To solve the integral \( I = \int \frac{x - \sin x}{1 - \cos x} \, dx \), we can follow these steps:
### Step 1: Split the Integral
We can separate the integral into two parts:
\[
I = \int \frac{x}{1 - \cos x} \, dx - \int \frac{\sin x}{1 - \cos x} \, dx
\]
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