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"Complement" to the Risch Algorithm


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?


2. Is there a theorem which proves that theorems as per 1. above can not exist?


3. Is this an undecidable problem?

Best regards,


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