I recently did an integration that came up with an answer different from what WolframAlpha comes up with. Here's the integral and my answer:

$\displaystyle \int \frac{dx}{|x|} = sgn(x) \cdot ln|x| + C$

Here's what WolframAlpha comes up with. (And here's the link.)

$\displaystyle \int \frac{dx}{|x|} = sgn(x) \cdot ln(x) + C$

The expressions are not the same. I'm inclined to believe WolframAlpha over my own work, but I can't see an error in my work, either. It's very basic, but I'll provide, for example, the case when x is negative:

$\displaystyle \int \frac{dx}{|x|} = \int \frac{dx}{-x} = -ln|x| + C$

The integration for positive x is similar.

Did I do anything wrong?

-Dan