Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 8: Techniques of Integration - Section 8.5 - Integration of Rational Functions by Partial Fractions - Exercises 8.5 - Page 475: 3



Work Step by Step

If the form of the rational function is $\frac{px+q}{(x-a)^{2}}$, then the form of the partial fraction is $\frac{A}{x-a}+\frac{B}{(x-b)^{2}}$. Therefore, $\frac{x+4}{(x+1)^{2}}=\frac{A}{x+1}+\frac{B}{(x+1)^{2}}$ A and B are to be determined. x+4= A(x+1)+B Equating the coefficients of x and the constant term, we get A+B=4 and A=1. Then, B=4-1=3. Therefore, $\frac{x+4}{(x+1)^{2}}=\frac{1}{x+1}+\frac{3}{(x+1)^{2}}$
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