The planar limit of integrated 4-point functions

We compute the planar limit, as all-order power series in the 't Hooft coupling, of various integrated 4-point functions of chiral primary operators of ${\cal N}=4$ SU(N) super Yang-Mills, and of moment map operators of ${\cal N}=2$ SU(N) SQCD. We do so by computing the planar free energy on $S^4$ of the respective massive deformations of these theories, and then taking advantage of the exact relation between these free energies and the integrated 4-point functions.