Nguyên hàm $I=\int{{\frac{{\sin 2xdx}}{{3+4\sin x-\cos 2x}}}}$ bằng?
A. $\displaystyle \frac{1}{2}\ln |{{\sin }^{2}}x+2\sin x+1|-\frac{1}{{\sin x+1}}+C$
B. $\displaystyle \frac{1}{2}\ln |{{\sin }^{2}}x+2\sin x+1|+\frac{1}{{\sin x+1}}+C$
C. $\displaystyle -\frac{1}{2}\ln |{{\sin }^{2}}x+2\sin x+1|-\frac{1}{{\sin x+1}}+C$
D. $\displaystyle -\frac{1}{2}\ln |{{\sin }^{2}}x+2\sin x+1|+\frac{1}{{\sin x+1}}+C$