`intsin^2b\ x\ dx`

Explanation

To solve the integral \(\int \sin^2(Bx) \, dx\), we can use the trigonometric identity for sine squared. Here’s a step-by-step solution:

### Step 1: Use the Identity for \(\sin^2\)
We know from trigonometric identities that:
\[ \sin^2(\theta) = \frac{1 - \cos(2\theta)}{2} \]
For our case, let \(\theta = Bx\). Thus, we can rewrite \(\sin^2(Bx)\) as:
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