Consider the indefinite integral The integrand decomposes into the form ax + b + where a = b = C = d= C x-1 + (3x³ + 3x² + 4x + 0 dx. x² - 1 d x + 1 Integrating term by term, we obtain that 3x³ + 3x² + 4x + 0 1³² dx = x² - 1
Consider the indefinite integral The integrand decomposes into the form ax + b + where a = b = C = d= C x-1 + (3x³ + 3x² + 4x + 0 dx. x² - 1 d x + 1 Integrating term by term, we obtain that 3x³ + 3x² + 4x + 0 1³² dx = x² - 1
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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![**Consider the Indefinite Integral**
\[
\int \frac{3x^3 + 3x^2 + 4x + 0}{x^2 - 1} \, dx.
\]
The integrand decomposes into the form:
\[
ax + b + \frac{c}{x-1} + \frac{d}{x+1}
\]
where
- \( a = \_\_\_\_ \)
- \( b = \_\_\_\_ \)
- \( c = \_\_\_\_ \)
- \( d = \_\_\_\_ \)
**Integrating Term by Term**
We obtain:
\[
\int \frac{3x^3 + 3x^2 + 4x + 0}{x^2 - 1} \, dx = \_\_\_\_ + C.
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb47bac88-cba5-40e5-9f3f-db7316eb95a3%2F4c0464b3-9001-4e1f-a6f1-39b04a61d3d7%2Fn1zgey_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Consider the Indefinite Integral**
\[
\int \frac{3x^3 + 3x^2 + 4x + 0}{x^2 - 1} \, dx.
\]
The integrand decomposes into the form:
\[
ax + b + \frac{c}{x-1} + \frac{d}{x+1}
\]
where
- \( a = \_\_\_\_ \)
- \( b = \_\_\_\_ \)
- \( c = \_\_\_\_ \)
- \( d = \_\_\_\_ \)
**Integrating Term by Term**
We obtain:
\[
\int \frac{3x^3 + 3x^2 + 4x + 0}{x^2 - 1} \, dx = \_\_\_\_ + C.
\]
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