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Re: int operator with various versions of Maple

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Subject	Re: int operator with various versions of Maple
From	acer <maple@rogers.com>
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Le mardi 27 mai 2014 22:38:29 UTC-4, pluton a écrit :
> Hello,
> 
> if you type: 
> 
> > assume(0<d,d<1);
> 
> > int(cos(theta)*sin(theta)/(1+d*cos(theta))^3,theta=0..Pi);
> 
> on various versions of Maple, you will notice that the output varies. A closed-form solution is given with versions 6 and 16 for instance (the final expression is not the same though), while version 13 fails (as far as I know). This is fairly annoying. 


I see success for that example in Maple 13.02 (64bit Windows), and also for 11.02, 12.02, 14.01, 15.01, 16.02, 17.02, and 18.01.

In each of those the result was as follows for 13.02,

restart:
assume(0<d,d<1); 

int(cos(theta)*sin(theta)/(1+d*cos(theta))^3,theta=0..Pi);

                                     2 d~               
                    - ----------------------------------
                      /      2       \ /              2\
                      \1 + d~  + 2 d~/ \-2 d~ + 1 + d~ /

kernelopts(version);

          Maple 13.02, X86 64 WINDOWS, Oct 12 2009, Build ID 436951


Those results were all generated by the `ftoc` method.

In later versions a variant with the denominator factored could also be obtained with the method=ftocms option.

restart:

assume(0<d,d<1); 

int(cos(theta)*sin(theta)/(1+d*cos(theta))^3,theta=0..Pi,method=ftocms);

                               2 d       
                      - -----------------
                               2        2
                        (1 + d)  (d - 1) 

kernelopts(version);

   Maple 18.01, X86 64 WINDOWS, Mar 28 2014, Build ID 935137


There may be some other example which regressed. But I don't see it for this one (on those 64bit Windows versions listed).

No, you cannot instruct `int` to act as in a previous version. You can instruct it to try various methods for symbolic definite integration, however.

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int operator with various versions of Maple pluton <plutonesque@gmail.com> - 2014-05-27 19:38 -0700
  Re: int operator with various versions of Maple "Nasser M. Abbasi" <nma@12000.org> - 2014-05-28 18:03 -0500
  Re: int operator with various versions of Maple acer <maple@rogers.com> - 2014-05-28 22:50 -0700
    Re: int operator with various versions of Maple pluton <plutonesque@gmail.com> - 2014-06-02 06:41 -0700
      Re: int operator with various versions of Maple acer <maple@rogers.com> - 2014-06-02 17:37 -0700
        Re: int operator with various versions of Maple pluton <plutonesque@gmail.com> - 2014-06-02 18:39 -0700

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