`intcos^(4)2xdx`

Explanation

`intcos^(4)2xdx=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 + cos8x)/(2))dx`
`=(1)/(8) int(3+4 cos 4x+cos 8x)dx`
`=(1)/(8)(3x+(4 sin 4x)/(4)+(sin 8x)/(8))+c`
`=(3x)/(8)+(1)/(8)sin 4x+(1)/(64)sin 8x+c`