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Re: Integrate bug and workaround

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  • Subject: [mg1058] Re: Integrate bug and workaround
  • From: withoff (David Withoff)
  • Date: Fri, 12 May 1995 15:00:48 -0400
  • Organization: Wolfram Research, Inc.

In article <3okes6$jh7 at> Steven Trainoff <steve at> writes:
>Hello all,
>I am constantly amazed at how fickle MMA's integrator is.  Perhaps  
>this example is well known, but it sure surprised me.  Can anyone  
>explain this behaviour, or is it a simple bug?  I am running MMA  
>version "NeXT 2.0 (November 14, 1991)"
>(* It can't do this... *)
>In[1]:= Integrate[x E^(Sqrt[z^2]*x), x ]
>                           2
>                   x Sqrt[z ]
>Out[1]= Integrate[E           x, x]		

Yes, this is a bug.  The Integrate function is being overly
pessimistic about its ability to handle algebraic expressions.
Handling algebraic subexpressions, even algebraic constants, is
indeed difficult in general, and it is best for Integrate to give
up than to get the wrong answer, but this particular algebraic
is in an innoccuous position and should not have caused any trouble.
The only workaround is, as you suggested, to temporarily remove the
algebraic constants so that Integrate doesn't see them.  This
problem will not lead to wrong answers, and has been fixed for
the next release of Mathematica.

Since this class of examples is fairly specific, I am concerned
that there must be other examples that led to your broader remark
about being "constantly amazed at how fickle" the integrator is.
If you have other examples like this, please send them to
support at so that we can make sure than they have been fixed.

Dave Withoff
Research and Development
Wolfram Research

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