`intsin^(4)xdx`

Explanation

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