Evaluate `int_0^(pi/2)logsinxdx`

Explanation

To evaluate the integral \( I = \int_0^{\frac{\pi}{2}} \log(\sin x) \, dx \), we can use a clever technique involving symmetry and properties of logarithms. Here’s a step-by-step solution:

### Step 1: Define the Integral
Let
\[ I = \int_0^{\frac{\pi}{2}} \log(\sin x) \, dx \]

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