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Re: A Problem with Simplify

  • To: mathgroup at smc.vnet.net
  • Subject: [mg87675] Re: A Problem with Simplify
  • From: Bill Rowe <readnews at sbcglobal.net>
  • Date: Tue, 15 Apr 2008 05:53:54 -0400 (EDT)

On 4/14/08 at 5:43 AM, popkov at gmail.com (Alexey Popkov) wrote:

>Try the following:
>Integrate[Exp[(a - 1)*x], x] /. a -> 1
>Integrate[Cos[(a - 1)*x], x] /. a -> 1
>Integrate[(a - 1)^x, {x, -1, 0}] /. a -> 1
>Integrate[Cos[a x]/Sin[x], x] /. a -> 1

>There is the ONE underlying BUG!

There is no bug here. Each of the integrals you do above result
in an expression divided by (a-1). The replacement rule simply
substitutes 1 for a everywhere. Consequently, the denominator of
each integral evaluates to 0 and Mathematica returns either
Indeterminate or ComplexInfinity as it should.

Where you expecting a to be replaced by 1 before the integration
was done? If so, the syntax should be written

Integrate[f/.a->1,x]

Or perhaps you were expecting Mathematica to simplify the
results of the integral before replacing a with 1. If so, you
need either

FullSimplify[Integrate[f,x]]/.a->1

or

Simplify[Integrate[f,x]]/.a->1

However, neither of these are guaranteed to remove the
singularity. So, these may result in exactly what you got.


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