From: nma@12000.org   
      
   so far, Maple 2017.3 and Mathematica 11.2 give wrong results   
   on this:   
      
   integrand := cos(x)* sin(x)^2*cos(n*x);   
      
   Now I wanted to integrate the above from 0..2PI   
   with the assumption that n above is integer and   
   positive.   
      
   What does your CAS give for the integral?  hint:   
   it should not be zero.  But....   
      
   Maple:   
   integrand := cos(x)* sin(x)^2*cos(n*x);   
   assume(n,integer,n>0);   
   int(integrand,x=0..2*Pi);   
      
               0   
      
   Mathematica:   
   Assuming[Element[n, Integers] && n > 0,   
                Integrate[integrand, {x, 0, 2 Pi}]]   
        0   
      
   But this integral is not zero for all integer n.   
      
   Table[Integrate[integrand, {x, 0, 2 Pi}], {n, 1, 5}]   
            {Pi/4,0,-Pi/4,0,0}   
      
   I do not know how to use assumptions yet in Fricas   
   to test this. Will try to learn how to.   
      
   I really do not understand how advanced and mature CAS   
   systems like Maple and Mathematica can get this wrong.   
      
   Or may be it is by design. I do not know. Someone told   
   me it is hard to program these exception cases into CAS   
   and have it check for each special case.  Any thoughts?   
      
   --Nasser   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)