Evaluate the Integral by Making a Substitution (Possibly Trigonometric) and Then

question 450

Multiple Choice

Evaluate the integral by making a substitution (possibly trigonometric) and then applying a reduction formula.
- $$\int \frac { d x } { \left( 25 - x ^ { 2 } \right) ^ { 2 } }$$

• A) \(\frac { 1 } { 10 } \ln \left| \frac { x + 5 } { x - 5 } \right| + C\)
• B) \(\frac { x } { 50 \left( 25 - x ^ { 2 } \right) } + C\)
• C) \(\frac { 1 } { 50 } \left( \frac { x } { 25 - x ^ { 2 } } + \frac { 1 } { 10 } \ln \left| \frac { x + 5 } { x - 5 } \right| \right) + C\)
• D) \(\frac { 1 } { 50 } \left( \frac { x } { 25 - x ^ { 2 } } - \frac { 1 } { 10 } \ln \left| \frac { x + 5 } { x - 5 } \right| \right) + C\)

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Definitions:

Neurotic Needs

These needs are excessive compulsions that individuals develop to deal with anxiety but ultimately lead to unhealthy behaviors or attitudes, as identified by psychoanalyst Karen Horney.

Trait Approach

A perspective in psychology that theorizes personality is comprised of broad, consistent behaviors or dispositions called traits, which this approach aims to identify and measure.

Heredity

The transmission of physical or mental traits from one generation to the next through genetics.

Mother

A female parent or guardian of a child, who may also play a pivotal role in the child's development and upbringing.