Question:medium

\( \int \frac{dx}{\sin x - \cos x + \sqrt{2}} \) is equal to

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For $\sin x \pm \cos x$, convert into single sine or cosine using $\sqrt{2}$ identity.
Updated On: Apr 23, 2026
  • $-\frac{1}{\sqrt{2}}\tan\left(\frac{x}{2} + \frac{\pi}{8}\right) + C$
  • $\frac{1}{\sqrt{2}}\tan\left(\frac{x}{2} + \frac{\pi}{8}\right) + C$
  • $\frac{1}{\sqrt{2}}\cot\left(\frac{x}{2} + \frac{\pi}{8}\right) + C$
  • $-\frac{1}{\sqrt{2}}\cot\left(\frac{x}{2} + \frac{\pi}{8}\right) + C$
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The Correct Option is D

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