$\int \frac{1}{\cos x}\left[\frac{1}{\sin x}-\frac{1}{\sin x+3 \cos x}\right] d x=$

• A

  $\frac{1}{3} \log \left|\frac{\sin x}{\sin x+3 \cos x}\right|+c$
• B

  $\log \left|\frac{\cos x}{\sin x+3 \cos x}\right|+c$
• C

  $\frac{1}{3} \log \left|\frac{\cos x}{\sin x+3 \cos x}\right|+c$
• Correct answer
  D

  $\log \left|\frac{\sin x}{\sin x+3 \cos x}\right|+c$

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