From: nma@12000.org   
      
   On 1/28/2018 2:27 AM, clicliclic@freenet.de wrote:   
      
   > In terms of a, the three solutions correspond to the integrals:   
   >   
   >    INT((x + a)/((x - a)*SQRT(x^3 - x^2*(a^2 + 1) + a^2*x)), x)   
   >   
   >    INT((x + a - 2)   
   >        /((x - a)*SQRT(x^3 + x^2*(a^2 - 2*a - 1) + a*x*(2 - a))), x)   
   >   
   >    INT((x*(2*a - 1) - a)   
   >        /((x - a)*SQRT(x^3*(2*a - 1) - x^2*(a^2 + 2*a - 1) + a^2*x)), x)   
   >   
   > I am confident that FriCAS can solve all three,   
      
   fyi,   
      
   The third one gives Fricas some trouble   
      
   ii:=integrate((x*(2*a - 1)-a)/((x - a)*sqrt(x^3*(2*a - 1)-x^2*(a^2 + 2*a - 1)   
   + a^2*x)), x)   
      
       >> Error detected within library code:   
       catdef: division by zero   
      
   But the strange thing, if I run it again, it works second time   
      
   ii:=integrate((x*(2*a - 1)-a)/((x - a)*sqrt(x^3*(2*a - 1)-x^2*(a^2 + 2*a - 1)   
   + a^2*x)), x)   
   log(((-2)*((2*a+(-1))*x^3+((-1)*a^2+(-2)*a+1)*x^2+a^2*x)^(1/2)+(x^2+(2*a+(-2   
      ))*x+(-1)*a^2))/(x^2+(-2)*a*x+a^2))   
      
   And if I run again I get division by zero. Again, it works, and so on.   
   It seems memory stored internally affect the result.   
      
   Very strange. I need to post this at Fricas forum.   
      
   Fricas 1.3.2 on Linux.   
      
   >and suspect that there   
   > are no other (i.e. non-Goursat) pseudo-elliptics of this general form.   
   > By the way, a rule-based integrator would not need to solve polynomial   
   > equations, it only needs to check if a given instance of the integrand   
   > satisfies them.   
   >   
   > Martin.   
   >   
      
   --Nasser   
      
   --- SoupGate-Win32 v1.05   
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