Re: ArcCos[x] with x > 1

*To*: mathgroup at smc.vnet.net*Subject*: [mg49354] Re: ArcCos[x] with x > 1*From*: "David W. Cantrell" <DWCantrell at sigmaxi.org>*Date*: Fri, 16 Jul 2004 06:06:36 -0400 (EDT)*References*: <cclev9$kb3$1@smc.vnet.net> <cco3io$4ig$1@smc.vnet.net> <cctaff$c11$1@smc.vnet.net> <cd0730$9g9$1@smc.vnet.net> <cd5p5r$b69$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

ab_def at prontomail.com (Maxim) wrote: > "David W. Cantrell" <DWCantrell at sigmaxi.org> wrote in message > news:<cd0730$9g9$1 at smc.vnet.net>... > > > But Paul's case is for version 5, as is what I showed above. So at > > least in the current version, some indefinite integrals are wrong. Ah, so I see below that I should have said "... some indefinite integrals are wrong _some of the time_."! > Actually this is a quite curious example, because Mathematica 5.0 > doesn't always return the same answer for this integral: [snip of very curious stuff, which I was able to reproduce on my machine] > This quirk is 100% reproducible on my machine (except for one time > when it crashed the kernel); apparently, evaluating In[3] changes some > internal states/settings Fascinating! (OK, call me hopelessly naive, but I hadn't thought about this sort of thing happening before. Thank you, Maxim, for opening my eyes!) I noticed that attempting to evaluate In[3] caused Mathematica to "think" for a while, before it gave up. So I'm wondering: In the future, when I encounter integrals (definite or indefinite) which Mathematica gets wrong, should I ask it to evaluate something like In[3] and then retry the original integral in the hope that Mathematica would now have been put in "a better frame of mind", so to speak? David Cantrell > and indef2, def2 are not the same as indef1, > def1. Out[4] and Out[5] are correct while Out[1] and Out[2] are not.