Strategy for Integration: Examples 2 to 5

in mathematics •  2 months ago  (edited)

In this video I go over more examples on illustrating how to apply the 4-step strategy for integration when deciding which integration technique to use. I go over 4 examples on just how to view and apply the strategy but I don't actually evaluate the integrals. This is a very useful technique to follow and these examples show the different types of integrals and integration techniques to use.

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Strategy for Integration: Examples 2 to 5

Strategy for Integration Example 2 to 5.jpeg

Recap from my earlier video on the 4-step integration strategy that I covered:

Four-Step Integration Strategy

  1. Simplify the Integrand if Possible
  2. Look for an Obvious Substitution
  3. Classify the Integrand According to its Form
  4. Try Again

Now in the following examples, I will go over the process of selecting a method to use to integrate but will not fully work out the integral:

Example 2:

The integral is now a product of u and a transcendental function eu and thus it can be integrated by parts.

Example 3:

No algebraic simplification or substitution is obvious so steps 1 and 2 don't apply.

The integrand is a rational function so we can solve this using the method of partial fractions.

Example 4:

Example 5:

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