# Differential Equation Involving Natural Log.

1. Sep 26, 2011

### theRukus

1. The problem statement, all variables and given/known data
Calculate the following:
$\int^{-4}_{-6} (x^-1+5x)dx$

2. Relevant equations

3. The attempt at a solution
I've worked this down to
$ln(-4) + 5(-4) - ln(-6) - 5(-6) =ln(-4)-ln(-6)+10$
The answer to the left half (the ln parts) of the equation is undefined, and the right is 10..
So... undefined + 10? I'm unsure what to say the definite answer is....

Thank you for any help.

2. Sep 26, 2011

### LCKurtz

The antiderivative is

$$\int \frac 1 x\,dx = \ln |x|+C$$

The absolute value signs matter when x < 0.