$\int \large\frac{1}{\Large\frac{\sqrt 3}{2} \sin x + \cos x }$$dx$
=>$\int \large\frac{1}{2} \bigg[\frac{1}{\Large\frac{\sqrt 3}{2} \sin x +\frac{1}{2} \cos (x) }\bigg]$
=> $ \large\frac{1}{2} \int \large\frac{1}{\sin (x + \frac{\pi}{6})}$
=> $\large\frac{1}{2}$$ \int \sec (x-\large\frac{\pi}{6})$$dx$
$\large\frac{1}{2}$$\log | \sec (x-\pi/6)+\tan (x-\pi/6) |+c$
Hence b is the correct answer.