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MathGroup Archive 1997

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Re: Integrate[x^x,x]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg8530] Re: [mg8449] Integrate[x^x,x]
  • From: seanross at worldnet.att.net
  • Date: Thu, 4 Sep 1997 02:20:34 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

seanross at worldnet.att.net wrote:
> 
> Fahad A Hoymany wrote:
> >
> > > Integrating x^n is not the same as integrating x^x.  Integrate[x^n,x] is
> > > a standard form found in any elementary calculus book.  x^x is not
> > > integrable in closed form.  n^n with n integer is a discrete sum and the
> > > term integral is incorrectly applied.
> >
> >    Do you know of a closed-form solution for SUM n^n, n=1,2,...k?
> >
> > Regards
> > Fahad
> Not off the top of my head, but If I were to try and look it up, I would
> start with Abrabowitz and Stegun, the CRC math handbook or Gradshteyn
> and Rhyzik.  If it is not in any of those books, I would dust off my old
> pre-calculus text to remind myself of the principles behind math
> induction.
> 
> A creative way might be to plot n^n as a list of data, then use
> NonlinearFit or Fit to match the data to a polynomial in n.


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