# RationalFunctionDefiniteIntegration R¶

RationalFunctionDefiniteIntegration provides functions to compute definite integrals of rational functions.

integrate: (Fraction Polynomial R, SegmentBinding OrderedCompletion Expression R) -> Union(f1: OrderedCompletion Expression R, f2: List OrderedCompletion Expression R, fail: failed, pole: potentialPole)
integrate(f, x = a..b) returns the integral of f(x)dx from a to b. Error: if f has a pole for x between a and b.
integrate: (Fraction Polynomial R, SegmentBinding OrderedCompletion Expression R, String) -> Union(f1: OrderedCompletion Expression R, f2: List OrderedCompletion Expression R, fail: failed, pole: potentialPole)
integrate(f, x = a..b, "noPole") returns the integral of f(x)dx from a to b. If it is not possible to check whether f has a pole for x between a and b (because of parameters), then this function will assume that f has no such pole. Error: if f has a pole for x between a and b or if the last argument is not “noPole”.
integrate: (Fraction Polynomial R, SegmentBinding OrderedCompletion Fraction Polynomial R) -> Union(f1: OrderedCompletion Expression R, f2: List OrderedCompletion Expression R, fail: failed, pole: potentialPole)
integrate(f, x = a..b) returns the integral of f(x)dx from a to b. Error: if f has a pole for x between a and b.
integrate: (Fraction Polynomial R, SegmentBinding OrderedCompletion Fraction Polynomial R, String) -> Union(f1: OrderedCompletion Expression R, f2: List OrderedCompletion Expression R, fail: failed, pole: potentialPole)
integrate(f, x = a..b, "noPole") returns the integral of f(x)dx from a to b. If it is not possible to check whether f has a pole for x between a and b (because of parameters), then this function will assume that f has no such pole. Error: if f has a pole for x between a and b or if the last argument is not “noPole”.