```Date: Jun 2, 2013 12:24 AM
Author: David Park
Subject: Re: Problems with solving integrals in Mathematica 9

It looks like the 8.04 result is only correct with conditions.  It is abasic change of variable example. The Presentations Application's Student'sIntegral routines with a little help from Mathematica Integrate allow us toevaluate the integral. The integrate routine is an unevaluated Integratethat allows us to manipulate the integral. It displays as a regular integralbut I'll just show the InputForm here. ChangeIntegralVariable does asubstitution. We then use Integrate but with the assumptions that thr f atthe endpoints are greater than zero. Mathematica does evaluate that.<< Presentations`integrate[D[f[x], x]/f[x], {x, 0, T}]% // ChangeIntegralVariable[t -> f[x], x]% // UseIntegrate[{f[0], f[T]} > 0] integrate[f[x]^(-1) Derivative[1][f][x], {x, 0, T}]integrate[t^(-1), {t, f[0], f[T]}] ConditionalExpression[Log[f[T]/f[0]], 0 < f[0] < f[T]] The routines in the Student's Integral sub-package are: integrate,BasicIntegralTable (basic table used by students), DisplayIntegralTable,BreakoutIntegral, OperateIntegrand, ChangeIntegralVariable,IntegrateByParts, TrigonometricSubsitute, LimitsBracket,EvaluateLimitsBracket, UseIntegralTable, UseIntegrate, UseNIntegrate.The use of integrate and UseIntegrate[assumptions] is a good method fordisplaying an unevaluated integral in a notebook and then evaluating it withassumptions.David Parkdjmpark@comcast.net http://home.comcast.net/~djmpark/index.html  From: Jost Adler [mailto:jost.adler@googlemail.com] Has anybody encountered the same problems with solving integrals in Ver. 9as 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 morecomplicated 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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