Finiteness of the total first curvature of a non-closed curve in ${\mathbb{E}}^n$

We consider a regular smooth curve in ${\mathbb{E}}^n$ such that its coordinates’ components are the fundamental solutions of the differential equation $y^{(n)}(x)-y(x)=0,$ $x\in \mathbb{R}$ of order $n$. We show that the total first curvature of this curve is infinite for odd $n$ and is finite for even $n$.