Evaluate: `int1/(1+sinx+cosx)\ dx`

Explanation

To evaluate the integral \( I = \int \frac{1}{1 + \sin x + \cos x} \, dx \), we can follow these steps:

### Step 1: Rewrite the integral using trigonometric identities
We know that:
\[ \sin x = \frac{2 \tan \frac{x}{2}}{1 + \tan^2 \frac{x}{2}} \quad \text{and} \quad \cos x = \frac{1 - \tan^2 \frac{x}{2}}{1 + \tan^2 \frac{x}{2}} \]
Substituting these into the integral gives:
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