Evaluate $\int \frac{1}{\cos 2x + 1}\,dx$.

Explanation

1. 01

   Rewrite first: $1 + \cos 2x = 2\cos^2 x$.

2. 02

   Then each term is standard: $\frac{\tan x}{2} + C$.

3. 03

   Check: differentiating the answer gives back the integrand.