= Integration by Parts =

'''Integration by parts''' is a method for solving complex [[Calculus/Integral|integrals]].

<<TableOfContents>>

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== Description ==

Given a complex integral, refactor it as ''∫udv''. The problem can then be rewritten as:

{{attachment:formula.svg}}

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== Derivation ==

The formula derives from the [[Calculus/Derivative#Product_Rule|product rule]]:

{{attachment:prod1.svg}}

Take the integral of both sides and breaking up the RHS into a sum of two integrals. Allowing for the improper notation, this can be written as:

{{attachment:prod2.svg}}

The LHS obviously reduces to ''uv''. The RHS further simplifies by rewriting in terms of the derivatives, creating [[Calculus/Differential|differentials]].

{{attachment:prod3.svg}}

This trivially can be rewritten into the familiar form above.



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CategoryRicottone