acer
Posts:
55
Registered:
5/8/07
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Re: A bug in Reduce package 'algint'?
Posted:
Jan 21, 2013 8:53 PM
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Le lundi 21 janvier 2013 16:16:30 UTC-5, Axel Vogt a écrit :
> On 21.01.2013 19:55, clicliclic wrote:
>
> >
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> > Wanting to refresh my knowledge of the capabilties of the Reduce algebra
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> > system, I have recently browsed the website. The system comes with the
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> > 'algint' package by J. Davenport which boosts the integrator
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> > capabilities for algebraic functions. The package documentation
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> >
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> > <http://www.reduce-algebra.com/docs/algint.pdf>
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> >
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> > introduces the example integrand sqrt(sqrt(a^2 + x^2) + x)/x. A correct
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> > antiderivative for this is
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> >
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> > 2*(sqrt(sqrt(a^2 + x^2) + x)
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> > - sqrt(a)*atanh(sqrt(sqrt(a^2 + x^2) + x)/sqrt(a))
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> > - sqrt(a)*atan(sqrt(sqrt(a^2 + x^2) + x)/sqrt(a)))
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> >
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> > The antiderivative printed in the documentation, however, is either very
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> > wrong or garbled beyond recognition.
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> >
>
> > Martin.
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>
>
> Maple 16 returns 2*sqrt(2*x)*hypergeom([-1/4, -1/4, 1/4],[1/2, 3/4],-a^2/x^2)
>
> May be right, but not that 'usefull' w.r.t. your result
Just because Axel's brought up Maple (and not wishing to side-track Martin), in Maple 16.02,
expr := sqrt(sqrt(a^2 + x^2) + x)/x:
p := u = sqrt(a^2 + x^2) + x:
new := student[changevar](p, Int(expr,x), u):
sol := eval(value(new),p):
lprint(sol);
-((2*a^2*((a^2+x^2)^(1/2)+x)^2+a^4+((a^2+x^2)^(1/2)+x)^4)/((a^2+x^2)^(1/2)+x)^2)^(1/2)*((a^2+x^2)^(1/2)+x)*4^(1/2)*(-((a^2+x^2)^(1/2)+x)^(1/2)+a^(1/2)*arctan(((a^2+x^2)^(1/2)+x)^(1/2)/a^(1/2))+a^(1/2)*arctanh(((a^2+x^2)^(1/2)+x)^(1/2)/a^(1/2)))/(a^2+((a^2+x^2)^(1/2)+x)^2)
other := expand(radnormal(sol),power):
lprint(other):
2*((a^2+x^2)^(1/2)+x)^(1/2)-2*a^(1/2)*arctan(((a^2+x^2)^(1/2)+x)^(1/2)/a^(1/2))-2*a^(1/2)*arctanh(((a^2+x^2)^(1/2)+x)^(1/2)/a^(1/2))
What should we expect from the system, automatically?
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