Tìm nguyên hàm
$\displaystyle \int{{\frac{{\sin 2x}}{{\sqrt{{{{{\cos }}^{2}}x+4{{{\sin }}^{2}}x}}}}dx.}}$
A. $\frac{2}{7}\sqrt{{{{{\cos }}^{2}}x+4{{{\sin }}^{2}}x}}+C.$
B. $\frac{1}{3}{{({{\cos }^{2}}x+4{{\sin }^{2}}x)}^{2}}+C.$
C. $\frac{2}{3}({{\cos }^{2}}x+4{{\sin }^{2}}x)+C.$
D. $\frac{2}{3}\sqrt{{{{{\cos }}^{2}}x+4{{{\sin }}^{2}}x}}+C.$