The Pareto case could be handled by using the fact that if $X$ is Pareto-dsitributed with minimal value $m$ and shape index $\alpha$, then $$Y = log(X) - log(m)$$ is exponentially distributed with rate parameter $\alpha$. Therefore, for any function $f$, $$\mathbb E(f(X)) = \mathbb E(f(m * e^Y))$$ and we can re-use the quadrature scheme of $Y$, which follows a Exponential(\alpha) distribution.