Evaluate the Integral $$\int \frac { d x } { \sqrt { x ^ { 2 } - 6 x - 7 } }$$

question 320

Multiple Choice

Evaluate the integral.
- $$\int \frac { d x } { \sqrt { x ^ { 2 } - 6 x - 7 } }$$

• A) \(\frac { 1 } { 4 } \tan ^ { - 1 } \left( \frac { x - 3 } { 4 } \right) + C\)
• B) \(\sin ^ { - 1 } \left( \frac { x - 3 } { 4 } \right) + C\)
• C) \(\sin ^ { - 1 } \left( \frac { x + 3 } { 4 } \right) + C\)
• D) \(\sin ^ { - 1 } \left( \frac { x - 6 } { 4 } \right) + C\)

Understand the basic concepts and assumptions of the quantity theory of money.

Grasp the relationship between money supply (M), velocity of money (V), price level (P), and real output (Q) in determining GDP.

Differentiate between the crude and sophisticated quantity theories of money.

Recognize the importance of velocity of money in economic transactions and its calculation.

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Definitions:

Birch Reduction

A chemical reaction that reduces aromatic rings to cyclohexadienes using sodium or lithium in liquid ammonia, often with an alcohol as a proton source.

T-Butylbenzoic Acid

T-Butylbenzoic Acid is an organic compound with the structure derived from benzoic acid where a tert-butyl group is attached to the benzene ring.

Synthetic Steps

The sequenced actions taken in the laboratory to synthetically create or modify molecules.

Toluene

Toluene is a clear, water-insoluble liquid, widely used as an industrial feedstock and solvent, known for its role in the manufacture of benzene and as a component in gasoline.