Evaluate: `inte^x\ (tan^(-1)x+1/(1+x^2))\ dx`

Explanation

To evaluate the integral \( I = \int e^x \left( \tan^{-1} x + \frac{1}{1+x^2} \right) \, dx \), we can follow these steps:

### Step 1: Identify the function and its derivative
We notice that the integrand consists of \( \tan^{-1} x \) and \( \frac{1}{1+x^2} \). The derivative of \( \tan^{-1} x \) is \( \frac{1}{1+x^2} \). Therefore, we can let:
\[ f(x) = \tan^{-1} x \]
Then, the derivative is:
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