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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Solve using partial fraction 211
![The following content is designed for an educational resource on evaluating integrals using the method of partial fractions.
---
**Exercises: Evaluate the following integrals using the method of partial fractions.**
**209.**
\[
\int \frac{x^3 + 6x^2 + 3x + 6}{x^3 + 2x^2} \, dx
\]
**210.**
\[
\int \frac{x}{(x - 1)(x^2 + 2x + 2)^2} \, dx
\]
Use the method of partial fractions to evaluate the following integrals.
**211.**
\[
\int \frac{3x + 4}{(x^2 + 4)(3 - x)} \, dx
\]
**212.**
\[
\int \frac{2}{(x + 2)^2(2 - x)} \, dx
\]
---
These exercises provide practice in decomposing complex rational expressions into simpler fractions that can be integrated individually.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03fd5f25-eded-4046-9c65-9e89b5e28b89%2Fd6f4d230-a0de-4610-b9d6-6fc7f5993158%2F9perjyq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The following content is designed for an educational resource on evaluating integrals using the method of partial fractions.
---
**Exercises: Evaluate the following integrals using the method of partial fractions.**
**209.**
\[
\int \frac{x^3 + 6x^2 + 3x + 6}{x^3 + 2x^2} \, dx
\]
**210.**
\[
\int \frac{x}{(x - 1)(x^2 + 2x + 2)^2} \, dx
\]
Use the method of partial fractions to evaluate the following integrals.
**211.**
\[
\int \frac{3x + 4}{(x^2 + 4)(3 - x)} \, dx
\]
**212.**
\[
\int \frac{2}{(x + 2)^2(2 - x)} \, dx
\]
---
These exercises provide practice in decomposing complex rational expressions into simpler fractions that can be integrated individually.
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