Series of powers of x with a logarithm as the sum

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

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1. A.
   $\frac{1}{2}e^{2}$
2. B.
   $2e$
3. C.
   $\frac{1}{2}\sqrt{e}$
4. D.
   $2e^{2}$

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