Answer
$\int\textbf{r}(t) dt = \langle \frac{-5}{3}t^{-3}-\frac{1}{3}t^3, \frac{1}{7}t^7-t^4, 2\ ln|t|\rangle + C$
Work Step by Step
To find the indefinite integral, compute the integral of each component.
$\int\textbf{r}(t) dt = \langle \int 5t^{-4} - t^2\ dt,\int t^6-4t^3\ dt,\int ,2/t\ dt\rangle = \langle \frac{-5}{3}t^{-3}-\frac{1}{3}t^3, \frac{1}{7}t^7-t^4, 2\ ln|t|\rangle + C$
