Integration by parts formula
∫udv= uv-∫vdu
The integration by parts formula is a technique used in calculus to simplify the integration of some types of functions.
It states that the integral of the product of two functions, u(x) and v'(x), can be simplified as follows:
∫u(x)v'(x)dx = u(x)v(x) – ∫v(x)u'(x)dx
In this formula, u(x) and u'(x) represents the antiderivative of some function and v(x) and v'(x) represents the derivative of another function. To use this technique, we would select u(x) and v'(x) in such a way that the integral on the right side of the equation is easier to solve than the original integral.
In practice, we often choose u(x) to be the more complicated function in the original integral and v'(x) to be a simpler function which differentiates to give a term that appears in the integral.
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