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

Question

The integral

$\int {{{{{\sin }^2}x{{\cos }^2}x} \over {{{\left( {{{\sin }^5}x + {{\cos }^3}x{{\sin }^2}x + {{\sin }^3}x{{\cos }^2}x + {{\cos }^5}x} \right)}^2}}}} dx$

is equal to

${{ - 1} \over {1 + {{\cot }^3}x}} + C$

${1 \over {3\left( {1 + {{\tan }^3}x} \right)}} + C$

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

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

Solution

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