clicliclic@freenet.de  wrote:   
   >   
   > antispam@math.uni.wroc.pl schrieb:   
   > >   
   > > clicliclic@freenet.de  wrote:   
   > > >   
   > > > Wow! In Legendre's pseudo-elliptic integral:   
   > > >   
   > > > INT(x/((4 - x^3)*SQRT(1 - x^3)), x)   
   > > >  = 2^(1/3)/18*(ATANH(SQRT(1 - x^3))   
   > > >  - 3*ATANH((1 + 2^(1/3)*x)/SQRT(1 - x^3))   
   > > >  - SQRT(3)*ATAN((2^(1/3) - 2^(2/3)*x - x^2)   
   > > > /(SQRT(3)*2^(1/3)*SQRT(1 - x^3))))   
   > > >   
   > >   
   > > This does not verify.  AFAICS the third atan should be   
   > >   
   > > atan((1 - 2^(1/3)*x - 2^(-1/3)*x^2)/(sqrt(3)*sqrt(1 - x^3)))   
   > >   
   >   
   > My arc tangent:   
   >   
   >   ATAN((2^(1/3) - 2^(2/3)*x - x^2)/(SQRT(3)*2^(1/3)*SQRT(1 - x^3)))   
   >   
   > and your arc tangent:   
   >   
   >   ATAN((1 - 2^(1/3)*x - 2^(-1/3)*x^2)/(SQRT(3)*SQRT(1 - x^3)))   
   >   
   > are exactly the same numerically. Your expression is somewhat shorter,   
   > however! I probably wanted to avoid the negative power. Also, I can   
   > symbolically verify my full antiderivative easily on Derive. Unless   
   > 2^(2/3) does not equal (2^(1/3))^2 in the FriCAS model of algebraic   
   > numbers, you may have a problem.   
      
   Sorry for the noise, you are right.  I messed the formula and it   
   did not verify.  Then I transformed the other case and got formula   
   that verifed.  It looked different, I did not notice that it is   
   the same...   
      
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