Evaluate the integral of cos^2(x) dx.

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

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

∫cos^2(x) dx = ∫(1/2)(1 + cos(2x)) 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 to obtain cos^2(x):

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

Therefore, our answer is correct.

Another way to evaluate the integral of cos^2(x) dx is to use the half-angle formula for cosine, which states that cos^2(x) = (1/2)(1 + cos(2x)). Using this formula, we have:

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

Again, we obtain the same answer as before.