Talk:Nonelementary integral
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"It can be shown (though not easily)" is there a citation for this line? I have been unable to find one 124.170.135.112 (talk) 17:37, 31 May 2008 (UTC)
- Well for instance (sin x)/x or exp(x2) don't have integrals in terms of elementary functions. In fact thst seems fairly obvious to me considering tht any of a number of things can stop one having an elementary integral so the chances of one of these happing in a big formula tends towards certainty. The mechanic might be a bit messy but the main theorem is the one that some such functions can't be integrated and it should at least be referenced and is missing - I'll put in a pointer to Liouvilles theorem about that. I don't know the theorem for the bit you wanted. Dmcq (talk) 10:56, 11 July 2010 (UTC)
Newsgroup discussion
[edit]I don't know whether this reference is acceptable, so I post it here instead of at the article.
Other Material
- "META-THEOREM: If you can't see how to integrate it easily, it probably, can't be integrated in closed form..." as stated in Subject: Re: CAN YOU SOLVE THIS INTEGRAL, PLEASE?. Newsgroup disccussion (sci.math). Last modified 13-Jan-2000 17:13; accessed 7 Dec 2012. Followed up by Subject: Re: Repost: Integral of x^x. Mathematical Atlas: A gateway to Mathematics, www.math-atlas.org. Last modified 09-Jan-2000 00:58; accessed 7 Dec 2012. 5.151.82.11 (talk) 01:11, 8 December 2012 (UTC)