Evaluate the Integral $\int x ^ { 3 } \ln 4 x d x$

question 37

Multiple Choice

Evaluate the integral.
- $\int x ^ { 3 } \ln 4 x d x$

• A) \(\frac { 1 } { 4 } x ^ { 4 } \ln 4 x - \frac { 1 } { 20 } x ^ { 5 } + C\)
• B) \(\frac { 1 } { 4 } x ^ { 4 } \ln 4 x - \frac { 1 } { 16 } x ^ { 4 } + C\)
• C) \(\frac { 1 } { 4 } x ^ { 4 } \ln 4 x + \frac { 1 } { 16 } x ^ { 4 } + C\)
• D) \(\ln 4 x - \frac { 1 } { 4 } x ^ { 4 } + C\)

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Definitions:

Extinction

In psychology, the gradual weakening and disappearance of a conditioned response when the conditioned stimulus is repeatedly presented without the unconditioned stimulus.

Discrimination

Discriminatory actions or attitudes against people belonging to distinct categories, mainly due to factors like ethnicity, age, or sexual orientation.

Classical Conditioning

A learning process that occurs through associations between an environmental stimulus and a naturally occurring stimulus, famously demonstrated by Ivan Pavlov's experiments with dogs.

Conditioned Stimulus (CS)

A stimulus that was neutral but becomes able to provoke a conditioned response after being paired with an unconditioned stimulus.