What is list of common integral that have no closed form?

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What is list of common integral that have no closed form?

It's diffucult for me to google it for some reason.

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See http://en.wikipedia.org/wiki/Lists_of_integrals#Definite_integrals_lacking_closed-form_antiderivatives. This link tells you a list of integrals not expressible in a closed form expression.

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$ e^{x^{2}} $, for starters. Hope this helps! :)