If $\int \frac{d x}{2 \cos x+3 \sin x+4}=\frac{2}{\sqrt{3}} f(x)+c$, then $f\left(\frac{2 \pi}{3}\right)=$

• A

  $\frac{\pi}{12}$
• B

  $\frac{\pi}{8}$
• Correct answer
  C

  $\frac{5 \pi}{12}$
• D

  $\frac{5 \pi}{8}$

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