How to evaluate $\int_0^\infty \exp \left(-\frac{A}{B + Cx} - Dx\right) dx$?

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How to evaluate the integral (or at least rewrite it in some form of special function)

$$\int_0^\infty \exp \left(-\frac{A}{B + Cx} - Dx\right) dx$$

where $A,B,C,D > 0$ ?

Also is this task even possible for the easy case $A = B = C = D = 1$ ?