# Problem with WolframAlpha integral?

• Apr 28th 2011, 02:16 AM
topsquark
Problem with WolframAlpha integral?
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
• Apr 28th 2011, 02:48 AM
Ackbeet
See here. WolframAlpha should have given ln|x|, but it didn't. Your answer is better than WolframAlpha's, I would say.
• Apr 28th 2011, 04:00 AM
topsquark
Quote:

Originally Posted by Ackbeet
See here. WolframAlpha should have given ln|x|, but it didn't. Your answer is better than WolframAlpha's, I would say.

I see. It makes the same mistake there, too.

Me more correct than WolframAlpha? That's a first. I feel giddy! (Dance)

-Dan

Edit: I sent a message to the Wolfram people. Hee hee. That was fun!
• Apr 28th 2011, 04:06 AM
Ackbeet
Computers make fast, very accurate mistakes. They're also incredibly stupid: they do what you tell them to do, not what you want them to do.