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

Barton Willis willisb at unk.edu
Wed May 16 07:54:23 CDT 2007

```-----maxima-bounces at math.utexas.edu wrote: -----

>To: Doug Stewart
>From: sen1 at math.msu.edu
>Sent by: maxima-bounces at math.utexas.edu
>Date: 05/16/2007 05:23AM
>cc: maxima list
>Subject: Re: [Maxima] integrate(sin(x)*cos(x),x)
>
>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?

(%i1) integrate(f(x) = sin(x) * cos(x),x);
(%o1) integrate(f(x),x)=integrationconstant1-cos(x)^2/2

Reasonable, maybe; easy to do, yes. But I'm not in favor of changing
integrate to always include an additive constant. For one, it would
make the logic behind the test suite more complicated. That's not a
compelling reason I suppose.  For another, with a simple
implementation, Maxima would generate gratuitous integration
constants: something like

integrate(x,x) + integrate(x^2,x) = x^2 / 2 + %c1 + x^3/4 + %c2

That would be distracting.

Barton
```