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Re: Problems with solving integrals in Mathematica 9

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  • 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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