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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![### Evaluating an Integral
**Problem Statement:**
Evaluate the integral. (Use \( C \) for the constant of integration.)
\[
\int \frac{1}{\sqrt{5x(1 + 5x)}} \, dx
\]
**Instructions:**
1. **Identify the Integral:**
We need to evaluate the given integral:
\[
\int \frac{1}{\sqrt{5x(1 + 5x)}} \, dx
\]
2. **Simplify the Expression:**
We can simplify the expression inside the integral using algebraic manipulations or substitutions if necessary.
3. **Integrate:**
Use the appropriate method to integrate the function, such as substitution, partial fractions, or recognizing a standard integral form.
4. **Add the Constant of Integration:**
Once the integral is found, include the constant of integration \( C \).
Here, there are no additional graphs or diagrams accompanying the problem statement. If there were, further explanation on interpreting these visual aids could be provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5abad2ef-7d64-4544-b6f7-dd3dfbff74f8%2Fe0656d15-2a50-46bf-82d6-4782b0dabf1a%2Fnvucffs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Evaluating an Integral
**Problem Statement:**
Evaluate the integral. (Use \( C \) for the constant of integration.)
\[
\int \frac{1}{\sqrt{5x(1 + 5x)}} \, dx
\]
**Instructions:**
1. **Identify the Integral:**
We need to evaluate the given integral:
\[
\int \frac{1}{\sqrt{5x(1 + 5x)}} \, dx
\]
2. **Simplify the Expression:**
We can simplify the expression inside the integral using algebraic manipulations or substitutions if necessary.
3. **Integrate:**
Use the appropriate method to integrate the function, such as substitution, partial fractions, or recognizing a standard integral form.
4. **Add the Constant of Integration:**
Once the integral is found, include the constant of integration \( C \).
Here, there are no additional graphs or diagrams accompanying the problem statement. If there were, further explanation on interpreting these visual aids could be provided.
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