patterns for integration



Richard Fateman wrote:
> Also, you could look at James Slagle's thesis, also at MIT.  
> 
> Ignoring the fact that what you are doing -- having a computer simulate the
> behavior that humans might use for these problems -- is often NOT the best
> way to write a program.
> 
> As a crude analogy, if you were simulating humans doing arithmetic, asking
> to show the fingers used for remembering "carries".  
> 

I know, but what could be optimal way to gain output similar to outputs 
on http://www.calc101.com/webMathematica/integrals.jsp or 
http://cgi.math.muni.cz/%7Exsrot/int/vyresene.htm from Maxima?

I know that the services like these cannot substitute the role of 
teacher and for example, I always tell the students that they are able 
to draw much much better graphs than computers (concerning intervals of 
monotonicity, maxima and minima, concavity up and down), but the tools 
like these may help in some simple problems and could provide hints to 
the students which are completely lost in mathmematics. And there are 
many students at our university of forestry and agriculture, who have to 
learn calculus, but have very poor knowledges of mathematics from 
higschools. But this is story for another discussion list :).

Thank you and thank also Raymond for the suggestions concerning theses 
from MIT and also for all your previous answers.

R.M.