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We consider a regular smooth curve in $\mathbb{E}^n$ such that itscoordinates' components are the fundamental solutions of the differentialequation $ y^{(n)} (x) - y(x) = 0 ,$ $x \in \mathbb{R} $ of order $n$. We showthat the total first curvature of this curve is infinite for odd $n$ and isfinite for even $n$.

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