CK12 Calculus - Single Variable

7. IntegrationTechniques................................................................................................................

Integrationby Substitution

Eachbasicrule of integrationthat you havestudiedso far was derivedfrom a correspondingdifferentiation
rule.Eventhoughyou havelearnedall the necessarytoolsfor differentiatingexponential,logarithmic,
trigonometric,and algebraicfunctions,your set of toolsfor integratingthesefunctionsis not yet complete.
In this chapterwe will exploredifferentwaysof integratingfunctionsand developseveralintegrationtechniques
that will greatlyexpandthe set of integralsto whichthe basicintegrationformulascan be applied.Before
we do that, let us reviewthe basicintegrationformulasthat you are alreadyfamiliarwith fromprevious
chapters.

1. The PowerRule :


2. The GeneralPowerRule :


3. The SimpleExponentialRule:


4. The GeneralExponentialRule:


5. The SimpleLog Rule:


6. The GeneralLog Rule:

It is importantthat you rememberthe aboverulesbecausewe will be usingthemextensivelyto solvemore
complicatedintegrationproblems.The skill that you needto developis to determinewhichof thesebasic