Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 7 - Principles Of Integral Evaluation - 7.2 Integration By Parts - Exercises Set 7.2 - Page 498: 40



Work Step by Step

By using $u=ln(x)$ and $dv=x^{3}$, $du=\frac{dx}{x}$ and $v=\frac{1}{4}x^{4}$. This means that $$\int{udv}=uv-\int{vdu}=\frac{1}{4}x^{4}ln(x)-\int{\frac{x^{4}}{4x}}dx$$ The newly formed integral $\int{vdu}$ can now be solved using power rule after dividing $x^4$ by $4x$.
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