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Integrate the functionssin^4x...

Integrate the functions`sin^4x`

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` int sin^(4) x dx = int (sin^(2) x)^(2) dx`
`= int ((1- cos 2x)/(2))^(2) dx`
` =(1)/(4) int (1-2 cos 2x+ cos^(2) 2x ) dx`
` = (1)/(4) int (1-2 cos 2x +.(1+cos 4x)/(2))dx`
`=(1)/(8) int (3-4 cos 2x + cos 4 x) dx`
` =(1)/(8) [3x -.(4 sin 2x)/(2) + (sin 4x)/(4)]+c`
` =(3x)/(8) -(1)/(4) sin 2x + (1)/(32) sin 4x +c`
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