What's the integral of cos^2(x)?

The integral of cos^2(x) is (1/2)x + (1/4)sin(2x) + C.

To find the integral of cos^2(x), we can use the identity cos^2(x) = (1 + cos(2x))/2. Therefore, we have:

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

Where C is the constant of integration. We can check our answer by differentiating it and verifying that we get cos^2(x) as the result.

d/dx [(1/2)x + (1/4)sin(2x) + C] = (1/2) - (1/2)cos(2x) = cos^2(x)

Therefore, our answer is correct.