Summary of Integration by Parts

Essential Concepts

  • The integration-by-parts formula allows the exchange of one integral for another, possibly easier, integral.
  • Integration by parts applies to both definite and indefinite integrals.

Key Equations

  • Integration by parts formula

    [latex]\displaystyle\int udv=uv-\displaystyle\int vdu[/latex]
  • Integration by parts for definite integrals

    [latex]{\displaystyle\int }_{a}^{b}udv={uv|}_{a}^{b}-{\displaystyle\int }_{a}^{b}vdu[/latex]

Glossary

integration by parts
a technique of integration that allows the exchange of one integral for another using the formula [latex]{\displaystyle\int}udv=uv-{\displaystyle\int}vdu[/latex]