x 18x² +81 Factor the denominator: - dx x²

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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can you please explai to me how did he get the partial fraction decomposition?

1
-1/2 √2+3
x
x²
(x − 3)²(x+3)²
Perform partial fraction decomposition:
1
- 1 (-126² = 21 - 414² +
=
+
(x+3)
dx +
1
Problem:
x²
S
x4
18x² +81
Factor the denominator:
4
=
:/
Apply linearity:
1
+
4(x+3)² 12 (x-
1
(x+3)²
dx
dx +
1
dx
J
12 X
3)
1
+
3
1
4(x - 3)²
dx +
1
dx
1
(x − 3)²
-
S
dx
Transcribed Image Text:1 -1/2 √2+3 x x² (x − 3)²(x+3)² Perform partial fraction decomposition: 1 - 1 (-126² = 21 - 414² + = + (x+3) dx + 1 Problem: x² S x4 18x² +81 Factor the denominator: 4 = :/ Apply linearity: 1 + 4(x+3)² 12 (x- 1 (x+3)² dx dx + 1 dx J 12 X 3) 1 + 3 1 4(x - 3)² dx + 1 dx 1 (x − 3)² - S dx
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