Integration by parts

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Graphical interpretation of the theorem. The pictured curve is parametrized by the variable t.

In calculus, and more generally in mathematical analysis, integration by parts is a theorem that relates the integral of a product of functions to the integral of their derivative and antiderivative. It is frequently used to find the antiderivative of a product of functions into an ideally simpler antiderivative. The rule can be derived in one line by simply integrating the product rule of differentiation.

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