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. x² Consider the indefinite integral (x-3)(x-4)² Then the integrand has partial fractions decomposition where a = b= C = Integrating term by term, we obtain that x² (x-3)(x-4)² dx = +C dx a x 3 + b C x-4 (x-4)² +
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. x² Consider the indefinite integral (x-3)(x-4)² Then the integrand has partial fractions decomposition where a = b= C = Integrating term by term, we obtain that x² (x-3)(x-4)² dx = +C dx a x 3 + b C x-4 (x-4)² +
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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![**Educational Material: Partial Fraction Decomposition and Integration**
**Problem Statement:**
Consider the indefinite integral:
\[ \int \frac{x^2}{(x - 3)(x - 4)^2} \, dx \]
**Partial Fractions Decomposition:**
The integrand can be decomposed into partial fractions as follows:
\[ \frac{a}{x - 3} + \frac{b}{x - 4} + \frac{c}{(x - 4)^2} \]
where:
- \( a = 1 \)
- \( b = \)
- \( c = \)
**Integration Method:**
By integrating each term separately, the following expression is obtained:
\[ \int \frac{x^2}{(x - 3)(x - 4)^2} \, dx = \]
\[ + C \]
**Note:**
You can earn full credit by answering just the final part of this problem. The preceding steps provide guidance and partial credit opportunities but are not mandatory for full credit.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb2133c9-e1e5-4d56-9c72-044227328930%2F997c41e4-cf32-4597-b180-91d036134a06%2Fc3t3547_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Material: Partial Fraction Decomposition and Integration**
**Problem Statement:**
Consider the indefinite integral:
\[ \int \frac{x^2}{(x - 3)(x - 4)^2} \, dx \]
**Partial Fractions Decomposition:**
The integrand can be decomposed into partial fractions as follows:
\[ \frac{a}{x - 3} + \frac{b}{x - 4} + \frac{c}{(x - 4)^2} \]
where:
- \( a = 1 \)
- \( b = \)
- \( c = \)
**Integration Method:**
By integrating each term separately, the following expression is obtained:
\[ \int \frac{x^2}{(x - 3)(x - 4)^2} \, dx = \]
\[ + C \]
**Note:**
You can earn full credit by answering just the final part of this problem. The preceding steps provide guidance and partial credit opportunities but are not mandatory for full credit.
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