If Integrate returns no result, can we conclude that no closed-form

*To*: mathgroup at smc.vnet.net*Subject*: [mg87759] If Integrate returns no result, can we conclude that no closed-form*From*: Szabolcs Horvát <szhorvat at gmail.com>*Date*: Wed, 16 Apr 2008 06:52:44 -0400 (EDT)*Organization*: University of Bergen

The documentation says: "In the most convenient cases, integrals can be done purely in terms of elementary functions such as exponentials, logarithms and trigonometric functions. In fact, if you give an integrand that involves only such elementary functions, then one of the important capabilities of Integrate is that if the corresponding integral can be expressed in terms of elementary functions, then Integrate will essentially always succeed in finding it." http://reference.wolfram.com/mathematica/tutorial/IntegralsThatCanAndCannotBeDone.html How precise is this? Can one rely on this information? Is it really true that if Mathematica cannot integrate an expression made up of elementary functions, then no closed-form result exists? Szabolcs (P.S. I do not know how Integrate works. I heard that CASs use a so-called "Risch-alogrithm", but there is relatively little information about this on the web (except in academic papers, most of which expect the reader to be familiar with the topic).)

**Follow-Ups**:**Re: If Integrate returns no result, can we conclude that no closed-form***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>