Evaluate: `intsinxsin2xsin3x\ dx`

Explanation

It is known that, `sin A sin B=frac{1}{2}{cos (A-B)-cos (A+B)}`

`therefore int sin x sin 2 x sin 3 x d x=int[sin x cdot frac{1}{2}{cos (2 x-3 x)-cos (2 x+3 x)}] d x`


`=frac{1}{2} int(sin x cos (-x)-sin x cos 5 x) d x`



`=frac{1}{2} int(sin x cos x-sin x cos 5 x) d x `

`=frac{1}{2} int frac{sin 2 x}{2} d x-frac{1}{2} int sin x cos 5 x d x `

...