If ∫ dx/((x² + x + 1)²) = a tan ⁻¹ ((2x + 1)/(3)) + b((2x + 1)/(x² + x + 1)) + C, x > 0 where C is the constant of integration, then the value of 9(3 a + b) is equal to _ _ _ _ _ _ _.

Integral Calculus: JEE Main 2021 Mathematics question

JEE Main 2021 · 27 Aug, Morning shift · Q36

JEE Main 202127 Aug, Morning shiftMathematicsMediumIntegral Calculus369× since 2002

\int {{{dx} \over {{{({x^2} + x + 1)}^2}}} = a{{\tan }^{ - 1}}\left( {{{2x + 1} \over {\sqrt 3 }}} \right) + b\left( {{{2x + 1} \over {{x^2} + x + 1}}} \right) + C}

, x > 0 where C is the constant of integration, then the value of

9\left( {\sqrt 3 a + b} \right)

is equal to _____________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2021 Integral Calculus Question with Answer (27 Aug Morning shift, Q36) | JEE Arc

JEE Main 2021 · 27 Aug, Morning shift · Q36

JEE Main 202127 Aug, Morning shiftMathematicsMediumIntegral Calculus369× since 2002

\int {{{dx} \over {{{({x^2} + x + 1)}^2}}} = a{{\tan }^{ - 1}}\left( {{{2x + 1} \over {\sqrt 3 }}} \right) + b\left( {{{2x + 1} \over {{x^2} + x + 1}}} \right) + C}

, x > 0 where C is the constant of integration, then the value of

9\left( {\sqrt 3 a + b} \right)

is equal to _____________.

Your answerType your answer. Integers and decimals are accepted.