ElementaryFunctionDefiniteIntegration(R, F)

defintef.spad line 1 [edit on github]

• R : Join(PolynomialFactorizationExplicit, Comparable, CharacteristicZero, RetractableTo(Integer), LinearlyExplicitOver(Integer))
• F : Join(TranscendentalFunctionCategory, PrimitiveFunctionCategory, AlgebraicallyClosedFunctionSpace(R))

ElementaryFunctionDefiniteIntegration provides functions to compute definite integrals of elementary functions.

innerint : (F, Symbol, OrderedCompletion(F), OrderedCompletion(F), Boolean) -> Union(:(f1, OrderedCompletion(F)), :(f2, List(OrderedCompletion(F))), :(fail, "failed"), :(pole, "potentialPole"))

innerint(f, x, a, b, ignore?) should be local but conditional

integrate : (F, SegmentBinding(OrderedCompletion(F))) -> Union(:(f1, OrderedCompletion(F)), :(f2, List(OrderedCompletion(F))), :(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 : (F, SegmentBinding(OrderedCompletion(F)), String) -> Union(:(f1, OrderedCompletion(F)), :(f2, List(OrderedCompletion(F))), :(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".