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Re: ArcCos[x] with x > 1
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 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 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 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 and Out are correct while Out and Out are not.