6.3 Integration By Parts Badlands, South Dakota Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 1993

6.3 Integration By Parts Start with the product rule: This is the Integration by Parts formula.

The Integration by Parts formula is a “product rule” for integration. u differentiates to zero (usually). dv is easy to integrate. Choose u in this order: LIPET Logs, Inverse trig, Polynomial, Exponential, Trig

Example 1: polynomial factor LIPET

Example: logarithmic factor LIPET

This is still a product, so we need to use integration by parts again. Example 4: LIPET

Example 5: LIPET This is the expression we started with!

Example 6: LIPET

Example 6:This is called “solving for the unknown integral.” It works when both factors integrate and differentiate forever.

A Shortcut: Tabular Integration Tabular integration works for integrals of the form: where: Differentiates to zero in several steps. Integrates repeatedly.

Compare this with the same problem done the other way:

Example 5: LIPET This is easier and quicker to do with tabular integration!

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