From: fateman@cs.berkeley.edu   
      
   Just to point out (again) that this discussion has rather   
   broader implications than integration, specifically.   
      
   If you just type log(x^2)  into Maxima, you get 2*log(x).   
      
   If you want to inhibit that transformation, you   
   must change the (default) setting by logexpand:false.   
      
   There are commands integrate(..)   
   and risch(...)  in Maxima.   
      
   if logexpand:false, then integrate() produces the   
   "approved" answer involving log(x^2).   
      
     risch() produces the one you don't like,   
   because it sets up a differential field and to do so it   
   uses parts of the radcan() program.   
      
   This is useful (essential in general) to detect   
   the dependency of the differential-algebraic extensions   
   log(x) and log(x^2) =[sometimes] 2*log(x).   
      
   As another example, entirely separate from integration,   
   radcan(log(x^2-1)-log(x+1))  returns log(x-1).   
      
   The behavior of the input and output expressions analytically   
   is different. e.g. at x=-1.   
      
   This is entirely deliberate.   
      
   RJF   
      
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