Integrate : $\int \large\frac{\sin 4x}{\sqrt {8+\sin ^4 2x}}$$dx$

Question

$(a)\;\log | \sin^2 2x -\sqrt {\sin ^4 2x+8}|+c \\(b)\; \log | \sin^2 2x +\sqrt {\sin ^4 2x+8}|+c \\(c)\; \frac{1}{2} \log | \sin^2 2x -\sqrt {\sin ^4 2x+8}|+c \\ (d)\;\frac{1}{2}\log | \sin^2 2x +\sqrt {\sin ^4 2x+8}|+c$