Suppose the only random number generator that you have is the one for log-normal distributions lnN(x|$\mu,\sigma^2$). Propose an MCMC algorithm for estimating the following integral
\begin{equation} I=\int_0^\infty e^{-x^4-x^6-x^8}\frac{e^x}{\alpha}dx, \end{equation}
where $\alpha=\int_0^\infty e^{-x^4-x^6-x^8}dx$ (is unknown). Describe the algorithm.