One of the strongest tools in integration is u-substitution, particularly when working with natural logs. In this step-by-step video presentation, a pleasant-voiced instructor walks through a number of integration problems. She begins with the basic application of the natural log as an anti-derivative and progresses through a number of more complicated examples, including one with polynomial synthetic division. A great tool to explain or re-explain how u-substitution and natural logs are linked in indefinite integration. 

Concepts

logarithms natural, antiderivatives, logarithmic functions, differential calculus

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Additional Tags

math

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Instructional Ideas

• Perfect for assigning as homework in a flipped-classroom model
• Would make a good re-teaching video for individual remediation

Classroom Considerations

• Consider creating a worksheet with the worked problems and having the class work along with the video
• Make this a whole lesson by pausing the video and allowing the class some time for working and collaboration with each problem
• While video is not YouTube linked, it does require streaming Internet access 

Pros

• Carefully worked examples, with the ability to pause and rewind as needed for clarification
• Examples scaffold in difficulty and complexity
• U-substitution and using the natural log as an anti-derivative clearly identified in each problem

Cons

• No accompanying student notes or worksheet

Common Core

HSF-BF.B.5 HSF-LE.A.4 MP1 MP2 MP7