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We compute systematically for the planar double box Feynman integral relevant to top pair production with a closed top loop the Laurent expansion in the dimensional regularization parameter ϵ. This is done by transforming the system of differential equations for this integral and all its sub-topologies to a form linear in ϵ, where the ϵ^{0} part is strictly lower triangular. This system is easily solved order by order in the dimensional regularization parameter ϵ. This is an example of an elliptic multiscale integral involving several elliptic subtopologies. Our methods are applicable to similar problems.