question_answer

If \[I=\int{\frac{(3\sin \theta -2)\cos \theta }{5-{{\cos }^{2}}\theta -4\sin \theta }\,\,d\theta ,}\] then I equals to ________.

A)  \[3\log |2-\sin \theta |+\frac{4}{2+\sin \theta }+C\]

B)  \[3\log \,\,(2+\sin \theta )-\frac{2}{2+cos\theta }+C\]

C)  \[3\log \,\,(2+\sin \theta )-\frac{2}{2-cos\theta }+C\]

D)  \[3\log \,\,(2-\sin \theta )+\frac{4}{2-\sin \theta }+C\]

E)  None of these