[en] We consider the conventional Laplace transform of f(x), denoted by $\mathcal{L}[f(x);p]\equiv <!--\; ???\; -->F(p)={{\displaystyle \int <!--\; ???\; -->}}_0^{\mathrm{\infty <!--\; ???\; -->}}{\mathrm{e}}^{-<!--\; ???\; -->px}f(x)\mathrm{d}x$ with $\mathfrak{R}\mathfrak{e}(p)><!--\; >\; -->0$. For $0<<!--\; <\; -->\mathrm{\alpha <!--\; ??\; -->}<<!--\; <\; -->1$ we furnish the closed form expressions for the inverse Laplace transforms ${\mathcal{L}}^{-<!--\; ???\; -->1}[F(p^{\mathrm{\alpha <!--\; ??\; -->}});x]$ and ${\mathcal{L}}^{-<!--\; ???\; -->1}[p^{\mathrm{\alpha <!--\; ??\; -->}-<!--\; ???\; -->1}F(p^{\mathrm{\alpha <!--\; ??\; -->}});x]$. In both cases they involve definite integration with kernels which are appropriately rescaled one-sided Lévy stable probability distribution functions $g_{\mathrm{\alpha <!--\; ??\; -->}}(x)$, $0<<!--\; <\; -->\mathrm{\alpha <!--\; ??\; -->}<<!--\; <\; -->1$, $x><!--\; >\; -->0$. Since $g_{\mathrm{\alpha <!--\; ??\; -->}}(x)$ are exactly and explicitly known for rational α, i.e. for $\mathrm{\alpha <!--\; ??\; -->}=l/k$ with $l,k=1,2,\dots <!--\; ???\; -->$, $l<<!--\; <\; -->k$, our results extend the known and tabulated case of $\mathrm{\alpha <!--\; ??\; -->}=1/2$ to any rational $0<<!--\; <\; -->\mathrm{\alpha <!--\; ??\; -->}<<!--\; <\; -->1$. We examine the integral kernels of this procedure as well as the resulting two kinds of Lévy integral transformations. (paper)