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Integration by parts : ウィキペディア英語版
Integration by parts

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 transform the antiderivative of a product of functions into an antiderivative for which a solution can be more easily found. The rule can be derived in one line simply by integrating the product rule of differentiation.
If and , while and , then integration by parts states that:
:\int u(x) v'(x) \, dx = u(x) v(x) - \int v(x) \, u'(x) dx
or more compactly:
:\int u \, dv=uv-\int v \, du.\!
More general formulations of integration by parts exist for the Riemann–Stieltjes integral and Lebesgue–Stieltjes integral. The discrete analogue for sequences is called summation by parts.
==Theorem==


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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