\[ \int \left (b \tan ^n(e+f x)\right )^{\frac {1}{n}} \, dx \]
Optimal antiderivative \[ -\frac {\cot \left (f x +e \right ) \ln \left (\cos \left (f x +e \right )\right ) \left (b \left (\tan ^{n}\left (f x +e \right )\right )\right )^{\frac {1}{n}}}{f} \]
command
int((b*tan(f*x+e)^n)^(1/n),x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| risch | \(\text {Expression too large to display}\) | \(12884\) |
Maple 2021.1 output
\[ \int \left (b \left (\tan ^{n}\left (f x +e \right )\right )\right )^{\frac {1}{n}}\, dx \]________________________________________________________________________________________