6.3– Integration By Parts

I. Evaluate the following indefinite integral Any easier than the original???

The choice of u and dv are very important!!!! The idea is to let dv be the easier function to integrate, as well as letting u be the function that produces a simpler derivative.

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

EX. 2 -

EX. 3 -

II. Tabular Integration - “Tic – Tac – Toe!” EX. 1 -

By Tables

EX. 2 -

TABLES ONLY WORK FOR REPEATED INTEGRATION BY PARTS WHEN ONE OF THE FUNCTIONS DERIVATIVES EVENTAULLY EQUALS 0!!!!!!!!!

For example…

EX. 3 - III. Repeated Integration by Parts