Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 8: Techniques of Integration - Section 8.1 - Using Basic Integration Formulas - Exercises 8.1 - Page 448: 1

Answer

$\ln5$

Work Step by Step

$$16\int_{0}^{1}\frac{x}{8x^{2}+2}dx=8\int_{0}^{1}\frac{d(x^{2})}{8x^{2}+2}$$ $$=\int_{0}^{1}\frac{d(8x^{2}+2)}{8x^{2}+2}$$ $$=\left | \ln(8x^{2}+2) \right |_{0}^{1}$$ $$=\ln10-\ln2$$ $$=\ln5$$
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