Is the following function known to be integrable? It is supposed to be a probability density function, i.e., integrates to one. However, it leaves the online Mathematica integrator stumped:
\begin{equation*} f(x) = \frac{k-1}{2(1+|x|^k)},\; x \in (-\infty, \infty),\; k \geq 2 \end{equation*}