Is there a way to integrate $\cos^{2} {3x}$ with a different technique than integration by parts?

Question

The question is just as it is on the title: Is there a way to integrate $\cos^{2} {3x}$ with a different technique than integration by parts? And in case there is, how can I do it?

Answer 1

Yes. By using the fact that $\cos^2t=\dfrac{1+\cos2t}2$ .

Answer 2

$$ \int \cos^2 (3x) = \int \frac{ 1 + \cos 6x }{2} dx = \frac{x}{2} + \frac{1}{12} \int \cos (6x ) d (6x) = \frac{x}{2} + \frac{1}{12} \sin (6x) + C $$