Evaluate the following integrals:
`intcos^(4)xdx`

Answer

`(3x)/(8)+(sin4x)/(32)+(sin2x)/(4)+C`

Explanation

`I=(1)/(4)int(2cos^(2)x)^(2)dx=(1)/(4)(1+cos2x)^(2)dx`
`=(1)/(4)int{:[(1+2cos2x)+((1+cos4x)/(2))]:}dx=int{:[(3)/(8)+(1)/(2)cos2x+(1)/(8)cos4x]:}dx`.