Chapter 14 - Calculus of Vector-Valued Functions - 14.2 Calculus of Vector-Valued Functions - Exercises - Page 720: 41

$ \left\langle 0,0\right\rangle.$

We can write \begin{align} \int_{-2}^{2}\left\langle u^3,u^5\right\rangle du&=\left\langle \frac{1}{4}u^4, \frac{1}{6}u^6\right\rangle|_{-2}^{2}\\ &=\left\langle4, \frac{64}{6}\right\rangle-\left\langle 4, \frac{64}{6}\right\rangle\\ &= \left\langle 0,0\right\rangle. \end{align}