Evaluate the Integral Using Integration by Parts $\int x ^ { 2 } e ^ { - x } d x$

question 125

Multiple Choice

Evaluate the integral using integration by parts.
- $\int x ^ { 2 } e ^ { - x } d x$

• A) -(2x +2) \(\mathrm { e } ^ { - \mathrm { x } }\) + C
• B) ( \(x ^ { 2 }\) + 2x +2) \(\mathrm { e } ^ { - \mathrm { x } }\) + C
• C) ( \(x ^ { 2 }\) + 2x) \(\mathrm { e } ^ { - \mathrm { x } }\) + C
• D) -( \(x ^ { 2 }\) + 2x +2) \(\mathrm { e } ^ { - \mathrm { x } }\) + C

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Definitions:

Schizophrenia

A group of severe disorders characterized by disorganized and delusional thinking, disturbed perceptions, and inappropriate emotions and actions.

Dopamine

A neurotransmitter in the brain that plays a major role in reward-motivated behavior, mood regulation, and control of movement.

Receptor Activity

The involvement of cellular receptors in responding to stimuli or drugs, affecting cell function.

Reuptake

Reuptake is a process by which neurotransmitters are absorbed back into the neuronal presynaptic cell after their release into the synaptic cleft, influencing neurotransmission.