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\text { 5.(20pts) An object travels in space with a velocity given by } \vec{v}(t)=(t+\cos t) \vec{i}-(t+1) \vec{j}+e^{t} \vec{k} \text { with an initial position } \vec{r}(0)=2 \vec{i}+\vec{j}+\vec{k} \text {.

Find its path. }

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