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:

Degree of Operating Leverage

A financial indicator that evaluates how changes in sales volume impact a company's operating earnings.

Break-even

The juncture where overall expenses match total income, indicating neither profit nor loss is present.

Unit Sales

The total quantity of an item or product sold.

Contribution Margin Ratio

A ratio that measures the proportion of each sales dollar remaining after variable costs have been deducted.