In
calculus, the
indefinite integral of a given function (i.e., the set of all
antiderivatives of the function) is only defined
up to an additive constant, the
constant of integration. This constant expresses an ambiguity inherent in the construction of antiderivatives. If a function
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=751)
is defined on an
interval and
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=3062)
is an antiderivative of
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=751)
, then the set of
all antiderivatives of
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=751)
is given by the functions
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=611)
, where
C is an arbitrary constant. The constant of integration is sometimes omitted in
lists of integrals for simplicity.