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

Jul 7, 2015

Do the division, then integrate to get ${x}^{3} / 3 + {x}^{2} + 4 x + 8 \ln \left\mid x - 2 \right\mid + C$

#### Explanation:

Perform the division:

${x}^{3} / \left(x - 2\right) = {x}^{2} + 2 x + 4 + \frac{8}{x - 2}$

So
$\int {x}^{3} / \left(x - 2\right) \mathrm{dx} = \int \left({x}^{2} + 2 x + 4 + \frac{8}{x - 2}\right) \mathrm{dx}$

$= {x}^{3} / 3 + {x}^{2} + 4 x + 8 \ln \left\mid x - 2 \right\mid + C$