One way I guess would be to set t=tan x, so you get an integral of a rational expression. Then you would have to solve the resulting integral with partial fractions.
By setting t=tan x I get
The rest of it is evaluating this integral. To begin with you should substitute for u=t^2. And so on. Hope this helps a little, and also hope someone has a more elegant solution.
Sorry, that way would have been hard, here is a better one. Note that:
So if you use that and substitute you should be able to solve the integral np.