oldk1331@gmail.com schrieb:   
   >   
   > > >   
   > > > FriCAS 1.3   
   > > > ==========   
   > > > integrate( sqrt(1 - x^4)/(1 + x^4), x)   
   > > >   
   > > > (log((2*x*((-1)*x^4+1)^(1/2)+((-1)*x^4+2*x^2+1))/(x^4+1))+   
   (-2)*atan((((-1)*   
   > > >    x^4+1)^(1/2)+x)/x)+2*atan(x^2)))/4   
   > >   
   > > This is (i) real and (ii) elementary, but (iii) discontinuous at x=0.   
   > > There are no other discontinuities.   
   > >   
   > > -   
   > >   
   > > Only Maple 2016.2 and FriCAS 1.3 return elementary answers, but both are   
   > > discontinuous at x=0.   
   > >   
   > > More work is therefore needed to make the output of these integrators   
   > > Davenport compatible.   
   > >   
   > > Martin.   
   >   
   > Hi Martin, FriCAS does an extra simplification, causes the result to be   
   > discontinuous at x=0.  This is caused by the same bug you mentioned   
   > in the previous thread.  I think there is a good enough fix, and the   
   > result after patching this bug is continuous:   
   >   
   > (log((2*x*((-1)*x^4+1)^(1/2)+((-1)*x^4+2*x^2+1))/(x^4+1))+2*atan((x^2*((-1)*   
   >   x^4+1)^(1/2)+(x^3+x))/(((-1)*x^4+1)^(1/2)+((-1)*x^3+x))))/4   
   >   
      
   This can still be simplified considerably:   
      
     1/2*ATANH(x*(1 - x^2)/SQRT(1 - x^4))   
     + 1/2*ATAN(x*(1 + x^2)/SQRT(1 - x^4))   
      
   Martin.   
      
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