$$\int_z^{\infty}f(z_1)\int_{z_1}^\infty f(z_2) \cdots \int_{z_{n-1}}^\infty f(z_n)dz_ndz_{n-1}\cdots dz_2dz_1$$ Just for reference we could also write it as
$$\int_z^\infty \int_{z_1}^\infty\cdots\int_{z_{n-2}}^\infty\int_{z_{n-1}}^\infty f(z_n)f(z_{n-1})\cdots f(z_2)f(z_1)dz_ndz_{n-1}\cdots dz_2dz_1$$ How is one to solve this integral I first thought to use cauchy but couldn't figure it out.