Evaluate $\int x ^ { 3 } \left( x ^ { 2 } - 3 \right) ^ { 7 } d x$

question 30

Multiple Choice

Evaluate $\int x ^ { 3 } \left( x ^ { 2 } - 3 \right) ^ { 7 } d x$ .

• A) \(\frac { \left( x ^ { 2 } - 3 \right) ^ { 8 } x ^ { 3 } } { 24 } + C\)
• B) \(\frac { x ^ { 2 } } { 16 } \left( x ^ { 2 } - 3 \right) ^ { 8 } + C\)
• C) \(\frac { x ^ { 2 } } { 16 } \left( x ^ { 2 } - 3 \right) ^ { 8 } - \frac { 1 } { 144 } \left( x ^ { 2 } - 3 \right) ^ { 9 } + C\)
• D) \(\frac { x ^ { 2 } } { 16 } \left( x ^ { 2 } - 3 \right) ^ { 8 } - \frac { 1 } { 72 } \left( x ^ { 2 } - 3 \right) ^ { 9 } + C\)

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Definitions:

Concentration Gradient

A variation in the concentration of a substance across a space, leading to diffusion or active transport phenomena.

Semipermeable Membrane

A membrane that allows the passage of certain molecules or ions but restricts others, crucial in processes like osmosis.

High Temperatures

Conditions involving elevated temperatures, often influencing chemical reactions or physical states of matter.

Activation Energy

The minimum amount of energy required to initiate a chemical reaction.