indefinite intergral

∫sin4(x/2)cos2(x/2) dx
= ∫sin2(x/2) (sin2(x/2)cos2(x/2)) dx
= ∫((1-cosx)/2 ) (sinx /2)2 dx
= (1/8)∫(1-cosx)sin2x dx
= (1/8) (∫sin2x dx - ∫sin2x cosx dx)

= (1/8) (∫ (1-cos2x)/2 dx - ∫sin2x d(sinx))
=(1/8) (x/2 - (sin2x /4) - (sin3x /3)) + C
= x/16 - (sin2x /32) - (sin3x /24) + C