Evaluate: (i) `intsin^3xcos^6x\ dx` (ii) `intcos^7x\ dx`

Explanation

(i)

`int sin ^{3} x cdot cos ^{6} x d x `

`=int sin ^{2} x cdot cos ^{6} x cdot sin x d x `

`=int(1-cos ^{2} x) cdot cos ^{6} x cdot sin x d x `

`text { Let } cos x=t `

`Rightarrow-sin x d x=d t `

`text { Now, } int(1-cos ^{2} x) cdot cos ^{6} x cdot sin x d x `

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