Integration Properties

Sum rule

$\displaystyle \int{\Big(f(x)+g(x)\Big)\,}dx$ $\,=\,$ $\displaystyle \int{f(x)\,}dx$ $+$ $\displaystyle \int{g(x)\,}dx$

Difference rule

$\displaystyle \int{\Big(f(x)-g(x)\Big)\,}dx$ $\,=\,$ $\displaystyle \int{f(x)\,}dx$ $-$ $\displaystyle \int{g(x)\,}dx$

Integration by Parts

$\displaystyle \int udv$ $\,=\,$ $uv$ $-$ $\displaystyle \int vdu$