If $\mathbf{r}(t)= \cos(-3t)\mathbf{i}+\sin( -3t)\mathbf{j}+2t \mathbf{k}$
compute $\mathbf{r}'(t)$= $\mathbf{i}+$ $\mathbf{j}+$ ${\mathbf{k}}$
and $\int{\mathbf{r}}(t)\, dt$= $\mathbf{i}+$ $\mathbf{j}+$ $\mathbf{k} + \mathbf{C}$
with $\mathbf{C}$ a constant vector.