how integrate x^x^x

Alejandroman8

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

HallsofIvy

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

Grufey

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.

Alejandroman8

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

JJacquelin

@ 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)

Alejandroman8	how integrate x^x^x Tweet how integrate x^x^x ???my teacher ask me)what do you think about it?

HallsofIvy Recognitions: Gold Member Science Advisor Staff Emeritus	I would suggest numerically! Certainly there is no elementary function that has that as its derivative.

Grufey	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.

Alejandroman8	how integrate x^x^x Thanks) but i think it took not one hour to take the result

JJacquelin	@ 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)