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Set up the following integral using partial fractions after showing the long division, then integrate. A. SHOW LONG DIVISION STEPS; B. SHOW PARTIAL FRACTION DECOMPOSITION AND WORK; C. INTEGRATE AND SHOW WORK. - 6x³ +3x² – 143x -80 -dx x² - 25

Set up the following integral using partial fractions after showing the long division, then integrate. A. SHOW LONG DIVISION STEPS; B. SHOW PARTIAL FRACTION DECOMPOSITION AND WORK; C. INTEGRATE AND SHOW WORK. - 6x³ +3x² – 143x -80 -dx x² - 25

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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## Partial Fractions and Integration ### Instructions Set up the following integral using **partial fractions** after **showing the long division**, then integrate. ### Steps **A. Show Long Division Steps** **B. Show Partial Fraction Decomposition and Work** **C. Integrate and Show Work** \[ \int \frac{6x^3 + 3x^2 - 143x - 80}{x^2 - 25} \, dx \] ### Explanation - **Long Division**: Dividing the polynomial \(6x^3 + 3x^2 - 143x - 80\) by \(x^2 - 25\) to simplify the integral. - **Partial Fraction Decomposition**: Breaking down the rational expression into simpler fractions that are easier to integrate. - **Integration**: Calculating the integral of the decomposed fractions with respect to \(x\). Each step should be detailed to ensure clarity in the process from division, through decomposition, to integration.
Transcribed Image Text:## Partial Fractions and Integration ### Instructions Set up the following integral using **partial fractions** after **showing the long division**, then integrate. ### Steps **A. Show Long Division Steps** **B. Show Partial Fraction Decomposition and Work** **C. Integrate and Show Work** \[ \int \frac{6x^3 + 3x^2 - 143x - 80}{x^2 - 25} \, dx \] ### Explanation - **Long Division**: Dividing the polynomial \(6x^3 + 3x^2 - 143x - 80\) by \(x^2 - 25\) to simplify the integral. - **Partial Fraction Decomposition**: Breaking down the rational expression into simpler fractions that are easier to integrate. - **Integration**: Calculating the integral of the decomposed fractions with respect to \(x\). Each step should be detailed to ensure clarity in the process from division, through decomposition, to integration.
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