On Saturday, March 25, 2017 at 5:25:59 PM UTC+8, Albert Rich wrote:   
   > On Friday, March 24, 2017 at 6:03:19 PM UTC-10, oldk...@gmail.com wrote:   
   > > Off topic a little, I find it interesting that Rubi fails Timofeev 493,   
   > >   
   > >      int(x^2/(x*cos(x)-sin(x))^2,x)  --> (cos(x) + x*sin(x))/(x*cos(x) -   
   sin(x))   
   > >   
   > > A pure transcendental function, and easy to solve by heuristic   
   > > methods.   
   >   
   > I'm a little slow.  What is the heuristic method used to integrate it?   
   >   
   > Albert   
      
   What I meant is:   
      
   This integral can be solved if transcendental case of Risch algorithm   
   is implemented.   
      
   Otherwise, a CAS system might try to solve it using heuristic method,   
   aka integration by parts, guess, etc.  For this integral, as Timofeev said,   
   it equals to int( x/sin(x) d(1/(x*cos(x)-sin(x)))), then integration by part,   
   result is x/sin(x)/(x*cos(x)-sin(x)) + int(1/sin(x)^2,x) .   
      
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