# How do you find the antiderivative of f(x)=(x-4)(x+2)?

Jan 29, 2017

$\frac{1}{3} {x}^{3} - {x}^{2} - 8 x + c$

#### Explanation:

distribute the factors.

$\Rightarrow \left(x - 4\right) \left(x + 2\right) = {x}^{2} - 2 x - 8$

$\Rightarrow \int \left({x}^{2} - 2 x - 8\right) \mathrm{dx} \leftarrow \text{ is required}$

Integrate each term using the $\textcolor{b l u e}{\text{power rule for integration}}$

color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(intax^ndx=a/(n+1)x^(n+1) ; n≠-1)color(white)(2/2)|)))

$\Rightarrow \int \left({x}^{2} - 2 x - 8\right) \mathrm{dx}$

$= \frac{1}{3} {x}^{3} - {x}^{2} - 8 x + c$

where c is the constant of integration.