Integral with Exponential and Algebraic function, need analytical solution

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Can anyone help me with following Integral? Mathematica may help, I don't have a Mathematica Licence.

\begin{equation} \int_{a^2}^{\infty} \frac{e^{-x} ~e^\frac{-a^2}{x}}{x^3 \sqrt{x-a^2}} ~dx \end{equation}

where $a$ is a real number.