MathematicsMedium64×since 2004Q4008The integral ∫sin2xcos2x(sin5x+cos3xsin2x+sin3xcos2x+cos5x)2dx\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∫(sin5x+cos3xsin2x+sin3xcos2x+cos5x)2sin2xcos2xdx is equal toA−11+cot3x+C{{ - 1} \over {1 + {{\cot }^3}x}} + C1+cot3x−1+CB13(1+tan3x)+C{1 \over {3\left( {1 + {{\tan }^3}x} \right)}} + C3(1+tan3x)1+CC−13(1+tan3x)+C{{ - 1} \over {3\left( {1 + {{\tan }^3}x} \right)}} + C3(1+tan3x)−1+CD11+cot3x+C{1 \over {1 + {{\cot }^3}x}} + C1+cot3x1+CCheck answerSkip