> Not off-topic: On page 344 of Timofeev's book as well as in Albert's   
   > pdf-file, this example problem reads:   
   >   
   >   INT((x/(x*COS(x) - SIN(x)))^2, x)   
   >   = (x*SIN(x) + COS(x))/(x*COS(x) - SIN(x))   
   >   
   > instead :(.   
   >   
   > Martin.   
      
   Back to topic: yes, the form of integrand matters, at least to heuristic   
   algorithm.  So we can grade integrator based on its output, we can   
   also grade integrator based on its input, although this will harder.   
      
   Take the famous risch algorithm wikipedia example #2:   
      
     int((x^2+2*x+1+(3*x+1)*sqrt(x+log(x)))/(x*sqrt(x+log(x))*(x+sq   
   t(x+log(x)))),x)   
      
   (Is this in the CAS test suite? Can Rubi solve it?)   
      
   The only winner to solve this integral so far is SymPy,   
   f=(x**2+2*x+1+(3*x+1)*sqrt(x+log(x)))/(x*sqrt(x+log(x))*(x+sqrt(x+log(x))))   
   integrate(f, x) can solve it, while   
   integrate(cancel(f), x) can't, 'cancel' expands the denominator.   
      
   That clearly shows the strength and limitation of heuristic algorithm.   
      
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