Integrate: `intsin2xsin4xsin6x\ dx`

Explanation

`int sin 2 x sin 4 x sin 6 xdx `

`=frac{1}{2} int(2 sin 2 x sin 4 x) sin 6 x d x `

`=frac{1}{2} int[cos (2 x-4 x)-cos (2 x+4 x)] sin 6 {x} d x `

`=frac{1}{2} int[cos (2 x)-cos (6 x)] sin 6 {x} {dx} `

`=frac{1}{2}[int cos (2 x) sin (6 x) d x-int cos (6 x) sin (6 x) d x] `

`=frac{1}{4}[int 2 cos (2 x) sin (6 x) d x-int 2 cos (6 x) sin (6 x) d x] `

`=frac{1}{4}{int[sin (2 x+6 x)-sin (2 x-6 x)] d x-int sin (12 x) d x} `

`=frac{1}{4}[int sin (8 x) d x+int sin (4 x) d x-int sin (12 x) d x] `

...