Question

Find the following integral.
$\int e^x({\sec }^{2}x+\tan x).dx$

Answer 1

Now,

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

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

$=e^x\int {\sec }^{2}x.dx-\int e^x\left(\tan x\right).dx$$+\int e^x\left(\tan x\right).dx$ [Using method of by parts]

$=e^x.\tan x-\int e^x\left(\tan x\right).dx$$+\int e^x\left(\tan x\right).dx$