Prove that the function `f(x)=(log)_e(x^2+1)-e^(-x)+1` is strictly increasing `AAx in Rdot`

Explanation

To prove that the function \( f(x) = \log_e(x^2 + 1) - e^{-x} + 1 \) is strictly increasing for all \( x \in \mathbb{R} \), we will follow these steps:

### Step 1: Differentiate the Function
We start by finding the derivative of the function \( f(x) \).

\[ f'(x) = \frac{d}{dx} \left( \log_e(x^2 + 1) \right) - \frac{d}{dx} \left( e^{-x} \right) + \frac{d}{dx}(1) \]
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