integrate(sin(x)*cos(x),x)



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?
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