• Integration of rational functions. Homework: do the exercise in this worksheet.
• More on integration of rational functions. Homework: Write a procedure with input: a rational function f, and output: rational functions A,g such that f = A' + g and denom(g) is squarefree. This way, the integration problem int(f,x) is reduced to an integration problem A+int(g,x) where g is a function with no poles of order > 1.
• The residue.
• More on residues.
• Summary of the previous worksheets: Integration of rational functions. (contains an assignment).
• Differential fields, logarithms polynomial case
• Logarithms general case.
• Another example for a logarithmic extension.
• valuations, Liouvilles Principle.
• The exponential case example 1. Example 2