\[ \int \frac {\cosh ^5\left (a+b \log \left (c x^n\right )\right )}{x} \, dx \]
Optimal antiderivative \[ \frac {\sinh \! \left (a +b \ln \! \left (c \,x^{n}\right )\right )}{b n}+\frac {2 \left (\sinh ^{3}\left (a +b \ln \! \left (c \,x^{n}\right )\right )\right )}{3 b n}+\frac {\sinh ^{5}\left (a +b \ln \! \left (c \,x^{n}\right )\right )}{5 b n} \]
command
int(cosh(a+b*ln(c*x^n))^5/x,x)
Maple 2022.1 output
\[\int \frac {\cosh ^{5}\left (a +b \ln \left (c \,x^{n}\right )\right )}{x}\, dx\]
Maple 2021.1 output
\[ \frac {\left (\frac {8}{15}+\frac {\left (\cosh ^{4}\left (a +b \ln \left (c \,x^{n}\right )\right )\right )}{5}+\frac {4 \left (\cosh ^{2}\left (a +b \ln \left (c \,x^{n}\right )\right )\right )}{15}\right ) \sinh \left (a +b \ln \left (c \,x^{n}\right )\right )}{n b} \]