Integrate : $\int \limits_0^{\large\frac{\pi}{2}} \large\frac{\cos ^3 x}{\sin ^3 x + \cos ^3 x }$$dx$

Question

$(A)\;\large\frac{\pi}{2} \\ (B)\;\large\frac{\pi}{4} \\ (C)\;2 \pi \\ (D)\;\large\frac{\pi}{6}$