TS EAMCET · Maths · Indefinite Integration
\(\int \frac{x+\cos x}{1-\sin x} d x=\)
- A \(x \tan \left(\frac{\pi}{4}+\frac{x}{2}\right)+\mathrm{c}\)
- B \(x \tan \frac{x}{2}+\mathrm{c}\)
- C \(x \cot \frac{x}{2}+\mathrm{c}\)
- D \(x \cot \left(\frac{\pi}{4}+\frac{x}{2}\right)+\mathrm{c}\)
Answer & Solution
Correct Answer
(A) \(x \tan \left(\frac{\pi}{4}+\frac{x}{2}\right)+\mathrm{c}\)
Step-by-step Solution
Detailed explanation
\( \frac{d}{dx} \left( x \tan \left(\frac{\pi}{4}+\frac{x}{2}\right) \right) = \tan \left(\frac{\pi}{4}+\frac{x}{2}\right) + x \cdot \frac{1}{2} \sec^2 \left(\frac{\pi}{4}+\frac{x}{2}\right) \). \( \tan \left(\frac{\pi}{4}+\frac{x}{2}\right) = \frac{\cos x}{1-\sin x} \).…
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