The integral ∫ (π)/6 ^((π)/3) tan ³x. sin ²3x(2 sec ²x. sin ²3x + 3 tan x. sin 6x)dx is equal to:

Integral Calculus: JEE Main 2020 Mathematics question

JEE Main 2020 · 4 Sep, Evening shift · Q3381

JEE Main 20204 Sep, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

The integral

\int\limits_{{\pi \over 6}}^{{\pi \over 3}} {{{\tan }^3}x.{{\sin }^2}3x\left( {2{{\sec }^2}x.{{\sin }^2}3x + 3\tan x.\sin 6x} \right)dx}

is equal to:

JEE Main 2020 · 4 Sep, Evening shift · Q3381

JEE Main 20204 Sep, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

The integral

\int\limits_{{\pi \over 6}}^{{\pi \over 3}} {{{\tan }^3}x.{{\sin }^2}3x\left( {2{{\sec }^2}x.{{\sin }^2}3x + 3\tan x.\sin 6x} \right)dx}

is equal to: