clicliclic@freenet.de schrieb:   
   >   
   > Thanks to the (still unpublished?) Masser-Zanier counterexample Waldek   
   > informed us about, we know that there are infinitely many (though   
   > increasingly complicated algebraic) u^2 for which   
   >   
   >   INT(x/((x^2 - u^2)*SQRT(x^3 - x)), x)   
   >   
   > has a solution (also of increasing complexity) in terms of elementary   
   > functions. Consequently, via the usual Moebius transformation of the   
   > integration variable, there are also infinitely many v = (u^2 - 1)/   
   > (u^2 + 1) for which   
   >   
   >   INT((y^2 - 1)/((y^2 + 2*v*y + 1)*SQRT(y^4 - 1)), y)   
   >   
   > has such an elementary solution. I too expect these patterns to be   
   > exceptions rather than the rule, the rule being that the number of   
   > pseudo-elliptic cases is finite and small. But does this pair already   
   > exhaust the store of patterns involving simple square-root radicands   
   > and giving rise to infinitely many pseudo-elliptic integrals?   
   >   
      
   The above relies on the transformation x = #i*(1 - y)/(1 + y).   
   Alternatively one may put x = z^2 to obtain:   
      
     INT(z^2/((z^4 - w^4)*SQRT(z^4 - 1)), z)   
      
   where w^2 = u. Now we have three simple patterns of this kind already.   
      
   Martin.   
      
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