cos^2(x) Integral..

iRaid

1. The problem statement, all variables and given/known data
[itex]\int cos^{2}x dx[/itex]

I know that

[itex]cos^{2}x = \frac{1+cos2x}{2}[/itex]

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

QuarkCharmer

Well, that leaves you with:
[tex]\int \frac{1}{2}+\frac{1}{2}cos(2x)dx[/tex]

Which you can break up into two integrals:
[tex]\int \frac{1}{2}dx + \int \frac{1}{2}cos(2x)dx[/tex]

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 thats not the answer..

Dick

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

iRaid

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