Integrate Cos^2(x)

{} = integral sign for purpose of this solutioncos²x = 1 - sin²x (1)cos 2x = cos²x - sin²x (2)cos²x = 1 - (cos²x - cos 2x)cos²x = 1 - cos²x + cos 2x2 cos²x = 1 + cos 2xcos²x = (1 + cos 2x)/2{} cos²(x) dx = {} (cos (2x) +1)/2 dx . = 1/2 {} 1 dx + 1/2 {} cos (2x) dx = 1/2 x + (sin 2x)/4 + C