Integrating cos^2(x) using two methods: substitution and integration by parts

[henryc09]

Homework Statement

1. Evaluate:
$$\oint cos^2(x)dx$$

Using two different methods

Homework Equations

The Attempt at a Solution

I have done it making the substitution of cos^2(x) = (1 + cos(2x))/2 but don't see how you can do this another way. Integration by parts doesn't seem to work and nor does substitution as far as I'm aware. Any ideas?

 

[Seannation]

You could maybe do something with this:

$$cos^2(x) + sin^2(x) = 1$$

 

[Jasso]

I have done it making the substitution of cos^2(x) = (1 + cos(2x))/2 but don't see how you can do this another way. Integration by parts doesn't seem to work and nor does substitution as far as I'm aware. Any ideas?

Integration by parts does indeed work on this integral, you just have to know where to use your trig identities as Seannation was hinting at.

 

[henryc09]

Ah ok I've got it now, thanks!