The series expansion of ` log[(1 + x)^((1 + x))(1-x)^(1-x)]` is
(1)`2[(x^(2))/(1.2) + (x^(4))/(3.4)+(x^(6))/(5.6)+...]`
(2) `[(x^(2))/(1.2) + (x^(4))/(3.4)+(x^(6))/(5.6)+...]`
(3)`2[(x^(2))/(1.2) + (x^(4))/(2.3)+(x^(6))/(3.4)+...]`
(4)`2[(x^(2))/(1.2) -(x^(4))/(2.3)+(x^(6))/(3.4)-...]`

Explanation

To find the series expansion of \( \log[(1 + x)^{(1 + x)}(1 - x)^{(1 - x)}] \), we will follow these steps:

### Step 1: Apply Logarithmic Properties
Using the properties of logarithms, we can rewrite the expression:
\[ \log[(1 + x)^{(1 + x)}(1 - x)^{(1 - x)}] = \log[(1 + x)^{(1 + x)}] + \log[(1 - x)^{(1 - x)}] \]
This simplifies to:
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