## Exponential Integration

Hello,
I have an integral and I can't figure out the solution,

The integral is,

$$\int_{0}^{L} dx\ \frac{e^{-(a y + \frac{b}{y})}}{y}$$

where $$L>0$$, $$a,b>0$$.

I know that the same integral from zero to infinity has a solution,

$$\int_{0}^{\infty} dx\ \frac{e^{-(a y + \frac{b}{y})}}{y} = 2 K_{0}\left( 2 \sqrt{a b}\right)$$
where $$K_{n}$$ is the BesselK function.

If anyone knows the solution, please let me know.!!!
Thanks

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