Indefinite Integration

$\log \left|\frac{\sec \left(x-\frac{\pi}{3}\right)}{\sec \left[x+\frac{\pi}{6}\right]}\right|+C$

$\log \left|\frac{\cos \left(x-\frac{\pi}{3}\right)}{\cos \left(x+\frac{\pi}{6}\right)}\right|+C$

$\log \left|\frac{\operatorname{cosec}\left(x-\frac{\pi}{3}\right)}{\operatorname{cosec}\left(x+\frac{\pi}{6}\right)}\right|+C$

$\log \left|\frac{\sin \left(x-\frac{\pi}{3}\right)}{\sin \left(x+\frac{\pi}{6}\right)}\right|+C$