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
![---
**Evaluate the following integral.**
\[ \int \frac{48x^2}{(x-15)(x+5)^2} \, dx \]
---
**Find the partial fraction decomposition of the integrand.**
\[ \int \frac{48x^2}{(x-15)(x+5)^2} \, dx = \int ( \Box ) \, dx \]
---
**Evaluate the indefinite integral.**
\[ \int \frac{48x^2}{(x-15)(x+5)^2} \, dx = \Box \]
---
Note: In the original image provided, there were blank boxes (represented as \(\Box\) ) used to indicate where answers or further steps are required.
In the first section, the task is to evaluate the integral \( \int \frac{48x^2}{(x-15)(x+5)^2} \, dx \).
In the second section, the goal is to decompose the integrand \( \frac{48x^2}{(x-15)(x+5)^2} \) into partial fractions.
In the final section, the integral obtained from the partial fraction decomposition needs to be evaluated to find the indefinite integral.
For more information on partial fraction decomposition and integration techniques, follow the relevant sections of the website.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F511d779c-bf10-4315-98b1-4f0038c55113%2F96e77245-195e-4924-aa9f-889eb1c092a8%2Ft2i9tl_processed.png&w=3840&q=75)
Transcribed Image Text:---
**Evaluate the following integral.**
\[ \int \frac{48x^2}{(x-15)(x+5)^2} \, dx \]
---
**Find the partial fraction decomposition of the integrand.**
\[ \int \frac{48x^2}{(x-15)(x+5)^2} \, dx = \int ( \Box ) \, dx \]
---
**Evaluate the indefinite integral.**
\[ \int \frac{48x^2}{(x-15)(x+5)^2} \, dx = \Box \]
---
Note: In the original image provided, there were blank boxes (represented as \(\Box\) ) used to indicate where answers or further steps are required.
In the first section, the task is to evaluate the integral \( \int \frac{48x^2}{(x-15)(x+5)^2} \, dx \).
In the second section, the goal is to decompose the integrand \( \frac{48x^2}{(x-15)(x+5)^2} \) into partial fractions.
In the final section, the integral obtained from the partial fraction decomposition needs to be evaluated to find the indefinite integral.
For more information on partial fraction decomposition and integration techniques, follow the relevant sections of the website.
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