  We show how to compute analytically time and space dependent correlations in
one dimensional quantum integrable systems with an impurity. Our approach is
based on a description of these systems in terms of massless scattering of
quasiparticles. Correlators follow then from matrix elements of local operators
between multiparticle states, the ``massless form factors''. Although an
infinite sum of these form factors has to be considered in principle, we find
that for current, spin, and energy operators, only a few (typically two or
three) are necessary to obtain an accuracy of more than $1\%$, for {\bf
arbitrary coupling strength}, that is all the way from short to large
distances. As examples we compute, at zero temperature, the frequency dependent
conductance in a Luttinger liquid with impurity, the spectral function in the
double well problem of dissipative quantum mechanics and part of the space
dependent succeptibility in the Kondo model .
