\[ \int (f x)^m \left (1+x^2\right ) \left (1+2 x^2+x^4\right )^5 \, dx \]
Optimal antiderivative \[ \frac {\left (f x \right )^{1+m}}{f \left (1+m \right )}+\frac {11 \left (f x \right )^{3+m}}{f^{3} \left (3+m \right )}+\frac {55 \left (f x \right )^{5+m}}{f^{5} \left (5+m \right )}+\frac {165 \left (f x \right )^{7+m}}{f^{7} \left (7+m \right )}+\frac {330 \left (f x \right )^{9+m}}{f^{9} \left (9+m \right )}+\frac {462 \left (f x \right )^{11+m}}{f^{11} \left (11+m \right )}+\frac {462 \left (f x \right )^{13+m}}{f^{13} \left (13+m \right )}+\frac {330 \left (f x \right )^{15+m}}{f^{15} \left (15+m \right )}+\frac {165 \left (f x \right )^{17+m}}{f^{17} \left (17+m \right )}+\frac {55 \left (f x \right )^{19+m}}{f^{19} \left (19+m \right )}+\frac {11 \left (f x \right )^{21+m}}{f^{21} \left (21+m \right )}+\frac {\left (f x \right )^{23+m}}{f^{23} \left (23+m \right )} \]
command
integrate((f*x)**m*(x**2+1)*(x**4+2*x**2+1)**5,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {output too large to display} \]
Sympy 1.8 under Python 3.8.8 output \[ \text {Timed out} \]_____________________________________________________