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

[colstat]

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?

 

[fauboca]

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=falseIs there a closed form of this?

Off the top of my head I would say Gamma function.

Wait are there any bounds?

 

[colstat]

wow, you are really good.

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

 

[fauboca]

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 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