$\int \frac{1}{(2 \cos x+\sin x)^2} d x=$

• A

  $\frac{1}{2+\tan x}+c$
• B

  $-\frac{1}{2 \tan x+1}+c$
• C

  $\frac{\cos x}{\cos x+2 \sin x}+c$
• Correct answer
  D

  $-\frac{\cos x}{2 \cos x+\sin x}+c$

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