Evaluate the Integral $$\int 4 \left( \frac { x - 1 } { x ^ { 2 } + 2 x } \right) d x$$

question 79

Multiple Choice

Evaluate the integral.
$$\int 4 \left( \frac { x - 1 } { x ^ { 2 } + 2 x } \right) d x$$

• A) \(4 \left( \frac { 1 } { 3 } x - \frac { 1 } { 3 } \ln x \right) + C\)
• B) \(4 \left( \frac { 3 } { 2 } \ln ( x + 2 ) - \frac { 1 } { 2 } \ln x \right) + C\)
• C) \(- 4 \left( \frac { \sqrt { 2 } } { 2 } \arctan x \right) + C\)
• D) \(- 4 ( \ln x - x ) + C\)
• E) None of these

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Definitions:

T-statistic

The t-statistic is a ratio calculated from the difference between a sample mean and a population mean, divided by the standard error of the mean.

Null

Often refers to a hypothesis which assumes no significant difference or effect in a statistical analysis.

Alpha

In statistics, the threshold probability of wrongly rejecting the null hypothesis, typically set at 0.05.

T-statistic

A ratio computed from the observed sample mean difference divided by the standard error of the mean, used in hypothesis testing.