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.