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Integration is the basic operation in integral calculus. While differentiation has straightforward rules by which the derivative of a complicated function can be found by differentiating its simpler component functions, integration does not, so tables of known integrals are often useful. This page lists some of the most common antiderivatives.
The slope field of () = +, showing three of the infinitely many solutions that can be produced by varying the arbitrary constant c.. In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral [Note 1] of a continuous function f is a differentiable function F whose derivative is equal to the original function f.
Lists of integrals; Integral transform; Leibniz integral rule; Definitions; Antiderivative; Integral Riemann integral; Lebesgue integration; Contour integration; Integral of inverse functions; Integration by; Parts; Discs; Cylindrical shells; Substitution (trigonometric, tangent half-angle, Euler) Euler's formula; Partial fractions (Heaviside's ...
Fundamental theorem of calculus; Integration by parts; Inverse chain rule method; Integration by substitution. Tangent half-angle substitution; Differentiation under the integral sign; Trigonometric substitution; Partial fractions in integration. Quadratic integral; Proof that 22/7 exceeds π; Trapezium rule; Integral of the secant function ...
The following is a list of integrals (antiderivative functions) of irrational functions. For a complete list of integral functions, see lists of integrals. Throughout this article the constant of integration is omitted for brevity.
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In calculus, and more generally in mathematical analysis, integration by parts or partial integration is a process that finds the integral of a product of functions in terms of the integral of the product of their derivative and antiderivative. It is frequently used to transform the antiderivative of a product of functions into an ...
Nonelementary antiderivatives can often be evaluated using Taylor series. Even if a function has no elementary antiderivative, its Taylor series can always be integrated term-by-term like a polynomial, giving the antiderivative function as a Taylor series with the same radius of convergence. However, even if the integrand has a convergent ...
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