Integrate : $\int \large\frac{\sin 2x }{a \cos ^2 x + b \sin ^2 x }$$dx$

Question

$(a)\;\frac{1}{b-a} \log _e |(a \cos ^2 x + b \sin ^2 x)|+c \qquad(b)\;\frac{1}{b-a} \log _e |(a \sin ^2 x + b \cos ^2 x)|+c \qquad(c)\;\frac{1}{b-a} \log _e |(a \sin ^2 x + b \sin ^2 x)|+c \qquad (d)\;None$