Re: Difficult antiderivative

*To*: mathgroup at smc.vnet.net*Subject*: [mg128858] Re: Difficult antiderivative*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Sat, 1 Dec 2012 04:31:29 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <20121129110606.EA8C968CD@smc.vnet.net> <20121130105445.3A2436857@smc.vnet.net>

On Nov 30, 2012, at 5:54 AM, Brambilla Roberto Luigi (RSE) <Roberto.Brambilla at rse-web.it> wrote: > > ...I'm asking if there exist any general criterion > (at least for simple combinations of elementary functions, as in my examples) that tell us about the existence of antiderivative > in the field of a set of chosen elementary functions. > Can I add to this set other less elementary functions (like Pailev=E9 trascendentans) in order to catch the missing antiderivative? You may wish to take a look at the article: http://en.wikipedia.org/wiki/Risch_algorithm --- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2838 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305