Express the Integrand as a Sum of Partial Fractions and Evaluate

question 293

Multiple Choice

Express the integrand as a sum of partial fractions and evaluate the integral.
- $$\int \frac { - 2 x ^ { 2 } + 8 x + 8 } { \left( x ^ { 2 } + 4 \right) ( x - 2 ) ^ { 3 } } d x$$

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

---

Definitions:

Mezzo Level Skills

Social work practices targeted at small-to-medium-sized groups, such as communities or institutions.

Generalist Practice

A broad approach in social work that applies a wide range of knowledge, skills, and methods to assess and address issues at individual, family, community, and societal levels.

Supervision

The act of overseeing the work or tasks of others to ensure standards are met and providing guidance, support, and feedback.