Indefinite Integration

The following quote from Reference [1] can clarify a lot of confusion about indefinite integration:

Today the process of finding the fluent of a given fluxion is called indefinite integration, or antidifferentiation, and the result of integrating a given function is its indefinite integral, or antiderivative (the “indefinite” refers to the existence of the arbitrary constant of integration).

It is possible to break down this quote.

First, the terms “fluent” and “fluxion” originate from Isac Newton. Consider a function $f(x)$. The indefinite integral is

$ \int f(x) dx $.

An indefinite integral has no limits of integration [2]. Note that $ \int f(x) dx $ is the antiderivative of $f(x)$, assuming the function $f(x)$ actually has an antiderivative.

The process of evaluating $ \int f(x) dx $ is called indefinite integration, which is the same process as antidifferentiation.

References

[1] Eli Maor. e, The Story of a Number. Princeton University Press. 1994.

[2] https://mathworld.wolfram.com/IndefiniteIntegral.html

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