The indefinite integral I = sin* x cos x dx can be calculated as following: 1. Using the double angle trig identities and also the trig identity COs u Cos U = [cos(u - U) + cos(u + v)] one obtains sin* x cos x = a + bcos(2x) + ccos(4x) + d cos(6x) where a = b = C = d = 2. The value of the integral is sin* xcos x dx = Ax + B sin(2x) + C sin(4x) + D sin(6x) + constant where A = B = C = D=