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CHAPTER 28: Methods of Integration
Section 10: Integration by Partial Fractions: Other Cases
1.
Use the method of partial fraction decomposition to perform the required integration.
a)
Begin by factoring an x from the denominator of the integrand.
b)
Notice that this expression can be factored further.
c)
Next decompose the integrand into a sum of simpler fractions.
d)
Multiply both sides by
to clear the fractions.
e)
The above equation can be rewritten in the following way to prepare us to solve
for A, B, and C.
f)
Now we have an equation that is an identity if and only if coefficients of like
powers of x on both sides are equal. We can write following equations to show
this.
g)
Solve the equations for A, B, and C.
h)
Now substitute these values into the decomposed form of the integrand.
i)
Next rewrite the integral.
j)
Lastly evaluate the integrals to obtain the final answer.
2.
Integrate the given function.
a)
This function can be integrated either by first setting up the appropriate partial
fractions, or by using the substitution u = s – 2. If there is one repeated factor in
the denominator and it is the only factor present in the denominator, a substitution
can be easier and more convenient than using partial fractions. Since there is one

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CHAPTER 28 Methods of Integration Section 10 Integration by Partial Fractions Other Cases

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