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Integrate the following functions: sin^4...

Integrate the following functions: `sin^4x`

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`sin^4x = (sinx)^2 = ((1-cos2x)/2)^2`
= `1/4(1-2cos 2x +cos^2 2x)`
=`1/4(1-2cos 2x +(1+cos 4x)/2)`
`=1/8(2-4 cos2x+1+cos4x)`
`=1/8(3-4 cos2x+cos4x)`
therefore` int sin^4x dx`
`=1/8[3x-4 (sin2x)/2+(sin4x)/4]+c`
`=3/8x- 1/4sin2x + (sin4x)/(32)+c`
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