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Math Help - Problem with WolframAlpha integral?

  1. #1
    Forum Admin topsquark's Avatar
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    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:
    \int \frac{dx}{|x|} = sgn(x) \cdot ln|x| + C

    Here's what WolframAlpha comes up with. (And here's the link.)
    \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:
    \int \frac{dx}{|x|} = \int \frac{dx}{-x} = -ln|x| + C

    The integration for positive x is similar.

    Did I do anything wrong?

    -Dan
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  2. #2
    A Plied Mathematician
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    See here. WolframAlpha should have given ln|x|, but it didn't. Your answer is better than WolframAlpha's, I would say.
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Ackbeet View Post
    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!

    -Dan

    Edit: I sent a message to the Wolfram people. Hee hee. That was fun!
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    A Plied Mathematician
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    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.
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