# cos^2(x) Integral..

by iRaid
Tags: cos2x, integral
 P: 519 1. The problem statement, all variables and given/known data $\int cos^{2}x dx$ I know that $cos^{2}x = \frac{1+cos2x}{2}$ but I don't see how that helps me. Can someone help walk me through it.. 2. Relevant equations 3. The attempt at a solution
 P: 1,035 Well, that leaves you with: $$\int \frac{1}{2}+\frac{1}{2}cos(2x)dx$$ Which you can break up into two integrals: $$\int \frac{1}{2}dx + \int \frac{1}{2}cos(2x)dx$$ The first one should be no problem. Isn't there some sort of substitution you can make for the second one?
 HW Helper Sci Advisor Thanks P: 24,462 Can you integrate cos(2x)? Use a u substitution.
P: 519

## cos^2(x) Integral..

u=2x du=(1/2)dx
(1/2)∫cosudu
=(1/4)sin2x

So then..
x/2 + (1/4)sin2x
but thats not the answer..
HW Helper
Sci Advisor
Thanks
P: 24,462
 Quote by iRaid u=2x du=(1/2)dx (1/2)∫cosudu =(1/4)sin2x So then.. x/2 + (1/4)sin2x but thats not the answer..
I think it is the correct answer. You should probably put a +C on it. Is that the problem?
P: 519
 Quote by Dick I think it is the correct answer. You should probably put a +C on it. Is that the problem?
Oh nevermind was looking at the wrong answer. Thanks for the help.

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