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:

Math Aptitude

The natural ability or talent for solving math problems and understanding mathematical concepts.

Spatial Visualization

The cognitive ability to manipulate, analyze, and comprehend two- and three-dimensional shapes and figures.

Third Sex

A term used to categorize individuals who do not fit traditional male or female gender roles, often seen in cultures recognizing more than two genders.

Hijras

A traditional term in South Asia for a transgender person who may take on the roles in various social and ceremonial aspects, often outside the conventional gender binary.