Evaluate the Integral by First Performing Long Division on the Integrand

question 8

Multiple Choice

Evaluate the integral by first performing long division on the integrand and then writing the proper fraction as a sum of partial fractions.
- $$\int \frac { x ^ { 4 } } { x ^ { 2 } - 9 } d x$$

• A) \(\frac { x ^ { 3 } } { 3 } + 9 x + \frac { 27 } { 2 } \ln | x - 9 | - \frac { 27 } { 2 } \ln | x + 9 | + C\)
• B) \(\frac { x ^ { 3 } } { 3 } + 9 x + \frac { 27 } { 2 } \ln | x - 3 | - \frac { 27 } { 2 } \ln | x + 3 | + C\)
• C) \(\frac { x ^ { 3 } } { 3 } + \frac { 9 } { 2 } \ln | x - 3 | - \frac { 9 } { 2 } \ln | x + 3 | + C\)
• D) \(\frac { x ^ { 3 } } { 3 } + 9 x - \frac { 27 } { 2 } \ln | x - 3 | + \frac { 27 } { 2 } \ln | x + 3 | + C\)

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