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Found in: Page 334

Essential Calculus: Early Transcendentals

Book edition 2nd
Author(s) James Stewart
Pages 830 pages
ISBN 9781133112280

Write out the form of the partial fraction decomposition of the function (as in Example 6). Do not determine the numerical values of the coefficients.(a)$$\frac{{{x^4} + 1}}{{{x^3} + 4{x^3}}}$$

$$\frac{A}{x} + \frac{B}{{{x^2}}} + \frac{C}{{{x^3}}} + \frac{{Dx + E}}{{{x^2} + 4}}$$ is the final answer.

See the step by step solution

Step 1: Given Data

$$\frac{{{x^4} + 1}}{{{x^3} + 4{x^3}}}$$

$$= \frac{{{x^4} + 1}}{{{x^3}\left( {{x^2} + 4} \right)}}$$

Step 2: Calculation of partial fraction.

$$\frac{{{x^4} + 1}}{{{x^3}\left( {{x^2} + 4} \right)}} = \frac{A}{x} + \frac{B}{{{x^2}}} + \frac{C}{{{x^3}}} + \frac{{Dx + E}}{{{x^2} + 4}}$$

Hence, $$\frac{A}{x} + \frac{B}{{{x^2}}} + \frac{C}{{{x^3}}} + \frac{{Dx + E}}{{{x^2} + 4}}$$ is the final answer.