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Re: Mathematica is not very clever

  • To: mathgroup at
  • Subject: [mg53073] Re: Mathematica is not very clever
  • From: "yehuda ben-shimol" <benshimo at>
  • Date: Wed, 22 Dec 2004 04:53:15 -0500 (EST)
  • Sender: owner-wri-mathgroup at

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.

-----Original Message-----
From: Clifford Martin [mailto:camartin at] 
To: mathgroup at
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

--- Klaus G <Karl_boehme_9 at> 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.

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