RationalFunctionDefiniteIntegration(R)

defintrf.spad line 259 [edit on github]

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".