Evaluate the Integral $$\int \frac { d x } { x ^ { 2 } \sqrt { 2 x - 7 } }$$

question 74

Multiple Choice

Evaluate the integral.
- $$\int \frac { d x } { x ^ { 2 } \sqrt { 2 x - 7 } }$$

• A) \(- \frac { \sqrt { 2 x - 7 } } { 7 x } - \frac { 2 } { 7 \sqrt { 7 } } \tan ^ { - 1 } \sqrt { \frac { 2 x - 7 } { 7 } } + C\)
• B) \(\frac { \sqrt { 2 x - 7 } } { 7 x } + \frac { 2 } { 7 \sqrt { 7 } } \tan ^ { - 1 } \sqrt { \frac { 2 x - 7 } { 7 } } + C\)
• C) \(\frac { \sqrt { 2 x - 7 } } { 7 x } + \frac { 2 } { 7 \sqrt { 7 } } \ln \left| \frac { \sqrt { 2 x - 7 } - \sqrt { 7 } } { \sqrt { 2 x - 7 } + \sqrt { 7 } } \right| + C\)
• D) \(\frac { \sqrt { 2 x - 7 } } { 7 } - \frac { 2 } { 7 \sqrt { 7 } } \tan ^ { - 1 } \sqrt { \frac { 2 x - 7 } { 7 x } } + C\)

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Definitions:

Inflation Tax

The revenue the government raises by creating money

Deadweight Loss

The fall in total surplus that results from a market distortion, such as a tax.

Money-Supply Growth Rate

The rate at which the amount of money available in an economy grows, impacting inflation and economic activity.

Hyperinflations

denotes extremely high and typically accelerating inflation rates, often resulting in the rapid erosion of the real value of the local currency.