Write a value

given,

$\int e^{x} \sec x(1+\tan x) d x=\int e^{x}(\sec x+\sec x \tan x) d x$

$=e^{x} \sec x+c$

$\because \int e^{x}\left(f(x)+f^{\prime}(x)\right) d x=e^{x} f(x)+c$