Thread: problem in integration

I'm supposed to integrate
pi
∫ (cos nx)(cosx)^2 dx
0

how do i integrate this?

My first guess would be convert to and then it becomes a trivial integral plus a u-sub one.

First, use the half angle identity to get rid of the cos^2(x).



Multiplying this with \cos{nx} will get you



First one should be easy. For the second one, you can use either integration by parts or the product to sum identity:

I didn't see the (nx) term. Sorry. Obviously the above substitution is the one to go with now.