PatternMatchIntegration(R, F)

intpm.spad line 1 [edit on github]

• R : Join(Comparable, RetractableTo(Integer), GcdDomain, LinearlyExplicitOver(Integer))
• F : Join(AlgebraicallyClosedField, TranscendentalFunctionCategory, FunctionSpace(R))

PatternMatchIntegration provides functions that use the pattern matcher to find some indefinite and definite integrals involving special functions and found in the literature.

pmintegrate : (F, Symbol, OrderedCompletion(F), OrderedCompletion(F)) -> Union(F, "failed") if R has ConvertibleTo(Pattern(Integer)) and F has SpecialFunctionCategory and R has PatternMatchable(Integer)

pmintegrate(f, x = a..b) returns the integral of f(x)dx from a to b if it can be found by the built-in pattern matching rules.

splitConstant : (F, Symbol) -> Record(const : F, nconst : F)

splitConstant(f, x) returns [c, g] such that f = c * g and c does not involve t.