Integral of Exponential function

1. The problem statement, all variables and given/known data

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)

2. Relevant equations

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

Thank you.
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


The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving