Evaluate: 2 x ^2 x ^2 x d x - Vidyadip

Question

Evaluate:
$\int \frac{\cos 2 x}{\sin ^2 x \cdot \cos ^2 x} \cdot d x$

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Answer

$\int \frac{\cos 2 x}{\sin ^2 x \cdot \cos ^2 x} d x$
$=\int \frac{\cos ^2 x-\sin ^2 x}{\sin ^2 x \cdot \cos ^2 x} d x$
$=\int\left(\frac{1}{\sin ^2 x}-\frac{1}{\cos ^2 x}\right) d x$
$=\int \operatorname{cosec}^2 x d x-\int \sec ^2 x d x$
$=-\cot x-\tan x+c$

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