Use a Table of Integrals to Evaluate the Integral $$\int \frac { \sqrt { 6 x + 5 } } { x ^ { 2 } } d x$$

question 16

Multiple Choice

Use a table of integrals to evaluate the integral. $$\int \frac { \sqrt { 6 x + 5 } } { x ^ { 2 } } d x$$

• A) \(- \frac { \sqrt { 6 x + 5 } } { x } + \frac { 3 \sqrt { 5 } } { 5 } \ln \left| \frac { \sqrt { 6 x + 5 } - \sqrt { 5 } } { \sqrt { 6 x + 5 } + \sqrt { 5 } } \right| + C\)
• B) \(- \frac { \sqrt { 6 x + 5 } } { x } + \frac { 6 \sqrt { 5 } } { 5 } \ln \left| \frac { \sqrt { 6 x + 5 } - \sqrt { 5 } } { \sqrt { 6 x + 5 } + \sqrt { 5 } } \right| + C\)
• C) \(- \frac { 6 \sqrt { 5 } } { 5 } \ln \left| \frac { \sqrt { 6 x + 5 } - \sqrt { 5 } } { \sqrt { 6 x + 5 } + \sqrt { 5 } } \right| + C\)
• D) \(- \frac { 3 \sqrt { 5 } } { 5 } \ln \left| \frac { \sqrt { 6 x + 5 } - \sqrt { 5 } } { \sqrt { 6 x + 5 } + \sqrt { 5 } } \right| + C\)

---

Definitions:

Long-run Equilibrium

A state in which all factors of production and costs are variable, and firms in the industry make just enough profit to stay in business.

Short-run Profits

Short-run profits occur when a company's revenue exceeds its operating costs within a particular, relatively brief period.

Long Run

A period in economics where all inputs, including capital and labor, can be adjusted.

Perfectly Competitive

A market structure characterized by a large number of small firms, identical products, and free entry and exit, leading to price taking behavior.