Is There an Analytical Solution for This Tough Definite Integral?

[Irid]

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 :(

 

[dextercioby]

Wolframalpha says the integral doesn't converge.

http://www.wolframalpha.com/input/?i=Integrate+from+0+to+1+Exp[1/(x-x^2)]/Sqrt[x-x^2]+

 

[Office_Shredder]

That integral does not converge. When x is near zero, the integrand looks like e^1/x, which is at least as large as 1+1/x. So for some small number a, that integral is going to be larger than
$$\int_{0}^{a} 1+1/x dx$$
which doesn't converge.

Alternatively,
http://www.wolframalpha.com/input/?i=integral_0^1+exp(1/(x*(1-x)))/sqrt(x*(1-x))+dx

 

[Irid]

Oops, sorry, I forgot the minus sign:

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

should converge now :)