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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Definitions:

Sum of Squares

The sum of the squared differences between each observation and the overall mean, used in various statistical models to measure variability.

Regression SSR

Sum of Squares due to Regression, representing the variation explained by the independent variables in a regression model.

API Gravity

A measure used to determine how heavy or light a petroleum liquid is compared to water, influencing product classification and market value.

Price Per Barrel

The cost of a barrel of commodities such as oil or other fluids, typically used in measuring large-scale transactions in the energy sector.