antispam@math.uni.wroc.pl schrieb:   
   >   
   > clicliclic@freenet.de wrote:   
   > >   
   > > [...]   
   > >   
   > > Anyway, I won't submit this nasty integral again. The problem of this   
   > > pseudo-elliptic integrand seems to be that it involves the constant root   
   > > SQRT(a^2 + 1) in addition to the main radical SQRT((x - a)*(x^2 + 1)).   
   > > So not only nested radicals but also separate constant roots may slow   
   > > the FriCAS integrator down to a crawl, and in this case even with   
   > > SimplifyDenomsFlag set!   
   > >   
   > > The elusive antiderivative is quite compact, however:   
   > >   
   > > INT((x - SQRT(a^2 + 1) - a)/((x + SQRT(a^2 + 1) - a)   
   > > *SQRT((x - a)*(x^2 + 1))), x) =   
   > > - SQRT(2)*SQRT(SQRT(a^2 + 1) + a)*ATAN(SQRT(2)*SQRT(SQRT(a^2 + 1) - a)   
   > > *((x - a)/SQRT((x - a)*(x^2 + 1))))   
   > >   
   > > Now left wondering how long _very_ long is in hours, say, or years ...   
   >   
   > This one has been running for few days.  There were examples that   
   > finished after a week or even a month.  Some other eventually   
   > run out of memory.  Other I have interrupred after about a month.   
   > Also, long running computation can mask a bug in later code.   
   > Namely, first part may be so slow that nobody is patient enough   
   > to see bug in following part.   
   >   
      
   Having found the web interface to be working again today, I have tried   
   the following special cases:   
      
   integrate((x - 2)/((2*x + 1)*sqrt((4*x - 3)*(x^2 + 1))), x)   
      
   integrate((x - sqrt(2) + 1)/((x + sqrt(2) + 1)*sqrt((x + 1)*(x^2 + 1))),   
   x)   
      
   integrate((x - sqrt(3) - sqrt(2))/((x + sqrt(3) - sqrt(2))*sqrt((x -   
   sqrt(2))*(x^2 + 1))), x)   
      
   preceded by setSimplifyDenomsFlag(true). All three were solved right   
   away. So the massive slow-down observed for a generic constant root   
   SQRT(a^2 + 1) disappears already for non-generic constant roots - the   
   constants need not be rational.   
      
   Martin.   
      
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