I am trying to obtain an analytic estimate of this integral:

$\int_0^1\frac{1}{\sqrt{x}}\exp\left(-a(x-x_0)^2\right) dx$,

where $a\gg1$, $x_0\in[0,1]$. Saddle-point approximation doesn't work due to infinite derivative of $1/\sqrt{x}$ at 0. Any tips on how to get a handle on this will be much appreciated.