$ \int \frac{\cos^{n-1}x}{\sin^{n+1}x} \, dx $, $n \neq 0$, is _____
$\cot^n x$
$\frac{-\cot^{n-1}x}{n-1}$
$\frac{-\cot^n x}{n}$
$\frac{\cot^{n-1}x}{n-1}$
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