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A) Write as a sum or difference of two fractions. (x+3)(x- 2) 3) 18 dx (x² +9)(x+3)

A) Write as a sum or difference of two fractions. (x+3)(x- 2) 3) 18 dx (x² +9)(x+3)

Calculus: Early Transcendentals
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
**A) Problem Statement:** Write \(\frac{x}{(x+3)(x-2)}\) as a sum or difference of two fractions. **B) Problem Statement:** Evaluate the integral \(\int \frac{18}{(x^2 + 9)(x + 3)} \, dx\). The tasks presented involve manipulating and integrating rational expressions. For task A, you'll perform partial fraction decomposition, rewriting a given rational expression as a sum or difference of simpler fractions. For task B, the focus is on solving an integral using techniques such as partial fraction decomposition, substitution, or integration by parts to simplify the process.
Transcribed Image Text:**A) Problem Statement:** Write \(\frac{x}{(x+3)(x-2)}\) as a sum or difference of two fractions. **B) Problem Statement:** Evaluate the integral \(\int \frac{18}{(x^2 + 9)(x + 3)} \, dx\). The tasks presented involve manipulating and integrating rational expressions. For task A, you'll perform partial fraction decomposition, rewriting a given rational expression as a sum or difference of simpler fractions. For task B, the focus is on solving an integral using techniques such as partial fraction decomposition, substitution, or integration by parts to simplify the process.
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