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AP EAMCET · Maths · Indefinite Integration

\(\int \frac{2 \cos 2 x}{(1+\sin 2 x)(1+\cos 2 x)} d x=\)

  1. A \(2 \tan x+\log (1+\tan x)+c\)
  2. B \(\tan x-2 \log (1+\tan x)+c\)
  3. C \(2 \log (1+\tan x)+\tan x+c\)
  4. D \(2 \log (1+\tan x)-\tan x+c\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(2 \log (1+\tan x)-\tan x+c\)

Step-by-step Solution

Detailed explanation

\(I=\int \frac{2 \cos 2 x}{(1+\sin 2 x)(1+\cos 2 x)} d x\)…