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Re: Problems with solving integrals in Mathematica 9
*To*: mathgroup at smc.vnet.net
*Subject*: [mg131002] Re: Problems with solving integrals in Mathematica 9
*From*: Andrzej Kozlowski <akozlowski at gmail.com>
*Date*: Sun, 2 Jun 2013 00:30:34 -0400 (EDT)
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In my opinion Mathematica is right.
Try the indefinite integral:
Integrate[f'[x]/f[x], x]
Log[f[x]]
No problem. Now, you claim that the correct answer for the definite
integral is -Log[f[0]] + Log[f[T]] but obviously this depends on various
assumptions on f. Simply by taking f(x)=x you will get a
non-convergent integral:
f[x_] := x
Integrate[f'[x]/f[x],{x,0,T}]
During evaluation of In[16]:= Integrate::idiv: Integral of 1/x does
not converge on {0,T}. >>
Integrate[1/x, {x, 0, T}]
Mathematica attempts to give an answer with full generality (expect
perhaps for non-generic cases) and in this no such answer can be given.
Thus, I would argue, this actually represents a fix of a bug in
Mathematica 8.
Andrzej Kozlowski
On 1 Jun 2013, at 12:26, Jost Adler <jost.adler at googlemail.com> wrote:
> Has anybody encountered the same problems with solving integrals in
Ver. 9 as I did?
>
> Here a very simple example:
>
> Integrate[D[f[x], x] / f[x], {x, 0, T}]
>
> Version 8.04 gives the correct results:
>
> -Log[f[0]] + Log[f[T]]
>
> In Version 9.00 as well as 9.01 this integral can't be solved. With
more complicated integrals I had the same problems. Version 8 gives a
solution, Version 9 doesn't!
>
> Could some other Version 9 users try it.
>
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