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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Question
![For each factor of the form \((px + q)^m\), the partial fraction decomposition must include the following sum of \(m\) fractions:
\[
\frac{A_1}{px + q} + \frac{A_2}{(px + q)^2} + \frac{A_3}{(px + q)^3} + \cdots + \frac{A_m}{(px + q)^m}
\]
For each factor of the form \((ax^2 + bx + c)^n\), the partial fraction decomposition must include the following sum of \(m\) fractions:
\[
\frac{B_1x + C_1}{ax^2 + bx + c} + \frac{B_2x + C_2}{(ax^2 + bx + c)^2} + \frac{B_3x + C_3}{(ax^2 + bx + c)^3} + \cdots + \frac{B_nx + C_n}{(ax^2 + bx + c)^n}
\]
**Example:**
\[
\int \frac{x^3}{x^2 + 4x + 3} \, dx
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe8a5b705-90e4-4486-988d-5f557495597a%2F7ab210f3-9a7d-4244-a404-c0fb43b013d6%2F3tvxxc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:For each factor of the form \((px + q)^m\), the partial fraction decomposition must include the following sum of \(m\) fractions:
\[
\frac{A_1}{px + q} + \frac{A_2}{(px + q)^2} + \frac{A_3}{(px + q)^3} + \cdots + \frac{A_m}{(px + q)^m}
\]
For each factor of the form \((ax^2 + bx + c)^n\), the partial fraction decomposition must include the following sum of \(m\) fractions:
\[
\frac{B_1x + C_1}{ax^2 + bx + c} + \frac{B_2x + C_2}{(ax^2 + bx + c)^2} + \frac{B_3x + C_3}{(ax^2 + bx + c)^3} + \cdots + \frac{B_nx + C_n}{(ax^2 + bx + c)^n}
\]
**Example:**
\[
\int \frac{x^3}{x^2 + 4x + 3} \, dx
\]
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