Integral of inverse cot of a quadratic from 0 to 1, split into a difference of inverse tans

1. A.
   $2\tan^{- 1}2 + \frac{1}{2}\log_{e}\left( \frac{5}{4} \right) + \frac{\pi}{2}$
2. B.
   $2\tan^{- 1}2 + \frac{1}{2}\log_{e}\left( \frac{5}{4} \right) - \frac{\pi}{2}$
3. C.
   $2\tan^{- 1}2 - \frac{1}{2}\log_{e}\left( \frac{5}{4} \right) + \frac{\pi}{2}$
4. D.
   $2\tan^{- 1}2 - \frac{1}{2}\log_{e}\left( \frac{5}{4} \right) - \frac{\pi}{2}$

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