Express the Integrand as a Sum of Partial Fractions and Evaluate

question 367

Multiple Choice

Express the integrand as a sum of partial fractions and evaluate the integral.
- $$\int \frac { 6 x - 12 } { x ^ { 2 } - 4 x - 5 } d x$$

• A) \(3 \ln | x - 5 | + 3 \ln | x + 1 | + C\)
• B) \(4 \ln | x - 5 | - 3 \ln | x + 1 | + C\)
• C) \(\ln | 3 ( x - 5 ) + 3 ( x + 1 ) | + C\)
• D) \(3 \ln | x + 5 | + 3 \ln | x - 1 | + C\)

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Definitions:

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The collective wealth, assets, or resources that a country possesses, which can contribute to its economic development and welfare.

Labor Costs

The total expenditure incurred by employers for the compensation of employees, including wages, benefits, and taxes.

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An equation or model that describes the relationship between inputs used in production and the output of goods or services.

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The financial assets or resources that businesses and individuals use to invest, produce goods and services, including buildings, machinery, and equipment.