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How integrate x^x^x

by Alejandroman8
Tags: integrate
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Alejandroman8
#1
Dec7-10, 03:59 PM
P: 3
how integrate x^x^x ???my teacher ask me)what do you think about it?
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HallsofIvy
#2
Dec8-10, 08:26 AM
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Thanks
PF Gold
P: 39,490
I would suggest numerically! Certainly there is no elementary function that has that as its derivative.
Grufey
#3
Dec8-10, 10:12 AM
P: 28
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
#4
Dec8-10, 02:25 PM
P: 3
How integrate x^x^x

Thanks)
but i think it took not one hour to take the result
JJacquelin
#5
Dec9-10, 12:01 AM
P: 759
@ 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)


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