# IntegrationTools(R, F)ΒΆ

- R: Comparable
- F: FunctionSpace R

Tools for the integrator Author: Manuel Bronstein Date Created: 25 April 1990 Keywords: elementary, function, integration.

- intPatternMatch: (F, Symbol, (F, Symbol) -> IntegrationResult F, (F, Symbol) -> Union(Record(special: F, integrand: F), failed)) -> IntegrationResult F if R has GcdDomain and F has LiouvillianFunctionCategory and F has ElementaryFunctionCategory and R has PatternMatchable Integer and R has ConvertibleTo Pattern Integer
`intPatternMatch(f, x, int, pmint)`

tries to integrate`f`

first by using the integration function`int`

, and then by using the pattern match intetgration function`pmint`

on any remaining unintegrable part.

- ksec: (Kernel F, List Kernel F, Symbol) -> Kernel F
`ksec(k, [k1, ..., kn], x)`

returns the second top-level`ki`

after`k`

involving`x`

.

- mkPrim: (F, Symbol) -> F if R has GcdDomain and F has ElementaryFunctionCategory
`mkPrim(f, x)`

makes the logs in`f`

which are linear in`x`

primitive with respect to`x`

.

- removeConstantTerm: (F, Symbol) -> F if R has IntegralDomain
`removeConstantTerm(f, x)`

returns`f`

minus any additive constant with respect to`x`

.

- union: (List Kernel F, List Kernel F) -> List Kernel F
`union(l1, l2)`

returns set-theoretic union of`l1`

and`l2`

.