If $\int {{e^{\sec x}}} (\sec x\tan x{\rm{ }}f(x) + (sec{\rm{ }}x\tan x + {\sec ^2}x)){\rm{ }}dx = {e^{\sec x}}f(x) + C$, then a possible choice of $f(x)$ is

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

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

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

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1

\int {{e^{\sec x}}} (\sec x\tan x\mathrm{ }f(x) + (sec\mathrm{ }x\tan x + {\sec ^2}x))\mathrm{ }dx = {e^{\sec x}}f(x) + C

, then a possible choice of

f(x)

View answer and explanation

Correct option: B

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

Option B (

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

) is correct because differentiating

e^{\sec x}f(x)

and comparing with the integrand allows us to identify

f(x)