We can start by using the formula:
cos²(x) = (1 + cos(2x))/2
We can then substitute this expression into our integral and simplify:
∫cos²(x)dx = ∫(1 + cos(2x))/2 dx
= (1/2)∫dx + (1/2)∫cos(2x)dx
= (1/2)x + (1/4)sin(2x) + C
Therefore, the antiderivative of cos²(x) is (1/2)x + (1/4)sin(2x) + C, where C is the constant of integration.
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