\[ \int x^4 \cosh ^{-1}(a x)^2 \, dx \]
Optimal antiderivative \[ \frac {16 x}{75 a^{4}}+\frac {8 x^{3}}{225 a^{2}}+\frac {2 x^{5}}{125}+\frac {x^{5} \mathrm {arccosh}\! \left (a x \right )^{2}}{5}-\frac {16 \,\mathrm {arccosh}\! \left (a x \right ) \sqrt {a x -1}\, \sqrt {a x +1}}{75 a^{5}}-\frac {8 x^{2} \mathrm {arccosh}\! \left (a x \right ) \sqrt {a x -1}\, \sqrt {a x +1}}{75 a^{3}}-\frac {2 x^{4} \mathrm {arccosh}\! \left (a x \right ) \sqrt {a x -1}\, \sqrt {a x +1}}{25 a} \]
command
int(x^4*arccosh(a*x)^2,x)
Maple 2022.1 output
\[\int x^{4} \mathrm {arccosh}\left (a x \right )^{2}\, dx\]
Maple 2021.1 output
\[ \frac {\frac {\mathrm {arccosh}\left (a x \right )^{2} a^{5} x^{5}}{5}-\frac {16 \sqrt {a x -1}\, \sqrt {a x +1}\, \mathrm {arccosh}\left (a x \right )}{75}-\frac {2 \,\mathrm {arccosh}\left (a x \right ) a^{4} x^{4} \sqrt {a x -1}\, \sqrt {a x +1}}{25}-\frac {8 \,\mathrm {arccosh}\left (a x \right ) \sqrt {a x -1}\, \sqrt {a x +1}\, a^{2} x^{2}}{75}+\frac {16 a x}{75}+\frac {2 x^{5} a^{5}}{125}+\frac {8 x^{3} a^{3}}{225}}{a^{5}} \]