Note: You can get full credit for this problem by just entering the final answer (to the last question) correctly. The initial questions are meant as hints towards the final answer and also allow you the opportunity to get partial credit. Consider the indefinite integral s 523+822+82+20 x4+4x² Then the integrand has partial fractions decomposition where a= b= C = d= Integrating term by term, we obtain that 5r3+8r+8r+20 dx = 24+422 +C dr a b 2 + + cx + d x² + 4
Note: You can get full credit for this problem by just entering the final answer (to the last question) correctly. The initial questions are meant as hints towards the final answer and also allow you the opportunity to get partial credit. Consider the indefinite integral s 523+822+82+20 x4+4x² Then the integrand has partial fractions decomposition where a= b= C = d= Integrating term by term, we obtain that 5r3+8r+8r+20 dx = 24+422 +C dr a b 2 + + cx + d x² + 4
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Partial Fraction Decomposition and Integration**
**Note:** You can get full credit for this problem by just entering the final answer (to the last question) correctly. The initial questions are meant as hints towards the final answer and also allow you the opportunity to get partial credit.
**Problem Statement:**
Consider the indefinite integral:
\[
\int \frac{5x^3 + 8x^2 + 8x + 20}{x^4 + 4x^2} \, dx
\]
The integrand has partial fractions decomposition in the form:
\[
\frac{a}{x^2} + \frac{b}{x} + \frac{cx + d}{x^2 + 4}
\]
**Where:**
- \( a = \) [blank box for user input]
- \( b = \) [blank box for user input]
- \( c = \) [blank box for user input]
- \( d = \) [blank box for user input]
**Integration by Term:**
By integrating term by term, we can obtain:
\[
\int \frac{5x^3 + 8x^2 + 8x + 20}{x^4 + 4x^2} \, dx = [blank box for user input] + C
\]
**Note:** You can earn full credit by answering just the last part.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb2133c9-e1e5-4d56-9c72-044227328930%2F29a97e1d-0d27-4b19-97da-bed814ddf51f%2Fbvg82na_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Partial Fraction Decomposition and Integration**
**Note:** You can get full credit for this problem by just entering the final answer (to the last question) correctly. The initial questions are meant as hints towards the final answer and also allow you the opportunity to get partial credit.
**Problem Statement:**
Consider the indefinite integral:
\[
\int \frac{5x^3 + 8x^2 + 8x + 20}{x^4 + 4x^2} \, dx
\]
The integrand has partial fractions decomposition in the form:
\[
\frac{a}{x^2} + \frac{b}{x} + \frac{cx + d}{x^2 + 4}
\]
**Where:**
- \( a = \) [blank box for user input]
- \( b = \) [blank box for user input]
- \( c = \) [blank box for user input]
- \( d = \) [blank box for user input]
**Integration by Term:**
By integrating term by term, we can obtain:
\[
\int \frac{5x^3 + 8x^2 + 8x + 20}{x^4 + 4x^2} \, dx = [blank box for user input] + C
\]
**Note:** You can earn full credit by answering just the last part.
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