Integral of log((a + x)^(a + x))

1. A.
   $(1+x)^2 \log(1+x) - \frac{1}{2} + c$
2. B.
   $\dfrac{(1+x)^2}{2} \log(1+x) + c$
3. C.
   $\dfrac{(1+x)^2}{2}\left(\log(1+x) - \frac{1}{2}\right) + c$
4. D.
   $\dfrac{1+x}{2}\log(1+x) + c$

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1. A.
   $\frac{(2 + x)^{2}}{2}\log\left( \frac{2 + x}{\sqrt{e}} \right) + c$, where c is the constant of integration
2. B.
   $\frac{(2 + x)^{2}}{2}\log\left( \frac{2 + x}{e} \right) + c$, where c is the constant of integration
3. C.
   $\ \frac{2 + x}{2}\log\left( \frac{2 + x}{\sqrt{e}} \right) + c$, where c is the constant of integration
4. D.
   $\frac{2 + x}{2}\log(2 + x)\sqrt{e} + c$, where c is the constant of integration

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