Express the Integrand as a Sum of Partial Fractions and Evaluate

question 308

Multiple Choice

Express the integrand as a sum of partial fractions and evaluate the integral.
- $$\int \frac { 5 x ^ { 2 } + x + 36 } { x ^ { 3 } + 9 x } d x$$

• A) \(4 \ln | x | + \frac { 1 } { 2 } \ln \left| x ^ { 2 } + 9 \right| + \frac { 1 } { 3 } \tan ^ { - 1 } \left( \frac { x } { 3 } \right) + C\)
• B) \(4 \ln | x | - \frac { 1 } { 2 } \ln \left| x ^ { 2 } + 9 \right| - \tan ^ { - 1 } x + C\)
• C) \(4 \ln | x | + \frac { 1 } { 2 } \ln \left| x ^ { 2 } + 9 \right| + \sin ^ { - 1 } \left( \frac { x } { 3 } \right) + C\)
• D) \(\ln | x | + \frac { 1 } { 2 } \ln \left| x ^ { 2 } + 9 \right| + \tan ^ { - 1 } \left( \frac { x } { 3 } \right) + C\)

Explain and differentiate between income, wealth, and other financial indicators.

Identify demographic characteristics associated with poverty in the United States and analyze these patterns through theoretical perspectives.

Describe the structure and characteristics of the U.S. class system.

Explore and explain theories related to stratification, including the works of Marx and Weber.

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Definitions:

Ions

Atoms or molecules with a net electric charge due to the loss or gain of one or more electrons.

Solution

A homogeneous mixture composed of two or more substances, where the solute is dissolved in the solvent.

Adrenal Cortex

The outer layer of the adrenal glands that produces steroid hormones such as cortisol and aldosterone, which regulate metabolism and blood pressure.

Hormones

Chemical messengers produced by the endocrine glands in the body, transported in the bloodstream to target organs to regulate physiology and behavior.