Re: Re: strange behavior of Integrate

*To*: mathgroup at smc.vnet.net*Subject*: [mg75322] Re: [mg75302] Re: strange behavior of Integrate*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Wed, 25 Apr 2007 05:35:06 -0400 (EDT)*References*: <200704220910.FAA20220@smc.vnet.net><f0hv8o$acb$1@smc.vnet.net> <200704240728.DAA27565@smc.vnet.net>

dimitris wrote: >>[...] I had asked: >>Why is this integral important? The reply: >>>int = HoldForm[(1/Pi)*Integrate[Log[x/(x^2 + 1)]*(1/(x^2 + 1)^m), {x,= > > 0, Infinity}, Assumptions -> m >= 1]] > > I study the book "Irresistible Integrals" by George Boros and Victor > Moll > (2nd Edition, Campridge University Press 2006). > I work various formulas by hand and Mathematica from this book and one > of worked examples is this integral (page 270). > > (BTW, very good performance of Mathematica) > > Is is a good reason or not? > > Best Regards > Dimitris It's a solid book and, hence, a sound reason. But only when stated explicitly. Problems that appear out of nowhere, so to speak, are likely to be taken less seriously. Integrals that appear in various books such as that of Boros and Moll come with a pedigree of sorts. That at least is my opinion (biased in part because they develop some methods involving what I find to be interesting mathematics). Needless to say, integrals, exact or numeric, that appear in the course of one's research are also quite important (especially to the researcher). In determining priority levels for purposes of triage, this question of origin is one thing I tend to take into account. Examples that exist merely to illustrate pathology are regarded as iteresting, but not, in general, as high priority bugs. Victor Moll also sometimes sends such examples. Daniel Lichtblau Wolfram Research

**Follow-Ups**:**Re: Re: Re: strange behavior of Integrate***From:*Daniel Lichtblau <danl@wolfram.com>

**References**:**strange behavior of Integrate***From:*dimitris <dimmechan@yahoo.com>

**Re: strange behavior of Integrate***From:*dimitris <dimmechan@yahoo.com>