Evaluate: (i) `intcot^n x\ cos e c^2\ x\ dx ,\ \ n!=-1` (ii) `intcot^5x\ cos e c^4\ x\ dx`

Explanation

(i)
`int cot ^{n} x cosec^{2} x d x `

`text { Let } cot x=t `

`Rightarrow-cosec^{2} x d x=d t `

`Rightarrow cosec^{2} x d x=-d t `

`text { Now, } int cot ^{n} x cosec^{2} x d x `

`=-int t^{n} d t `

`=frac{-t^{n+1}}{n+1}+C `

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