Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.2 Exercises - Page 334: 8


$-\frac{1}{3}$$\ln|5-x^{3}|$ + C

Work Step by Step

$\int\frac{x^{2}}{5-x^{3}} dx $ Let $u =5-x^{3}$ $\frac{du}{dx}$ = $-3x^{2}$ $\frac{du}{-3x^{2}}$ = $dx$ Substitute $u$ and $dx$ into the original equation $\int\frac{x^{2}}{u}\frac{du}{-3x^{2}}$ = $\int\frac{x^{2}}{-3x^{2}}\frac{1}{u} du$ = $\int\frac{1}{-3}\frac{1}{u} du$ = $-\frac{1}{3}$$\int\frac{1}{u} du$ = $-\frac{1}{3}$$\ln|u|$ + C Since $u =5-x^{3}$, substituting it back will give you $-\frac{1}{3}$$\ln|5-x^{3}|$ + C
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