  If the $n-th$ order differential equation is not exact, under certain
conditions, an integrating factor exists which transforms the differential
equation into an exact one. Hence, its order can be reduced to the lower order.
In this paper, the principle of finding an integrating factor of a none exact
differential equations is extended to the class of $n$-th order differential
equations \begin{align}
F_n\left(t,y,y^\prime,y^{\prime\prime},\ldots,y^{(n-1)}\right)y^{(n)}&+F_{n-1}\left(t,y,y^\prime,y^{\prime\prime},\ldots,y^{(n-1)}\right)y^{(n-1)}+\cdots
+\nonumber\\
&+F_{1}\left(t,y,y^\prime,y^{\prime\prime},\ldots,y^{(n-1)}\right)y^{\prime}+F_{0}\left(t,y,y^\prime,y^{\prime\prime}\ldots,y^{(n-1)}\right)\nonumber\\
&=0,\nonumber \end{align} where $F_0,F_1,F_2, \cdots,F_n$ are continuous
functions with their first partial derivatives on some simply connected domain
$\Omega \subset\R^{n+1}$. In particular, we prove some explicit forms of
integrating factors for this class of differential equations. Moreover, as a
special case of this class, we consider the class of third order differential
equations in more details. We also present some illustrative examples.
