Evaluate the Integral $$\int \frac { d x } { x ^ { 2 } + 6 x + 25 }$$

question 211

Multiple Choice

Evaluate the integral.
- $$\int \frac { d x } { x ^ { 2 } + 6 x + 25 }$$

• A) \(\frac { 1 } { 4 } \tan ^ { - 1 } \left( \frac { \mathrm { x } + 3 } { 4 } \right) + \mathrm { C }\)
• B) \(\frac { 1 } { 4 } \sin ^ { - 1 } \left( \frac { x + 3 } { 4 } \right) + C\)
• C) \(( 2 x + 6 ) \ln \left| x ^ { 2 } + 6 x + 25 \right| + C\)
• D) \(4 \tan ^ { - 1 } \left( \frac { \mathrm { x } + 3 } { 4 } \right) + \mathrm { C }\)

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Definitions:

Discretionary Policy

This involves government policies, like fiscal and monetary policy decisions, that are deliberately formulated and applied in response to economic conditions to manage aggregate demand.

Economic Fluctuations

Variations in the level of economic activity in a country over a period of time, characterized by periods of boom and recession.

Fiscal Policy

The use of government spending and taxation levels to influence the economy, aiming at managing economic fluctuations, controlling inflation, and stimulating economic growth.

Tax Cut

A reduction in the amount of taxes imposed by a government, often aimed at stimulating economic growth or achieving political goals.