Integral of Exponential with Polynomial Argument

[LayMuon]

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

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

 

[Dr. Courtney]

Wolfram Alpha.

 

[LayMuon]

Doesn't evaluate the first one.

 

[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.