Find the Indefinite Integral $\int \frac { x } { - 4 x ^ { 2 } + 9 } d x$

question 119

Multiple Choice

Find the indefinite integral. $\int \frac { x } { - 4 x ^ { 2 } + 9 } d x$

• A) \(\frac { \ln \left| - 4 x ^ { 2 } + 9 \right| } { - 4 x ^ { 2 } + 9 } + C\)
• B) \(\frac { - 1 } { 8 } \ln \left| - 4 x ^ { 2 } + 9 \right| + C\)
• C) \(\ln \left| - 4 x ^ { 2 } + 9 \right| + C\)
• D) \(\ln \left| - 4 x ^ { 2 } - 9 \right| + C\)
• E) \(\frac { 1 } { - 8 x } + C\)

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Definitions:

Tragedy of the Commons

A situation in a shared-resource system where individual users acting independently according to their own self-interest behave contrary to the common good of all users by depleting or spoiling that resource.

Excludable

A characteristic of a good or service that means it can be restricted to only those who pay for it; the opposite of a public or non-excludable good.

Rival in Consumption

A characteristic of goods where one individual's consumption prevents or decreases others' ability to consume the same good.

Corrective Tax

A tax designed to correct market outcomes by accounting for externalities, encouraging more efficient allocation of resources.