Find the indefinite integral of cos^2 x

First, we need to write cos²x in a form that is easily integrable. We can use the double angle formula cos(2x) = 2cos²x - 1 to see that cos²x = 1/2cos(2x)+1/2. Now, we can integrate the terms seperately. Using the chain rule, we see that the integral of 1/2cos(2x) is 1/4sin(2x). Also, the integral of 1/2 is 1/2x. This gives us the answer of: 1/4sin(2x) + 1/2x + const.