For any integer $\mathrm{n} \geq 2$, if $\mathrm{I}_n=\int \cot ^n x d x$ then $\mathrm{I}_5=$

• Correct answer
  A

  $\frac{-\cot ^4 x}{4}+\frac{\cot ^2 x}{2}+\log |\sin x|+c$
• B

  $\frac{-\cot ^4 x}{4}+\frac{\cot ^2 x}{2}-\log |\sin x|+c$
• C

  $\frac{\cot ^4 x}{4}+\frac{\cot ^2 x}{2}+\log |\cos x|+c$
• D

  $\frac{\cot ^4 x}{4}-\frac{\cot ^2 x}{2}-\cot x+c$

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