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

For any integer $\mathrm{n} \geq 2$, if $\mathrm{I}_n=\int \cot ^n x d x$ then $\mathrm{I}_5=$
  1. $\frac{-\cot ^4 x}{4}+\frac{\cot ^2 x}{2}+\log |\sin x|+c$
  2. $\frac{-\cot ^4 x}{4}+\frac{\cot ^2 x}{2}-\log |\sin x|+c$
  3. $\frac{\cot ^4 x}{4}+\frac{\cot ^2 x}{2}+\log |\cos x|+c$
  4. $\frac{\cot ^4 x}{4}-\frac{\cot ^2 x}{2}-\cot x+c$

Solution

No solution. Refer to answer key.

Asked in: AP EAMCET 2018 (24 Apr Shift 2)

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