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