Re: Definite Integration in Mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg74564] Re: Definite Integration in Mathematica*From*: "Michael Weyrauch" <michael.weyrauch at gmx.de>*Date*: Mon, 26 Mar 2007 02:08:35 -0500 (EST)*References*: <etqo3f$10i$1@smc.vnet.net>

Hello, thanks, Dimitris, for bringing up this issue. (By the way, as I just realized, Michael Trott in his book on symbolics has quite some interesting things to say related to this issue.) My remark in this thread clearly was written in the spirit of "functions of one real variable". As I see my statements are clearly incorrect in the sense of "functions of a complex variable". However, in many practical applications people want to have an integral in the former sense, and it is very disconcerting to fall down a discontinuity step along an integral of a continous integrand on the real line due to a singularity of the integrand somewhere in the complex plane. Therefore, I guess, the designers of "the other CAS", which Dimitris uses for comparison, obviously opted to return an integral, which is continuous along the real axis (if such an integral is available in the set of possible solutions). This is not just a matter of aestetics or simplicity as Dimitris remark in this thread may suggest >Do you prefer the extend antiderivative over the compact one obtained >directly >by Mathematica only because is real in the real axis? >As regards myself, no! In applications we have to use that solution which makes practical sense, and in many applications it's the integral which is continouus (and differentiable) for a continouus integrand on the real axis. Of course, it's my task as a physicist or engineer to see if a mathematical solution serves my purposes or not, however, in such rather intriguing cases, it would be desirable that the designers of Mathematica would help me by providing an Option to Integrate, in which I could ask for an integral which is continuous on the real axis if such an integral exists for a particular integrand. (As I understand the remark of Daniel Lichtblau in some future version of Mathematica they may provide such an Option). Thanks again Michael Weyrauch

**Follow-Ups**:**Re: Re: Definite Integration in Mathematica***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>