Calculus 8th Edition

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

Chapter 7 - Techniques of Integration - 7.1 Integration by Parts - 7.1 Exercises: 2

Answer

$\int\sqrt{x}\ln{x}dx$

Work Step by Step

Let $u=\ln{x}$ and $dv=\sqrt{x}dx$ then $du=\frac{1}{x}dx$ and $v=\frac{2}{3}x^\frac{3}{2}$ then $\int\sqrt{x}\ln{x}dx=\sqrt{x}\ln{x}-\int\frac{2}{3}x^\frac{3}{2}\times\frac{1}{x}dx=\sqrt{x}\ln{x}-\int\frac{2}{3}x^\frac{1}{2}dx$ \begin{equation*}=\sqrt{x}\ln{x}-\frac{4}{9}x^\frac{3}{2}+C\end{equation*}
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