  A new integral formula, which has not been compiled in any integral tables or
mathematical softwares, is proposed to obtain the analytical energy-angular
spectra of the particles that are sequentially emitted from the discrete energy
levels of the residual nuclei in the statistical theory of light nucleus
reaction (STLN). In the cases of the neutron induced light nucleus reactions,
the demonstration of the kinetic energy conservation in the sequential emission
processes becomes straightforward thanks to this new integral formula and it is
also helpful to largely reduce the volume of file-6 in nuclear reaction
databases. Furthermore, taking p+$^9$Be reaction at 18 MeV as an example, this
integral formula is extended to calculate the energy-angular spectra of the
sequentially emitted neutrons for proton induced light nucleus reactions in the
frame of STLN.
