We saw last week that there was a plethora of algorithms to integrate where p and q were polynomials in x.
where the are the distinct roots of and the are computed by . This algorithm is very impressive.
And they get worse in the elementary function case. In some sense we
are going to see that the Hermite reduction/ Rothstein-Trager algorithm
generalizes nicely to the elementary function case, and this is good in
the sense that we will have an algorithm, but it is bad in the
sense that we will inherit all the branch cut problems.