4)[(x+3)(x-2)dx;

4) $$ \int (x+3)(x-2) dx = \int (x^2 - 2x + 3x - 6) dx = \int (x^2 + x - 6) dx = \int x^2 dx + \int x dx - 6 \int dx = \frac{x^3}{3} + \frac{x^2}{2} - 6x + C $$.

Ответ: $$\frac{x^3}{3} + \frac{x^2}{2} - 6x + C$$