clicliclic@freenet.de  wrote:   
   >   
   > antispam@math.uni.wroc.pl schrieb:   
   > >   
   > > clicliclic@freenet.de  wrote:   
   > > >   
   > > > [...]   
   > > >   
   > > > The last two evaluations are not wrong, but they are certainly   
   > > > suboptimal :(. I suspect that Rubi can do better!   
   > >   
   > > There are many things in FriCAS that could be improved.  This   
      
   > Some bad oldies are:   
   >   
   >   integrate(log(log(x))^n/x, x)   
   >   
   > whose evaluation cos(n*pi())*Gamma(n+1,(-1)*log(log(x))) differentiates   
   > to (cos(n*pi())*((-1)*log(log(x)))^n)/x, which fails to reproduce the   
   > integrand.   
      
   Yes, this is a bug.  In fact, I consider this high priority bug,   
   but solving it requires rather large changes to FriCAS.  More   
   precisly, FriCAS assumes that integral of real function is   
   real and computes real part of the integral.  Gamma above is   
   complex and need complex constant.  Real bug is that FriCAS   
   integral freqently contains spurious imaginary parts and ATM taking   
   real part is needed to "clean up" them.  After other parts   
   are corrected (which is substantial work) there will be no   
   need to take real part of integral and the above will give   
   correct result.   
      
   > And then:   
   >   
   >   integrate((5*x - 9*sqrt(6) + 26)   
   >     /((x^2 - 4*x - 50)*sqrt(x^3 - 30*x - 56)), x)   
   >   
   > >> Error detected within library code: catdef: division by zero.   
   >   
   > And the recently recalled:   
   >   
   >   integrate(1/((p*sqrt(1 - x^2) - 1)*sqrt(p*sqrt(1 - x^2) - x^2)), x)   
   >   
   > >> Error detected within library code: Denominator not equal to 1.   
   >   
   > And also:   
   >   
   >   integrate((cos(2*x) - sqrt(sin(2*x)))/sqrt(cos(x)^3*sin(x)), x)   
   >   
   > whose evaluation involves the expected radical sqrt(2*cos(x)*sin(x))   
   > along with a mangled radical sqrt(2*cos(x)^3*sin(x)); the latter must   
   > be replaced by sqrt(2)*sqrt(cos(x)^3*sin(x)) for a valid result.   
      
   Yes, there are several problems.   
      
   --   
                                 Waldek Hebisch   
      
   --- SoupGate-Win32 v1.05   
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