Problem with integration



Richard Fateman writes:
 > As is often the case, you get unusual answers when if you
 > have not conformed to the expected syntax. Certainly
 > cos^3(x) is not the same as  (cos(x))^3, nor is
 > sin*(2*x)  the same as sin(2*x).
 > 
 > Do you mean  f1(x):=  ( cos(sin(2*x)))^3  ?
 > 
 > RJF
 > 
 > 
Hi Richard-

   Ok, my bad.
   I take back what I said! ;-)

   The correct syntax yields the correct answer.

   Thanks for pointing this out!

   Best regards,

   Henry





 > synthespian wrote:
 > > 
 > > Hi James-
 > > 
 > >    I disagree that Maxima is trustworthy. There are little bugs here
 > > and there. More than I have time to report or annotate.
 > >    I gave up on using it for graphics altogether.
 > >    I hope for better days.
 > > 
 > >    Let me give you another bug, involving differentiation:
 > > 
 > > (C1) f1(x):= (cos^3*(sin*(2*x)));
 > > (C2) diff(f1(x),x);
 > >    This evaluates to the bizarre answer:
 > > 
 > >    2 x cos^3 DEL(sin) + 6 x cos^2 sin DEL(COS) + 2 cos^3 sin DEL(x)
 > > 
 > >    The correct answer, by hand and confirme with Maple, is:
 > > 
 > >    6 cos^2(sin(2x))*sin(sin(2x))*cos(2x);
 > > 
 > >    Regs,
 > > 
 > >    Henry
 > >    synthespian@uol.com.br
 > > 
 > > James Amundson writes:
 > >  > Great. Not too long ago, I wrote that none of the bugs found recently in
 > >  > Maxima resulted in mathematically incorrect answers. Now you have to go
 > >  > an ruin the streak.
 > >  >
 > >  > This bug deserves *careful* consideration.
 > >  >
 > >  > Thanks for the report.
 > >  >
 > >  > --Jim
 > >  >
 > >  >
 > >  > On Fri, 2002-04-05 at 14:36, C Y wrote:
 > >  > > I've run into a problem with the Maxima integration ability.  I tried
 > >  > > to integrate 3^log(x), and according to both hand and mathematica
 > >  > > calculations the answer should be (x*3^log(x))/(1+log(3)).  Maxima,
 > >  > > however, gives 3^(2*log(x))/(2*log(3)).  Here is a simple test to show
 > >  > > the problem:
 > >  > >
 > >  > > (C1) c:3^log(x);
 > >  > >
 > >  > >                                      LOG(x)
 > >  > > (D1)                                3
 > >  > > (C2) diff(integrate(c,x),x);
 > >  > >
 > >  > >                                     2 LOG(x)
 > >  > >                                    3
 > >  > > (D2)                               ---------
 > >  > >                                        x
 > >  > >
 > >  > >
 > >  > > CY
 > >  > >
 > >  > >
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