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

Discussion in 'Mathematica' started by Klaus Engel, Apr 16, 2010.

1. ### Klaus EngelGuest

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.

Klaus

Klaus Engel, Apr 16, 2010

2. ### Andreas HinzeGuest

Hi Klaus

Why do you assume that Integrate[2 f[x], {x, 0, 1}] exist ?
(Assume i.e. f[x] has a pole at 1)

it leaves the intgral expression untouched.

What happens when you define f[x] ?

Just my \$0.01
Regards
AHz

Andreas Hinze, Apr 17, 2010