In calculus [Calculus], the constant of integration, often denoted by $$C$$ (or $$c$$), is a constant term added to an antiderivative [Antiderivative] of a function $$f(x)$$ to indicate that the indefinite integral of $$f(x)$$ (i.e., the set of all antiderivatives of $$f(x)$$), on a connected domain, is only defined up to an additive constant. This constant expresses an ambiguity inherent in the construction of antiderivatives.

More specifically, if a function $$f(x)$$ is defined on an interval, and $$F(x)$$(x)} is an antiderivative of $$f(x)$$, then the set of all antiderivatives of $$f(x)$$ is given by the functions $$F(x) + C$$, where $$C$$ is an arbitrary constant (meaning that any value of $$C$$ would make $$F(x) + C$$ a valid antiderivative). For that reason, the indefinite integral is often written as $$\int f(x)\,dx=F(x)+C$$, although the constant of integration might be sometimes omitted in lists of integrals for simplicity.

## Bibliography¶

“Constant of Integration.” 2022. Wikipedia, December. https://en.wikipedia.org/w/index.php?title=Constant_of_integration&oldid=1127887875.