The correct option is D log ( logsin x ) Let nbsp;I=∫ nbsp; nbsp;x /log nbsp;sin nbsp;x dx Put nbsp;log nbsp;sin nbsp;x=t⇒ nbsp; ...

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Variable Separable Method

∫ x/logsin xd...

Question

$\int \frac{cot x}{log sin x} d x .$

(log sin x)

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log (log cos x)

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log \frac{1}{2} (log sin x)

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log (log sin x)

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Solution

The correct option is D $log (log sin x)$
Let $I = \int \frac{cot x}{log sin x} d x$
Put $log sin x = t \Rightarrow cot x d x = d t$
$I = \int \frac{d t}{t} = log t = log (log sin x)$

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