Integrate: `intsinxcos2xsin3x\ dx`

Explanation

To solve the integral \( \int \sin x \cos 2x \sin 3x \, dx \), we can follow these steps:

### Step 1: Use the Product-to-Sum Formula
We start by applying the product-to-sum identities. The identity we will use is:
\[ 2 \sin A \cos B = \sin(A + B) + \sin(A - B) \]
In our case, we can treat \( \sin x \) and \( \sin 3x \) together with \( \cos 2x \).
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