\[ \int x^2 \cos ^3\left (a+b \log \left (c x^n\right )\right ) \, dx \]
Optimal antiderivative \[ \frac {2 b^{2} n^{2} x^{3} \cos \left (a +b \ln \left (c \,x^{n}\right )\right )}{b^{4} n^{4}+10 b^{2} n^{2}+9}+\frac {x^{3} \left (\cos ^{3}\left (a +b \ln \left (c \,x^{n}\right )\right )\right )}{3 b^{2} n^{2}+3}+\frac {2 b^{3} n^{3} x^{3} \sin \left (a +b \ln \left (c \,x^{n}\right )\right )}{3 \left (b^{4} n^{4}+10 b^{2} n^{2}+9\right )}+\frac {b n \,x^{3} \left (\cos ^{2}\left (a +b \ln \left (c \,x^{n}\right )\right )\right ) \sin \left (a +b \ln \left (c \,x^{n}\right )\right )}{3 b^{2} n^{2}+3} \]
command
integrate(x^2*cos(a+b*log(c*x^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 \[ \text {Timed out} \]_______________________________________________________