If ∫ (sin x)/(sin ³x + cos ³x)dx = α log e |1 + tan x| + β log e |1 - tan x + tan ²x| + γ tan ⁻¹((2 tan x - 1)/(3)) + C, when C is constant of integration, then the value of 18(α + β + γ ²) is _ _ _ _ _ _ _.

Integral Calculus: JEE Main 2021 Mathematics question

JEE Main 2021 · 31 Aug, Evening shift · Q33

JEE Main 202131 Aug, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

\int {{{\sin x} \over {{{\sin }^3}x + {{\cos }^3}x}}dx = }

\alpha {\log _e}|1 + \tan x| + \beta {\log _e}|1 - \tan x + {\tan ^2}x| + \gamma {\tan ^{ - 1}}\left( {{{2\tan x - 1} \over {\sqrt 3 }}} \right) + C

, when C is constant of integration, then the value of

18(\alpha + \beta + {\gamma ^2})

is ______________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2021 Integral Calculus Question with Answer (31 Aug Evening shift, Q33) | JEE Arc

JEE Main 2021 · 31 Aug, Evening shift · Q33

JEE Main 202131 Aug, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

\int {{{\sin x} \over {{{\sin }^3}x + {{\cos }^3}x}}dx = }

\alpha {\log _e}|1 + \tan x| + \beta {\log _e}|1 - \tan x + {\tan ^2}x| + \gamma {\tan ^{ - 1}}\left( {{{2\tan x - 1} \over {\sqrt 3 }}} \right) + C

, when C is constant of integration, then the value of

18(\alpha + \beta + {\gamma ^2})

is ______________.

Your answerType your answer. Integers and decimals are accepted.