Use the substitution u = cos 2x to find ∫(cos^2*(2x) *sin3 (2x)) dx

∫(cos² 2x *sin³ 2x)dx u = cos2x - u =(du/dx) = -2sin2x - differentiate u dx = du/(-2sin(2x)) - dx = -1/2 ∫cos²2x * sin²2x du - sub in dx-1/2 ∫u²(1-u²)du - put in terms if u -1/2 [ u³/3 - u⁵/5 ] + c - integrate in terms of u (cos⁵2x)/10 - (cos³2x)/6 - Final answer