JEE PYQ: Definite Integration Question 51
Question 51 - 2019 (11 Jan Shift 2)
The integral $\int_{\pi/6}^{\pi/4} \dfrac{dx}{\sin 2x(\tan^5 x + \cot^5 x)}$ equals:
(1) $\dfrac{1}{20}\tan^{-1}\left(\dfrac{1}{9\sqrt{3}}\right)$
(2) $\dfrac{1}{10}\left(\dfrac{\pi}{4} - \tan^{-1}\left(\dfrac{1}{9\sqrt{3}}\right)\right)$
(3) $\dfrac{\pi}{40}$
(4) $\dfrac{1}{5}\left(\dfrac{\pi}{4} - \tan^{-1}\left(\dfrac{1}{3\sqrt{3}}\right)\right)$