\[ \int \frac {\sinh ^4\left (a+b \log \left (c x^n\right )\right )}{x} \, dx \]
Optimal antiderivative \[ \frac {3 \ln \! \left (x \right )}{8}-\frac {3 \cosh \! \left (a +b \ln \! \left (c \,x^{n}\right )\right ) \sinh \! \left (a +b \ln \! \left (c \,x^{n}\right )\right )}{8 b n}+\frac {\cosh \! \left (a +b \ln \! \left (c \,x^{n}\right )\right ) \left (\sinh ^{3}\left (a +b \ln \! \left (c \,x^{n}\right )\right )\right )}{4 b n} \]
command
int(sinh(a+b*ln(c*x^n))^4/x,x)
Maple 2022.1 output
\[\int \frac {\sinh ^{4}\left (a +b \ln \left (c \,x^{n}\right )\right )}{x}\, dx\]
Maple 2021.1 output
\[ \frac {\cosh \left (a +b \ln \left (c \,x^{n}\right )\right ) \left (\sinh ^{3}\left (a +b \ln \left (c \,x^{n}\right )\right )\right )}{4 b n}-\frac {3 \cosh \left (a +b \ln \left (c \,x^{n}\right )\right ) \sinh \left (a +b \ln \left (c \,x^{n}\right )\right )}{8 b n}+\frac {3 \ln \left (c \,x^{n}\right )}{8 n}+\frac {3 a}{8 b n} \]