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

Explanation

(i)
We know that `sin 3 x=3 sin x-4 sin ^{3} x`

`Rightarrow sin ^{3} x=frac{1}{4}(3 sin x-sin 3 x) `

`int sin ^{3} x d x `

`=frac{1}{4} int(3 sin x-sin 3 x) d x `

`=frac{1}{4}[-3 cos x-(frac{-cos 3 x}{3})]+c `

`=frac{1}{4}[-3 cos x+frac{cos 3 x}{3}]+c`



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