# Tough definite integral

Hello,
I would like to evaluate the following definite integral

$\int_0^1 \frac{exp(1/(x(1-x)))}{\sqrt{x(1-x)}}$

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 :(

$\int_0^1 \frac{exp(-1/(x(1-x)))}{\sqrt{x(1-x)}}$