# How do you evaluate the integral intdx/(2x+3)?

Feb 7, 2017

The answer is $= = \frac{1}{2} \ln \left(| 2 x + 3 |\right) + C$

#### Explanation:

We need

$\int \frac{\mathrm{dx}}{x} = \ln x + C$

Let $u = 2 x + 3$

$\mathrm{du} = 2 \mathrm{dx}$

$\mathrm{dx} = \mathrm{du} \left(\frac{1}{2}\right)$

$\int \frac{\mathrm{dx}}{2 x + 3} = \frac{1}{2} \int \frac{\mathrm{du}}{u}$

$= \frac{1}{2} \ln u$

$= \frac{1}{2} \ln \left(| 2 x + 3 |\right) + C$