JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Analyzing +4 | -1

The integral

\int\limits_{{\pi / 6}}^{\pi / 4} \frac{\mathrm{d} x}{\sin 2 x\left(\tan ^5 x+\cot ^5 x\right)}

equals :

View answer and explanation

Correct option: D

\frac{1}{5}\left(\frac{\pi}{4}-\tan ^{-1}\left(\frac{1}{3 \sqrt{3}}\right)\right)

Option D (

\frac{1}{5}(\frac{\pi}{4}-\tan ^{-1}(\frac{1}{3 \sqrt{3}}))

) is correct because the integral is solved by using trigonometric substitution and simplification.

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