In this paper, we consider a Kaehlerian manifold M of complex dimension n admitting a holomorphically projective vector field ^1,2,5. The purpose of the paper is to obtain the integral formulas and inequalities in a simply connected, compact Kaehlerian manifold without putting restriction on the scalar curvature of M such as the constancy of scalar curvature K on M and to generalize some of the integral formulas, inequalities and some of the propositions of K.Yano and H. Hiramatu⁷. In section 4 , we introduce GH-projective vector field and study its properties and further generalize a Theorem of S.Tanno^9,10 and a Theorem of T Nagano¹¹.