Evaluate: `intxsin^3x\ dx`

Explanation

To evaluate the integral \( I = \int x \sin^3 x \, dx \), we will use integration by parts and some trigonometric identities. Here is the step-by-step solution:

### Step 1: Rewrite the Integral
First, we can rewrite \( \sin^3 x \) using the identity:
\[ \sin^3 x = \sin x (1 - \cos^2 x) \]
Thus, we can express the integral as:
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