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How integrate x^x^xby Alejandroman8
Tags: integrate 
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#1
Dec710, 03:59 PM

P: 3

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



#2
Dec810, 08:26 AM

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Thanks
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P: 39,490

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



#3
Dec810, 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. 


#4
Dec810, 02:25 PM

P: 3

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


#5
Dec910, 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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