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Q3E

Expert-verifiedFound in: Page 334

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.

\(\frac{{{x^4} + 1}}{{{x^3} + 4{x^3}}}\)

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

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

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

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