Find the Integral Using an Appropriate Trigonometric Substitution $$\int \frac { x ^ { 3 } } { \sqrt { x ^ { 2 } + 1 } } d x$$

question 153

Multiple Choice

Find the integral using an appropriate trigonometric substitution. Select the correct answer.
$$\int \frac { x ^ { 3 } } { \sqrt { x ^ { 2 } + 1 } } d x$$

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

Assess whether specific groups such as women and African Americans are more prone to low self-esteem based on research findings.

Identify the "positive illusions" that contribute to the mental health of well-adjusted individuals as described by Taylor and Brown.

Understand various methods individuals use to escape self-awareness and the implications of these methods.

Describe the endowment effect and give examples to illustrate this concept.

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