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Topic: can your system handle 4th-root pseudo-elliptics?
Replies: 17   Last Post: Sep 24, 2017 12:37 PM

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clicliclic@freenet.de

Posts: 1,245
Registered: 4/26/08
Re: can your system handle 4th-root pseudo-elliptics?
Posted: Sep 24, 2017 12:37 PM
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Albert Rich schrieb:
>
> According to Mathematica, 1/(2*(1-x^2)^(1/4)) is the derivative of
> Elliptic[ArcSin[x]/2,2]. At the FriCASIntegration website
>
> \begin{axiom}
> setSimplifyDenomsFlag(true)
> integrate(1/(1-x^2)^(1/4), x)
> \end{axiom}
>
> is unable to find a closed-form antiderivative. So apparently FriCAS
> concurs it is elliptic.
>


While integrals returned unevaluated by FriCAS are thereby declared
non-integrable in elementary terms, occasional error exits or endless
computations have no such implication. One may then only rephrase the
integral and try again.

There have also been bugs causing integrals to be mistakenly returned
unevaluated; thus INT(x/((3*x^2 + 2*SQRT(3) - 3)*SQRT(x^3 - x)), x) was
declared non-integrable in elementary terms by FriCAS version 1.3.0 and
earlier.

Martin.



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