Cos^2(x) Integral

1. Apr 12, 2012

iRaid

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

2. Apr 12, 2012

QuarkCharmer

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?

3. Apr 12, 2012

Dick

Can you integrate cos(2x)? Use a u substitution.

4. Apr 12, 2012

iRaid

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

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

Last edited: Apr 12, 2012
5. Apr 12, 2012

Dick

I think it is the correct answer. You should probably put a +C on it. Is that the problem?

6. Apr 12, 2012

iRaid

Oh nevermind was looking at the wrong answer. Thanks for the help.