# [Maxima] integrate(sin(x)*cos(x),x)

Stavros Macrakis macrakis at alum.mit.edu
Wed May 16 08:14:14 CDT 2007

```On 5/16/07, sen1 at math.msu.edu <sen1 at math.msu.edu> wrote:
>
> Agreed that this might be low on the list of things to do, but, isn't it
> reasonable to

have indefinite integrals return constants to show the non-uniqueness?...

If so, how hard would it be to add constants to indefinite integrals?

It would be trivial to implement if we decide to do it -- a couple of lines
of code in \$integrate and simpinteg.  From the user's point of view, one
complication might be a profusion of arbitrary constants, e.g.

integrate(x+x^2,x) => x^2/2+x^3/3+%c1

but

integrate(x,x)+integrate(x^2,x) => x^2/2+x^3/3+%c2+%c3

Also, it is curious that Maple 10 returns
>    sin(x)^2/2
> while Mathematica 3.0 returns
>   -cos(x)^2/2

Most integrals in computer algebra systems are not handled by lookup in a
table of integrals, but are derived algorithmically.  The details of the
algorithm determine the result.   As a general rule, they try to preserve
the shape of the expression, so that the equivalent integral -cos(2*x)/4
isn't generated, but even that is not guaranteed in general.

>From this discussion, it seems that the indefinite integration and ode2
> routines in maxima have little to do with each other.

They have a lot to do with each other: the ode2 routines use integration as
a subroutine.

-s
-------------- next part --------------
An HTML attachment was scrubbed...
URL: http://www.math.utexas.edu/pipermail/maxima/attachments/20070516/eecd6df2/attachment.htm
```