Re: "Complement" to the Risch Algorithm

*To*: mathgroup at smc.vnet.net*Subject*: [mg131455] Re: "Complement" to the Risch Algorithm*From*: David Bailey <dave at removedbailey.co.uk>*Date*: Fri, 26 Jul 2013 05:46:34 -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 25/07/2013 02:58, 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 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? > > This question would clearly have to be asked with respect to some class of functions. For example, Exp[-x^2] isn't integrable, except that the special function Erf was introduced specifically to represent this integral! David Bailey http://www.dbaileyconsultancy.co.uk