### 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]