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Integrate the functionscos^4 2x...

Integrate the functions`cos^4 2x`

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` int cos^(4) 2x dx = int (cos^(2) 2x)^(2) dx`
`= int ((1+cos4x)/(2))^(2) dx`
` =(1)/(4) int (1+ 2 cos 4x+ cos^(2) 4x) dx`
` =(1)/(4) int (1+2 cos 4x + .(1+ cos 8x)/(2) )dx`
`=(1)/(8) int (3 x+ .(4sin 4x)/(4) +(sin 8x)/(8))+c`
` =(3x)/(8)+(1)/(8) sin 4x +(1)/(64) sin 8x +c`
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