This does not – according to what I can see from the code and comments – implement the case of algebraic extensions. As someone only really familiar with the implementation of the transcendental case[1], my understanding is that the algebraic case is where the major difficulty lies.

[1]: Manuel Bronstein, Symbolic Integration I. Online: https://archive.org/details/springer_10.1007-978-3-662-03386...

Unfortunately this is not complete, because it does not work with integrals that require algebraic extensions (they are more complicated than transcendental extensions).