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

*To*: mathgroup at smc.vnet.net*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>