Solution Found!
Repeated linear factors Evaluate the following
Chapter 4, Problem 25E(choose chapter or problem)
Repeated linear factors Evaluate the following integrals.
\(\int \frac{x-5}{x^{2}(x+1)} d x\)
Questions & Answers
QUESTION:
Repeated linear factors Evaluate the following integrals.
\(\int \frac{x-5}{x^{2}(x+1)} d x\)
ANSWER:Step 1 of 4
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.