\[ \int x^4 \sinh ^{-1}(a x)^4 \, dx \]
Optimal antiderivative \[ \frac {16576 x}{5625 a^{4}}-\frac {1088 x^{3}}{16875 a^{2}}+\frac {24 x^{5}}{3125}+\frac {32 x \arcsinh \! \left (a x \right )^{2}}{25 a^{4}}-\frac {16 x^{3} \arcsinh \! \left (a x \right )^{2}}{75 a^{2}}+\frac {12 x^{5} \arcsinh \! \left (a x \right )^{2}}{125}+\frac {x^{5} \arcsinh \! \left (a x \right )^{4}}{5}-\frac {16576 \arcsinh \! \left (a x \right ) \sqrt {a^{2} x^{2}+1}}{5625 a^{5}}+\frac {1088 x^{2} \arcsinh \! \left (a x \right ) \sqrt {a^{2} x^{2}+1}}{5625 a^{3}}-\frac {24 x^{4} \arcsinh \! \left (a x \right ) \sqrt {a^{2} x^{2}+1}}{625 a}-\frac {32 \arcsinh \! \left (a x \right )^{3} \sqrt {a^{2} x^{2}+1}}{75 a^{5}}+\frac {16 x^{2} \arcsinh \! \left (a x \right )^{3} \sqrt {a^{2} x^{2}+1}}{75 a^{3}}-\frac {4 x^{4} \arcsinh \! \left (a x \right )^{3} \sqrt {a^{2} x^{2}+1}}{25 a} \]
command
int(x^4*arcsinh(a*x)^4,x)
Maple 2022.1 output
\[\int x^{4} \arcsinh \left (a x \right )^{4}\, dx\]
Maple 2021.1 output
\[ \frac {\frac {a^{5} x^{5} \arcsinh \left (a x \right )^{4}}{5}-\frac {32 \arcsinh \left (a x \right )^{3} \sqrt {a^{2} x^{2}+1}}{75}-\frac {4 a^{4} x^{4} \arcsinh \left (a x \right )^{3} \sqrt {a^{2} x^{2}+1}}{25}+\frac {16 a^{2} x^{2} \arcsinh \left (a x \right )^{3} \sqrt {a^{2} x^{2}+1}}{75}+\frac {32 a x \arcsinh \left (a x \right )^{2}}{25}-\frac {16576 \sqrt {a^{2} x^{2}+1}\, \arcsinh \left (a x \right )}{5625}+\frac {16576 a x}{5625}+\frac {12 a^{5} x^{5} \arcsinh \left (a x \right )^{2}}{125}-\frac {24 a^{4} x^{4} \arcsinh \left (a x \right ) \sqrt {a^{2} x^{2}+1}}{625}+\frac {1088 \arcsinh \left (a x \right ) \sqrt {a^{2} x^{2}+1}\, a^{2} x^{2}}{5625}+\frac {24 a^{5} x^{5}}{3125}-\frac {1088 a^{3} x^{3}}{16875}-\frac {16 a^{3} x^{3} \arcsinh \left (a x \right )^{2}}{75}}{a^{5}} \]