Iterated Differential Forms III: Integral Calculus
  Basic elements of integral calculus over algebras of iterated differential forms, are presented. In particular, defining complexes for modules of integral forms are described and the corresponding berezinians and complexes of integral forms are computed. Various applications and the integral calculus over the algebra $\Lambda_{\infty}$ will be discussed in subsequent notes. 
A. M. Vinogradov, L. Vitagliano