Integration involving exponential function

Question

I am trying to find the following integral

$\int_t^s e^{-\frac{(\sqrt{x^2-a^2}-u)^2}{\sigma^2} } e^{-\frac{b^2}{x^2}} dx$

where $t<u<s$, I can find a solution for $u=0$, but I need the solution for general case.