\[ \int (d x)^m \left (A+B x+C x^2\right ) \left (a+b x^2+c x^4\right )^3 \, dx \]
Optimal antiderivative \[ \frac {a^{3} A \left (d x \right )^{1+m}}{d \left (1+m \right )}+\frac {a^{3} B \left (d x \right )^{2+m}}{d^{2} \left (2+m \right )}+\frac {a^{2} \left (3 A b +a C \right ) \left (d x \right )^{3+m}}{d^{3} \left (3+m \right )}+\frac {3 a^{2} b B \left (d x \right )^{4+m}}{d^{4} \left (4+m \right )}+\frac {3 a \left (A \left (a c +b^{2}\right )+a b C \right ) \left (d x \right )^{5+m}}{d^{5} \left (5+m \right )}+\frac {3 a B \left (a c +b^{2}\right ) \left (d x \right )^{6+m}}{d^{6} \left (6+m \right )}+\frac {\left (A \left (6 a b c +b^{3}\right )+3 a \left (a c +b^{2}\right ) C \right ) \left (d x \right )^{7+m}}{d^{7} \left (7+m \right )}+\frac {b B \left (6 a c +b^{2}\right ) \left (d x \right )^{8+m}}{d^{8} \left (8+m \right )}+\frac {\left (3 A c \left (a c +b^{2}\right )+b \left (6 a c +b^{2}\right ) C \right ) \left (d x \right )^{9+m}}{d^{9} \left (9+m \right )}+\frac {3 B c \left (a c +b^{2}\right ) \left (d x \right )^{10+m}}{d^{10} \left (10+m \right )}+\frac {3 c \left (A b c +\left (a c +b^{2}\right ) C \right ) \left (d x \right )^{11+m}}{d^{11} \left (11+m \right )}+\frac {3 b B \,c^{2} \left (d x \right )^{12+m}}{d^{12} \left (12+m \right )}+\frac {c^{2} \left (A c +3 b C \right ) \left (d x \right )^{13+m}}{d^{13} \left (13+m \right )}+\frac {B \,c^{3} \left (d x \right )^{14+m}}{d^{14} \left (14+m \right )}+\frac {c^{3} C \left (d x \right )^{15+m}}{d^{15} \left (15+m \right )} \]
command
integrate((d*x)**m*(C*x**2+B*x+A)*(c*x**4+b*x**2+a)**3,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 \[ \text {Timed out} \]_____________________________________________________