Yes I should just read,
"integrate may carry out a change of variable if the integrand has the
form f(g(x)) * diff(g(x), x). integrate attempts to find a subexpression
g(x) such that the derivative of g(x) divides the integrand. This search
may make use of derivatives defined by the gradef function. See also
changevar and antid."
http://maxima.sourceforge.net/docs/manual/en/maxima_20.html
thank you
On Wed, 2007-05-16 at 12:53 -0700, Richard Fateman wrote:
> No. the technique used by this is "derivative divides".
>
> Integrate U*V by seeing if dU/dx divides V. It does. Integral is U^2/2.
> U=sin
> V=cos
> one has to take care of constant factors too.
>
> Substitution as taught "by hand" is not needed.
> RJF
>
>
> Yigal Weinstein wrote:
>
> >Does the algorithm in Maxima use something like substitution as used by
> >hand?
> >y= cos(x) or sin(x)
> >=> dy = -sin(x)dx or cos(x)dx
> >=> I(x)=integrate(sin(x)*cos(x),x) = -cos^2(x) or sin^2(x)?
> >Or does substitution not factor in at all?