` x sin x`

Explanation

To solve the integral \( \int x \sin x \, dx \), we will use the method of integration by parts. Here are the steps:

### Step 1: Identify \( u \) and \( dv \)
We choose:
- \( u = x \) (which is algebraic)
- \( dv = \sin x \, dx \) (which is trigonometric)

### Step 2: Differentiate \( u \) and Integrate \( dv \)
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