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Integrate the following w.r.t.x. sin^(4...

Integrate the following w.r.t.x. `sin^(4)x`

Text Solution

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`int sin^(4)x dx=int(sin^(2)x)dx`
`=int((1-cos2x)/(2))^(2)dx`
`=(1)/(4)int(1-2cos 2x+cos^(2)2x)dx`
`=(1)/(4)int(1-2cos2x+(1+cos4x)/(2))dx`
`=(1)/(4)int((3)/(2)-2cos 2x+(1)/(2)cos 4x)dx`
`=(3)/(8)int 1dx-(2)/(4)int cos 2 dx+(1)/(8) int cos 4xdx`
`=(3)/(8)x-(1)/(2).(sin 2x)/(2)+(1)/(8).(sin4x)/(4)+c`
`=(3)/(8)x-(1)/(4)sin 2x+(1)/(32)sin4x+c`
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