Evaluate the integral. 66² = Step 1 30 6x² + 7x + 1 +6²= Q(x) = The integrand of 30 where P(x) = 30 and Q(x) = 6x² + 7x + 1. Since the degree of the 6x² + 7x + 1 numerator P(x) is less than the degree of the denominator Q(x), we do not need to divide. However, we note that the denominator can be factored as follows. x6 x² + x 7 x + 1 dx = (x6 x + 1) dx is a rational function of the form f(x) = X P(x) Q(x) )

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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Evaluate the integral.
Step 1
'1
30
bo 5x² + 2x + 1 x
dx
7x
1
30
6²
where P(x): = 30 and Q(x) = 6x² + 7x + 1. Since the degree of the
10 6x² + 7x + 1
numerator P(x) is less than the degree of the denominator Q(x), we do not need to divide. However, we note that the denominator can be factored as
follows.
Q(x) = X 6 X² + x 7 x + 1
The integrand of
=
(x6x + 1)(
dx is a rational function of the form f(x) :
=
X
)
P(x)
Q(x)
Transcribed Image Text:Evaluate the integral. Step 1 '1 30 bo 5x² + 2x + 1 x dx 7x 1 30 6² where P(x): = 30 and Q(x) = 6x² + 7x + 1. Since the degree of the 10 6x² + 7x + 1 numerator P(x) is less than the degree of the denominator Q(x), we do not need to divide. However, we note that the denominator can be factored as follows. Q(x) = X 6 X² + x 7 x + 1 The integrand of = (x6x + 1)( dx is a rational function of the form f(x) : = X ) P(x) Q(x)
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