The integral $\;\int \large\frac{sin^{2}x cos^{2}x}{(sin^{3} x +cos^{3} x )^{2}} dx\;$ is equal to :

Question

$(a)\;\large\frac{1}{(1+cot^{3} x)} +c \qquad(b)\;-\large\frac{1}{3(1+tan^{3} x)} +c \qquad(c)\;\large\frac{sin^{3} x}{(1+cos^{3} x)} +c \qquad(d)\;-\large\frac{cos^{3}x}{3(1+sin^{3} x)} +c $