Use a Trigonometric Substitution to Evaluate the Integral $$\int \frac { d x } { x \sqrt { 9 + \ln ^ { 2 } x } }$$

question 64

Multiple Choice

Use a trigonometric substitution to evaluate the integral.
- $$\int \frac { d x } { x \sqrt { 9 + \ln ^ { 2 } x } }$$

• A) \(\cosh ^ { - 1 } \left( \frac { \ln x } { 3 } \right) + C\)
• B) \(\sin ^ { - 1 } \left( \frac { \ln x } { 3 } \right) + C\)
• C) \(\tan ^ { - 1 } \left( \frac { \ln x } { 3 } \right) + C\)
• D) \(\sinh ^ { - 1 } \left( \frac { \ln x } { 3 } \right) + C\)

---

Definitions:

Middle Class

Refers to the social group between the upper and working classes, including professionals, business people, and others with a moderate to high income level.

Lower Class

A term often used in sociology to describe a social group that is at the bottom of a societal hierarchy based on wealth, education, or occupation.

Education Levels

Classifications that describe the highest degree of education completed by individuals or required for certain jobs.