Is there a way to represent this integral in terms of summation of series? $$ \int_0^\infty {1 \over x^x}dx$$ Like for example: $$ \int_0^1 {1 \over x^x}dx = \sum_{n=1}^\infty {1 \over n^n}$$ I am not getting an answer from Mathematica.
How to evaluate $ \int_0^\infty {1 \over x^x}dx$ in terms of summation of series?
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sequences-and-series
integration
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2thanks @Sasha I didn't know that ... but how to evaluate the integral with $ \infty $? – 2012-08-20
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0Oops, sorry. I guess I missed the question. – 2012-08-20
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0your info was helpful ;) – 2012-08-20
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6This doesn't look like an exact duplicate to me. I vote not to close. – 2012-08-20
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0To start talking about this integral i think you have first to define what is $1/x^x$ when $x=0$. – 2012-08-20
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0it's an improper integral – 2012-08-20
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0thats true. ^_^ – 2012-08-20
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0The numerical value is 1.995455957500138000... and the [Inverse Symbolic Calculator](http://isc.carma.newcastle.edu.au/index) finds nothing. – 2012-08-20