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|    sci.math.symbolic    |    Symbolic algebra discussion    |    10,432 messages    |
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|    Message 9,870 of 10,432    |
|    clicliclic@freenet.de to clicliclic@freenet.de    |
|    Re: elementarily integrable or not?    |
|    17 Mar 18 19:31:26    |
      clicliclic@freenet.de schrieb:       >       > "Nasser M. Abbasi" schrieb:       > >       > > On 3/16/2018 10:18 AM, clicliclic@freenet.de wrote:       > > >       > > > A different problem for a similar integrand:       > > >       > > > setSimplifyDenomsFlag(true)       > > >       > > > integrate((5*x-9*sqrt(6)+26)/((x^2-4*x-50)*sqrt(x^3-30*x-56)), x)       > > >       > > > on the FriCAS web interface currently results in:       > > >       > > >>> Error detected within library code:       > > > catdef: division by zero       > > >       > > > The FriCAS )version command reports 1.3.2. Can earlier or later       > > > versions decide if this integral is elementary or not?       > > >       > >       > > Same thing on 1.3.3 on Linux:       > >       > > >fricas       > > FriCAS Computer Algebra System       > > Version: FriCAS 1.3.3       > > Timestamp: Tue Mar 13 22:58:43 CDT 2018       > > (1) -> setSimplifyDenomsFlag(true)       > > (1) false       > > (3) -> ii:=integrate((5*x-9*sqrt(6)+26)/((x^2-4*x-50)*sqrt(x^3-30*x-56)),       x)       > >       > > >> Error detected within library code:       > > catdef: division by zero       > >       >       > Thanks. "Is there any moderately-sized square-root pseudo-elliptic       > integral on which FriCAS is still known to fail?" I asked a while ago.       > The present integral would be one if it is integrable in elementary       > terms.       >              Here's a much more deadly failure:              setSimplifyDenomsFlag(true)              integrate((7*x + 6*sqrt(17*sqrt(2) + 23) + 9*sqrt(2) + 34)       /((x^2 + 2*x*(3*sqrt(sqrt(2) + 1) + 1) + 6*sqrt(58*sqrt(2) + 82)        - 18*sqrt(2) - 26)*sqrt(x^3 - 30*x - 56)), x)              is returned unevaluated on the web interface. But my oracle says that       the integand is pseudo-elliptic according to Goursat:              goursat3((7*x + 6*SQRT(17*SQRT(2) + 23) + 9*SQRT(2) + 34)       /(x^2 + 2*x*(3*SQRT(SQRT(2) + 1) + 1) + 6*SQRT(58*SQRT(2) + 82)        - 18*SQRT(2) - 26), x, -56, -30, 0, 1)              [false, false, false, true]              The last answer counts.              Martin.              --- SoupGate-Win32 v1.05        * Origin: you cannot sedate... all the things you hate (1:229/2)    |
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