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

question 67

Multiple Choice

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

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

Recognize the effects of quality improvement initiatives on decision-making speed.

Comprehend the relationship between uncertainty and decision confidence.

Identify the conditions of risk and how they differ from certainty and uncertainty.

Acknowledge the time implications of seeking interdisciplinary inputs in decision making.

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Definitions:

Peroxide Initiator

A compound that decomposes to form free radicals, initiating polymerization reactions.

Propylene

A flammable gas that is a colorless hydrocarbon used as a fuel and a petrochemical feedstock.

3-ethyl-3-hexene

An organic compound, specifically an alkene, with a double bond between two of the carbon atoms, and an ethyl group attached to the third carbon atom.

Regio-

A prefix indicating the region or position in a molecule where a chemical reaction occurs, often used in organic chemistry.