  Scattering amplitudes at loop level can be expressed in terms of Feynman
integrals. The latter satisfy partial differential equations in the kinematical
variables. We argue that a good choice of basis for (multi-)loop integrals can
lead to significant simplifications of the differential equations, and propose
criteria for finding an optimal basis. This builds on experience obtained in
supersymmetric field theories that can be applied successfully to generic
quantum field theory integrals. It involves studying leading singularities and
explicit integral representations. When the differential equations are cast
into canonical form, their solution becomes elementary. The class of functions
involved is easily identified, and the solution can be written down to any
desired order in epsilon within dimensional regularization. Results obtained in
this way are particularly simple and compact. In this letter, we outline the
general ideas of the method and apply them to a two-loop example.
