From: nma@12000.org   
      
   On 3/25/2017 3:38 AM, clicliclic@freenet.de wrote:   
   >   
   > oldk1331@gmail.com schrieb:   
   >>   
   >> 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.   
   >   
   > 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.   
   >   
      
   Hello Martin;   
      
   The input file used also has the same form as you shown.   
      
   The issue is just display of the input.   
      
   When converting the input expression to Latex   
   for display, and when converting the input to InputForm   
   for showing it in verbatim, Mathematica re-writes it   
   as shown in the report.   
      
   But the actual input to Rubi is exactly as you show, as   
   read from the input file:   
      
   ----------------------   
   ShowSteps=False;   
   ClearAll[x];   
   input=(x/(x*Cos[x]-Sin[x]))^2;   
   Int[input,x]   
   --------------------------   
      
   Rubi does not solve this one, it returns   
      
   Int[x^2/(x*Cos[x] - Sin[x])^2, x]   
      
   But the InputForm changes   
      
   In[53]:= InputForm[input]   
   Out[53]//InputForm= x^2/(x*Cos[x] - Sin[x])^2   
      
   Also the TeXForm   
      
   In[54]:= TeXForm[input]   
   Out[54]//TeXForm= \frac{x^2}{(x \cos (x)-\sin (x))^2}   
      
   So it is all just display of the same expression.   
      
   But the two expressions are the same any way?   
      
   input = (x/(x*Cos[x] - Sin[x]))^2;   
   input2 = x^2/(x*Cos[x] - Sin[x])^2;   
   Simplify[input - input2]   
      
   Out[60]= 0   
      
   This re-write of the expression is done automatically by   
   Mathematica.  I myself do not touch the input or change it   
   in any way :)   
      
   ps. this integral, Rubi did not solve also in earlier   
   versions. This is not new to 4.11   
      
   --Nasser   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)