$I=\int e^{x}\left(\frac{\sin x+\cos x}{1-\sin ^{2} x}\right) d x$
$I=\int e^{x}\left(\frac{\sin x+\cos x}{\cos ^{2} x}\right) d x$
$I=\int e^{x} \tan x \cdot \sec x d x+\int \frac{e^{x}}{ II } \cdot \frac{\sec}{{I}} x d x$
$I=\int e^{x} \tan x \cdot \sec x d x+\left\{\sec x \cdot e^{x}\right.$
$\left.-\int \sec x \cdot \tan x e^{x} d x\right\}$
$I=\int e^{x} \tan x \cdot \sec x d x+e^{x} \sec x$
$-\int e^{x} \tan x \cdot \sec x d x$
$I \equiv e^{x} \cdot \sec x+C$