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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![### Integral Calculation Problem:
Evaluate the integral:
\[
\int \frac{x}{81 + 9x^4} \, dx
\]
Below are the multiple-choice options with potential solutions:
1. \(\frac{1}{6} \arctan \left( \frac{x^2}{3} \right) + C\)
\[
\bigcirc \quad \frac{1}{6} \arctan \left( \frac{x^2}{3} \right) + C
\]
2. \(\frac{1}{54} \arctan \left( \frac{x^2}{3} \right) + C\)
\[
\bigcirc \quad \frac{1}{54} \arctan \left( \frac{x^2}{3} \right) + C
\]
3. \(\frac{1}{302} \ln |81 + 9x^4| + C\)
\[
\bigcirc \quad \frac{1}{302} \ln |81 + 9x^4| + C
\]
4. \(\frac{1}{9} \arctan \left( \frac{x^2}{3} \right) + C\)
\[
\bigcirc \quad \frac{1}{9} \arctan \left( \frac{x^2}{3} \right) + C
\]
**Instructions for Students:**
Choose the correct option from the given multiple-choice answers by carefully evaluating the integral provided. Remember, the typical approach for solving such integrals might involve trigonometric substitutions or direct integration techniques. Evaluate each option and confirm which one accurately represents the integration result.
**Graph/Diagram Explanation:**
- There are no graphs or diagrams provided in this problem. The focus is solely on the mathematical expression and its evaluation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4143f45a-5c96-4449-af2f-abda697f3e91%2Fe75d1df3-5675-4266-ab40-798bf7df72f5%2Fibvgne_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Integral Calculation Problem:
Evaluate the integral:
\[
\int \frac{x}{81 + 9x^4} \, dx
\]
Below are the multiple-choice options with potential solutions:
1. \(\frac{1}{6} \arctan \left( \frac{x^2}{3} \right) + C\)
\[
\bigcirc \quad \frac{1}{6} \arctan \left( \frac{x^2}{3} \right) + C
\]
2. \(\frac{1}{54} \arctan \left( \frac{x^2}{3} \right) + C\)
\[
\bigcirc \quad \frac{1}{54} \arctan \left( \frac{x^2}{3} \right) + C
\]
3. \(\frac{1}{302} \ln |81 + 9x^4| + C\)
\[
\bigcirc \quad \frac{1}{302} \ln |81 + 9x^4| + C
\]
4. \(\frac{1}{9} \arctan \left( \frac{x^2}{3} \right) + C\)
\[
\bigcirc \quad \frac{1}{9} \arctan \left( \frac{x^2}{3} \right) + C
\]
**Instructions for Students:**
Choose the correct option from the given multiple-choice answers by carefully evaluating the integral provided. Remember, the typical approach for solving such integrals might involve trigonometric substitutions or direct integration techniques. Evaluate each option and confirm which one accurately represents the integration result.
**Graph/Diagram Explanation:**
- There are no graphs or diagrams provided in this problem. The focus is solely on the mathematical expression and its evaluation.
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