AP EAMCET · Maths · Indefinite Integration
\(\int \frac{\sqrt{2} \sin x}{\sin \left(x+\frac{\pi}{4}\right)} d x\) is equal to
- A \(x+\log \left|\sin \left(x-\frac{\pi}{4}\right)\right|+c\)
- B \(x-\log \left|\sin \left(x-\frac{\pi}{4}\right)\right|+c\)
- C \(x+\log \left|\sin \left(x+\frac{\pi}{4}\right)\right|+c\)
- D \(x-\log \left|\sin \left(x+\frac{\pi}{4}\right)\right|+c\)
Answer & Solution
Correct Answer
(D) \(x-\log \left|\sin \left(x+\frac{\pi}{4}\right)\right|+c\)
Step-by-step Solution
Detailed explanation
\(\int \frac{\sqrt{2} \sin x}{\sin \left(x+\frac{\pi}{4}\right)} d x\) Let \(x+\frac{\pi}{4}=t \Rightarrow x=t-\frac{\pi}{4}\)…
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