$\displaystyle \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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- Jul 19th 2010, 11:28 AMANDS!Anyone with Mathematica, help evaluating integral:
$\displaystyle \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. - Jul 19th 2010, 11:52 AMAckbeet
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.

- Jul 19th 2010, 02:38 PMANDS!
Already tried, that's why I am stuck at this point. All Alpha does is give me the symbolic representation of my request.

- Jul 19th 2010, 03:32 PMAckbeet
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:

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

That's about as far as Mathematica will take you, I think. - Jul 19th 2010, 03:37 PMANDS!
. . .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. - Jul 19th 2010, 03:38 PMAckbeet
Out of curiosity, what's this "larger function", and what are you trying to do with it?

- Jul 19th 2010, 03:48 PMANDS!
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. - Jul 19th 2010, 05:10 PMAckbeet
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!