AP EAMCET · Maths · Indefinite Integration
\(\int \frac{\sin x+\cos x}{\sin x-\cos x} d x=\)
- A \(-x+\log |\cos x-\sin x|+c\)
- B \(x-\log |\cos x-\sin x|+c\)
- C \(-\log |\cos x-\sin x|+c\)
- D \(\log |\cos x-\sin x|+c\)
Answer & Solution
Correct Answer
(D) \(\log |\cos x-\sin x|+c\)
Step-by-step Solution
Detailed explanation
Let \(u = \sin x - \cos x\). \(du = (\cos x - (-\sin x)) dx = (\cos x + \sin x) dx\). \(\int \frac{1}{u} du\). \(=\log |u| + C\). \(=\log |\sin x - \cos x| + C\). \(=\log |\cos x - \sin x| + C\).
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