Indefinite integral

An indefinite integral is the family of functions whose derivatives equal a given function, conventionally written with an arbitrary constant of integration.

Antiderivative: A function whose derivative equals a specified function. Each member of an indefinite integral is an antiderivative of its integrand.
Derivative: The instantaneous rate of change of a function, defined by a limit of difference quotients. An indefinite integral reverses differentiation by seeking functions with a specified derivative.
Initial value problem: A differential equation together with conditions specifying a solution at one or more points. An initial condition selects one function from the indefinite integral’s family.
Numerical integration: Methods for approximating the value of a definite integral using finite computations. It approximates endpoint-defined values rather than expressing an antiderivative family.
Constant of integration: An arbitrary constant added to an antiderivative to represent all functions with the same derivative. It distinguishes the full family of antiderivatives from a single one.
Differential operator: An operator that maps functions to expressions involving their derivatives. Differentiation is the operator that indefinite integration seeks to invert.
Separable differential equation: A differential equation whose variables can be separated into expressions involving one variable each. Solving it often requires integrating both sides without fixed endpoints.
Differentiation: The process of finding a function's derivative. It is the operation reversed by indefinite integration.
Power rule: A differentiation rule stating that the derivative of xⁿ is n xⁿ⁻¹. Reversing this rule gives a basic method for finding many indefinite integrals.
Function: A rule that assigns each input in a domain exactly one output. Both the integrand and its antiderivatives are functions.

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