Evaluate the Line Integral Using the Fundamental Theorem of Line $\int \frac { 2 x } { C \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } } d x + \frac { 2 y } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } } d y$

Multiple Choice

Evaluate the line integral using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results. $\int \frac { 2 x } { C \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } } d x + \frac { 2 y } { \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } } d y$ $C$ : circle $( x - 2 ) ^ { 2 } + ( y - 10 ) ^ { 2 } = 9$ clockwise from $( 5,10 )$ to $( - 1,10 )$

A) $- \frac { 24 } { 16,261 }$
B) $- \frac { 12 } { 12,625 }$
C) $\frac { 24 } { 12,625 }$
D) $- \frac { 24 } { 12,625 }$
E) $\frac { 12 } { 12,625 }$