clicliclic@freenet.de schrieb:   
   >   
   > By contrast, your Maple result is valid for all real a < 0, but   
   > invalid for all real a > 0. This is a *bug* since all real a with |a|   
   > > 1 were admitted and the answer does not restrict itself to a < 0.   
   > The validity for all real a < 0 is readily exhibited by conditional   
   > simplification:   
   >   
   > 1/4*LN(a^2+2*a+1)*pi+1/4*pi^(1/2)*(a^2+2*a+1)^(1/2)*(-(-1+LN(a^2~   
   > +2*a+1)-LN(-a))*pi^(1/2)*(-a)^(1/2)/(a^2+2*a+1)^(1/2)+1/2*pi^(1/~   
   > 2)*(a^2+2*a+1)^(1/2)/(-a)^(1/2)-pi^(1/2)*(-1/4*(a^2+2*a+1)/a+1)^~   
   > (1/2)+2*pi^(1/2)*a^(1/2)*ASIN(1/2*(a^2+2*a+1)^(1/2)/a^(1/2))/(a^~   
   > 2+2*a+1)^(1/2))/(-a)^(1/2)   
   >   
   > a :epsilon Real(-inf, -1)   
   >   
   > pi*(2*a*LN(-a) - 1)/(4*a)   
   >   
   > a :epsilon Real(-1, 0)   
   >   
   > -pi*a/4   
   >   
   > a :epsilon Real(0, 1)   
   >   
   > pi*(2*a*LN(a) - 1)/(4*a)   
   >   
   > a :epsilon Real(1, inf)   
   >   
   > -pi*a/4   
   >   
   > Analyzed using plots and simplification on Derive 6.10.   
   >   
      
   My detection of a bug may have been premature: Maple's arcsin(z) could   
   be defined differently from Derive's ASIN(z) = #i*LN(SQRT(1-z^2) -   
   #i*z), in which case Maple's result might in fact be correct for all   
   real a with |a| > 1, and perhaps even for all real a.   
      
   I haven't tried to look Maple's definition up.   
      
   Martin.   
      
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