How do you integrate (cosx)^2?

Answer 1

Using the trig identity cos² x = (cos (2x) + 1)/2. So we have:

∫cos² x dx
1/2 ∫cos (2x) + 1 dx
1/2 (sin (2x)/2 + x) + C
sin (2x)/4 + x/2 + C

And we are done.