Express the Integrand as a Sum of Partial Fractions and Evaluate

question 294

Multiple Choice

Express the integrand as a sum of partial fractions and evaluate the integral.
- $$\int \frac { 7 x ^ { 3 } + 35 x ^ { 2 } + 55 x + 23 } { ( x + 3 ) ( x + 1 ) ^ { 3 } } d x$$

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

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