In Exercises 112, use the Exponential Rule to find the indefinite integral. 2e dx 2x dx
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0.1
The Real Number Line and Order
0.2
Absolute Value and Distance on the Real Number Line
0.3
Exponents and Radicals
0.4
Factoring Polynomials
0.5
Fractions and Rationalization
1
Functions, Graphs, and Limits
1.1
The Cartesian Plane and the Distance Formula
1.2
Graphs of Equations
1.3
Lines in the Plane and Slope
1.4
Functions
1.5
Limits
1.6
Continuity
2
Differentiation
2.1
The Derivative and the Slope of a Graph
2.2
Some Rules for Differentiation
2.3
Rates of Change: Velocity and Marginals
2.4
The Product and Quotient Rules
2.5
The Chain Rule
2.6
Higher-Order Derivatives
2.7
Implicit Differentiation
2.8
Related Rates
3
Applications of the Derivative
3.1
Increasing and Decreasing Functions
3.2
Extrema and the First-Derivative Test
3.3
Concavity and the Second-Derivative Test
3.4
Optimization Problems
3.5
Business and Economics Applications
3.6
Asymptotes
3.7
Curve Sketching: A Summary
3.8
Differentials and Marginal Analysis
4
Exponential and Logarithmic Functions
4.1
Exponential Functions
4.2
Natural Exponential Functions
4.3
Derivatives of Exponential Functions
4.4
Logarithmic Functions
4.5
Derivatives of Logarithmic Functions
4.6
Exponential Growth and Decay
5
Integration and Its Applications
5.1
Antiderivatives and Indefinite Integrals
5.2
The General Power Rule
5.3
Exponential and Logarithmic Integrals
5.4
Area and the Fundamental Theorem of Calculus
5.5
The Area of a Region Bounded by Two Graphs
5.6
The Definite Integral as the Limit of a Sum 3
5.7
Volumes of Solids of Revolution
6
Techniques of Integration
6.1
Integration by Substitution
6.2
Integration by Parts and Present Value
6.3
Partial Fractions and Logistic Growth
6.4
Integration Tables and Completing the Square
6.5
Numerical Integration
6.6
Improper Integrals
7
Functions of Several Variables
7.1
The Three-Dimensional Coordinate System
7.2
Surfaces in Space
7.3
Functions of Several Variables
7.4
Partial Derivatives
7.5
Extrema of Functions of Two Variables
7.6
Lagrange Multipliers
7.7
Least Squares Regression Analysis
7.8
Double Integrals and Area in the Plane
7.9
Applications of Double Integrals
Textbook Solutions for Brief Calculus: An Applied Approach
Chapter 5.3 Problem 31
Question
In Exercises 2938, use a symbolic integration utility to find the indefinite integral. 1 x ex dx
Solution
The first step in solving 5.3 problem number 31 trying to solve the problem we have to refer to the textbook question: In Exercises 2938, use a symbolic integration utility to find the indefinite integral. 1 x ex dx
From the textbook chapter Exponential and Logarithmic Integrals you will find a few key concepts needed to solve this.
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full solution
Title
Brief Calculus: An Applied Approach 7
Author
Ron Larson, Bruce H. Edwards
ISBN
9780618547197
Solution: In Exercises 2938, use a symbolic integration utility to find the indefinite
Chapter 5.3 textbook questions
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Chapter 5: Problem 1 Brief Calculus: An Applied Approach 7
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Chapter 5: Problem 2 Brief Calculus: An Applied Approach 7
In Exercises 112, use the Exponential Rule to find the indefinite integral.3e3x 2e dx
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Chapter 5: Problem 3 Brief Calculus: An Applied Approach 7
In Exercises 112, use the Exponential Rule to find the indefinite integral. e dx 4x dx
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Chapter 5: Problem 4 Brief Calculus: An Applied Approach 7
In Exercises 112, use the Exponential Rule to find the indefinite integral. e0.25x e dx
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Chapter 5: Problem 5 Brief Calculus: An Applied Approach 7
In Exercises 112, use the Exponential Rule to find the indefinite integral. 9xe dx x2 dx
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Chapter 5: Problem 6 Brief Calculus: An Applied Approach 7
In Exercises 112, use the Exponential Rule to find the indefinite integral. 3xe0.5x2 9xe dx
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Chapter 5: Problem 7 Brief Calculus: An Applied Approach 7
In Exercises 112, use the Exponential Rule to find the indefinite integral. 5x dx 2 ex3 dx
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Chapter 5: Problem 8 Brief Calculus: An Applied Approach 7
In Exercises 112, use the Exponential Rule to find the indefinite integral.2x 1ex2x 5x dx 2 ex
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Chapter 5: Problem 9 Brief Calculus: An Applied Approach 7
In Exercises 112, use the Exponential Rule to find the indefinite integral. x dx 2 2xex33x21 dx 2
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Chapter 5: Problem 10 Brief Calculus: An Applied Approach 7
In Exercises 112, use the Exponential Rule to find the indefinite integral. 3x 4ex28x x dx 2
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Chapter 5: Problem 11 Brief Calculus: An Applied Approach 7
In Exercises 112, use the Exponential Rule to find the indefinite integral. 5e dx 2x dx
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Chapter 5: Problem 12 Brief Calculus: An Applied Approach 7
In Exercises 112, use the Exponential Rule to find the indefinite integral.3ex1 5e dx 2x
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Chapter 5: Problem 13 Brief Calculus: An Applied Approach 7
In Exercises 1328, use the Log Rule to find the indefinite integral. dx 1 x 1 dx
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Chapter 5: Problem 14 Brief Calculus: An Applied Approach 7
In Exercises 1328, use the Log Rule to find the indefinite integral. 1 x 5 dx
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Chapter 5: Problem 15 Brief Calculus: An Applied Approach 7
In Exercises 1328, use the Log Rule to find the indefinite integral. 1 3 2x dx
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Chapter 5: Problem 16 Brief Calculus: An Applied Approach 7
In Exercises 1328, use the Log Rule to find the indefinite integral. 1 6x 5 dx
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Chapter 5: Problem 17 Brief Calculus: An Applied Approach 7
In Exercises 1328, use the Log Rule to find the indefinite integral. 2 3x 5 dx
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Chapter 5: Problem 18 Brief Calculus: An Applied Approach 7
In Exercises 1328, use the Log Rule to find the indefinite integral. 5 2x 1 dx
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Chapter 5: Problem 19 Brief Calculus: An Applied Approach 7
In Exercises 1328, use the Log Rule to find the indefinite integral. x x2 1 dx
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Chapter 5: Problem 20 Brief Calculus: An Applied Approach 7
In Exercises 1328, use the Log Rule to find the indefinite integral. x2 3 x3 dx
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Chapter 5: Problem 21 Brief Calculus: An Applied Approach 7
In Exercises 1328, use the Log Rule to find the indefinite integral. x2 x3 1 dx
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Chapter 5: Problem 22 Brief Calculus: An Applied Approach 7
In Exercises 1328, use the Log Rule to find the indefinite integral. x x2 4 dx x
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Chapter 5: Problem 23 Brief Calculus: An Applied Approach 7
In Exercises 1328, use the Log Rule to find the indefinite integral. x 3 x2 6x 7 dx
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Chapter 5: Problem 24 Brief Calculus: An Applied Approach 7
In Exercises 1328, use the Log Rule to find the indefinite integral. x2 2x 3 x3 3x2 9x 1 dx x
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Chapter 5: Problem 25 Brief Calculus: An Applied Approach 7
In Exercises 1328, use the Log Rule to find the indefinite integral. 1 x ln x dx
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Chapter 5: Problem 26 Brief Calculus: An Applied Approach 7
In Exercises 1328, use the Log Rule to find the indefinite integral.1 xln x2 dx 1
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Chapter 5: Problem 27 Brief Calculus: An Applied Approach 7
In Exercises 1328, use the Log Rule to find the indefinite integral. ex 1 ex dx
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Chapter 5: Problem 28 Brief Calculus: An Applied Approach 7
In Exercises 1328, use the Log Rule to find the indefinite integral. ex 1 e x dx e
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Chapter 5: Problem 29 Brief Calculus: An Applied Approach 7
In Exercises 2938, use a symbolic integration utility to find the indefinite integral. dx 1 x2 e2x dx
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Chapter 5: Problem 30 Brief Calculus: An Applied Approach 7
In Exercises 2938, use a symbolic integration utility to find the indefinite integral. 1 x3 e14x2 dx
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Chapter 5: Problem 31 Brief Calculus: An Applied Approach 7
In Exercises 2938, use a symbolic integration utility to find the indefinite integral. 1 x ex dx
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Chapter 5: Problem 32 Brief Calculus: An Applied Approach 7
In Exercises 2938, use a symbolic integration utility to find the indefinite integral. e1x x32 dx
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Chapter 5: Problem 33 Brief Calculus: An Applied Approach 7
In Exercises 2938, use a symbolic integration utility to find the indefinite integral. e dx x 22 dx
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Chapter 5: Problem 34 Brief Calculus: An Applied Approach 7
In Exercises 2938, use a symbolic integration utility to find the indefinite integral. ex ex 2 e dx x
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Chapter 5: Problem 35 Brief Calculus: An Applied Approach 7
In Exercises 2938, use a symbolic integration utility to find the indefinite integral. ex 1 ex dx
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Chapter 5: Problem 36 Brief Calculus: An Applied Approach 7
In Exercises 2938, use a symbolic integration utility to find the indefinite integral. 3ex 2 e x dx
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Chapter 5: Problem 37 Brief Calculus: An Applied Approach 7
In Exercises 2938, use a symbolic integration utility to find the indefinite integral. 4e2x 5 e2x dx
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Chapter 5: Problem 38 Brief Calculus: An Applied Approach 7
In Exercises 2938, use a symbolic integration utility to find the indefinite integral. e3x 2 e3x dx
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Chapter 5: Problem 39 Brief Calculus: An Applied Approach 7
In Exercises 3954, use any basic integration formula or formulas to find the indefinite integral. dx e2x 2ex 1 ex dx S
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Chapter 5: Problem 40 Brief Calculus: An Applied Approach 7
In Exercises 3954, use any basic integration formula or formulas to find the indefinite integral. 6x ex 3x2 e x dx e2x
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Chapter 5: Problem 41 Brief Calculus: An Applied Approach 7
In Exercises 3954, use any basic integration formula or formulas to find the indefinite integral. e dx x1 e x dx
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Chapter 5: Problem 42 Brief Calculus: An Applied Approach 7
In Exercises 3954, use any basic integration formula or formulas to find the indefinite integral. 2ex ex e x ex 2 e dx x1
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Chapter 5: Problem 43 Brief Calculus: An Applied Approach 7
In Exercises 3954, use any basic integration formula or formulas to find the indefinite integral. 1 x 12 dx
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Chapter 5: Problem 44 Brief Calculus: An Applied Approach 7
In Exercises 3954, use any basic integration formula or formulas to find the indefinite integral. 1 x 1 dx 1
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Chapter 5: Problem 45 Brief Calculus: An Applied Approach 7
In Exercises 3954, use any basic integration formula or formulas to find the indefinite integral. 4e 2x 1 dx 2x1 dx
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Chapter 5: Problem 46 Brief Calculus: An Applied Approach 7
In Exercises 3954, use any basic integration formula or formulas to find the indefinite integral. 5e 4e 2x 1 dx 2x
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Chapter 5: Problem 47 Brief Calculus: An Applied Approach 7
In Exercises 3954, use any basic integration formula or formulas to find the indefinite integral. x3 8x 2x2 dx
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Chapter 5: Problem 48 Brief Calculus: An Applied Approach 7
In Exercises 3954, use any basic integration formula or formulas to find the indefinite integral. x 1 4x dx
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Chapter 5: Problem 49 Brief Calculus: An Applied Approach 7
In Exercises 3954, use any basic integration formula or formulas to find the indefinite integral. 2 1 ex dx
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Chapter 5: Problem 50 Brief Calculus: An Applied Approach 7
In Exercises 3954, use any basic integration formula or formulas to find the indefinite integral. 3 1 e3x dx
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Chapter 5: Problem 51 Brief Calculus: An Applied Approach 7
In Exercises 3954, use any basic integration formula or formulas to find the indefinite integral. x2 2x 5 x 1 dx
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Chapter 5: Problem 52 Brief Calculus: An Applied Approach 7
In Exercises 3954, use any basic integration formula or formulas to find the indefinite integral. x 3 x 3 dx x
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Chapter 5: Problem 53 Brief Calculus: An Applied Approach 7
In Exercises 3954, use any basic integration formula or formulas to find the indefinite integral. 1 ex 1 xex dx
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Chapter 5: Problem 54 Brief Calculus: An Applied Approach 7
In Exercises 3954, use any basic integration formula or formulas to find the indefinite integral. 5 e5x 7 dx 1
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Chapter 5: Problem 55 Brief Calculus: An Applied Approach 7
In Exercises 55 and 56, find the equation of the function f whose graph passes through the point. x 2, 4 x2 4x 3 x 1 ; 5 e
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Chapter 5: Problem 56 Brief Calculus: An Applied Approach 7
In Exercises 55 and 56, find the equation of the function f whose graph passes through the point. fx 4, 1 x3 4x2 3 x 3 ; fx
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Chapter 5: Problem 57 Brief Calculus: An Applied Approach 7
Biology A population of bacteria is growing at the rate of where t is the time in days. When the population is 1000. (a) Write an equation that models the population P in terms of the time t. (b) What is the population after 3 days? (c) After how many days will the population be 12,000?
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Chapter 5: Problem 58 Brief Calculus: An Applied Approach 7
. Biology Because of an insufficient oxygen supply, the trout population in a lake is dying. The populations rate of change can be modeled by where t is the time in days. When the population is 2500. (a) Write an equation that models the population P in terms of the time t. (b) What is the population after 15 days? (c) According to this model, how long will it take for the entire trout population to die?
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Chapter 5: Problem 59 Brief Calculus: An Applied Approach 7
Demand The marginal price for the demand of a product can be modeled by where x is the quantity demanded. When the demand is 600 units, the price is $30. (a) Find the demand function, (b) Use a graphing utility to graph the demand function. Does price increase or decrease as demand increases? (c) Use the zoom and trace features of the graphing utility to find the quantity demanded when the price is $22.
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Chapter 5: Problem 60 Brief Calculus: An Applied Approach 7
Revenue The marginal revenue for the sale of a product can be modeled by where x is the quantity demanded. (a) Find the revenue function. (b) Use a graphing utility to graph the revenue function. (c) Find the revenue when 1500 units are sold. (d) Use the zoom and trace features of the graphing utility to find the number of units sold when the revenue is $60,230.
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Chapter 5: Problem 61 Brief Calculus: An Applied Approach 7
Average Salary From 1995 through 2002, the average salary for superintendents S (in dollars) in the United States changed at the rate of where corresponds to 1995. In 2001, the average salary for superintendents was $118,496. (Source: Educational Research Service) (a) Write a model that gives the average salary for superintendents per year. (b) Use the model to find the average salary for superintendents in 1999.
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Chapter 5: Problem 62 Brief Calculus: An Applied Approach 7
Sales The rate of change in sales for The Yankee Candle Company from 1998 through 2003 can be modeled by where S is the sales (in millions) and corresponds to 1998. In 1999, the sales for The Yankee Candle Company were $256.6 million. (Source: The Yankee Candle Company) (a) Find a model for sales from 1998 through 2003. (b) Find The Yankee Candle Companys sales in 2002.
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Chapter 5: Problem 63 Brief Calculus: An Applied Approach 7
True or False? In Exercises 63 and 64, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. ln x12 C 1 2ln x t
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Chapter 5: Problem 64 Brief Calculus: An Applied Approach 7
True or False? In Exercises 63 and 64, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. ln x 1 x ln x12 C 1
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