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

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Definitions:

Aversive

Something unpleasant or repelling, often used in the context of behaviors or stimuli that an organism seeks to avoid.

Unwanted Behaviours

Actions or habits exhibited by individuals that are inappropriate, disruptive, or undesirable in a specific social or professional context.

Stop Reinforcement

The cessation of reinforcements (reward or punishment), leading to an extinction of learned behavior.

Extinguish

To put out or bring to an end, often used in the context of extinguishing a fire or gradually reducing a behavior through the process of elimination in psychology.