Evaluate: `intx^2sin^2x\ dx`

Explanation

To evaluate the integral \( I = \int x^2 \sin^2 x \, dx \), we will use integration by parts and some trigonometric identities.

### Step 1: Use the Trigonometric Identity
We start by using the identity for \(\sin^2 x\):
\[ \sin^2 x = \frac{1 - \cos(2x)}{2} \]
Thus, we can rewrite the integral:
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