# How do you find the integral of (x+6)/(x+10) dx?

Jul 5, 2015

I found: $x - 4 \ln | x + 10 | + c$

#### Explanation:

You can write:
$\int \frac{x + 6}{x + 10} \mathrm{dx} = \int \left[1 - \frac{4}{x + 10}\right] \mathrm{dx} =$ integrating:
$= x - 4 \ln | x + 10 | + c$

Jul 5, 2015

There is a small trick to this some people don't see.

$\int \frac{x + 6}{x + 10} \mathrm{dx}$

$= \int \frac{x + 6 + 4 - 4}{x + 10} \mathrm{dx}$

$= \int \frac{x + 10 - 4}{x + 10} \mathrm{dx}$

$= \int \frac{x + 10}{x + 10} - \frac{4}{x + 10} \mathrm{dx}$

$= \int 1 - \frac{4}{x + 10} \mathrm{dx}$

$= \textcolor{b l u e}{x - 4 \ln | x + 10 | + C}$