\(\left\{ \begin{array}{l}du = g'\left( x \right)dx\\v = \int {h\left( x \right)dx} \end{array} \right.\)

\(\left\{ \begin{array}{l}du = g\left( x \right)dx\\v = \int {h\left( x \right)dx} \end{array} \right.\)           

\(\left\{ \begin{array}{l}du = \int {g\left( x \right)dx} \\v = h\left( x \right)\end{array} \right.\)  

\(\left\{ \begin{array}{l}du = g'\left( x \right)dx\\v = h\left( x \right)\end{array} \right.\)