Re: Problems with solving integrals in Mathematica 9

*To*: mathgroup at smc.vnet.net*Subject*: [mg130998] Re: Problems with solving integrals in Mathematica 9*From*: "djmpark" <djmpark at comcast.net>*Date*: Sun, 2 Jun 2013 00:29:13 -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*: <3939930.66166.1370082482241.JavaMail.root@m06>

It looks like the 8.04 result is only correct with conditions. It is a basic change of variable example. The Presentations Application's Student's Integral routines with a little help from Mathematica Integrate allow us to evaluate the integral. The integrate routine is an unevaluated Integrate that allows us to manipulate the integral. It displays as a regular integral but I'll just show the InputForm here. ChangeIntegralVariable does a substitution. We then use Integrate but with the assumptions that thr f at the 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 for displaying an unevaluated integral in a notebook and then evaluating it with assumptions. David Park djmpark at comcast.net http://home.comcast.net/~djmpark/index.html From: Jost Adler [mailto:jost.adler at googlemail.com] 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.