Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 8 - Techniques of Integration - 8.6 Strategies for Integration - Exercises - Page 431: 50


$$\frac{1}{8}x^8+\frac{1}{4}x^4 +\frac{1}{4}\ln|x^4-1|+C$$

Work Step by Step

Given $$\int \frac{x^{11}}{x^{4}-1} d x$$ Use long division \begin{align*} \int \frac{x^{11}}{x^{4}-1} d x&= \int \left(x^7+x^3+\frac{x^3}{x^4-1}\right)dx\\ &= \frac{1}{8}x^8+\frac{1}{4}x^4 +\frac{1}{4}\ln|x^4-1|+C \end{align*}
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