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The transformation, may be achieved purely by integration by substitution.
For this and other reasons, integration by substitution is an important tool for mathematicians.
In geometric measure theory, integration by substitution is used with Lipschitz functions.
This result can be established for n a natural number by induction, or using integration by substitution.
Integration by substitution can be derived from the fundamental theorem of calculus as follows.
The chain rule and integration by substitution rules are especially easy to express here, because the "d" terms cancel:
In calculus, integration by substitution, also known as u-substitution, is a method for finding integrals.
Integration by substitution, also known as "udu substitution"
Integration by substitution:
(One could view the method of integration by substitution as a major justification of Leibniz's notation for integrals and derivatives.)
The reduction formula can be derived using any of the common methods of integration, like integration by substitution, integration by parts, integration by trigonometric substitution, integration by partial fractions, etc.
Formally, the differential appearing under the integral behaves exactly as a differential: thus, the integration by substitution and integration by parts formulae for Stieltjes integral correspond, respectively, to the chain rule and product rule for the differential.
