Evaluate the Integral $$\int \frac { 7 d x } { \left( x ^ { 2 } + 2 x + 2 \right) ^ { 2 } }$$

question 4

Multiple Choice

Evaluate the integral.
$$\int \frac { 7 d x } { \left( x ^ { 2 } + 2 x + 2 \right) ^ { 2 } }$$

• A) \(\frac { 1 } { 2 } \left( \tan ( x + 1 ) + \frac { 17 } { x ^ { 2 } + 2 x + 2 } \right) + C\)
• B) \(\frac { 1 } { 2 } \left( \tan ^ { - 1 } ( x + 2 ) + \frac { 7 } { x ^ { 2 } + 2 } \right) + C\)
• C) \(\frac { 1 } { 2 } \left( \tan ^ { - 1 } ( x + 7 ) + \frac { 1 } { x ^ { 2 } + 2 x + 2 } \right) + C\)
• D) \(\frac { 7 } { 2 } \left( \tan ( x + 2 ) + \frac { x + 1 } { x ^ { 2 } + 2 x + 2 } \right) + C\)
• E) \(\frac { 7 } { 2 } \left( \tan ^ { - 1 } ( x + 1 ) + \frac { x + 1 } { x ^ { 2 } + 2 x + 2 } \right) + C\)

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Definitions:

Latency Stage

A phase in Freudian psychosexual development occurring between ages six and puberty, characterized by a decrease in sexual interest and activities.

Psychosexual Development

A Freudian theory in psychology that suggests human development occurs in stages based around the erogenous zones.

Social Contacts

Social contacts refer to interactions and relationships with other people, ranging from casual acquaintances to deep, personal connections, which are vital for emotional well-being and social support.

Genital Stage

In psychoanalytic theory, the final stage of psychosexual development, typically beginning at puberty, where sexual maturity is reached, and sexual interests become concentrated on the genitals.