Evaluate the Integral by Using a Substitution Prior to Integration $$\int \frac { x ^ { 2 } } { \sqrt { x ^ { 2 } + 13 } } d x$$

question 127

Multiple Choice

Evaluate the integral by using a substitution prior to integration by parts.
- $$\int \frac { x ^ { 2 } } { \sqrt { x ^ { 2 } + 13 } } d x$$

• A) \(\frac { 3 x } { 2 } \sqrt { x ^ { 2 } + 13 } + \frac { 13 } { 2 } \ln \left( x + \sqrt { x ^ { 2 } + 13 } \right) + C\)
• B) \(\frac { 3 x } { 2 } \sqrt { x ^ { 2 } + 13 } - \frac { 13 } { 2 } \ln \left( x + \sqrt { x ^ { 2 } + 13 } \right) + C\)
• C) \(\frac { x } { 2 } \sqrt { x ^ { 2 } + 13 } - \frac { 13 } { 2 } \ln \left( x + \sqrt { x ^ { 2 } + 13 } \right) + C\)
• D) \(\frac { x } { 2 } \sqrt { x ^ { 2 } + 13 } + \frac { 13 } { 2 } \ln \left( x + \sqrt { x ^ { 2 } + 13 } \right) + C\)

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Definitions:

Subliminal Stimulation

The process of influencing individuals with signals or messages delivered below the threshold of conscious perception.

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The part of the cerebral cortex responsible for processing visual information, located in the occipital lobe.

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The light-sensitive inner surface of the eye, containing the receptor rods and cones plus layers of neurons that begin the processing of visual information.

Thalamus

A part of the brain located above the brainstem that acts as a relay center, directing sensory and motor signals to other parts of the brain.