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Math Help - Anyone with Mathematica, help evaluating integral:

  1. #1
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    Anyone with Mathematica, help evaluating integral:

    \int_0^\frac{x}{x-1} \frac{ln(1-t)}{t} dt

    Someone mind spitting that out? Computers on campus lack current code, and it take some time to get Mathematica folks down here to initialize a copy.
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  2. #2
    A Plied Mathematician
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    Check out WolframAlpha: it's basically a Mathematica calculator online. It's really cool in that it can often show the steps used to compute something.
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  3. #3
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    Already tried, that's why I am stuck at this point. All Alpha does is give me the symbolic representation of my request.
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  4. #4
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    Hmm. You're right. The antiderivative is a polylogarithm, which is not a very nice function to work with. If WolframAlpha doesn't crack it, you can be sure even the latest version of Mathematica won't crack it. They have the same engine underneath, I think. You've got this, at least:

    \int\frac{\ln(1-t)}{t}\,dt=-\text{Li}_{2}(t)+C.

    That's about as far as Mathematica will take you, I think.
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  5. #5
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    . . .which is a bummer since the PolyLog is what I don't want. This bit is part of a larger function in R, and was hoping there was something simpler to work with than the integral representation. Cest la vie. We'll go with that.

    Thanks for spitting it in Math for me.
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  6. #6
    A Plied Mathematician
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    Out of curiosity, what's this "larger function", and what are you trying to do with it?
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  7. #7
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    I misspoke - I don't mean a math function but a program function; we are creating a mini program that will help calculate the variance of a continuous distribution. We found the integral involves PolyLog's, and were hoping there was a closed form we could use. We can use the integral; I was just hoping there was an actual form that didn't involve PolyLog's or integrals.

    As for what its for, we will be using it to investigate certain stat-analysis techniques and their efficacy.
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  8. #8
    A Plied Mathematician
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    Well, you could use numerical integration if you know what x is. You could also try using a truncated Taylor series. I doubt that you're going to get all the way to where you want to go, however.

    Good luck!
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