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Re: A bug in Reduce package 'algint'?
Posted:
Jan 21, 2013 7:47 PM
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clicliclic@freenet.de schrieb:
>
> Wanting to refresh my knowledge of the capabilties of the Reduce algebra
> system, I have recently browsed the website. The system comes with the
> 'algint' package by J. Davenport which boosts the integrator
> capabilities for algebraic functions. The package documentation
>
> <http://www.reduce-algebra.com/docs/algint.pdf>
>
> introduces the example integrand sqrt(sqrt(a^2 + x^2) + x)/x. A correct
> antiderivative for this is
>
> 2*(sqrt(sqrt(a^2 + x^2) + x)
> - sqrt(a)*atanh(sqrt(sqrt(a^2 + x^2) + x)/sqrt(a))
> - sqrt(a)*atan(sqrt(sqrt(a^2 + x^2) + x)/sqrt(a)))
>
> The antiderivative printed in the documentation, however, is either very
> wrong or garbled beyond recognition.
>
I took another look and - the Reduce result printed in the documentation
is correct:
SQRT(a)*ATAN((SQRT(a)*SQRT(SQRT(a^2+x^2)+x)*SQRT(a^2+x^2)-SQRT(a~
)*SQRT(SQRT(a^2+x^2)+x)*a-SQRT(a)*SQRT(SQRT(a^2+x^2)+x)*x)/(2*a^~
2))+2*SQRT(SQRT(a^2+x^2)+x)+SQRT(a)*LOG(SQRT(SQRT(a^2+x^2)+x)-SQ~
RT(a))-SQRT(a)*LOG(SQRT(SQRT(a^2+x^2)+x)+SQRT(a))
DIF(SQRT(a)*ATAN((SQRT(a)*SQRT(SQRT(a^2+x^2)+x)*SQRT(a^2+x^2)-SQ~
RT(a)*SQRT(SQRT(a^2+x^2)+x)*a-SQRT(a)*SQRT(SQRT(a^2+x^2)+x)*x)/(~
2*a^2))+2*SQRT(SQRT(a^2+x^2)+x)+SQRT(a)*LOG(SQRT(SQRT(a^2+x^2)+x~
)-SQRT(a))-SQRT(a)*LOG(SQRT(SQRT(a^2+x^2)+x)+SQRT(a)),x)
[x:epsilonComplex,a:epsilonComplex]
SQRT(SQRT(x^2+a^2)+x)/x
as required (I had made a mistake inputting the pretty-printed result
into Derive). Sorry for that - but then it was this mistake what made me
find a more compact antiderivative!
Martin.
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