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) \(\frac { 1 } { 2 } \tan ^ { - 1 } \left( \frac { x } { 2 } \right) - \frac { 1 } { ( x - 2 ) ^ { 2 } } + \frac { 1 } { ( x - 2 ) ^ { 3 } } + C\)

Understand the advantages of internal over external fertilization and the biological implications for species.

Identify and describe the structure and function of male reproductive anatomy, including the significance of sperm components.

Recognize the cellular development process of sperm from spermatogonia to mature sperm.

Understand the process and biological significance of sexual and asexual reproduction, including environmental factors that influence reproductive strategies.

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