Find the Given Integral $$\int \frac { 2 \tan ^ { - 1 } 2 x } { 1 + 4 x ^ { 2 } } d x$$

question 94

Short Answer

Find the given integral.
$$\int \frac { 2 \tan ^ { - 1 } 2 x } { 1 + 4 x ^ { 2 } } d x$$

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Definitions:

Invisible Hand Principle

Adam Smith's concept that individuals' self-interested actions can lead to positive social and economic outcomes, guided as if by an invisible hand.

Economic Welfare

The overall well-being and standard of living of people in an economy, typically measured by indicators like wealth, health, and happiness, alongside economic factors.

Competitive Market

A market structure characterized by a large number of buyers and sellers, free entry and exit, and products that are similar but differentiated.

Invisible Hand Concept

A term coined by Adam Smith describing the self-regulating nature of the marketplace, where individuals pursuing their self-interest unwittingly contribute to the economic wellbeing of society.