Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 7 - Techniques of Integration - Review - Exercises - Page 577: 1


$$\frac{7}{2} +\ln 2$$

Work Step by Step

Given $$\int_{1}^{2} \frac{(x+1)^{2}}{x} d x$$ Since \begin{align*} \int_{1}^{2} \frac{(x+1)^{2}}{x} d x&=\int_{1}^{2} \frac{ x^2+2x+1 }{x} d x\\ &=\int_{1}^{2} \left( x+2+\frac{1 }{x} \right)d x\\ &=\frac{1}{2}x^2+2x+\ln x\bigg|_{1}^2\\ &=\frac{3}{2} +2+\ln 2\\ &=\frac{7}{2} +\ln 2 \end{align*}
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