∫exsec⁡x(1+tan⁡x)dx is equal to

Let $I = \int e^{x} \sec x (1 + \tan x) dx$

$\Rightarrow I = \int e^{x} \sec xdx + \int e^{x} \sec xtan xdx - - - - - (i)$

Now $\int e^{x} \sec xdx = \sec x \int e^{x} dx - \int [\frac{d}{dx} \sec x \int e^{x} dx] dx$

$= e^{x} \sec x - \int \sec xtan {xe}^{x} dx - - - - (ii)$

$On putting the value from Eq . (ii) inEq . (i), we get$

$\begin{array}{l} I = e^{x} \sec x - \int e^{x} \sec xtan xdx + \int \sec xtan {xe}^{x} dx + C \\ \Rightarrow I = e^{x} \sec x + C \end{array}$

$\int e^{x} \sec x (1 + \tan x) dx$ is equal to