Provide an Appropriate Response $\ln \left( 1 + x ^ { 2 } \right)$

question 198

Multiple Choice

Provide an appropriate response.
-Derive a series for $\ln \left( 1 + x ^ { 2 } \right)$ for $x > 1$ by first finding the series for $\frac { x } { 1 + x ^ { 2 } }$ and then integrating. $\left( \right.$ Hint: $\left. \frac { x } { 1 + x ^ { 2 } } = \frac { 1 } { x } \frac { 1 } { 1 + 1 / x ^ { 2 } } \right)$

• A) \(2 \ln x + \sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { n x ^ { 2 n } }\)
• B) \(\ln x + \sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n - 1 } } { n x ^ { 2 n } }\)
• C) \(\ln x + \sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } } { n x ^ { 2 n } }\)
• D) \(2 \ln x + \sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } } { n x ^ { 2 n } }\)

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Definitions:

Psychoanalytic Techniques

Methods developed by Freud and his successors to explore the unconscious mind, such as free association, dream analysis, and transference.

Insight

The capacity to gain a deep, intuitive understanding of a person or situation, often resulting in a clear comprehension of complex patterns or issues.

Free Association

A psychoanalytic technique in which a patient says whatever comes to mind without censorship as a way to uncover unconscious thoughts.

Biomedical Therapy

Involves the treatment of psychological disorders through medical procedures and medication, addressing the biological aspects of disorders.