question_answer

lf \[\int_{2}^{e}{\left[ \frac{1}{\log x}-\frac{1}{{{(\log x)}^{2}}} \right]}\,dx=\alpha +\frac{\beta }{\log 2},\] then

A)  \[\alpha =e,\]\[\beta =-2\]          

B)  \[\alpha =e,\]\[\beta =2\]

C)  \[\alpha =-e,\]\[\beta =2\]          

D)  \[\alpha =-e,\]\[\beta =-2\]

E)  None of these