The Constant of Integration: Why the Most General Antiderivative Needs + C

Two functions with the same derivative on an interval differ by a constant, so every antiderivative of f is F(x) + C and the constant has to come from an extra condition. The rule only holds on an interval, which is why 1/x can carry two different constants.

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Find the Most General Antiderivative or Indefinite Integral of 8 sec x (sec x − 4 tan x)