Indefinite integral

An indefinite integral gives the antiderivative F of a function f, which is any function whose derivative is f, plus an arbitrary constant C. It is used to find families of functions with a given derivative.

\int f(x)\,\mathrm{d}x = F(x) + C \quad \text{where } F'(x) = f(x)

What the symbols mean

the integrand, the function being integrated
an antiderivative of f, so that F'(x) = f(x)
the constant of integration, an arbitrary real number
the variable of integration

About this formula

  • FieldMathematics
  • TopicIntegral calculus
  • LevelHigh school
  • Also calledindefinite integration, antiderivative, integral of a function, constant of integration, indefinite integral formula, antiderivative formula
  • SourceWikidata Q8437543

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