Integral of Exponential function

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Homework Help Overview

The discussion revolves around the evaluation of integrals involving exponential functions, specifically the integrals of the forms \(\int^{\infty}_{-\infty}e^{-ax^2 - bx^{\frac{5}{2}}}dx\) and \(\int^{\infty}_{-\infty}x^ne^{-ax^2 - bx^{\frac{5}{2}}}dx\), where \(n\) is an integer. The original poster seeks closed forms or references for these integrals.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants inquire about the difficulties faced by the original poster and request any workings out to better understand the problem. Suggestions for external resources are provided to assist in finding closed forms for the integrals.

Discussion Status

The discussion is ongoing, with participants offering guidance and resources. The original poster expresses gratitude for the suggestions and indicates a willingness to share any solutions found in the future.

Contextual Notes

The original poster is looking for closed forms of the integrals, which may not exist, as indicated by the references shared in the discussion.

macauor
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Homework Statement



1. [tex]\int^{\infty}_{-\infty}e^{-ax^2 - bx^{\frac{5}{2}}}dx[/tex]

2. [tex]\int^{\infty}_{-\infty}x^ne^{-ax^2 - bx^{\frac{5}{2}}}dx[/tex]

(n is integer)

Homework Equations



Does anyone can give me the integral in the closed form or introduce any useful references?

Thank you.
 
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Hi macauor, Welcome to PF!

What is putting you off? Can you show us any workings out?

The Bob
 
Hello, The Bob
Thank you for your warm welcome!
I want to obtain the closed forms of the integration of the above two integrals.
Do you have any suggestion about that?
 
Dear The Bob,

It is really helpful.

Thank you for your kindness.

If I find the solution, I would like to share it on PF

macauor
 

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