Find the Value of the Integral $\int _ { 1 } ^ { 2 } \sqrt { u ^ { 2 } - 1 } d u$

Find the value of the integral $\int _ { 1 } ^ { 2 } \sqrt { u ^ { 2 } - 1 } d u$

A) $\sqrt { 3 } + \frac { 1 } { 2 } \ln ( 4 - \sqrt { 3 } )$
B) $\sqrt { 3 } - \frac { 1 } { 2 } \ln ( 2 + \sqrt { 3 } )$
C) $\sqrt { 3 } - \frac { 1 } { 2 } \ln ( 4 + \sqrt { 3 } )$
D) $\sqrt { 3 } + \frac { 1 } { 2 } \ln ( 2 - \sqrt { 3 } )$
E) $\sqrt { 3 } - \frac { 1 } { 2 } \ln ( 4 - \sqrt { 3 } )$
F) $\sqrt { 3 } + \frac { 1 } { 2 } \ln ( 4 + \sqrt { 3 } )$
G) $\sqrt { 3 } + \frac { 1 } { 2 } \ln ( 2 + \sqrt { 3 } )$
H) $\sqrt { 3 } - \frac { 1 } { 2 } \ln ( 2 - \sqrt { 3 } )$

Correct Answer:

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