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8.2 Integration By Parts

8.2 Integration By Parts. That is, what to do when integrating a product. There are times that the tricks we have learned so far won’t work. What happens when you need to integrate a product? That is, something that fits the pattern Such as. What is the derivative of a product?.

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8.2 Integration By Parts

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  1. 8.2 Integration By Parts That is, what to do when integrating a product

  2. There are times that the tricks we have learned so far won’t work. What happens when you need to integrate a product? That is, something that fits the pattern Such as

  3. What is the derivative of a product?

  4. Integration by Parts Therefore, you will let f(x)=u and g(x)=dv. Remember: we are looking at the form

  5. How do I know which is u and which is dv? A good rule of thumb (although NOT always a guarantee) is this: u = the one that could differentiate to 0 dv = the one that can be integrated easily. This isn’t a guarantee, but it at least gives a starting place.

  6. Examples

  7. Now that last problem was quite long. There is a shortcut, called Tabular Integration, which can be used when many repetitions are needed to get to f(x) = 0 and the integration of g(x) is easy. Simply list in 2 columns the sequential derivatives of f(x) next to the sequential integrations of g(x). Use diagonal arrows (with + - + -) to connect each f(x) derivative with each g(x) integration. See next problem.

  8. + - + -

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