1 x- x dx =____ - Vidyadip

MCQ

$\int \frac{1}{\cos x-\sin x} dx =$____

A
$\frac{1}{\sqrt{2}} \log \left[\operatorname{cosec}\left(x+\frac{\pi}{4}\right)-\cot \left(x+\frac{\pi}{4}\right)\right]+ c$
B
$\sqrt{2} \log \left[\operatorname{cosec}\left(x+\frac{\pi}{4}\right)+\cot \left(x+\frac{\pi}{4}\right)\right]+ c$
✓
$\frac{1}{\sqrt{2}} \log \left[\sec \left(x+\frac{\pi}{4}\right)+\tan \left(x+\frac{\pi}{4}\right)\right]+ c$
D
$\sqrt{2} \log \left[\sec \left(x+\frac{\pi}{4}\right)-\tan \left(x+\frac{\pi}{4}\right)\right]+ c$

✓

Answer

Correct option: C.

$\frac{1}{\sqrt{2}} \log \left[\sec \left(x+\frac{\pi}{4}\right)+\tan \left(x+\frac{\pi}{4}\right)\right]+ c$

$\frac{1}{\sqrt{2}} \log \left[\sec \left(x+\frac{\pi}{4}\right)+\tan \left(x+\frac{\pi}{4}\right)\right]+ c$

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