The integral  $\int \frac{{\sin }^{2}x{\cos }^{2}x}{{\sin }^{6}x+2{\sin }^{3}x{\cos }^{3}x+{\cos }^{6}x}dx$  is equal to 
(Where  $C$  is a constant of integration)

 $$\begin{gathered} \int \frac{{\sin }^{2}x{\cos }^{2}x}{{({\sin }^{5}x+{\cos }^{3}x{\sin }^{2}x+{\sin }^{3}x{\cos }^{2}x+{\cos }^{5}x)}^2}dx \\ \int \frac{{\sin }^{2}x{\cos }^{2}x}{{({\sin }^3+{\cos }^{3}x)}^2}dx \\ \int \frac{{\tan }^{2}x.{\sec }^{2}x}{{(1+{\tan }^{3}x)}^2}dx \end{gathered}$$
 Put  $1+{\tan }^{3}x=t$
 $=\frac{1}{3}\int \frac{dt}{t^2}\Rightarrow -\frac{1}{3t}+c$
  $=-\frac{1}{3(1+{\tan }^{3}x)}+c$