In this manuscript, a new identity for functions defined on an open invex subset of set of real numbers is established. We present new type integral inequalities for functions whose powers of 𝑛𝑡ℎ derivatives in absolute value are preinvex and prequasiinvex functions. This paper is a generalization of studies being done for functions whose first, second, third and fourth derivatives are preinvex and prequasiinvex. Moreover, the results we obtained in this article coincide with the previous ones in special cases.