# Integral of Exponential function

#### macauor

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

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)

2. Relevant equations

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

Thank you.

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#### 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

Last edited by a moderator:

#### macauor

Dear The Bob,

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

macauor

"Integral of Exponential function"

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