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Q13E

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Essential Calculus: Early Transcendentals
Found in: Page 306
Essential Calculus: Early Transcendentals

Essential Calculus: Early Transcendentals

Book edition 2nd
Author(s) James Stewart
Pages 830 pages
ISBN 9781133112280

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Short Answer

Evaluate the indefinite integral\(\int {\frac{{dx}}{{5 - 3x}}} \).

The indefinite integral value of the given equation is\(\int {\frac{{dx}}{{5 - 3x}}} = - \frac{1}{3}\ln (5 - 3x) + c\).

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Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1 Definition of the indefinite integral

An integral that has no upper bound and no lower bound is known as indefinite integral.

Step 2: Expand the number of variables in the equation.

Given:\(I = \int {\frac{{dx}}{{5 - 3x}}} \)

Let \(u = 5 - 3x\)

\(\begin{aligned}{c}du &= - 3dx\\dx &= - \frac{{du}}{3}\end{aligned}\)

Substitute\(5 - 3x\)and \( - 3dx\)for \({\rm{u}}\) and \({\rm{du}}\)

\(I = - \frac{1}{3}\int {\frac{1}{u}} \)

Step 3: Evaluate the equation.

Integrate

\(I = - \frac{1}{3}\ln u + c\)

Substitute \(u = 5 - 3x\)

\(I = - \frac{1}{3}\ln (5 - 3x) + c\)

Therefore, the indefinite integral value of the given equation is\(\int {\frac{{dx}}{{5 - 3x}}} = - \frac{1}{3}\ln (5 - 3x) + c\).

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