Evaluate $\int \cos^{2} 2x\,dx$.

Explanation

1. 01

   $\cos^{2} 2x = \frac{1 + \cos 4x}{2}$.

2. 02

   $\int \frac{1 + \cos 4x}{2}\,dx = \frac{x}{2} + \frac{\sin 4x}{8} + C$.