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...
Related questions
Question
Please simplify this equation.
![The expression shown in the image is a mathematical equation involving logarithms. Here it is transcribed:
\[
\frac{1}{(2)(1) - (3)(-1)} \left(\frac{1}{-1} \ln |1 - x + 1| - \frac{3}{2} \ln |2x + 3|\right) + C
\]
**Explanation:**
This equation includes the following components:
- **Fraction**: The entire expression is multiplied by a fraction, \(\frac{1}{(2)(1) - (3)(-1)}\).
- **Logarithms**:
- The first term within the parentheses is \(\frac{1}{-1} \ln |1 - x + 1|\).
- The second term is \(- \frac{3}{2} \ln |2x + 3|\).
- **Constant of Integration**: The equation includes an arbitrary constant \(C\), which is typical in indefinite integrals.
This expression likely results from integrating a function and simplifying the terms. The use of absolute value symbols around expressions inside the logarithms (\(| \cdot |\)) ensures that the arguments are positive, as required by the domain of the natural logarithm function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F35e72b1b-10a7-4bb2-8cf5-54093c302f79%2F91b77a00-735f-40f1-ab51-6ffd534aa11f%2Fxop1sd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The expression shown in the image is a mathematical equation involving logarithms. Here it is transcribed:
\[
\frac{1}{(2)(1) - (3)(-1)} \left(\frac{1}{-1} \ln |1 - x + 1| - \frac{3}{2} \ln |2x + 3|\right) + C
\]
**Explanation:**
This equation includes the following components:
- **Fraction**: The entire expression is multiplied by a fraction, \(\frac{1}{(2)(1) - (3)(-1)}\).
- **Logarithms**:
- The first term within the parentheses is \(\frac{1}{-1} \ln |1 - x + 1|\).
- The second term is \(- \frac{3}{2} \ln |2x + 3|\).
- **Constant of Integration**: The equation includes an arbitrary constant \(C\), which is typical in indefinite integrals.
This expression likely results from integrating a function and simplifying the terms. The use of absolute value symbols around expressions inside the logarithms (\(| \cdot |\)) ensures that the arguments are positive, as required by the domain of the natural logarithm function.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning