Integration Problem with a Trig substitution Okay I am a little stuck on this problem.
$$\int \tan^5(x)\sqrt{\sec(x)} \; dx$$
What should be my first step for a u sub or a trig sub? I have tried to use $u=\sec(x)$ and then $u=\tan(x)$, but I get stuck.  A little help?

Let $u=\cos x$ then $du=\sin x dx$ and then the anti derivative becomes:
$$\int\frac{(1-u^2)^2}{u^5}\frac{du}{\sqrt u}$$
now let $u=t^2$ so we find
$$2\int \frac{(1-t^4)^2}{t^{10}}dt=2\int t^{-10}dt-4\int t^{-6}dt+2\int t^{-2}dt$$
I'm sure that you can take it from here.
