Optimal antiderivative \[ -\frac {x^{1+m} \Gamma \left (\frac {1+m}{n}, -x^{n}\right ) \left (-x^{n}\right )^{-\frac {1+m}{n}}}{n} \]
command
int(exp(x^n)*x^m,x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| meijerg | \(\frac {\left (-1\right )^{-\frac {m}{n}-\frac {1}{n}} \left (\frac {n \,x^{1+m} \left (-1\right )^{\frac {m}{n}+\frac {1}{n}} \left (x^{n} n +m +n +1\right ) L_{-\frac {1+m}{n}}^{\left (\frac {1+m +n}{n}\right )}\left (x^{n}\right ) \Gamma \left (-\frac {1+m}{n}+1\right ) \Gamma \left (\frac {1+m +n}{n}+1\right )}{\left (1+m \right ) \left (1+m +n \right ) \Gamma \left (-\frac {1+m}{n}+\frac {1+m +n}{n}+1\right )}-\frac {\left (-1\right )^{\frac {m}{n}+\frac {1}{n}} n^{2} x^{1+m +n} L_{-\frac {1+m}{n}}^{\left (\frac {1+m +n}{n}+1\right )}\left (x^{n}\right ) \Gamma \left (-\frac {1+m}{n}+1\right ) \Gamma \left (\frac {1+m +n}{n}+1\right )}{\left (1+m \right ) \left (1+m +n \right ) \Gamma \left (-\frac {1+m}{n}+\frac {1+m +n}{n}+1\right )}\right )}{n}\) | \(219\) |
Maple 2021.1 output
\[ \int x^{m} {\mathrm e}^{x^{n}}\, dx \]________________________________________________________________________________________