Integrate the expression cos^2(x).

This is a common question in C4 and the trick used to solve it is often used in sub-sections to full questions.

To solve it, we must simplify the expression in terms of cos(2x) using two trigonometric identities: "cos(2x) = cos²x - sin²x" and "sin²x + cos²x = 1". The result of these two expressions gives us "cos²x = 0.5cos(2x) + 0.5". We can now obtain the final solution by integrating this expression knowing that cos(x) integrates to sin(x), giving "0.25sin(2x) + 0.5x + c". The c term, representing a constant, is essential in the answer as we have not defined the integral between any limits.