Re: Mathematica is not very clever

*To*: mathgroup at smc.vnet.net*Subject*: [mg53073] Re: Mathematica is not very clever*From*: "yehuda ben-shimol" <benshimo at bgu.ac.il>*Date*: Wed, 22 Dec 2004 04:53:15 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Solving integrals analytically usually follows some technique (eg., interchange of variables). There is no one technique that works for all types of integrals. From the software engineering perspective each such solution method may be considered as a heuristic, and from the perspective of Mathematica's implementation it may be considered as a heuristic rules that a specific symbolic function such as Integrate uses. Since Integrate "cannot" solve this specific integral, you may assume that the specific rule is not part of the checking of Integrate implementation or that it decides somehow not to use it. The power of Mathematica is to let you define additional rules so it will be solvable. It is not about the "smartness" of Mathematica, it is all about the implementation decisions. yehuda -----Original Message----- From: Clifford Martin [mailto:camartin at snet.net] To: mathgroup at smc.vnet.net Subject: [mg53073] Mathematica is not very clever If you use NIntegrate (as your answer is numerical) you get the answer you were looking for, at least in 5.01. Cliff --- Klaus G <Karl_boehme_9 at msn.com> wrote: > Mathematica refuses to compute the following > integral: > > Integrate [ArcTan[Sqrt[x^2 + 2]]/((x^2 + 1)*Sqrt[x^2 > + 2]), {x, 0, 1}] > > Why is that? > The correct result is 5*Pi^2 / 96, which can be > proved. > > Klaus G. > >