Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 7 - Integration Techniques - 7.5 Partial Fractions - 7.5 Exercises - Page 549: 39

Answer

$$\frac{A}{{x - 1}} + \frac{B}{{{{\left( {x - 1} \right)}^2}}} + \frac{{Cx + D}}{{{x^2} + 1}}$$

Work Step by Step

$$\eqalign{ & \frac{{20x}}{{{{\left( {x - 1} \right)}^2}\left( {{x^2} + 1} \right)}} \cr & {\text{factors}} \cr & {\left( {x - 1} \right)^2}{\text{ and }}{x^2} + 1 \cr & {\left( {x - 1} \right)^2}{\text{, repeated linear factor}} \cr & {x^2} + 1,{\text{ irreductible quadratic factor}} \cr & \cr & {\text{the partial fraction decomposition is}} \cr & \frac{{20x}}{{{{\left( {x - 1} \right)}^2}\left( {{x^2} + 1} \right)}} = \frac{A}{{x - 1}} + \frac{B}{{{{\left( {x - 1} \right)}^2}}} + \frac{{Cx + D}}{{{x^2} + 1}} \cr} $$
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