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

question 50

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) \(\frac { 7 } { 2 } \left( \tan ^ { - 1 } ( x + 1 ) + \frac { x + 1 } { x ^ { 2 } + 2 x + 2 } \right) + C\)

---

Definitions:

Primary Appraisal

The initial evaluation process where the individual assesses the significance of a stressor as being positive, neutral, or negative.

Potential Stressor

An event, situation, or stimulus that has the capacity to induce stress, depending on the individual's perception, experiences, and coping mechanisms.

Abstract Painting

A style of painting that does not attempt to represent external reality, but seeks to achieve its effect through shapes, colors, and textures.

Projective Test

A psychological assessment tool in which a subject's response to ambiguous stimuli, such as pictures or patterns, is interpreted to uncover unconscious desires, thoughts, or emotions.