$\int \frac{x+\cos x}{1-\sin x} d x=$

• Correct answer
  A

  $x \tan \left(\frac{\pi}{4}+\frac{x}{2}\right)+\mathrm{c}$
• B

  $x \tan \frac{x}{2}+\mathrm{c}$
• C

  $x \cot \frac{x}{2}+\mathrm{c}$
• D

  $x \cot \left(\frac{\pi}{4}+\frac{x}{2}\right)+\mathrm{c}$

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