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From: Golam Mortuza Hossain <gmhoss...@gmail.com>
Date: Tue, 18 Aug 2009 22:48:19 -0300
Message-ID: <141c154a0908181848p67e2d31ev4af175bfd3996...@mail.gmail.com>
Subject: Re: [sage-devel] Re: Serious bug in integral using Maxima?
To: sage-devel@googlegroups.com
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Hi,

On Tue, Aug 18, 2009 at 8:42 PM, rjf<fate...@gmail.com> wrote:
>
> did you mean to integrate with respect to "x^2" ?

Yes.

> Well, x^2 doesn't occur in =C2=A0 f(x). =C2=A0So let's rename x^2 as y.
> What is the integral of f(x) with respect to y?
>
> It is y*f(x).
>
> substituting back x^2 for y, =C2=A0you get x^2*f(x).

Are you saying during integration maxima is not aware
that "x^2" is the square of "x"?

Take following examples:
----------
(%i4) integrate(log(x), x);
(%o4)                            x log(x) - x

(%i5) integrate(log(x^2), x^2);
                                     2
(%o5)                             2 x  log(x)
----------

"log" is certainly aware of it.

> Certainly Maxima expects "the variable of integration" as
> the second argument. =C2=A0Anything else is asking for trouble.

Then maxima should throw error instead of giving a wrong
answer silently. This is rather bizarre given maxima is known
to be over-cautious during integration and sometime
it asks too many questions, even something like
--------
(%i6) integrate(1/x, x, 0, 1);
Is  x + 1  positive, negative, or zero?
--------

Cheers,
Golam