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int(0)^(pi)log(1+cosx)dx=-pi(log2)...

`int_(0)^(pi)log(1+cosx)dx=-pi(log2)`

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To solve the integral \( I = \int_0^{\pi} \log(1 + \cos x) \, dx \), we can follow these steps: ### Step 1: Rewrite the integrand We start by using the trigonometric identity: \[ 1 + \cos x = 2 \cos^2\left(\frac{x}{2}\right) \] Thus, we can rewrite the integral: ...
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