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sin x sin 2x sin 3x...

`sin x sin 2x sin 3x`

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` int " sin x sin 2x sin 3x dx "`
`=(1)/(2) int" (2 sin 3x sin x) sin 2x dx "`
` =(1)/(2) int " (cos 2x - cos 4x ) sin 2x dxb "`
`=(1)/(4) int " (2 sin 2x cos 2x - 2 cos 4x sin 2x ) dx "`
`=(1)/(4) int " (sin 4x - (sin 6x - sin2x) dx "`
`=(1)/(4) int " (sin 4x- sin 6x + sin 2x) dx "`
`=(1)/(4) [-(1)/(4) cos 4x + (1)/(24) cos 6x -(1)/(8) cos 2x + c`
`=-(1)/(16) cos 4x +(1)/(24) cos 6x -(1)/(8) cos 2x +c`
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