Re: warning!!! I would suggest numerically! Certainly there is no elementary function that has that as its derivative.
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.
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" : http://www.scribd.com/JJacquelin/documents A so simple answer ! (ยง.12) :rofl: