The integration of the function x^(-a) * e^(-b/x), where a and b are constants, can be approached using various methods. Users in the discussion noted that tools like Wolfram Alpha and Maple provide solutions, with Maple yielding results in terms of exponentials and Whittaker M functions. The substitution u = b/x is suggested for simplifying the integral. The discussion also touches on the Gamma function and its relevance to the problem, particularly in the context of posterior distributions.
PREREQUISITESMathematicians, students studying calculus, and professionals in fields requiring integration of complex functions, particularly those interested in statistical distributions and special functions.
colstat said: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?
colstat said:wow, you are really good.
Yes, I wrote a simplified version of inverse-gamma. I am looking for the posterior distribution.
colstat said: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?