Exponential Integration

coyote_001

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

The integral is,

[tex]\int_{0}^{L} dx\ \frac{e^{-(a y + \frac{b}{y})}}{y}[/tex]

where [tex]L>0[/tex], [tex]a,b>0[/tex].

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

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


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