Integrate the Function $$\int \frac { x ^ { 3 } } { \sqrt { x ^ { 2 } + 8 } } d x$$

question 97

Multiple Choice

Integrate the function.
- $$\int \frac { x ^ { 3 } } { \sqrt { x ^ { 2 } + 8 } } d x$$

• A) \(\frac { 1 } { 3 } \left( x ^ { 2 } + 8 \right) ^ { 3 / 2 } + \tan ^ { - 1 } \left( \frac { x } { 8 } \right) + C\)
• B) \(\frac { 1 } { 3 } \left( x ^ { 2 } + 8 \right) ^ { 3 / 2 } - 8 \sqrt { x ^ { 2 } + 8 } + C\)
• C) \(\frac { 1 } { 3 } \sqrt { x ^ { 2 } + 8 } - \frac { 8 } { \sqrt { x ^ { 2 } + 8 } } + C\)
• D) \(\frac { 1 } { 8 } \left( x ^ { 2 } + 8 \right) ^ { 3 / 2 } - \sqrt { x ^ { 2 } + 8 } + C\)

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Definitions:

Neurons

Unique cells within the nervous system that convey data to other neurons, muscles, or glands.

Communicate

To convey or exchange information, thoughts, or messages through speech, writing, or signals.

Graded Potential

Graded Potential is a variable electric potential change in neurons that decreases in magnitude with distance from the stimulus source, contrary to the all-or-none response of action potentials.

Electrical Charge

A fundamental property of matter that causes it to experience a force when placed in an electromagnetic field.