Evaluate: (i) `intcot^2x cos e c^4x\ \ dx` (ii) `intcos e c^4x\ dx`

Explanation

(i)
`int cot ^{2} x cosec^{4} x d x `

`=int cot ^{2} x(1+cot ^{2} x) cosec^{2} x d x `

`text { Let } cot x=t `

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

`=-int t^{2}(1+t^{2}) d t `

`=-int(t^{4}+t^{2}) d t `

`=-(t^{5} / 5)+(t^{3} / 3)+c `

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