Answer
$\int\textbf{r}(t) dt = \langle 2sin(t), \frac{-2}{3}cos(3t), \frac{1}{2}sin(8t) \rangle + C$
Work Step by Step
To find the indefinite integral, compute the integral of each component.
$\int\textbf{r}(t) dt = \langle \int 2cos(t)\ dt,\int 2sin(3t)\ dt,\int 4cos(8t)\ dt\rangle = \langle 2sin(t), \frac{-2}{3}cos(3t), \frac{1}{2}sin(8t) \rangle + C$
