  We integrate the Lifting cocycles $\Psi_{2n+1},\Psi_{2n+3},\Psi_{2n+5},...$
([Sh1], [Sh2]) on the Lie algebra $\Dif_n$ of holomorphic differential
operators on an $n$-dimensional complex vector space to the cocycles on the Lie
algebra of holomorphic differential operators on a holomorphic line bundle
$\lambda$ on an $n$-dimensional complex manifold $M$ in the sense of
Gelfand-Fuks cohomology [GF] (more precisely, we integrate the cocycles on the
sheaves of the Lie algebras of finite matrices over the corresponding
associative algebras). The main result is the following explicit form of the
Feigin-Tsygan theorem [FT1]:
  $H^\bullet_\Lie(\gl^\fin_\infty(\Dif_n);\C) = \wedge^\bullet(\Psi_{2n+1},
\Psi_{2n+3},\Psi_{2n+5}, ...)$.
