Now that we have finished our study of techniques of integration, we take stock of everything we have learned, and summarize when to use which method, and what to do if none of our methods (seem to) work: In those cases, we can use a Table of Integrals or a Computer Algebra System (CAS) like WolframAlpha.com or Sage (on CoCalc.com) to help us.

Basic Learning Objectives

These are the tasks you should be able to perform with reasonable fluency when you arrive at your next class meeting. Important new vocabulary words are indicated in italics.

  • Given an indefinite integral, recognize whether it is best evaluated with a Substitution, Integration by Parts, Partial Fraction Decomposition, Trigonometric Substitution, Weierstrass Substitution, or neither, and justify your choice.

  • Be proficient with asking Integral-Calculator.com or WolframAlpha to calculate derivatives and integrals.

  • (Optional:) Be proficient with asking Sage (on CoCocalc.com) to calculate derivatives and integrals.

Advanced Learning Objectives

In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:

  • Given an indefinite integral, make an informed and justified choice for the best approach to calculate it.

To prepare for class


Charles Fortin Avatar Charles Fortin
Gabriel Indurskis Avatar Gabriel Indurskis


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