oldk1331@gmail.com schrieb:   
   >   
   > On Friday, August 19, 2016 at 1:00:37 PM UTC+8, clicl...@freenet.de wrote:   
   > > But the result for number six does not differentiate back; it looks like   
   > > an attempt at approximating the antiderivative.   
   >   
   > All five differentiate back, can you check again?   
   >   
      
   Yes, I fell into an old trap: multi-digit numbers split over consecutive   
   lines are read as products when copied into Derive, this affects the   
   sixth result only.   
      
   The FriCAS antiderivative shows 18 jumps along the real axis. A smooth   
   alternative is:   
      
   -2^(1/3)/4*(LN(2*(1-x)^3+(1-x^3))-3*LN(2^(1/3)*(1-x)+(1-x^3)^(1/~   
   3))-2*SQRT(3)*ATAN(1/SQRT(3)*(1-2*2^(1/3)*((1-x)/(1-x^3)^(1/3)))~   
   ))-2^(1/3)/12*(LN(2-(1-x^3))-3*LN(2^(1/3)-(1-x^3)^(1/3))+2*SQRT(~   
   3)*ATAN((1+2^(2/3)*(1-x^3)^(1/3))/SQRT(3)))+2^(1/3)/12*(LN(2*x^3~   
   +(1-x^3))-3*LN(2^(1/3)*x+(1-x^3)^(1/3))-2*SQRT(3)*ATAN(1/SQRT(3)~   
   *(1-2*2^(1/3)*(x/(1-x^3)^(1/3)))))-1/6*(LN(x^3+(1-x^3))-3*LN(x+(~   
   1-x^3)^(1/3))-2*SQRT(3)*ATAN(1/SQRT(3)*(1-2*x/(1-x^3)^(1/3))))   
      
   Martin.   
      
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