# What is the antiderivative of  x/(x+1)?

Jul 7, 2015

$x + \ln \left\mid x + 1 \right\mid + C$
Note: This is the same answer as the one Selim has given. It just has a different constant.

#### Explanation:

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

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

$= x + \ln \left\mid x + 1 \right\mid + C$