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