Integrate the functions `sinxsin2xsin3x`

Explanation

To integrate the function \( \sin x \sin 2x \sin 3x \), we can use trigonometric identities to simplify the expression. Here’s a step-by-step solution:

### Step 1: Use the Product-to-Sum Formulas
We can use the product-to-sum identities to rewrite the product of sine functions. The identity we will use is:
\[ \sin A \sin B = \frac{1}{2} [\cos(A - B) - \cos(A + B)] \]
We will first combine \( \sin 2x \) and \( \sin 3x \).
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