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How to simplify "Integrate[2 f[x], {x, 0, 1}]/2" to "Integrate[f[x],

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  • Subject: [mg109199] How to simplify "Integrate[2 f[x], {x, 0, 1}]/2" to "Integrate[f[x],
  • From: Klaus Engel <klaus.engel at tiscali.it>
  • Date: Fri, 16 Apr 2010 05:53:30 -0400 (EDT)

Dear group,

I tried to simplify an awkward looking integral with "Mathematica 7" 
using its "(Full)Simplify[...]" function. Unfortunately it failed to do 
so, even though I know that this would be possible. I boiled down the 
problem to the following very simple example ("f" is just a generic, 
undefined function): The input

         Integrate[2 f[x], {x, 0, 1}]/2 // FullSimplify

returns just the input

         Integrate[2 f[x], {x, 0, 1}]/2

(same result for "Simplify" instead of "FullSimplify"), i.e., 
Mathematica seems not to be aware that the factor "2" can be canceled 
out. Even worse, the expressions

         TrueQ[Integrate[2 f[x], {x, 0, 1}]/2  == Integrate[f[x], {x, 0, 
1}]]
         SameQ[Integrate[2 f[x], {x, 0, 1}]/2 , Integrate[f[x], {x, 0, 1}]]
         Integrate[2 f[x], {x, 0, 1}]/2  === Integrate[f[x], {x, 0, 1}]

return the (wrong) result "False".

So my question: Is there something I am overlooking, or what is the 
right "Mathematica" way to treat expressions like the one above.

Thanks a lot in advance,

Klaus
------------

Klaus Engel <klaus.engel at tiscali.it>


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