Evaluate the Integral Using the Indicated Trigonometric Substitution $\int \frac{x^{3}}{\sqrt{x^{2}+16}} d x ; x=4 \tan \theta$

question 45

Multiple Choice

Evaluate the integral using the indicated trigonometric substitution. $\int \frac{x^{3}}{\sqrt{x^{2}+16}} d x ; x=4 \tan \theta$

• A) \(\frac{3}{2}(x+16)^{3 / 2}-16 \sqrt{x+16}+C\)
• B) \(\left(x^{2}+16\right)^{3 / 2}-\sqrt{x^{2}+16}+C\)
• C) \(\frac{1}{3}\left(x^{2}+16\right)^{3 / 2}-\sqrt{x^{2}+16}+C\)
• D) \(\frac{1}{3}\left(x^{2}+16\right)^{3 / 2}+16 \sqrt{x^{2}+16}+C\)
• E) \(\left(x^{2}+16\right)^{3 / 2}-4 \sqrt{x^{2}+16}+C\)

Grasp the global perception of the Civil War and its key figures post-war.

Identify the ongoing struggle and progress toward racial equality and civil rights post-Civil War.

Understand the concepts of marginal utility and how it influences consumer purchasing behavior.

Comprehend the composition and implications of the consumer's budget line.

---

Definitions:

Falling Prices

Falling prices indicate a decrease in the cost of goods and services over a period, which can be symptomatic of deflation or market corrections.

Behavioral Finance

A field of finance that examines how psychological influences and biases affect the financial behaviors of investors and financial markets.

Psychological Factors

Elements of human behavior and cognition that influence financial decision-making and market movements.

Investor Behavior

The study of how psychology influences financial decision-making and market movements.