Express the Integrand as a Sum of Partial Fractions and Evaluate

question 297

Multiple Choice

Express the integrand as a sum of partial fractions and evaluate the integral.
- $$\int \frac { x ^ { 3 } } { x ^ { 2 } + 4 x + 4 } d x$$

• A) \(\frac { x ^ { 2 } } { 2 } - 4 x + 12 \ln | x + 2 | + \frac { 8 } { x + 2 } + C\)
• B) \(\frac { x ^ { 2 } } { 2 } - 4 x + 6 \ln | x + 2 | - \frac { 4 } { x + 2 } + C\)
• C) \(12 \ln | x - 4 | + \frac { 12 } { x + 2 } - \frac { 8 } { ( x + 2 ) ^ { 2 } } + C\)
• D) \(\frac { x ^ { 2 } } { 2 } - 4 x - 12 \ln | x + 2 | + \frac { 8 } { ( x + 2 ) ^ { 2 } } + C\)

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Definitions:

Mixed Messages

Communications or signals that contain conflicting or contradictory information, often leading to confusion or misunderstanding.

Active Listening

The process of taking action to help someone say exactly what he or she really means or wants to communicate.

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The act of rewording or restating text or speech using different words, often to achieve clearer understanding.

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The capacity to recognize, understand, and appropriately react to the emotions of others.