The integral $\int \frac{{\sin }^{2}x{\cos }^{2}x}{{\left({\sin }^{5}x+{\cos }^{3}x{\sin }^{2}x+{\sin }^{3}x{\cos }^{2}x+{\cos }^{5}x\right)}^2}dx$, is equal to

(where $C$ is the constant of integration).

• A

  $\frac{-1}{1+{\cot }^{3}x}+C$
• B

  $\frac{1}{3\left(1+{\tan }^{3}x\right)}+C$
• Correct answer
  C

  $\frac{-1}{3\left(1+{\tan }^{3}x\right)}+C$
• D

  $\frac{1}{1+{\cot }^{3}x}+C$

Hence, the correct answer is option: 'C'.