Richard Fateman schrieb:   
   >   
   > [...]   
   >   
   > It seems to me that the integrand  log(x)*log(x^2), considered   
   > algebraically, is 2*log(x)^2.  Are you trying to say something   
   >   subtle about it by stating it in that form?   
      
   With this identification of distinct integrands you are pointing to the   
   root of the problem. The systems I know insist that LN(x)*LN(x^2) /=   
   2*LN(x)^2 for any x < 0, in violation of your identification. For x =   
   -1, Mathematica and Derive thus simplify the left-hand side to zero and   
   the right-hand side to -2*pi^2. I expect Maxima to do so too.   
      
   Maxima and Mathematica both claim to employ Risch techniques for   
   transcendental integrands. Judging from the respective antiderivatives,   
   Maxima seems to rely on the problematic identification like FriCAS does,   
   whereas Mathematica manages without.   
      
   Instances where DIF(INT(f(x), x), x) /= f(x) must be considered   
   manifestations of a bug as both sides are usually understood to be   
   mathematically equal. Like FriCAS, you are therefore having a   
   consistency problem if this equality is violated by your system in the   
   case of f(x) = LN(x)*LN(x^2).   
      
   I am not surprised that Maxima too isn't perfect :). Sympy would be   
   another candidate to check.   
      
   Martin.   
      
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