Auto-correlation function for a time signal

For a time signal $$x(t)= \cos^2(2\pi t)$$, solve for the Auto-correlation Function.

Basically I have been following a guide on how to compute the auto-correlation function and am getting hung-up on this Trig equation. The steps I have taken so far are

1. $$\cos^2(2\pi t) = (1/2)[1+\cos(4\pi t)]$$
2. the integral I used to solve for the correlation function (1/T) in front of the integral My main question is if this is the correct process, how would I go about solving this integral when the time delay is present in the second cosine?
• I'm not sure what your question is? – Mattos Dec 4 '18 at 23:26