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

question 34

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:

Stimulus Generalization

The process by which a response conditioned to one stimulus is evoked by similar, but not identical, stimuli.

Higher-Order Conditioning

Higher-order conditioning is a form of learning in which a stimulus is paired with a previously conditioned stimulus, leading to an association and conditioned response to the new stimulus, even though it was never directly associated with the unconditioned stimulus.

Sensory Preconditioning

A learning process where a neutral stimulus becomes capable of eliciting a response after being paired with another stimulus that naturally evokes a reaction.

Conditioned Response

A learned response to a previously neutral stimulus that has been repeatedly paired with an unconditioned stimulus.