"Complement" to the Risch Algorithm

*To*: mathgroup at smc.vnet.net*Subject*: [mg131447] "Complement" to the Risch Algorithm*From*: Matthias Bode <lvsaba at hotmail.com>*Date*: Wed, 24 Jul 2013 22:03:47 -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

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? Or: 2. Is there a theorem which proves that theorems as per 1. above can not exist? Or: 3. Is this an undecidable problem? Best regards, MATTHIAS BODE.