$\int \frac{d x}{12 \cos x+5 \sin x}=$

• Correct answer
  A

  $\frac{1}{13} \log \left|\tan \left(\frac{\pi}{4}+\frac{x}{2}-\frac{1}{2} \operatorname{Tan}^{-1} \frac{5}{12}\right)\right|+c$
• B

  $\frac{5}{12} \log \left|\tan \left(\frac{\pi}{4}+\frac{\mathrm{x}}{2}-\frac{1}{2} \operatorname{Tan}^{-1} \frac{5}{12}\right)\right|+\mathrm{c}$
• C

  $\frac{1}{13} \log \left|\tan \left(\frac{\pi}{4}+\frac{\mathrm{x}}{2}+\frac{1}{2} \operatorname{Tan}^{-1} \frac{5}{12}\right)\right|+\mathrm{c}$
• D

  $\frac{5}{12} \log \left|\tan \left(\frac{\pi}{4}+\frac{\mathrm{x}}{2}+\frac{1}{2} \operatorname{Tan}^{-1} \frac{5}{12}\right)\right|+\mathrm{c}$

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