# How do you find the definite integral of int 1/(x+2) from [-1,1]?

Dec 4, 2016

$\ln 3$

#### Explanation:

Let $u = x + 2$
$\text{ }$
then $\text{ } \mathrm{du} = \mathrm{dx}$
$\text{ }$
$\int \frac{1}{x + 2} \mathrm{dx}$
$\text{ }$
$= \int \frac{\mathrm{du}}{u}$
$\text{ }$
$= \ln u + C$
$\text{ }$
$= \ln \left\mid x + 2 \right\mid + C$
$\text{ }$
$\text{ }$
${\int}_{-} {1}^{1} \frac{1}{x + 2} \mathrm{dx}$
$\text{ }$
$= \ln \left\mid 1 + 2 \right\mid - \ln \left\mid - 1 + 2 \right\mid$
$\text{ }$
$= \ln \left\mid 3 \right\mid - \ln \left\mid 1 \right\mid$
$\text{ }$
$= \ln 3 - \ln 1$
$\text{ }$
$= \ln 3 - 0$
$\text{ }$
$= \ln 3$