Evaluate: `int1/(2+cosx)\ dx`

Explanation

To evaluate the integral \( I = \int \frac{1}{2 + \cos x} \, dx \), we can use the substitution involving the tangent half-angle formula. Here’s a step-by-step solution:

### Step 1: Use the half-angle substitution
We use the substitution:
\[ t = \tan\left(\frac{x}{2}\right) \]
From this substitution, we can express \( \cos x \) in terms of \( t \):
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