I'm supposed to integrate

pi

∫ (cos nx)(cosx)^2 dx

0

how do i integrate this?

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- Sep 23rd 2008, 10:37 AMpandaproblem in integration
I'm supposed to integrate

pi

∫ (cos nx)(cosx)^2 dx

0

how do i integrate this? - Sep 23rd 2008, 10:55 AMJameson
My first guess would be convert to and then it becomes a trivial integral plus a u-sub one.

- Sep 23rd 2008, 10:55 AMChop Suey
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:

- Sep 23rd 2008, 10:59 AMJameson
I didn't see the (nx) term. Sorry. Obviously the above substitution is the one to go with now.