Integral of 1/(sin 2x (tan^5 x + cot^5 x)) from pi/6 to pi/4

1. A.
   $\frac{1}{5}\left[\frac{\pi}{4}-\tan^{-1}\!\left(\frac{1}{3\sqrt{3}}\right)\right]$
2. B.
   $\frac{1}{2}\left[\frac{\pi}{4}-\tan^{-1}\!\left(\frac{1}{9\sqrt{3}}\right)\right]$
3. C.
   $\frac{1}{10}\left[\frac{\pi}{4}-\tan^{-1}\!\left(\frac{1}{9\sqrt{3}}\right)\right]$
4. D.
   $\frac{1}{10}\left[\frac{\pi}{4}-\tan^{-1}\!\left(\frac{1}{3\sqrt{3}}\right)\right]$

Tap an option to check your answer.

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

Tap an option to check your answer.