I wish to compute the integral of
$$\displaystyle \int_0^{\infty} \dfrac{1}{x^2} \exp{\left(-\dfrac{a}{x}-bx\right)} dx$$
I found something similar in Gradshteyn and Ryzhik 7th Ed. p336 (Sec 3.324) in terms of the modified Bessel function of the second kind $K_\nu (x)$ but it didn't include the factor of $\dfrac{1}{x^2}$.
Can you help? Thank you.