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Please how to find indefinite integral

$$\int x^{x^x}\mathrm dx$$ Thank for any one help me to find it

Ahmed
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    Why do you expect a nice closed form for the antiderivative to exist? – Henry T. Horton Feb 09 '13 at 21:09
  • Source?${}{}{}{}$ – Clayton Feb 09 '13 at 21:17
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    @Clayton, such functions (and their derivatives and integrals) did intrige me when in my calculus classes. Sadly, there was no http://math.stackexchange.com around in those days. Don't quench the kid's curiosity. – vonbrand Feb 09 '13 at 21:43
  • @vonbrand: I'm not sure if you thought I was trying to be rude; I was simply curious myself. – Clayton Feb 09 '13 at 21:51
  • @Clayton, I don't believe you tried to be rude, it just came across that it could be interpreted that way to me. – vonbrand Feb 09 '13 at 21:55
  • @vonbrand, we can choose less abrupt language for asking, but it will always be helpful to know the background of a question. Especially in the middle ground, if I think I might be able to contribute but am not sure of solving a problem without a good deal of work: for example, see my forlorn comments at http://math.stackexchange.com/questions/296931/find-x-such-that-1213x-be-a-perfect-square#comment645600_296931 Sometime before that, i put related language in my user profile. – Will Jagy Feb 09 '13 at 22:19

2 Answers2

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Maybe this is possible for the definite integrals as (in the sense of getting an alternative form) $$\int_0^1 x^x \mathrm{dx} = \sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{n^n} $$ and then we can think of a generalization of sophomore’s dream integral/series identities.
In the spirit of this way I think you're also interested in this useful paper.

user 1591719
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For your reference:${}{}{}{}{}$

http://hk.knowledge.yahoo.com/question/question?qid=7008010201949

JSCB
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