Integral of log(x + sqrt(x^2 + 1)) by parts

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

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1. A.
   $\sqrt{5} - \sqrt{2} + \log_{e}\left( \frac{9 + 4\sqrt{5}}{1 + \sqrt{2}} \right)$
2. B.
   $\sqrt{2} - \sqrt{5} + \log_{e}\left( \frac{9 + 4\sqrt{5}}{1 + \sqrt{2}} \right)$
3. C.
   $\sqrt{5} - \sqrt{2} + \log_{e}\left( \frac{7 + 4\sqrt{5}}{1 + \sqrt{2}} \right)$
4. D.
   $\sqrt{2} - \sqrt{5} + \log_{e}\left( \frac{7 + 4\sqrt{5}}{1 + \sqrt{2}} \right)$

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