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Simple Integration Rules and Examples

Learn basic integration rules by manipulating integrals to fit rules. Find derivative of u, take antiderivatives, and replace u with original function. Follow examples to understand integration better. Practice problems included.

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Simple Integration Rules and Examples

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  1. F.1 Basic Integration Rules

  2. This Section is basically using your integration rules and manipulating whatever it is they are asking to fit one of the rules.

  3. Integral Rules made simple • Let u equal the most complicated part of your integral. • Then find derivative of u with respect to x • Then replace what you have in your integral • Take antiderivatives • Replace u with your original function

  4. Example 1 • dt Let u = t-9, so = 1, therefore du = dt • dt = dt (When finding antiderivative for power rule, add one and divide by that number) = 2 ( = + C =

  5. Example 2 • let u = 3x, so = 3, therefore du = 3dx = du = = 1/3 goes in front to account for the 3 in du = 3dx

  6. Example 3 • Let u = x² + 9. Then = 2x, therefore du = 2x dx • = = du = 2ln + C = 2ln(x²+9) + C

  7. Example 4 • Let u = ln(sinx) then du = dx = cotxdx • = + C • = [ln(sinx)]² + C

  8. HW • Pg. 522 • #15, 17, 21, 25, 29, 33

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