# How integrate x^x^x

1. ### Alejandroman8

3
how integrate x^x^x ???my teacher ask me)what do you think about it?

2. ### HallsofIvy

41,060
Staff Emeritus
Re: warning!!!

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

3. ### Grufey

29
Re: warning!!!

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.

4. ### Alejandroman8

3
Re: warning!!!

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

5. ### JJacquelin

781
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 ! (§.12) :rofl: