Let $X$ be a real random variable with density
$$
f(x)=c^{-1} \frac{e^{-|x|}}{1+|x|^{3}}
$$
where $c=\int_{-\infty}^{\infty} \frac{e^{-|x|}}{1+|x|^{3}} d x$. Check if the logarithmic moment generating function $\Lambda$ is continuous and sketch the graph of $\Lambda$.