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