Solve this following

Question:

If $\int e^{\sec x}\left(\sec x \tan x f(x)+\left(\sec x \tan x+\sec ^{2} x\right) d x=\right.$

$e^{\sec x} f(x)+C$, then a possible choice of $f(x)$ is :-

 

  1. $\sec x-\tan x-\frac{1}{2}$

  2. $x \sec x+\tan x+\frac{1}{2}$

  3. $\sec x+x \tan x-\frac{1}{2}$

  4. $\sec x+\tan x+\frac{1}{2}$


Correct Option: , 4

Solution:

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