∫x(3-x)²dx

1. Expand the integrand: ∫x(9 - 6x + x²) dx = ∫(9x - 6x² + x³) dx.

2. Integrate term by term: 9(x²/2) - 6(x³/3) + x⁴/4 + C.

3. (9x²/2) - 2x³ + x⁴/4 + C.