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