The integral ∫ sin ²x cos ² x (sin ⁵x + cos ³x sin ² x + sin ³x cos ² x + cos ⁵x) ² dx is equal to

Integral Calculus: JEE Main 2018 Mathematics question

JEE Main 2018 · Session, Shift 1 · Q4008

JEE Main 2018Session, Shift 1MathematicsMediumIntegral Calculus369× since 2002

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

JEE Main 2018 · Session, Shift 1 · Q4008

JEE Main 2018Session, Shift 1MathematicsMediumIntegral Calculus369× since 2002

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