Definite Integration

If $f(x)=\left|\begin{array}{ccc}2 \cos ^2 x & \sin 2 x & \sin x \\ \sin 2 x & 2 \sin ^2 x & -\cos x \\ \sin x & -\cos x & 0\end{array}\right|$, then

\(\left.\int_0^{\pi / 4}|2| f(x) \mid+5 f^{\prime}(x)\right) d x=\)