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AP EAMCET · Maths · Indefinite Integration

\(\int \frac{x+\sin x}{1+\cos x} d x\) is equal to

  1. A \(x \cot \left(\frac{x}{2}\right)+c\)
  2. B \(\cot \left(\frac{x}{2}\right)+c\)
  3. C \(\tan \left(\frac{x}{2}\right)+c\)
  4. D \(x \tan \left(\frac{x}{2}\right)+c\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(x \tan \left(\frac{x}{2}\right)+c\)

Step-by-step Solution

Detailed explanation

Let \(I=\int \frac{x+\sin x}{1+\cos x} d x\) \(I=\frac{1}{2} \int\left(x \sec ^2 x / 2\right) d x+\int \tan x / 2 d x\)…