Evaluate the following integral: `int_(-2)^2x e^(|x|)dx`

Explanation

To evaluate the integral \( I = \int_{-2}^{2} x e^{|x|} \, dx \), we need to consider the absolute value function \( |x| \). The integral can be split into two parts based on the definition of \( |x| \):

1. For \( x \) in the interval \([-2, 0]\), \( |x| = -x \).
2. For \( x \) in the interval \([0, 2]\), \( |x| = x \).

Thus, we can rewrite the integral as:

\[
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