Chapter 12 - Vector-Valued Functions - 12.2 Exercises - Page 830: 43

$$\int(2 \mathfrak{t} \mathbf{i}+\mathbf{j}+\mathbf{k}) d t=t^{2} \mathbf{i}+t \mathbf{j}+t \mathbf{k}+ C$$

Given $$\int(2 \mathfrak{t} \mathbf{i}+\mathbf{j}+\mathbf{k}) d t $$ Integrating on a component-by-component basis produces $$\int(2 \mathfrak{t} \mathbf{i}+\mathbf{j}+\mathbf{k}) d t=t^{2} \ \mathbf{i}+t \ \mathbf{j}+t \ \mathbf{k}+ C$$