Express the Integrand as a Sum of Partial Fractions and Evaluate

question 321

Multiple Choice

Express the integrand as a sum of partial fractions and evaluate the integral.
- $$\int \frac { 2 x ^ { 3 } + 5 x ^ { 2 } + 14 x + 7 } { \left( x ^ { 2 } + 2 x + 5 \right) ^ { 2 } } d x$$

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

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