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

• A

  $2 \operatorname{Tan}^{-1}\left(2 e^x\right)$
• Correct answer
  B

  $\frac{1}{2} \operatorname{Tan}^{-1}\left(\frac{e^x}{2}\right)$
• C

  $2 \operatorname{Tan}^{-1}\left(\frac{e^x}{2}\right)$
• D

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

Hence, the correct answer is option: 'B'.