# Exponential Integration

by coyote_001
Tags: exponential, integration
 P: 7 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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