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