Mark the correct alternative in each of the following:

Question:

Mark the correct alternative in each of the following:

The value of $\int \frac{\sin x+\cos x}{\sqrt{1-\sin 2 x}} d x$ is equal to

A. $\sqrt{\sin 2 x}+C$

B. $\sqrt{\cos 2 x}+C$

C. $\pm(\sin x-\cos x)+C$

D. $\pm \log (\sin x-\cos x)+C$

Solution:

$I=\int \frac{\sin x+\cos x}{\sin x-\cos x} d x(\sqrt{1-\sin 2 x}=\pm\{\sin x-\cos x\})$

Let $\mathrm{t}=\sin \mathrm{x}-\cos \times\left(\frac{d t}{d x}=\sin x+\cos x\right)$

$I=\int \frac{d t}{t}$

$I=\pm \log (\sin x-\cos x)+c$

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