Express the Integrand as a Sum of Partial Fractions and Evaluate

question 321

Multiple Choice

Express the integrand as a sum of partial fractions and evaluate the integral.
- $$\int \frac { 2 x ^ { 3 } + 5 x ^ { 2 } + 14 x + 7 } { \left( x ^ { 2 } + 2 x + 5 \right) ^ { 2 } } d x$$

• A) \(\ln \left| x ^ { 2 } + 2 x + 5 \right| - \frac { 1 } { 2 } \tan ^ { - 1 } \left( \frac { x + 1 } { 2 } \right) + C\)
• B) \(\ln \left| x ^ { 2 } + 2 x + 5 \right| - \frac { 1 } { 2 } \tan ^ { - 1 } \left( \frac { x + 1 } { 2 } \right) - \frac { 1 } { x ^ { 2 } + 2 x + 5 } + C\)
• C) \(- \frac { 1 } { 2 } \tan ^ { - 1 } \left( \frac { \mathrm { x } + 1 } { 2 } \right) - \frac { 1 } { \mathrm { x } ^ { 2 } + 2 \mathrm { x } + 5 } + \mathrm { C }\)
• D) \(\ln \left| x ^ { 2 } + 2 x + 5 \right| - \frac { 1 } { x ^ { 2 } + 2 x + 5 } + C\)

Identify the legal frameworks and consumer rights under bankruptcy law.

Recognize the impact of bankruptcy among different demographic groups.

Differentiate between various types of bankruptcy and their consequences.

Understand the function and regulation of credit insurance and debt collection practices.

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Organizational structures where decision-making authority is concentrated at a high level, with few individuals or a single entity controlling the organization.

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The flow of information from lower levels of a hierarchy to the higher-ups, aiding in decision-making and organizational effectiveness.