Integrate the functions `sin 4x sin8x`

Explanation

To solve the integral of the function \( \sin(4x) \sin(8x) \), we will use a trigonometric identity to simplify the expression before integrating. Here's the step-by-step solution:

### Step 1: Use the Product-to-Sum Identity
We can use the product-to-sum identity for sine functions:
\[ \sin A \sin B = \frac{1}{2} [\cos(A - B) - \cos(A + B)] \]
In our case, let \( A = 8x \) and \( B = 4x \). Thus, we have:
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