Answer
$$\int \frac{(\ln x)^3}{x}dx=\frac{(\ln x)^4}{4}+C$$
Work Step by Step
$$A=\int \frac{(\ln x)^3}{x}dx$$
We set $u=\ln x$. We then have $$du=\frac{dx}{x}$$
Therefore, $$A=\int u^3du$$ $$A=\frac{u^4}{4}+C$$ $$A=\frac{(\ln x)^4}{4}+C$$
University Calculus: Early Transcendentals (3rd Edition)
by Hass, Joel R.; Weir, Maurice D.; Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0321999584
ISBN 13:
978-0-32199-958-0
Chapter 8 - Section 8.1 - Integration by Parts - Exercises - Page 427: 36
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