We are given a vector function \(\mathbf{r}(t)=\left\langle 2 e^{t}, 2 \sqrt{2} t, 2 e^{-t}\right\rangle\) that defines a curve \(C\) and a scalar field \(f(x, y, z)=x^{2} z\). Our goal is to compute the line integral of \(f\) along \(C\), which is denoted as
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