Chapter 11 - Vectors and Vector-Valued Functions - 11.6 Calculus of Vector-Valued Functions - 11.6 Exercises - Page 815: 50

$\int\textbf{r}(t) dt = \langle te^{-t}-e^t, \frac{-1}{2}cos(t^2), -2\sqrt {t^2+4}\rangle + C$

To find the indefinite integral, compute the integral of each component. $\int\textbf{r}(t) dt = \langle \int te^t\ dt,\int t\ sin(t^2)\ dt,\int \frac{-2t}{\sqrt {t^2 + 4}}\ dt\rangle = \langle te^{-t}-e^t, \frac{-1}{2}cos(t^2), -2\sqrt {t^2+4}\rangle + C$