Problem with integrals

How can I solve it?? ∫exp(x²)dx=??

I would like to know if there is any method to make an estimation on how big it is a number, in terms of orders of magnitude of n! when n is a big number.

(x^2) (2-x)^2 = 1 + 2(2-x)^2 I asked this problem on this page a few months ago, but didn’t get any satisfactory answer. I think there is a trick solution to it