Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 5 - The Integral - 5.3 The Indefinite Integral - Exercises: 3

Answer

$\int(2x^4 -24x^2 +12x^{-1}) dx = \frac{2}{5}x^5 - 8x^3 + 12ln|x| + C$

Work Step by Step

Anti-differentiating: $\int(2x^4 -24x^2 +12x^{-1}) dx = 2\times\frac{1}{5}x^5 -24 \times\frac{1}{3}x^3 + 12ln|x| + C = \frac{2}{5}x^5 - 8x^3 + 12ln|x| + C$ Checking with differentiation: $(\frac{2}{5}x^5 - 8x^3 + 12ln|x| + C)' = \frac{2}{5} \times5 x^4-8\times3x^2 + 12\times\frac{1}{x} = 2x^4 -24x^2 + 12x^{-1}$
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