Evaluate: (i) `intsin^4xcos^3x\ dx` (ii) `intsin^5x\ dx`

Explanation

(i)

`int sin ^{4} x cos ^{3} x d x `

`=int sin ^{4} x cdot cos ^{2} x cos x d x `

`=int sin ^{4} x cdot(1-sin ^{2} x) cos x d x `

`text { Let } sin x=t `

`Rightarrow cos x d x=d t `

`text { Now } int sin ^{4} x cdot(1-sin ^{2} x) cos x d x `

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