How integrate x^x^x

by Alejandroman8
Tags: integrate
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 P: 3 how integrate x^x^x ???my teacher ask me)what do you think about it?
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,322 I would suggest numerically! Certainly there is no elementary function that has that as its derivative.
 P: 28 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.
 P: 3 How integrate x^x^x Thanks) but i think it took not one hour to take the result
 P: 756 @ 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)