\[ \int \sec ^6(a+b x) (d \tan (a+b x))^n \, dx \]
Optimal antiderivative \[ \frac {\left (d \tan \left (b x +a \right )\right )^{1+n}}{b d \left (1+n \right )}+\frac {2 \left (d \tan \left (b x +a \right )\right )^{3+n}}{b \,d^{3} \left (3+n \right )}+\frac {\left (d \tan \left (b x +a \right )\right )^{5+n}}{b \,d^{5} \left (5+n \right )} \]
command
int(sec(b*x+a)^6*(d*tan(b*x+a))^n,x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| risch | \(\text {Expression too large to display}\) | \(10923\) |
Maple 2021.1 output
\[ \int \left (\sec ^{6}\left (b x +a \right )\right ) \left (d \tan \left (b x +a \right )\right )^{n}\, dx \]________________________________________________________________________________________