The value of $\sqrt{2}\displaystyle\int\frac {sin\;{x}{dx}}{sin(x-\frac{\pi}{4})}$ is

Question

( A ) $x+log|sin(x-\frac{\pi}{4})|+c$
( B ) $x-log|cos(x-\frac{\pi}{4})|+c$
( C ) $x-log|sin(x-\frac{\pi}{4})|+c$
( D ) $x+log|sin(x-\frac{\pi}{4})|+c$