + 10 a^{3} b^{2} \log {\left (x \right )} + 10 a^{2} b^{3} \log {\left (x \right )} + 5 a b^{4} \log {\left (x \right )} + b^{5} \log {\left (x \right )} & \text {otherwise} \end {cases} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________