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: