Express the Integrand as a Sum of Partial Fractions and Evaluate

question 222

Multiple Choice

Express the integrand as a sum of partial fractions and evaluate the integral.
- $$\int \frac { 2 x ^ { 2 } + x + 1 } { \left( x ^ { 2 } + 3 \right) ( x - 5 ) } d x$$

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