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Indefinite Integrals question

2021 · 31 Aug · Shift 2 · Q39

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JEE Main
Mathematics
Indefinite Integrals
2021 · 31 Aug · Shift 2 · Q39

Indefinite Integrals question

2021 · 31 Aug · Shift 2 · Q39

JEE MainMathematicsIndefinite IntegralsNumerical+4 / −1

If

\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

\underline{\hspace{2cm}}

.

Numerical answer

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