Use the Substitution 8 *4(In x)³ 1 b n Formula, Sf(g(x)) • gʻ a g(b) (x)) • g'(x) dx = [ f(u) du where g(x) = u, to evaluate the following integral. g(a)
Use the Substitution 8 *4(In x)³ 1 b n Formula, Sf(g(x)) • gʻ a g(b) (x)) • g'(x) dx = [ f(u) du where g(x) = u, to evaluate the following integral. g(a)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![Use the Substitution Formula, \(\int_{a}^{b} f(g(x)) \cdot g'(x) \, dx = \int_{g(a)}^{g(b)} f(u) \, du \text{ where } g(x)=u,\) to evaluate the following integral.
\[
\int_{1}^{8} \frac{(4 \ln x)^3}{x} \, dx
\]
\[
\int_{1}^{8} \frac{(4 \ln x)^3}{x} \, dx = \boxed{\phantom{()} \text{(Type an exact answer.)}}
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Transcribed Image Text:Use the Substitution Formula, \(\int_{a}^{b} f(g(x)) \cdot g'(x) \, dx = \int_{g(a)}^{g(b)} f(u) \, du \text{ where } g(x)=u,\) to evaluate the following integral.
\[
\int_{1}^{8} \frac{(4 \ln x)^3}{x} \, dx
\]
\[
\int_{1}^{8} \frac{(4 \ln x)^3}{x} \, dx = \boxed{\phantom{()} \text{(Type an exact answer.)}}
\]
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