Integration by Parts/Corollary

Corollary to Integration by Parts
Let $u$ and $v$ be real functions which are integrable on their domain.

Then:
 * $\ds \int u v \rd x = \paren {\int u \rd x} v - \int \paren {\int u \rd x} \dfrac {\d v} {\d x} \rd x$

Proof
From Integration by Parts:


 * $(1): \quad \ds \int u \dfrac {\d v} {\d x} \rd x = u v - \int v \dfrac {\d u} {\d x} \rd x$

In $(1)$, let us make the identifications:

This gives: