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Topic: The Charlwood Fifty
Replies: 52   Last Post: Jun 24, 2013 10:24 PM

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Richard Fateman

Posts: 1,404
Registered: 12/7/04
Re: The Charlwood Fifty and Macsyma
Posted: Jun 9, 2013 9:12 PM
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On 6/8/2013 10:17 AM, clicliclic@freenet.de wrote:
> I haven't checked the evaluations in the file systematically, but a new
> look has revealed further possibilities for improvement.
>
> The present solutions of problems #21 and #22 from Charlwood's appendix,
> INT(x^3*ASIN(x)/SQRT(1-x^4), x) and INT(x^3*ASEC(x)/SQRT(x^4-1), x), can
> be written as:
>
> 1/4*(x*SQRT(1-x^4)/SQRT(1-x^2)
> + LN(1-x^2) - LN(-x + x^3 + SQRT(1-x^2)*SQRT(1-x^4)))
> - 1/2*SQRT(1-x^4)*ASIN(x)


How about
((asinh(x))/4) - ((sqrt(1 - x^4) * asin(x))/2) + ((x * sqrt(x^2 + 1))/4)

from Macsyma. Which has the advantage of using no logs, just asin() and
asinh(). Since the integrand has asin, I think it is nice.

I have tried only a few others in the file, and Macsyma stumbled on one
or two of them. I am not inclined generally to spend my time to see if
the Macsyma solutions are smaller, neater, continuous etc, and maybe
it is of no interest since Macsyma is not easily available. But then
neither is Derive.. I suppose I can run the file through Macsyma if
someone else is willing to look at the results :)

RJF





Date Subject Author
5/23/13
Read The Charlwood Fifty
Albert D. Rich
5/23/13
Read Re: The Charlwood Fifty
Nasser Abbasi
5/23/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/16/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/16/13
Read Re: The Charlwood Fifty
Nasser Abbasi
6/17/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/17/13
Read Re: The Charlwood Fifty
Nasser Abbasi
6/17/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/17/13
Read Re: The Charlwood Fifty
Nasser Abbasi
6/17/13
Read Re: The Charlwood Fifty
Waldek Hebisch
6/18/13
Read Re: The Charlwood Fifty
Albert D. Rich
6/24/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/24/13
Read Re: The Charlwood Fifty
Albert D. Rich
5/23/13
Read Re: The Charlwood Fifty
Albert D. Rich
5/23/13
Read Re: The Charlwood Fifty
Waldek Hebisch
5/24/13
Read Re: The Charlwood Fifty
Andreas Dieckmann
5/25/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/1/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/3/13
Read Re: The Charlwood Fifty
Albert D. Rich
6/6/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/6/13
Read Re: The Charlwood Fifty
Nasser Abbasi
6/6/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/8/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/8/13
Read Re: The Charlwood Fifty
Albert D. Rich
6/8/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/8/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/9/13
Read Re: The Charlwood Fifty
Albert D. Rich
6/9/13
Read Re: The Charlwood Fifty
Nasser Abbasi
6/9/13
Read Re: The Charlwood Fifty
Albert D. Rich
6/9/13
Read Re: The Charlwood Fifty
Nasser Abbasi
6/10/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/10/13
Read Re: The Charlwood Fifty
Nasser Abbasi
6/10/13
Read Re: The Charlwood Fifty
Nasser Abbasi
6/12/13
Read Re: The Charlwood Fifty
Nasser Abbasi
6/13/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/13/13
Read Re: The Charlwood Fifty
Nasser Abbasi
6/13/13
Read Re: The Charlwood Fifty
Waldek Hebisch
6/13/13
Read Re: The Charlwood Fifty
Nasser Abbasi
6/13/13
Read Re: The Charlwood Fifty
Waldek Hebisch
6/14/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/14/13
Read Re: The Charlwood Fifty
Waldek Hebisch
6/14/13
Read Re: The Charlwood Fifty / Sage and sympy
Richard Fateman
6/14/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/9/13
Read Re: The Charlwood Fifty and Macsyma
Richard Fateman
6/9/13
Read Re: The Charlwood Fifty and Macsyma
Albert D. Rich
6/9/13
Read Re: The Charlwood Fifty, another Macsyma result
Richard Fateman
6/9/13
Read Re: The Charlwood Fifty, another Macsyma result
Albert D. Rich
6/10/13
Read Re: The Charlwood Fifty, another Macsyma result
Richard Fateman
6/10/13
Read Re: The Charlwood Fifty, another Macsyma result
clicliclic@freenet.de
6/10/13
Read Re: The Charlwood Fifty, another Macsyma result
Waldek Hebisch
6/11/13
Read Re: The Charlwood Fifty, another Macsyma result
Nasser Abbasi
6/11/13
Read Re: The Charlwood Fifty, another Macsyma result
clicliclic@freenet.de
6/11/13
Read Re: The Charlwood Fifty, another Macsyma result
Nasser Abbasi

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