For the given ordinary differential equation, $\frac{dx}{dy}+x{\sec }^{2}y=e^{-\tan y}$, the integrating factor will be equal to:

The equation is a linear differential equation of the form $\frac{dx}{dy}+Px=Q$, where $P$ and $Q$ are functions of $y$.Here, $P={\sec }^{2}y$.The Integrating Factor ($IF$) is given by:
$$IF=e^{\int Pdy}$$
$$IF=e^{\int {\sec }^{2}ydy}$$
$$IF=e^{\tan y}$$