\[ \int x^2 \cosh ^{-1}(a x)^4 \, dx \]
Optimal antiderivative \[ \frac {160 x}{27 a^{2}}+\frac {8 x^{3}}{81}+\frac {8 x \mathrm {arccosh}\! \left (a x \right )^{2}}{3 a^{2}}+\frac {4 x^{3} \mathrm {arccosh}\! \left (a x \right )^{2}}{9}+\frac {x^{3} \mathrm {arccosh}\! \left (a x \right )^{4}}{3}-\frac {160 \,\mathrm {arccosh}\! \left (a x \right ) \sqrt {a x -1}\, \sqrt {a x +1}}{27 a^{3}}-\frac {8 x^{2} \mathrm {arccosh}\! \left (a x \right ) \sqrt {a x -1}\, \sqrt {a x +1}}{27 a}-\frac {8 \mathrm {arccosh}\! \left (a x \right )^{3} \sqrt {a x -1}\, \sqrt {a x +1}}{9 a^{3}}-\frac {4 x^{2} \mathrm {arccosh}\! \left (a x \right )^{3} \sqrt {a x -1}\, \sqrt {a x +1}}{9 a} \]
command
int(x^2*arccosh(a*x)^4,x)
Maple 2022.1 output
\[\int x^{2} \mathrm {arccosh}\left (a x \right )^{4}\, dx\]
Maple 2021.1 output
\[ \frac {\frac {a^{3} x^{3} \mathrm {arccosh}\left (a x \right )^{4}}{3}-\frac {8 \mathrm {arccosh}\left (a x \right )^{3} \sqrt {a x -1}\, \sqrt {a x +1}}{9}-\frac {4 \mathrm {arccosh}\left (a x \right )^{3} a^{2} x^{2} \sqrt {a x -1}\, \sqrt {a x +1}}{9}+\frac {8 a x \mathrm {arccosh}\left (a x \right )^{2}}{3}-\frac {160 \sqrt {a x -1}\, \sqrt {a x +1}\, \mathrm {arccosh}\left (a x \right )}{27}+\frac {160 a x}{27}+\frac {4 a^{3} x^{3} \mathrm {arccosh}\left (a x \right )^{2}}{9}-\frac {8 \,\mathrm {arccosh}\left (a x \right ) \sqrt {a x -1}\, \sqrt {a x +1}\, a^{2} x^{2}}{27}+\frac {8 x^{3} a^{3}}{81}}{a^{3}} \]