Express the Integrand as a Sum of Partial Fractions and Evaluate

question 134

Multiple Choice

Express the integrand as a sum of partial fractions and evaluate the integral.
- $$\int \frac { 3 x ^ { 3 } - 3 x ^ { 2 } + 6 x - 6 } { \left( x ^ { 2 } + 2 \right) ( x - 2 ) ^ { 3 } } d x$$

• A) \(- \frac { 3 } { x - 2 } - \frac { 3 } { 2 ( x - 2 ) ^ { 2 } } + C\)
• B) \(\frac { 1 } { x ^ { 2 } + 2 } - \frac { 2 } { x - 2 } - \frac { 3 } { 2 ( x - 2 ) ^ { 2 } } + C\)
• C) \(2 \ln | x - 2 | - \frac { 2 } { x - 2 } - \frac { 3 } { 2 ( x - 2 ) ^ { 2 } } + C\)
• D) \(\frac { 4 } { x - 2 } - \frac { 5 } { 2 ( x - 2 ) ^ { 3 } } + C\)

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