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I would like to evaluate the following definite integral

[itex] \int_0^1 \frac{exp(1/(x(1-x)))}{\sqrt{x(1-x)}} [/itex]

Numerically I get the result of about 1.4695 and it appears to converge nicely in the domain of interest (0;1). However, I'm wondering whether some kind of analytical integral exists as well... couldn't find anything myself :(

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# Tough definite integral

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