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)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net*References*: <20130601102628.B6E6B69C7@smc.vnet.net>

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. >

**References**:**Problems with solving integrals in Mathematica 9***From:*Jost Adler <jost.adler@googlemail.com>