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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.4 - Problem 9e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.4 - Problem 9e

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# Simple linear factors Evaluate the following integrals. ISBN: 9780321570567 2

## Solution for problem 9E Chapter 7.4

Calculus: Early Transcendentals | 1st Edition

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Problem 9E

Simple linear factors Evaluate the following integrals.

$$\int \frac{d x}{(x-1)(x+2)}$$

Step-by-Step Solution:

Step 1 of 3

Proper fraction definition ; In a rational fraction , if the degree of f(x) < the degree of g(x) , then the rational fraction is called a proper fraction.

The sum of two proper fractions is a proper fraction.

Example; Partial fractions Depending upon the nature of factors of Denominator ;

1) When the denominator has non-repeated linear factors;

A non - repeated linear factor (x-a) of denominator corresponds a partial fraction of the form , where A is a constant to be determined’

If g(x) = (x-a)(x-b)(x-c)............(x-n), then we assume that = + + +...............+ Where A, B, C,............N are constants which can be determined by equating the numerator of L.H.Sto the numerator of R.H.S , and substituting x = a,b ,c ….n.

Step 2 of 3

Step 3 of 3

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Simple linear factors Evaluate the following integrals.