Integral of Exponential function

[macauor]

Homework Statement

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

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

(n is integer)

Homework Equations

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

Thank you.

 

[The Bob]

Hi macauor, Welcome to PF!

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

The Bob

 

[macauor]

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?

 

[The Bob]

Ok, try here (http://en.wikipedia.org/wiki/Lists_...integrals_lacking_closed-form_antiderivatives) under the section 'Definite integrals lacking closed-form antiderivatives' and see if that helps.

If not look at this (http://www.soton.ac.uk/~adf/pubstore/pub20.pdf ).

The Bob

 

[macauor]

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