If $$\int_{}^{}\left(\frac{1-5\cos^{2} x}{\sin^{5} x \cos^{2} x}\right)dx=f(x)+C$$, where C is the constant of integration, then $$f\left(\frac{\pi}{6}\right)-f\left(\frac{\pi}{4}\right)$$ is equal to

A

$$\frac{2}{\sqrt{3}}(4+\sqrt{6})$$

B

$$\frac{1}{\sqrt{3}}(26+\sqrt{3})$$

C

$$\frac{1}{\sqrt{3}}(26-\sqrt{3})$$

D

$$\frac{4}{\sqrt{3}}(8-\sqrt{6})$$