  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 regularisation parameter $\varepsilon$. This is done by
transforming the system of differential equations for this integral and all its
sub-topologies to a form linear in $\varepsilon$, where the
$\varepsilon^0$-part is strictly lower triangular. This system is easily solved
order by order in the dimensional regularisation parameter $\varepsilon$. This
is an example of an elliptic multi-scale integral involving several elliptic
sub-topologies. Our methods are applicable to similar problems.
