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

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

On 5/16/07, Doug Stewart <dastew at sympatico.ca> wrote:
> I was just wondering how it picks U and V, because if it picked it the
> other way around then then it would give sin^2(x)/2 as the answer.

Whatever the pattern-matcher picks up first, I suspect, that is, essentially
an accident of implementation.  And no, there is no way to control that.

I also tried
> integrate(cos(n*x)*sin(n*x),x,0, t)
> but this doesn't give an answer. Does Maxima know how to do the definite
> integral from zero to t ?

This works fine for me (see below), as does the corresponding indefinite
integral.  Perhaps this Web interface doesn't support asking questions?

integrate(cos(n*x)*sin(n*x),x,0, t);

Is  t  positive, negative, or zero?

       1    cos (n t)
      --- - ---------
      2 n      2 n
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