Question

Integrate with respect to $x$:
$e^x({\sec }^{2}x+\tan x)$

Answer 1

Consider the given integral.

$I=\int e^x({\sec }^{2}x+\tan x)dx$

$I=\int e^x{\sec }^{2}xdx+\int e^x\tan xdx$

$I=e^x\tan x-\int e^x\tan xdx+\int e^x\tan xdx$

$I=e^x\tan x+C$

Hence, this is the answer.