Evaluate: `intsin^3xcos^4x\ dx`

Explanation

`text { Let I }=int sin ^{3} x cdot cos ^{4} x d x `

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

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

`=int(cos ^{4} x-cos ^{6} x) cdot sin x d x `

`text { Putting } cos {x}={t} `

`Rightarrow-sin x d x=d t `

`Rightarrow sin x d x=-d t `

`therefore I=-int(t^{4}-t^{6}) d t `

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