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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[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.


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