Re: "Complement" to the Risch Algorithm

*To*: mathgroup at smc.vnet.net*Subject*: [mg131459] Re: "Complement" to the Risch Algorithm*From*: Richard Fateman <fateman at cs.berkeley.edu>*Date*: Sat, 27 Jul 2013 05:38:54 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net*References*: <ksq0os$8na$1@smc.vnet.net>

On 7/24/13 6:58 PM, Matthias Bode wrote: > Hola: > > Motivated by An analytical solution to an integral not currently in Mathematica? and by the interview with Mr. Daniel Lichtblau on omega tau Huh? oh, I found it using Google. three questions arose to me: > > 1. Are there theorems that prove that particular types of functions - e. g. x^(1/x) - can not be integrated? Yes. You can find "integration in finite terms" discussions (including by Risch, and successors e.g. Bronstein) via Google. > > > Or: > > > 2. Is there a theorem which proves that theorems as per 1. above can not exist? No, see above. > > > Or: > > > 3. Is this an undecidable problem? Since you cannot tell in general if a factor of an integrand is zero or not, you cannot tell if you can integrate or not. Suggestion: Google for {undecidable integration} Important hint for effective use of the internet. Instead of posting a question or 3 here first, try to use the Google. It is your friend. RJF >