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