# How do you integrate int (2x-3x^2)dx?

Oct 29, 2016

$\therefore \int \left(2 x - 3 {x}^{2}\right) \mathrm{dx} = {x}^{2} - {x}^{3} + C$

#### Explanation:

You should learn the power rule for integration, which is the opposite of that for differentiation, ie

$\int {x}^{n} \mathrm{dx} = {x}^{n + 1} / \left(n + 1\right) \forall x \in \mathbb{R} , x \ne - 1$

So $\int \left(2 x - 3 {x}^{2}\right) \mathrm{dx} = 2 {x}^{1 + 1} / \left(1 + 1\right) - 3 {x}^{2 + 1} / \left(2 + 1\right) + C$
$\therefore \int \left(2 x - 3 {x}^{2}\right) \mathrm{dx} = 2 {x}^{2} / 2 - 3 {x}^{3} / 3 + C$
$\therefore \int \left(2 x - 3 {x}^{2}\right) \mathrm{dx} = {x}^{2} - {x}^{3} + C$