This concept covers the power rule for antiderivatives: the antiderivative of xⁿ (for n ≠ −1) is x^(n+1)/(n+1) plus an arbitrary constant, reflecting that differentiation and antidifferentiation are inverse operations where the exponent moves in opposite directions (down when differentiating, up when antidifferentiating). It also relies on the linearity of antidifferentiation — the antiderivative of a sum is the sum of the antiderivatives, and constant multiples pass through unchanged — and establishes differentiation as the verification method for a proposed antiderivative. This belongs to single-variable calculus, within the theory of antiderivatives (indefinite integration) as the formal inverse of differentiation.
This concept covers the power rule for antiderivatives: the antiderivative of xⁿ (for n ≠ −1) is x^(n+1)/(n+1) plus an arbitrary constant, reflecting that differentiation and antidifferentiation are …