\[ \int (f x)^m \left (d+e x^2\right ) \left (1+2 x^2+x^4\right )^5 \, dx \]
Optimal antiderivative \[ \frac {d \left (f x \right )^{1+m}}{f \left (1+m \right )}+\frac {\left (10 d +e \right ) \left (f x \right )^{3+m}}{f^{3} \left (3+m \right )}+\frac {5 \left (9 d +2 e \right ) \left (f x \right )^{5+m}}{f^{5} \left (5+m \right )}+\frac {15 \left (8 d +3 e \right ) \left (f x \right )^{7+m}}{f^{7} \left (7+m \right )}+\frac {30 \left (7 d +4 e \right ) \left (f x \right )^{9+m}}{f^{9} \left (9+m \right )}+\frac {42 \left (6 d +5 e \right ) \left (f x \right )^{11+m}}{f^{11} \left (11+m \right )}+\frac {42 \left (5 d +6 e \right ) \left (f x \right )^{13+m}}{f^{13} \left (13+m \right )}+\frac {30 \left (4 d +7 e \right ) \left (f x \right )^{15+m}}{f^{15} \left (15+m \right )}+\frac {15 \left (3 d +8 e \right ) \left (f x \right )^{17+m}}{f^{17} \left (17+m \right )}+\frac {5 \left (2 d +9 e \right ) \left (f x \right )^{19+m}}{f^{19} \left (19+m \right )}+\frac {\left (d +10 e \right ) \left (f x \right )^{21+m}}{f^{21} \left (21+m \right )}+\frac {e \left (f x \right )^{23+m}}{f^{23} \left (23+m \right )} \]
command
integrate((f*x)**m*(e*x**2+d)*(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 \[ \text {Timed out} \]_____________________________________________________