\[ \int x^2 \sinh ^{-1}(a x)^3 \, dx \]
Optimal antiderivative \[ -\frac {2 \left (a^{2} x^{2}+1\right )^{\frac {3}{2}}}{27 a^{3}}-\frac {4 x \arcsinh \! \left (a x \right )}{3 a^{2}}+\frac {2 x^{3} \arcsinh \! \left (a x \right )}{9}+\frac {x^{3} \arcsinh \! \left (a x \right )^{3}}{3}+\frac {14 \sqrt {a^{2} x^{2}+1}}{9 a^{3}}+\frac {2 \arcsinh \! \left (a x \right )^{2} \sqrt {a^{2} x^{2}+1}}{3 a^{3}}-\frac {x^{2} \arcsinh \! \left (a x \right )^{2} \sqrt {a^{2} x^{2}+1}}{3 a} \]
command
int(x^2*arcsinh(a*x)^3,x)
Maple 2022.1 output
\[\int x^{2} \arcsinh \left (a x \right )^{3}\, dx\]
Maple 2021.1 output
\[ \frac {\frac {a^{3} x^{3} \arcsinh \left (a x \right )^{3}}{3}+\frac {2 \arcsinh \left (a x \right )^{2} \sqrt {a^{2} x^{2}+1}}{3}-\frac {\arcsinh \left (a x \right )^{2} \sqrt {a^{2} x^{2}+1}\, a^{2} x^{2}}{3}-\frac {4 a x \arcsinh \left (a x \right )}{3}+\frac {40 \sqrt {a^{2} x^{2}+1}}{27}+\frac {2 a^{3} x^{3} \arcsinh \left (a x \right )}{9}-\frac {2 a^{2} x^{2} \sqrt {a^{2} x^{2}+1}}{27}}{a^{3}} \]