Integration by Parts

Indefinite Integral

{(f g)}^{'} = f^{'} g + f g^{'}

Written as

\int f^{'} (x) g (x) ⅆ x = f (x) g (x) - \int f (x) g^{'} (x) ⅆ x

\int u ⅆ v = u v - \int v ⅆ u

\int_{𝒶}^{𝒷} f^{'} (x) g (x) ⅆ x = {f (x) g (x) |}_{𝒶}^{𝒷} - \int_{𝒶}^{𝒷} f (x) g^{'} (x) ⅆ x

\int_{𝒶}^{𝒷} u ⅆ v = {u v |}_{𝒶}^{𝒷} - \int_{𝒶}^{𝒷} v ⅆ u