We have to find the integral of y = (cos x)^2 - (sin x)^2.

We know that cos 2x = (cos x)^2 - (sin x)^2

=> y = cos 2x

Int[ cos 2x dx]

let 2x = y, dy/2 = dx

=> Int[(1/2)cos y dy]

=> (1/2) sin y + C

substitute y = 2x

=> (1/2)*sin 2x + C

**The required integral is (1/2)*sin 2x + C**