\[ \int (d x)^m \left (a+b x^n+c x^{2 n}\right )^3 \, dx \]
Optimal antiderivative \[ \frac {3 a^{2} b \,x^{1+n} \left (d x \right )^{m}}{1+m +n}+\frac {3 a \left (a c +b^{2}\right ) x^{1+2 n} \left (d x \right )^{m}}{1+m +2 n}+\frac {b \left (6 a c +b^{2}\right ) x^{1+3 n} \left (d x \right )^{m}}{1+m +3 n}+\frac {3 c \left (a c +b^{2}\right ) x^{1+4 n} \left (d x \right )^{m}}{1+m +4 n}+\frac {3 b \,c^{2} x^{1+5 n} \left (d x \right )^{m}}{1+m +5 n}+\frac {c^{3} x^{1+6 n} \left (d x \right )^{m}}{1+m +6 n}+\frac {a^{3} \left (d x \right )^{1+m}}{d \left (1+m \right )} \]
command
integrate((d*x)^m*(a+b*x^n+c*x^(2*n))^3,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {output too large to display} \]
Giac 1.7.0 via sagemath 9.3 output \[ \text {Timed out} \]_______________________________________________________