DE-BOOK Breaking Down the Integration by Parts Formula

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Subsection B.2.1 Breaking Down the Integration by Parts Formula

Let’s break down the formula for integration by parts:

\begin{equation*} \int u\, dv = uv - \int v\, du \text{.} \end{equation*}

Here’s how it works:

$u$ is a function that you choose to differentiate (it should get simpler when differentiated).
$dv$ is a part of the integrand that you choose to integrate (it should get easier when integrated).
$uv$ is the new term after applying the product of $u$ and the integral of $dv\text{.}$
$\int v\, du$ is the remaining integral, now simpler than the original.

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