The integral int_π/6^π/4 dx/(sin 2x(tan^5 x + cot^5 x)) equals

1/10 ((π)/4 - tan^-1 (dfrac19√(3) ) )

1/5 ((π)/4 - tan^-1 (dfrac13√(3) ) )

The integral int_π/6^π/4 dx/(sin 2x(tan^5 x + cot^5 x))… — JEE Main 2019 Mathematics PYQ

JEE Main 2019 · 11 Jan · Shift II

The integral

\int_{\pi/6}^{\pi/4} \dfrac{dx}{\sin 2x(\tan^5 x + \cot^5 x)}

equals

A.
$\dfrac{1}{5}\left(\dfrac{\pi}{4} - \tan^{-1}\left(\dfrac{1}{3\sqrt{3}}\right)\right)$
B.
$\dfrac{1}{20}\tan^{-1}\left(\dfrac{1}{9\sqrt{3}}\right)$
C.
$\dfrac{1}{10}\left(\dfrac{\pi}{4} - \tan^{-1}\left(\dfrac{1}{9\sqrt{3}}\right)\right)$
D.
$\dfrac{\pi}{40}$

Show answer

Correct option: C

[JEE Main 2019 · 11 Jan · Shift II]

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