The following is a list of integrals (antiderivative functions) of rational functions.
Any rational function can be integrated by partial fraction decomposition of the function into a sum of functions of the form: which can then be integrated term by term.
For other types of functions, see lists of integrals.
Many of the following antiderivatives have a term of the form ln |ax + b|.
Because this is undefined when x = −b / a, the most general form of the antiderivative replaces the constant of integration with a locally constant function.
[1] However, it is conventional to omit this from the notation.
where C is to be understood as notation for a locally constant function of x.