Integrate x^x^x: What do you think?

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In summary, the conversation discusses the integration of x^x^x and the suggestion to use numerical methods. It is noted that there is no elementary function with x^x^x as its derivative and that the Lambert function could be used to solve the problem. It is also mentioned that the integration process is complicated and may take more than an hour to complete. However, there is a simple function, Sphd(1,1;x), that can be used as a primitive of x^(x^x).
  • #1
Alejandroman8
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how integrate x^x^x ?my teacher ask me)what do you think about it?
 
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  • #2


I would suggest numerically! Certainly there is no elementary function that has that as its derivative.
 
  • #3


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


Thanks)
but i think it took not one hour to take the result
 
  • #5


@ 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:
 

1. What is the formula for integrating x^x^x?

The formula for integrating x^x^x is not a simple one and cannot be written out in terms of basic mathematical operations. It involves the use of special functions, such as the exponential integral, and cannot be easily expressed in closed form.

2. Can x^x^x be integrated using traditional integration techniques?

No, x^x^x cannot be integrated using traditional integration techniques. As mentioned before, it requires the use of special functions and cannot be easily expressed in closed form.

3. What is the significance of integrating x^x^x?

The integral of x^x^x has various applications in mathematics, physics, and engineering. It can be used to solve problems in areas such as probability, number theory, and differential equations.

4. Is there a general strategy for integrating x^x^x?

There is no general strategy for integrating x^x^x, as each problem may require a different approach. However, some common techniques used include substitution, integration by parts, and using special functions.

5. What are some examples of problems that involve integrating x^x^x?

Problems that involve integrating x^x^x can include calculating areas under curves, finding the volume of certain shapes, and solving differential equations. It can also be used in various physics and engineering problems, such as calculating work done or determining energy functions.

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