Trig Integral S (1+cos(x))^2 dx

[csmajor86]

First of all, I'm not sure how to properly notate integrals on this forum. I probably should look around and figure it out but being that I'm in a pinch for time I will just use:
S f(x) dx to mean the integral of f(x). If there is a better notation someone please fill me in.

So the problem I am attempting to complete is this:

"Evaluate the integral S (1+cos(x))[sup:2m93acrq]2[/sup:2m93acrq] dx ."

I attempted just foiling out (1+cos(x))[sup:2m93acrq]2[/sup:2m93acrq] to get S cos[sup:2m93acrq]2[/sup:2m93acrq](x) + 2cos(x) + 1 dx but I don't know how to evaluate that either. I'm assuming I need to use a trig identity but I don't know how to approach it.

Any help would be greatly appreciated!

Thanks

 

[galactus]

You are doing OK. Expand it out.

\(\displaystyle (1+cos(x))^{2}=cos^{2}(x)+2cos(x)+1\)

Now, 2cos(x) and 1 should be easy enough to integrate. Correct?.

Just use the identity \(\displaystyle cos^{2}(x)=\frac{1}{2}+\frac{cos(2x)}{2}\) to finish the other portion.

Now, is it easier. Just use a simple u substitution.

 

[csmajor86]

OK...So I end up with:

3x/2 + 2 sin(x) + sin(2x)/4 +C

I believe that is correct. Thank you for your help!