Find: ^ 2 x - ^ 2 x x x dx - Vidyadip

Question

Find:
$\int \frac{\sin^{2} \text{x} - \cos^{2} \text{x}}{\sin \text{x} \cos \text{x}} \text{dx}$

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Answer

$\int \frac{\sin^{2} \text{x} - \cos^{2} \text{x}}{\sin \text{x} \cos \text{x}} \text{dx}$
$= \int \frac{\sin^{2}\text{x}}{\sin \text{x} \cos \text{x}} - \int \frac{\cos^{2}\text{x}}{\sin \text{x} \cos \text{x}} \text{dx}$
$ = \int \tan \text{x dx} - \int\cot \text{x dx}$
$= \log | \text{Sec} \text{ x}| - \log |\sin \text{x}| + C$

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