Find the Indefinite Integral $$\int \frac { 2 x - 4 } { x ^ { 2 } + 4 x + 13 } d x$$

question 16

Multiple Choice

Find the indefinite integral. $$\int \frac { 2 x - 4 } { x ^ { 2 } + 4 x + 13 } d x$$

• A) \(\ln \left| x ^ { 2 } + 4 x + 13 \right| - \frac { 8 } { 3 } \arctan \left( \frac { x + 2 } { 3 } \right) + C\)
• B) \(\ln \left| x ^ { 2 } + 4 x + 13 \right| + C\)
• C) \(- \frac { 8 } { 3 } \arctan \left( \frac { x + 2 } { 3 } \right) + C\)
• D) \(\ln \left| x ^ { 2 } + 4 x + 13 \right| + \frac { 8 } { 3 } \arctan \left( \frac { x + 2 } { 3 } \right) + C\)
• E) \(\frac { 8 } { 3 } \arctan \left( \frac { x + 2 } { 3 } \right) + C\)

Understand the influence of geographical features on climate and biome distribution.

Explain the ecological role of organisms in extreme environments such as thermal vents.

Understand the basic trophic levels and their roles in ecosystems (producers, consumers, decomposers).

Grasp the concepts of energy flow and nutrient cycling within ecosystems.

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