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Re: bug in Integrate (5.2)

• To: mathgroup at smc.vnet.net
• Subject: [mg74942] Re: [mg74918] bug in Integrate (5.2)
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Thu, 12 Apr 2007 04:49:54 -0400 (EDT)
• References: <200704110557.BAA02816@smc.vnet.net>

dimitris wrote:
> Consider the integral of the following function in [0,Infinity).
> 
> In[710]:=
> f[x_, a_, b_] := (ArcTan[x/a] - ArcTan[x/b])/x
> 
> The integrand can be proved that converges for a, b>0.
> [proof snipped --dl]
> 
> However Mathematica returns
> 
> In[725]:=
> Block[{Message}, Integrate[f[x, a, b], {x, 0, Infinity}]]
> 
> Out[725]=
> Infinity
> 
> result which came from a very bad performance of Mathematica's
> Integrate algorithm.
 >
> (The ommited message is Integrate::idiv, generated when Mathematica
> considers an integral
> divergent.)
> [...]

This has been discussed in past.

http://forums.wolfram.com/mathgroup/archive/2006/Sep/msg00468.html

To recap:

(1) Integrate can misjudge convergence and incorrectly claim divergence.
(2) As mentioned in the post at the above URL, if this happens, and if 
Message is blocked by Block, then Integrate can claim the result is 
infinite. This was a small (in my opinion) bug, fixed for the next release.

Daniel Lichtblau
Wolfram Research

• References:
  • bug in Integrate (5.2)
    • From: "dimitris" <dimmechan@yahoo.com>