\[ \int \frac {\sin ^4\left (a+b \log \left (c x^n\right )\right )}{x^3} \, dx \]
Optimal antiderivative \[ -\frac {3 b^{4} n^{4}}{4 \left (4 b^{4} n^{4}+5 b^{2} n^{2}+1\right ) x^{2}}-\frac {3 b^{3} n^{3} \cos \left (a +b \ln \left (c \,x^{n}\right )\right ) \sin \left (a +b \ln \left (c \,x^{n}\right )\right )}{2 \left (4 b^{4} n^{4}+5 b^{2} n^{2}+1\right ) x^{2}}-\frac {3 b^{2} n^{2} \left (\sin ^{2}\left (a +b \ln \left (c \,x^{n}\right )\right )\right )}{2 \left (4 b^{4} n^{4}+5 b^{2} n^{2}+1\right ) x^{2}}-\frac {b n \cos \left (a +b \ln \left (c \,x^{n}\right )\right ) \left (\sin ^{3}\left (a +b \ln \left (c \,x^{n}\right )\right )\right )}{\left (4 b^{2} n^{2}+1\right ) x^{2}}-\frac {\sin ^{4}\left (a +b \ln \left (c \,x^{n}\right )\right )}{2 \left (4 b^{2} n^{2}+1\right ) x^{2}} \]
command
integrate(sin(a+b*ln(c*x**n))**4/x**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 \[ \text {Timed out} \]_____________________________________________________