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TS EAMCET · Maths · Indefinite Integration

\(\int \frac{\sec ^2 x}{(\sec x+\tan x)^2} d x=\)

  1. A \(\frac{3+(\sec x+\tan x)^2}{2(\sec x+\tan x)^3}+c\)
  2. B \(-\frac{1+3(\sec x+\tan x)^2}{6(\sec x+\tan x)^3}+c\)
  3. C \(-\frac{3+(\sec x+\tan x)^2}{2(\sec x+\tan x)^3}+c\)
  4. D \(-\frac{1+(\sec x+\tan x)}{3(\sec x+\tan x)^2}+c\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(-\frac{1+3(\sec x+\tan x)^2}{6(\sec x+\tan x)^3}+c\)

Step-by-step Solution

Detailed explanation

\(\int \frac{\sec ^2 x d x}{(\sec x+\tan x)^2}\) Let \(\sec x+\tan x=t\) and \(\sec x-\tan x=\frac{1}{t}\)…