Integration of (a-b)^n



On Tue, Sep 21, 2010 at 12:04:20PM -0400, Raymond Toy wrote:
>  On 9/19/10 12:50 PM, Ian Bell wrote:
> > integrate((a-b)^2,a) to give me the factored solution (a-b)^3/3 .
> > Maxima (and Mathematica for that matter), expand the product and then
> > group all the constants together since mathematically they all drop
> > out when you plug in limits.  In this way it makes it impossible to
> > refactor the anti-derivative back to the form (a-b)^3 .   I've got a
> > lot of other integrals that I have a similar problem with, like
> > (a-b)^n*sin(a) with n an integer.  For what its worth, in MATLAB (w/
> > MuPaD) int((a-b)^2,a) yields (a-b)^3/3
> >
> This has come up before in some bug report.  Currently, you can't do
> that. 

Well, you can, if you think a little. Like this:

(%i1) integrate((x-a)^5,x,a,x),factor;
                                          6
                                   (x - a)
(%o1)                              --------
                                      6
                                      
Sorry for bringing back a topic from one month ago (I was not
reading the list for about a month), but I simply could not resist
commenting.

-- 
Stanislav