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
