Section 13.2: Derivatives and Integrals of Vector Functions

Find \(\mathbf{r}(t)\) if \(\mathbf{r}'(t) = t\mathbf{i} + e^t\mathbf{j} + te^t\mathbf{k}\) and \(\mathbf{r}(0) = \mathbf{i} + \mathbf{j} + \mathbf{k}\).