Evaluate: `intsin^4x\ dx`

Explanation

To evaluate the integral \(\int \sin^4 x \, dx\), we can follow these steps:

### Step 1: Use the identity for \(\sin^2 x\)
We know that:
\[ \sin^2 x = \frac{1 - \cos 2x}{2} \]
Thus, we can express \(\sin^4 x\) as:
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