Integration By Parts - Several Examples.

THE FORMULA FOR INTEGRATION BY PARTS

Let $u(x), v(x)$ be two functions of $x$.
$$\int u(x) v'(x)\,dx=u(x) v(x)-\int u'(x) v(x)\,dx$$
or the 'quick formula' 
$$\int uv'=uv-\int u'v$$

[Remark: This is like the product rule for derivatives]