II. Integrating Improper Rational Functions
Although the method of partial fractions only applies to proper rational functions, an improper rational function can be integrated by performing long division (or synthetic division). If is a rational function where and are polynomial functions and the degree of is greater than or equal to the degree of , then by long division, where is a proper rational fraction. Since is a proper rational function, it can be decomposed into partial fractions.
Example 12: Find .
. Thus, .
.
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