Evaluate: `int(sinx)/(sin4x)dx`

Explanation

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

### Step 1: Rewrite \( \sin 4x \) using the double angle formula
We know that \( \sin 4x = 2 \sin 2x \cos 2x \). We can further express \( \sin 2x \) as \( 2 \sin x \cos x \). Thus, we have:
\[ \sin 4x = 2(2 \sin x \cos x) \cos 2x = 4 \sin x \cos x \cos 2x \]
Now, substituting this back into the integral gives:
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