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Integration by Substitution (Section 4-5)

Learn how to use integration by substitution to rewrite functions and find their indefinite integrals. Includes examples and explanations.

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Integration by Substitution (Section 4-5)

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  1. Integration by Substitution(Section 4-5)

  2. The chain rule allows us to differentiate a wide variety of functions, but we are able to find antiderivatives for only a limited range of functions. We can sometimes use substitution to rewrite functions in a form that we can integrate.

  3. Find the indefinite integral. Example 1: The variable of integration must match the variable in the expression. Don’t forget to substitute the value for u back into the problem!

  4. Find the indefinite integral. Example 2

  5. Find the indefinite integral. Example 3

  6. Find the indefinite integral. Example 4: Solve for dx.

  7. Find the indefinite integral. Example 5:

  8. Find the indefinite integral. One of the clues that we look for is if we can find a function and its derivative in the integrand. The derivative of is . Note that this only worked because of the 2x in the original. Many integrals can not be done by substitution. Example 6:

  9. Find the indefinite integral. We solve for because we can find it in the integrand. Example 7:

  10. Find the indefinite integral. Example 8:

  11. Example 9: Find the indefinite integral by the method shown in Example 5.

  12. HW #1 pg 304 (1-33odd)

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