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"Complement" to the Risch Algorithm


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.


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