Find the Indefinite Integral $\int \frac { x ^ { 2 } - 25 } { x ^ { 2 } + 25 } d x$

question 152

Multiple Choice

Find the indefinite integral $\int \frac { x ^ { 2 } - 25 } { x ^ { 2 } + 25 } d x$ .

• A) \(\frac { x ^ { 3 } - 25 x } { x ^ { 3 } + 25 x } + C\)
• B)
• \(x - 10 \arctan \left( \frac { x } { 5 } \right) + C\)
• C)
• \(x - 6 \arctan \left( \frac { x } { 5 } \right) + C\)
• D) \(\frac { x ^ { 3 } - 75 x } { x ^ { 3 } + 75 x } + C\)

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Definitions:

Marginal Product

The additional output resulting from a one-unit increase in the use of a particular input, holding all other inputs constant.

Monopsony

A market condition where there is only one buyer for a product or service, giving them significant control over prices.

Hourly Wage

The rate an employee is paid for each hour of work.

Labor-Supply Curve

A graphical representation showing the relationship between the amount of labor workers are willing to provide at different wage rates.