Chapter 14 - Calculus of Vector-Valued Functions - 14.2 Calculus of Vector-Valued Functions - Exercises - Page 720: 46

$\left\langle\frac{3}{2}t^2, 2t^3, 9t \right\rangle.$

We have \begin{align} \int_{0}^{t}\left\langle 3s, 6s^2, 9 \right\rangle ds &=\left\langle \frac{3}{2}s^2, 2s^3, 9s \right\rangle|_{0}^{t}\\ &=\left\langle \frac{3}{2}t^2, 2t^3, 9t \right\rangle-\left\langle 0, 0 ,0 \right\rangle\\ &=\left\langle\frac{3}{2}t^2, 2t^3, 9t \right\rangle. \end{align}