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Substitution Rule

Substitution Rule. Substitution Rule. Basic Problems. Example (1). Example (2). Example (3). Example (4). Example (5). Example (6). Example (7). Example (8). Example (9). Substitution Rule. Definite Integral Case. Example (1). Example (2). Example (3). Substitution Rule.

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Substitution Rule

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  1. Substitution Rule

  2. Substitution Rule Basic Problems

  3. Example (1)

  4. Example (2)

  5. Example (3)

  6. Example (4)

  7. Example (5)

  8. Example (6)

  9. Example (7)

  10. Example (8)

  11. Example (9)

  12. Substitution Rule Definite Integral Case

  13. Example (1)

  14. Example (2)

  15. Example (3)

  16. Substitution Rule More Challenging Problems

  17. Example (1)

  18. Method 1

  19. Note that the first method can be used to find the integral of any function of the form:f(x) = x(2n-1) (axn+b)kfor any positive integer n and any real number k (where k is not -1) as the following examples show:

  20. Example (2)

  21. In all of the first three examples, we let:u = 2x+ 4and so:du = 2dx → dx = du/2andx = (u - 4)/2

  22. In the fourth example, we let:u = 2x2+ 4and so:du = 4xdx → dx = du/4xandx2 = (u - 4)/2

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