The value of 2 x ~d x (x- 4 ) is

Mathematics · JEE Main · NTA ExamsIntegral Calculus

The value of \[\sqrt{2} \int \frac{\sin x \mathrm{~d} x}{\sin \left(x-\frac{\pi}{4}\right)}\] is
  1. \(x-\log \left|\cos x\left(x-\frac{\pi}{4}\right)\right|+C\)
  2. \(x+\log \left|\cos \left(x-\frac{\pi}{4}\right)\right|+C\)
  3. \(x-\log \left|\sin \left(x-\frac{\pi}{4}\right)\right|+C\)
  4. \(x+\log \left|\sin \left(x-\frac{\pi}{4}\right)\right|+C\)

Answer

(D) x+ | (x- 4 ) |+C

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