Evaluate the Definite Integral $\int _ { 1 } ^ { 2 } \frac { 1 - \cos ( 9 \theta ) } { 9 \theta - \sin ( 9 \theta ) } d \theta$

Multiple Choice

Evaluate the definite integral. $\int _ { 1 } ^ { 2 } \frac { 1 - \cos ( 9 \theta ) } { 9 \theta - \sin ( 9 \theta ) } d \theta$

A) $\frac { 1 } { 9 } \ln \left| \frac { 1 - \cos ( 18 ) } { 9 - \sin ( 9 ) } \right|$
B) $\frac { 1 } { 9 } \ln \left| \frac { 1 - \sin ( 18 ) } { 9 - \sin ( 9 ) } \right|$
C) $\frac { 1 } { 18 } \ln \left| \frac { 18 - \sin ( 18 ) } { 9 - \sin ( 9 ) } \right|$
D) $\frac { 1 } { 9 } \ln \left| \frac { 18 - \sin ( 18 ) } { 9 - \sin ( 9 ) } \right|$
E) $\frac { 1 } { 9 } \ln \left| \frac { 2 - \cos ( 18 ) } { 9 - \sin ( 9 ) } \right|$