\[ \int x^5 \sqrt [3]{1+x^3} \, dx \]
Optimal antiderivative \[ \frac {\left (x^{3}+1\right )^{\frac {1}{3}} \left (4 x^{6}+x^{3}-3\right )}{28} \]
command
int(x^5*(x^3+1)^(1/3),x)
Maple 2022.1 output
hanged
Maple 2021.1 output
| method | result | size |
| meijerg | \(\frac {\hypergeom \left (\left [-\frac {1}{3}, 2\right ], \left [3\right ], -x^{3}\right ) x^{6}}{6}\) | \(17\) |
| risch | \(\frac {\left (x^{3}+1\right )^{\frac {1}{3}} \left (4 x^{6}+x^{3}-3\right )}{28}\) | \(20\) |
| trager | \(\left (\frac {1}{7} x^{6}+\frac {1}{28} x^{3}-\frac {3}{28}\right ) \left (x^{3}+1\right )^{\frac {1}{3}}\) | \(21\) |
| gosper | \(\frac {\left (1+x \right ) \left (x^{2}-x +1\right ) \left (4 x^{3}-3\right ) \left (x^{3}+1\right )^{\frac {1}{3}}}{28}\) | \(28\) |