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: 32



Work Step by Step

Given $$\int \frac{x^{4}+1}{x^{2}+1} d x$$ By using long division, we get \begin{align*} \int \frac{x^{4}+1}{x^{2}+1} d x&=\int( x^{2}-1) d x+\int \frac{2}{x^{2}+1} d x\\ &=\frac{1}{3}x^3-x+2\tan^{-1}x+C \end{align*}
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