Optimal antiderivative \[ -\frac {f^{a} x \Gamma \left (\frac {1}{n}, -b \,x^{n} \ln \left (f \right )\right ) \left (-b \,x^{n} \ln \left (f \right )\right )^{-\frac {1}{n}}}{n} \]
command
int(f^(a+b*x^n),x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| meijerg | \(\frac {f^{a} \left (-b \right )^{-\frac {1}{n}} \ln \left (f \right )^{-\frac {1}{n}} \left (\frac {n x \left (-b \right )^{\frac {1}{n}} \ln \left (f \right )^{\frac {1}{n}} \left (\ln \left (f \right ) x^{n} b n +n +1\right ) \Gamma \left (1-\frac {1}{n}\right ) \Gamma \left (\frac {1+n}{n}+1\right ) L_{-\frac {1}{n}}^{\left (\frac {1+n}{n}\right )}\left (b \,x^{n} \ln \left (f \right )\right )}{\left (1+n \right ) \Gamma \left (-\frac {1}{n}+\frac {1+n}{n}+1\right )}-\frac {n^{2} x^{1+n} \left (-b \right )^{\frac {1}{n}} \ln \left (f \right )^{1+\frac {1}{n}} b L_{-\frac {1}{n}}^{\left (\frac {1+n}{n}+1\right )}\left (b \,x^{n} \ln \left (f \right )\right ) \Gamma \left (1-\frac {1}{n}\right ) \Gamma \left (\frac {1+n}{n}+1\right )}{\left (1+n \right ) \Gamma \left (-\frac {1}{n}+\frac {1+n}{n}+1\right )}\right )}{n}\) | \(201\) |
Maple 2021.1 output
\[ \int f^{b \,x^{n}+a}\, dx \]________________________________________________________________________________________