MATH138 Lecture 6: Week 3 (Lecture 6-8) Lecture Notes

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Lec 6 - integration by rational function by partial fraction. We will learn how to do this backwards so that the integrand can be rewritten as a sum of terms each of which we can be rewritten as a sum of terms each of which we can integrate. The function is proper rational function if the degree of the degree of . We only apply partial fractions on proper rational functions. If not proper then we long division to reduce it where are polynomials. Step 1: use long division to get a proper fraction. Case 1: the denominator is a product of distinct linear factors. The method i present is different from the textbook. Step 1: it is proper, no long division. Case 1: a product of distinct linear roots. Case 2: is a product of linear factors where some of the roots are repeated.

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