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