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

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Presentation transcript:

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

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

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

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?

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

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:

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

Find