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

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) $2 \ln x + \sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } } { n x ^ { 2 n } }$