Express the Integrand as a Sum of Partial Fractions and Evaluate

question 78

Multiple Choice

Express the integrand as a sum of partial fractions and evaluate the integral.
- $$\int \frac { 5 x + 12 } { x ^ { 3 } + 4 x ^ { 2 } + 4 x } d x$$

• A) \(3 \ln \left| \frac { x } { x + 2 } \right| + \frac { 1 } { x + 2 } + C\)
• B) \(2 \ln \left| \frac { x } { x + 2 } \right| - \frac { 1 } { x + 2 } + C\)
• C) \(3 \ln \left| \frac { x } { x + 2 } \right| - \frac { 6 } { x + 2 } + C\)
• D) \(3 \ln \left| \frac { x } { x + 2 } \right| + \frac { 5 } { x + 2 } + C\)

Recognize and apply the processes that enhance effective communication.

Identify the roles individuals play in various communication scenarios.

Grasp the importance of adapting communication strategies to audience needs.

Comprehend the sophisticated nature of human communication beyond mere message exchange.

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Definitions:

Psychoanalysis

A therapeutic technique and theory of psychological disorders, emphasizing unconscious conflicts and childhood experiences.

Cognitive Therapies

Psychological treatments that focus on changing faulty or irrational thinking patterns, beliefs, and attitudes.

Systematic Desensitization

A therapeutic method used to cure phobias and other behavior problems involving anxiety, by gradual exposure to the feared object or situation in a controlled environment.

Token Economy

An operant conditioning procedure in which people earn a token for exhibiting a desired behavior and can later exchange the tokens for privileges or treats.