Integrate x^x^x: What do you think?

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Discussion Overview

The discussion revolves around the integration of the function x^x^x, exploring various methods and perspectives on how to approach this problem. Participants consider both numerical and analytical techniques, as well as the potential use of special functions.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant suggests that numerical integration may be the best approach, noting the absence of an elementary function for its derivative.
  • Another participant proposes using the Lambert function, defining x^x as z and attempting to express x in terms of z to facilitate integration.
  • A different participant challenges the previous suggestion, pointing out an oversight regarding the differential dx, implying that the integration process is even more complex than initially thought.
  • Another claim is made about a primitive function related to x^(x^x), referencing a specific function and a document that purportedly contains a simple answer.

Areas of Agreement / Disagreement

Participants express differing views on the methods for integrating x^x^x, with no consensus reached on a definitive approach or solution.

Contextual Notes

Some participants highlight the complexity of the integration process and the potential for missing assumptions or steps in their reasoning.

Alejandroman8
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how integrate x^x^x ?my teacher ask me)what do you think about it?
 
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I would suggest numerically! Certainly there is no elementary function that has that as its derivative.
 


I don't know, but I thougt in the Lambert function

If we define x^x=z, then, x=\frac{ln(z)}{W(ln(z)}, where W is the Lambert function. So we can write

x^z=\left(\frac{ln(z)}{W(ln(z)}\right)^z, and then integrate.

I know, that this is awfull, but, maybe it can help or give any clue.
 


Thanks)
but i think it took not one hour to take the result
 


@ Grufey : False because you forgot the dx.
So, even more complicated !
.
@ Alejandroman8 : a primitive of x^(x^x) is the function Sphd(1,1;x)
Is it a joke ? Just read the preamble of "The Somophore's Dream Function" :
http://www.scribd.com/JJacquelin/documents
A so simple answer ! (§.12) :smile:
 

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