Integrate the function (1/2 sin(2x) * 3x²) dx. Which of the following options correctly represents the integral of the function?
A) ∫(1/2 sin(2x) * 3x²) dx
B) ∫(sin(2x) * 3x²) dx
C) ∫(1/2 sin(2x) * 3x²) dx
D) ∫(1/2 sin(2x) * 3x²) dx