Evaluate the Integral $$\int \frac { \sqrt { 25 x ^ { 2 } - 9 } } { x } d x$$

question 256

Multiple Choice

Evaluate the integral.
- $$\int \frac { \sqrt { 25 x ^ { 2 } - 9 } } { x } d x$$

• A) \(\sqrt { x ^ { 2 } - 9 } - 3 \sec - 1 \left| \frac { x } { 3 } \right| + C\)
• B) \(\ln \left| x + \sqrt { 25 x ^ { 2 } - 9 } \right| - \frac { \sqrt { 25 x ^ { 2 } - 9 } } { x } + C\)
• C) \(\ln \left| x + \sqrt { x ^ { 2 } - 9 } \right| - \frac { \sqrt { x ^ { 2 } - 9 } } { x } + C\)
• D) \(\sqrt { 25 x ^ { 2 } - 9 } - 3 \sec - 1 \left| \frac { 5 x } { 3 } \right| + C\)

---

Definitions:

Despair

A profound sense of hopelessness, often accompanied by a loss of motivation and decreased emotional well-being.

Indifferent

Having no particular interest or sympathy; unconcerned or neutral towards something.

Psychological State

An individual's current mental condition or mind state, which can affect perceptions, emotions, and behavior.

Detachment

For Bowlby, the state of indifference toward others experienced by children who have been separated from their caregivers for an extended time and have not formed new stable relationships.