Cos^2(x) Integral: Get Help Solving

[iRaid]

Homework Statement

$\int cos^{2}x dx$

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..

Homework Equations

The Attempt at a Solution

 

[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?

 

[Dick]

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

 

[iRaid]

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

So then..
x/2 + (1/4)sin2x
but that's not the answer..

 

[Dick]

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

So then..
x/2 + (1/4)sin2x
but that's not the answer..

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

 

[iRaid]

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.