Originally Posted by

**ElBartoV** I was just curious to see if there was alternative methods to solving

$\displaystyle \displaystyle\int \tan^6(x)\sec(x)\,dx$

asides from using integrations by parts since it tends to yield a very lengthy solution. Although, I believe the reduction formula for sec(x) could probably be applied in this case instead of integration by parts

$\displaystyle \displaystyle\int\sec^n(x)\,dx = -\frac{1}{n-1}\cot^{n-1}(x) - \cot^{n-2}(x)$

but, still is there any other methods asides from these two that could be used?

(P.S. sorry if the format is not completely correct, this is the first time i have used LaTex)