Evaluate: `intcos^4x\ dx`

Explanation

`intcos^(4)xdx=int((1+cos2x)/(2))^(2)dx=(1)/(4)(1+2cos2x+cos^(2)2x)dx`
`=(1)/(4)int(1+2cos2x+(1+cos4x)/(2))dx=(1)/(4)int((3)/(2)+2cos2x+(cos4x)/(2))dx`
`=(1)/(4)[(3)/(2)x+(2sin2x)/(2)+(sin4x)/(2xx4)]+C=(3)/(8)x+(sin2x)/(4)+(sin4x)/(32)+C`