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”.