DE-BOOK Breaking Down the Integration by Parts Formula

Subsection B.2.1 Breaking Down the Integration by Parts Formula

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

\int u d v = u v - \int v d u .

Here’s how it works:

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