# How to integrate x^(-a)*e^(-b/x), where a, b are constants?

wow, you are really good.

Yes, I wrote a simplified version of inverse-gamma. I am looking for the posterior distribution.

wow, you are really good.

Yes, I wrote a simplified version of inverse-gamma. I am looking for the posterior distribution.

Try the substitution u = b/x

I am assuming you have 0 to infinite has bounds of the integral

Ray Vickson
Homework Helper
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## Homework Statement

How do you integrate this?
x-ae-b/x, where a and b are some constants.

## The Attempt at a Solution

I have tried this
http://integrals.wolfram.com/index.jsp?expr=x+*+e^%28-1%2Fx%29&random=false

Is there a closed form of this?

Maple gets an answer in terms of exponentials and Whittaker M functions. Of course, you might not regard that as a "closed form", since Whittaker functions are not "elementary".

RGV