  The construction of supersymmetric invariant integrals is discussed in a
superspace setting. The formalism is applied to D=4, N=4 SYM and used to
construct the F^2, F^4 and (F^5 + \del^2 F^4) terms in the effective action of
coincident D-branes. The results are in agreement with those obtained by other
methods. A simple derivation of the abelian \del^4 F^4 invariant is given and
generalised to the non-abelian case. We also find some double-trace invariants.
The invariants are interpreted in terms of superconformal multiplets: the F^2
and F^4 terms are given by one-half BPS multiplets, the (F^5+\del^2F^4) arises
as a full superspace integral of the Konishi multiplet K and the abelian \del^4
F^4 term comes from integrating the fourth power of the field strength
superfield. Counterparts of the abelian invariants are exhibited for the
D=6,(2,0) tensor multiplet and the D=3, N=8 scalar multiplet. The method is
also applied to D=4, N=8 supergravity. All invariants in the linearised theory
(with SU(8) symmetry) which arise from partial superspace integrals are
constructed.
