1. ## Trigonometric integral cot^5(x)

I need to integrate:
$
\int \cot^{5}\left(3x\right)dx
$

I started to set u=3x then 1/3du=dx and I get

$
\frac{1}{3}\int \cot^{5}\left(u\right)dx
$

I know that
$
\frac{d}{dx} \cot x = -\csc^{2} x
$

and that

$
\cot^{2} x = \csc^{2} x -1
$

But now I am not sure how to go on. In the case of cot^3 I would write it as cotx and cot^2 x and set t=cotx.
Since I have cot^5 I do not know what to do.
Thanks for any help.

2. We have $\cot^5 u =\frac{\cos^5 u}{\sin ^5 u}
=\frac{\cos u \left(1-\sin^2 u\right)^2}{\sin ^5 u}$
so you can try to set $t =\sin u$