why can't you integrate e^x^2

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why can't you integrate e^x^2

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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I suppose its because there is no function whose slope at any point cannot be in the form e^x^2. Actually only about 20% of functions can be integrated. I read that some where though I'm not sure about the figure of 20.
so you can't integrate it unless there is 2x in front of e^x^2
http://www.rangevoting.org/MarchisottoZint.pdf

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Other answers:

The integral is exist but we can't express it in terms of elementary functions (say all functions that you know in calculus)
hmm ok thanks
actually zero % of functions can be integrated if by "integrate" you mean find a formula for a function whose derivative is what you want.

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