Answer
$\int\textbf{r}(t) dt = \langle \frac{1}{5}t^5-\frac{3}{2}t^2, t^2-t, 10t\rangle + C$
Work Step by Step
To find the indefinite integral, compute the integral of each component.
$\int\textbf{r}(t) dt = \langle \int t^4-3t\ dt,\int 2t-1\ dt,\int 10\ dt\rangle = \langle \frac{1}{5}t^5-\frac{3}{2}t^2, t^2-t, 10t\rangle + C$
