Express the Integrand as a Sum of Partial Fractions and Evaluate

question 338

Multiple Choice

Express the integrand as a sum of partial fractions and evaluate the integral.
- $$\int \frac { 72 d x } { x ^ { 3 } - 9 x }$$

• A) \(- \frac { 8 } { x } + 4 \ln | x - 3 | + 4 \ln | x + 3 | + C\)
• B) \(8 \ln | x | - 4 \ln | x - 3 | - 4 \ln | x + 3 | + C\)
• C) \(- 8 \ln | x | + 4 \ln | x - 3 | + 4 \ln | x + 3 | + C\)
• D) \(- 8 \ln | x | + \frac { 1 } { 3 } \tan ^ { - 1 } \frac { x } { 3 } + C\)

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Definitions:

Social Loafing

The phenomenon where individuals exert less effort when working in a group than when working alone.

Collective Action

Action taken together by a group of people whose goal is to enhance their status and achieve a common objective.

System Justification Theory

A theory suggesting that people have a psychological tendency to defend and justify the status quo, even at the expense of personal or group interest.

Social Identity Theory

Social identity theory is a psychological framework that posits individuals derive part of their identity and self-esteem from the groups to which they belong.