# RationalFunctionDefiniteIntegration RΒΆ

- R: Join(EuclideanDomain, Comparable, CharacteristicZero, RetractableTo Integer, LinearlyExplicitOver Integer)

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”.