## 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

$\displaystyle\int udv=uv-\displaystyle\int vdu$
• Integration by parts for definite integrals

${\displaystyle\int }_{a}^{b}udv={uv|}_{a}^{b}-{\displaystyle\int }_{a}^{b}vdu$

## Glossary

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