If $I=\int \frac{d x}{e^x+4 e^{-x}}=f(x)+c$, then $f(x)$ is equal to

$2 \tan ^{-1}\left(2 \mathrm{e}^x\right)$

$\frac{1}{2} \tan ^{-1}\left(2 e^{2 x}\right)$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

I=\int \frac{d x}{e^x+4 e^{-x}}=f(x)+c

, then

f(x)

is equal to

View answer and explanation

Correct option: B

\frac{1}{2} \tan ^{-1}\left(\frac{e^x}{2}\right)

Option B (

\frac{1}{2} \tan ^{-1}\left(\frac{e^x}{2}\right)

) is correct because the integral can be solved using a simple substitution, resulting in the given expression.