# Integral of Exponential with Polynomial Argument

1. Jul 4, 2015

### LayMuon

How can I find an Integral of an exponential with Polynomial argument with finite limits:

$\int_0^\pi \exp^{-a x^2 -b x^4} dx \\ \int_0^\pi \exp^{-a x^2 -b x^4} (x - x^3)dx$

2. Jul 4, 2015

### Dr. Courtney

Wolfram Alpha.

3. Jul 4, 2015

### LayMuon

Doesn't evaluate the first one.

4. Jul 4, 2015

### Dr. Courtney

There likely is no closed form solution for the top one in terms of a and b. Put in numbers for a and b and there are a lot of tools that will integrate it numerically, including Wolfram Alpha.