Evaluate the Improper Integral or State That It Is Divergent $$\int _ { 1 } ^ { \infty } \frac { 9 } { \left( 1 + x ^ { 2 } \right) \tan ^ { - 1 } x } d x$$

question 421

Multiple Choice

Evaluate the improper integral or state that it is divergent.
- $$\int _ { 1 } ^ { \infty } \frac { 9 } { \left( 1 + x ^ { 2 } \right) \tan ^ { - 1 } x } d x$$

• A) \(\frac { 9 } { 2 } \left( 1 + \frac { \pi } { 2 } \right) ^ { 2 }\)
• B) \(9 \ln 2\)
• C) \(9 \ln \frac { \pi } { 2 }\)
• D) \(9 \ln \left( 1 + \frac { \pi } { 2 } \right)\)

---

Definitions:

Cultural Interpretation

The process of understanding and evaluating behaviors, values, and beliefs within the context of a specific culture.

Empathic

The capacity to understand and share the feelings of another person, often leading to compassionate action.

Touch

The physical sensation perceived when something comes into contact with the skin, one of the five senses.

Nonverbal Communication

The process of conveying messages and meanings without the use of spoken or written words, through facial expressions, gestures, and body language.