Closed form of $\int_{x = 0}^{C} \exp\left(-\frac{x}{A}-\frac{B}{x}\right)\,dx$

Question

Is there a closed-form expression for the following definite integral?

\begin{equation} \int_{x = 0}^{C} \exp\left(-\frac{x}{A}-\frac{B}{x}\right)\,dx, \end{equation} where $A$, $B$, and $C$ are positive constants. Here, $C < \infty$. I know that, when $C = \infty$, a closed-form expression in the form of a Bessel function exists.

Answer 1

$\int_0^Ce^{-\frac{x}{A}-\frac{B}{x}}~dx$

$=\int_0^1e^{-\frac{Cx}{A}-\frac{B}{Cx}}~d(Cx)$

$=C\int_0^1e^{-\frac{Cx}{A}-\frac{B}{Cx}}~dx$

$=C\int_\infty^1e^{-\frac{C}{Ax}-\frac{Bx}{C}}~d\left(\dfrac{1}{x}\right)$

$=C\int_1^\infty\dfrac{e^{-\frac{Bx}{C}-\frac{C}{Ax}}}{x^2}dx$

$=CK_1\left(\dfrac{B}{C},\dfrac{C}{A}\right)$ (according to https://core.ac.uk/download/pdf/81935301.pdf)