It seems like I am stuck on such a simple problem:
How to I find the antiderivative of cos2x?
I have tried partial integration, it doesn't seem to work (for me). Some help on how to integrate it would be nice.
Answer
You use the identity (e.g. solving from cos(2x)=2cos2x−1):
cos2x=1+cos(2x)2
Addendum: the previous hint will give you the easiest solution, but you mentioned an attempt with integration by parts - that would work too:
∫cos2xdx=∫cosxdsinx=cosxsinx−∫sinxdcosx=cosxsinx+∫sin2xdx=cosxsinx+∫1−cos2xdx=cosxsinx+x−∫cos2xdx⇒2∫cos2xdx=cosxsinx+x+C
Then you divide by 2.
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