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.
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:
That's about as far as Mathematica will take you, I think.
. . .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.
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.