Question

Integrate: $\int e^x\left[\tan x+\log \sec x\right]dx$

Answer 1

$\int e^x\tan xdx+\int e_{II}^x\log {\sec }_{I}xdx$

$=\int e^x\tan xdx+\log \sec x.e^x-\int \frac{\sec x\tan {x_e}^{x}dx}{\sec x}$

$=\int e^x\tan xdx+e^x\log \sec x-\int e^x\tan xdx$

$=e^x\log \sec x+c$