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Integration by substitution

Definitions
Derivative (generalizations) Differential infinitesimal of a function total
Concepts
Differentiation notation Second derivative Implicit differentiation Logarithmic differentiation Related rates Taylor's theorem
Rules and identities
Sum Product Chain Power Quotient L'Hôpital's rule Inverse General Leibniz Faà di Bruno's formula Reynolds

Definitions
Lists of integrals Integral transform Leibniz integral rule
Antiderivative Integral (improper) 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 method) Changing order Reduction formulae Differentiating under the integral sign Risch algorithm

Convergence tests
Geometric (arithmetico-geometric) Harmonic Alternating Power Binomial Taylor
Summand limit (term test) Ratio Root Integral Direct comparison Limit comparison Alternating series Cauchy condensation Dirichlet Abel

In calculus, integration by substitution, also known as u-substitution, reverse chain rule or change of variables,^[1] is a method for evaluating integrals and antiderivatives. It is the counterpart to the chain rule for differentiation, and can loosely be thought of as using the chain rule "backwards."

^ Swokowski 1983, p. 257

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تكامل بالتعويض Arabic Integració per canvi de variable Catalan Substituční metoda (integrování) Czech Integration durch Substitution German Métodos de integración#Método de integración por sustitución Spanish Sijoitusmenetelmä Finnish Intégration par changement de variable French Integración por cambio de variábeis GL אינטגרציה באמצעות החלפת משתנים HE प्रतिस्थापन द्वारा समाकलन HI

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