How to solve $\int \sqrt{x} e^{x} \mathrm{d}x$

Asked Jun 11 '22 at 06:44

Active Jun 11 '22 at 08:27

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I can't solve this integral. I have tried all the things that I could think of, but I keep getting stuck.

edited Jun 11 '22 at 08:27

Eunuch Dave

asked Jun 11 '22 at 06:44

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https://socratic.org/questions/how-do-you-integrate-int-sqrtx-e-x-dx-using-integration-by-parts#628186 – Alessandro Della Corte Jun 11 '22 at 07:10
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See also: Strange integrand: $\int \sqrt{x} e^{x}dx$. You can check the search results from Approach0 and from SearchOnMath to see whether you find some other interesting posts there. (I reposted this - the comment was deleted in the migration.) – Martin Sleziak Jun 11 '22 at 07:41
the indefinite integral (which is what you want) cannot be expressed in terms of elementary functions; it's this function: https://en.wikipedia.org/wiki/Incomplete_gamma_function – Carlo Beenakker Jun 11 '22 at 09:18

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