Evaluate $\int_0^{\pi} \frac{\sin x}{2 - \cos x}\,dx$.

Explanation

1. 01

   Put $t = 2 - \cos x$, $dt = \sin x\,dx$; $x = 0 \to t = 1$, $x = \pi \to t = 3$.

2. 02

   $\int_1^3 \frac{dt}{t} = \log 3$.