# How do you integrate (x/(x+2))?

May 29, 2016

$x - 2 \ln \left\mid x + 2 \right\mid + C$

#### Explanation:

We can simplify this way is written:

$\int \frac{x}{x + 2} \mathrm{dx} = \int \frac{x + 2 - 2}{x + 2} \mathrm{dx} = \int \left(\frac{x + 2}{x + 2} - \frac{2}{x + 2} \mathrm{dx}\right)$

$\int \left(1 - \frac{2}{x + 2}\right) \mathrm{dx} = \int 1 \mathrm{dx} - 2 \int \frac{1}{x + 2} \mathrm{dx}$

From here the integration is fairly simple:

$= x - 2 \ln \left\mid x + 2 \right\mid + C$