$\text { Use partial fractions to find } \int \frac { x ^ { 2 } + x + 5 } { x ^ { 4 } + 10 x ^ { 2 } + 25 } d x \text {. }$

question 48

Multiple Choice

$\text { Use partial fractions to find } \int \frac { x ^ { 2 } + x + 5 } { x ^ { 4 } + 10 x ^ { 2 } + 25 } d x \text {. }$

• A)
• \(\int \frac { x ^ { 2 } + x + 5 } { x ^ { 4 } + 10 x ^ { 2 } + 25 } d x = ( 1 / \sqrt { 5 } ) \arctan ( x / \sqrt { 5 } ) - \frac { 1 } { 2 \left( x ^ { 2 } + 5 \right) } + C\)
• B)
• \(\int \frac { x ^ { 2 } + x + 5 } { x ^ { 4 } + 10 x ^ { 2 } + 25 } d x = \frac { 1 } { 2 \left( x ^ { 2 } + 10 \right) } + C\)
• C)
• \(\int \frac { x ^ { 2 } + x + 5 } { x ^ { 4 } + 10 x ^ { 2 } + 25 } d x = ( 1 / \sqrt { 5 } ) \arcsin ( x / \sqrt { 5 } ) + C\)
• D)
• \(\int \frac { x ^ { 2 } + x + 5 } { x ^ { 4 } + 10 x ^ { 2 } + 25 } d x = - \frac { 1 } { 2 \left( x ^ { 2 } + 5 \right) } + C\)
• E)
• \(\int \frac { x ^ { 2 } + x + 5 } { x ^ { 4 } + 10 x ^ { 2 } + 25 } d x = \arctan ( x / \sqrt { 10 } ) - \frac { 1 } { 2 \left( x ^ { 2 } + 5 \right) } + C\)

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Definitions:

Conscientiousness

How neat, organized, and achievement oriented a person is; part of the Big Five personality traits.

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The length of time that an individual lives or a thing exists; often used in the context of life expectancy.

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A predisposition or likelihood of developing certain traits, behaviors, or conditions based on one's genetic makeup.

Self-Control

Willpower; the ability to control one’s own behavior.