I need to evaluate the following integral

$\displaystyle \int{\frac{e^{(-at-bt^2)}}{t}}dt$

It seems there is no closed from expression for this integral. But if we do the power series expansion for either $\displaystyle e^{-at}$ or $\displaystyle e^{-bt^2}$, then the closed form is possible but with an infinite power series. Kindly suggest if any alternative is available?