\[ \int x^5 \sinh ^{-1}(a x)^4 \, dx \]
Optimal antiderivative \[ \frac {245 x^{2}}{1152 a^{4}}-\frac {65 x^{4}}{3456 a^{2}}+\frac {x^{6}}{324}+\frac {245 \arcsinh \! \left (a x \right )^{2}}{1152 a^{6}}+\frac {5 x^{2} \arcsinh \! \left (a x \right )^{2}}{16 a^{4}}-\frac {5 x^{4} \arcsinh \! \left (a x \right )^{2}}{48 a^{2}}+\frac {x^{6} \arcsinh \! \left (a x \right )^{2}}{18}+\frac {5 \arcsinh \! \left (a x \right )^{4}}{96 a^{6}}+\frac {x^{6} \arcsinh \! \left (a x \right )^{4}}{6}-\frac {245 x \arcsinh \! \left (a x \right ) \sqrt {a^{2} x^{2}+1}}{576 a^{5}}+\frac {65 x^{3} \arcsinh \! \left (a x \right ) \sqrt {a^{2} x^{2}+1}}{864 a^{3}}-\frac {x^{5} \arcsinh \! \left (a x \right ) \sqrt {a^{2} x^{2}+1}}{54 a}-\frac {5 x \arcsinh \! \left (a x \right )^{3} \sqrt {a^{2} x^{2}+1}}{24 a^{5}}+\frac {5 x^{3} \arcsinh \! \left (a x \right )^{3} \sqrt {a^{2} x^{2}+1}}{36 a^{3}}-\frac {x^{5} \arcsinh \! \left (a x \right )^{3} \sqrt {a^{2} x^{2}+1}}{9 a} \]
command
int(x^5*arcsinh(a*x)^4,x)
Maple 2022.1 output
\[\int x^{5} \arcsinh \left (a x \right )^{4}\, dx\]
Maple 2021.1 output
\[ \frac {\frac {a^{6} x^{6} \arcsinh \left (a x \right )^{4}}{6}-\frac {a^{5} x^{5} \arcsinh \left (a x \right )^{3} \sqrt {a^{2} x^{2}+1}}{9}+\frac {5 a^{3} x^{3} \arcsinh \left (a x \right )^{3} \sqrt {a^{2} x^{2}+1}}{36}-\frac {5 a x \arcsinh \left (a x \right )^{3} \sqrt {a^{2} x^{2}+1}}{24}+\frac {5 \arcsinh \left (a x \right )^{4}}{96}+\frac {\arcsinh \left (a x \right )^{2} a^{6} x^{6}}{18}-\frac {\arcsinh \left (a x \right ) \sqrt {a^{2} x^{2}+1}\, a^{5} x^{5}}{54}+\frac {65 a^{3} x^{3} \arcsinh \left (a x \right ) \sqrt {a^{2} x^{2}+1}}{864}-\frac {245 \arcsinh \left (a x \right ) \sqrt {a^{2} x^{2}+1}\, a x}{576}-\frac {115 \arcsinh \left (a x \right )^{2}}{1152}+\frac {a^{6} x^{6}}{324}-\frac {65 a^{4} x^{4}}{3456}+\frac {245 a^{2} x^{2}}{1152}+\frac {245}{1152}-\frac {5 a^{4} x^{4} \arcsinh \left (a x \right )^{2}}{48}+\frac {5 \left (a^{2} x^{2}+1\right ) \arcsinh \left (a x \right )^{2}}{16}}{a^{6}} \]