Question

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

Answer 1

`1/3x^3-x^2-8x+c`

Explanation:

distribute the factors.

`rArr(x-4)(x+2)=x^2-2x-8`

`rArrint(x^2-2x-8)dxlarr" is required"`

Integrate each term using the `color(blue)"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)|)))`

`rArrint(x^2-2x-8)dx`

`=1/3x^3-x^2-8x+c`

where c is the constant of integration.