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What is the integration of $$\int x^x dx$$ And how can I understand whether an integration is possible or not? Is there any rule to understand whether a function is integrable or not?

Martin Sleziak
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user10379
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  • WA shows that there is no integral in terms of standard elementary functions. – zz20s Jan 12 '16 at 15:30
  • this question was asked hundreds of times before. use the search function properly next time! – tired Jan 12 '16 at 15:39
  • That is a duplicate only for the first question, and not the other two. For help on understanding when an integral can be done in finite terms, I like this introductory paper: Rosenlicht, Maxwell, Integration in finite terms. Amer. Math. Monthly 79 (1972), 963–972. – GEdgar Jan 12 '16 at 16:06
  • @ user103379 : This paper may give you some clue : https://fr.scribd.com/doc/34977341/Sophomore-s-Dream-Function – JJacquelin Jan 12 '16 at 16:08

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