# cos^2(x) Integral..

by iRaid
Tags: cos2x, integral
 P: 542 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?
 Sci Advisor HW Helper Thanks P: 25,171 Can you integrate cos(2x)? Use a u substitution.
P: 542

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

So then..
x/2 + (1/4)sin2x