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: 9

Answer

$\ln|x^{4}+3x|$ + C

Work Step by Step

$\int\frac{4x^{3}+3}{x^{4}+3x} dx $ Let $u =x^{4}+3x$ $\frac{du}{dx}$ = $4x^{3}+3$ $\frac{du}{4x^{3}+3}$ = $dx$ Substitute $u$ and $dx$ into the original equation $\int\frac{4x^{3}+3}{u}\frac{du}{4x^{3}+3}$ = $\int\frac{4x^{3}+3}{4x^{3}+3}\frac{1}{u} du$ = $\int\frac{1}{u} du$ = $\ln|u|$ + C Since $u =x^{4}+3x$, substituting it back will give you $\ln|x^{4}+3x|$ + C
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