If ∫ π/6 ^(π/4)(cot (x-(π)/3) cot (x+(π)/3)+1)dx=α log e (3-1), then 9α² is equal to _ _ _.

Integral Calculus: JEE Main 2026 Mathematics question

JEE Main 2026 · 8 Apr, Evening shift · Q22

JEE Main 20268 Apr, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

\int_{\pi/6}^{\pi/4}\left(\cot\left(x-\frac{\pi}{3}\right)\cot\left(x+\frac{\pi}{3}\right)+1\right)dx=\alpha\log_e(\sqrt3-1)

, then

9\alpha^2

is equal to ______.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2026 · 8 Apr, Evening shift · Q22

JEE Main 20268 Apr, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

\int_{\pi/6}^{\pi/4}\left(\cot\left(x-\frac{\pi}{3}\right)\cot\left(x+\frac{\pi}{3}\right)+1\right)dx=\alpha\log_e(\sqrt3-1)

, then

9\alpha^2

is equal to ______.

Your answerType your answer. Integers and decimals are accepted.