How integrate x^x^x

  1. how integrate x^x^x ???my teacher ask me)what do you think about it?
  2. jcsd
  3. HallsofIvy

    HallsofIvy 41,260
    Staff Emeritus
    Science Advisor

    Re: warning!!!

    I would suggest numerically! Certainly there is no elementary function that has that as its derivative.
  4. Re: warning!!!

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

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

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

    I know, that this is awfull, but, maybe it can help or give any clue.
  5. Re: warning!!!

    but i think it took not one hour to take the result
  6. Re: warning!!!

    @ 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" :
    A so simple answer ! (ยง.12) :rofl:
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