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Topic: Charlwood Fifty test results
Replies: 16   Last Post: Sep 19, 2013 10:09 PM

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Nasser Abbasi

Posts: 5,686
Registered: 2/7/05
Re: Charlwood Fifty test results
Posted: Jul 6, 2013 5:53 PM
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On 7/6/2013 3:32 PM, Albert Rich wrote:

> Nasser and I agree that Maple failed to integrate problem 9. On problem 10, I entered the integrand as
>
> x^3*exp(1)^arcsin(x)/sqrt(1-x^2)
>
> whereas he probably entered it as
>
> x^3*exp(arcsin(x))/sqrt(1-x^2)
>
> Because of some bazaar quirk in Maple, it succeeds in integrating the former and not the latter!
>Perhaps some Maple aficionado can justify, or at least explain, this phenomena...
>
> Albert
>


That is interesting. I wonder how you discovered this. It would
never have occurred to me to try that.

I updated the table for the 10 integrals, I suppose it is fair to give
this one to Maple now. I am using now Maple 17.01 (version just came out).
So maple now has 9/10 as well.

I also made a full trace of this problem 10, one with

x^3*exp(1)^arcsin(x)/sqrt(1-x^2)

and another trace with

x^3*exp(arcsin(x))/sqrt(1-x^2)

to try to find why Maple gives an answer for one case and not the other.

Will look at the traces more later. But if someone like to try find out,
the traces are uploaded as well in HTML and PDF format. They are under the
Maple download section:

http://www.12000.org/my_notes/ten_hard_integrals/index.htm

ps. HTML export by Maple are little strange, one needed to scroll
down a bit to see start seeing the actual text. PDF export is better.

pps. I did not use full tracing, as that would have generated huge amount
of data.

ppps. I did not do timing on results, so, yes some Mathematica results
took more than 30 seconds.

--Nasser



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