# How do you integrate f(x)=(2-3x-x^2+x^3)(-1+2x^2+3x^3) using the product rule?

$\int \left(2 - 3 x - {x}^{2} + {x}^{3}\right) \left(- 1 + 2 {x}^{2} + 3 {x}^{3}\right) \mathrm{dx} = \int \left(3 {x}^{6} - {x}^{5} - 11 {x}^{4} - {x}^{3} + 5 {x}^{2} + 3 x - 2\right) \mathrm{dx}$
$= \frac{3}{7} {x}^{7} - \frac{1}{6} {x}^{6} - \frac{11}{5} {x}^{5} - \frac{1}{4} {x}^{4} + \frac{5}{3} {x}^{3} + \frac{3}{2} {x}^{2} - 2 x + C$