Evaluate: (i) `intcos^5x\ dx` (ii) `intsin^5xcosx\ dx`

Explanation

(i)

`int cos ^{5} x d x `

`=int cos ^{4} x cdot cos x d x `

`=int(1-sin ^{2} x)^{2} cos x d x `

`text { Let } sin x=t `

`Rightarrow cos x d x=d t `

`text { Now, } int(1-sin ^{2} x)^{2} cos x d x `

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