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CHAPTER 28: Methods of Integration
Section 9: Integration by Partial Fractions: Nonrepeated Linear Factors
1. Write out the form of the partial fractions that would be use to perform the indicated
integration. Do not evaluate the constants.
a)
Note that the degree of the numerator is 1 and that of the denominator is 2.
Because degree of the denominator is higher, next step is to factor the
denominator.
b)
To find form of the partial fractions, first factor the denominator of the given
integrand.
c)
Notice no common factors in the numerator and denominator.
d)
For each factor ax + b that occurs once in the denominator, there will be a partial
fraction of the form
, where A is a constant.
e)
There are two linear factors, 2x and x + 2, in denominator, and they are different.
Means that there are two partial fractions.
f)
Therefore, the form of the partial fractions is
2. Integrate the given function
a)
In order to express the rational fraction f(x)/g(x) in terms of simpler partial
fractions, the degree of the numerator f(x) must be less than that of the
denominator g(x). The given integrand satisfies this condition.
b)
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