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In this section, we will look at integrating more complicated rational functions using the technique of partial fraction decomposition.

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Presentation on theme: "In this section, we will look at integrating more complicated rational functions using the technique of partial fraction decomposition."— Presentation transcript:

1 In this section, we will look at integrating more complicated rational functions using the technique of partial fraction decomposition.

2 The integral seems difficult to evaluate. The integral is not.

3 The integral seems difficult to evaluate. The integral is not. They are the same integral!

4 The integral seems difficult to evaluate. The integral is not. They are the same integral! How do we convert the first integral into the second?

5

6 Consider the function. By going through the long division process, we can rewrite this as:

7 All polynomials can be written as a product of linear and irreducible quadratic factors raised to powers. Thus, all partial fractions will have one of two forms:

8 1. Make the integrand proper 2. Factor the denominator completely 3. Write as a sum of partial fractions with undetermined numerator coefficients 4. Algebraically find the value of these coefficients. 5. Antidifferentiate the result fraction by fraction

9 Find

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