Evaluate: `int_0^pi log(1+cosx)dx`

Explanation

To evaluate the integral \( I = \int_0^{\pi} \log(1 + \cos x) \, dx \), we can use a property of definite integrals. Let's go through the steps systematically.

### Step 1: Use the property of definite integrals
We know that:
\[ \int_0^a f(x) \, dx = \int_0^a f(a - x) \, dx \]
For our integral, we have \( a = \pi \) and \( f(x) = \log(1 + \cos x) \). Thus, we can write:
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