Question

Write a value of $\int e^x\sec x\left(1+\tan x\right)dx$.

Answer 1

Let I=$\int$ e^x sec x(1 + tan x) dx
=$\int$ e^x (sec x + sec x tan x) dx
Let e^x sec x = t
⇒ (e^x sec x + e^x sec x tan x)dx = dt
⇒​ e^x sec x (1 + tan x) dx = dt
$\therefore I=$$\int$ dt
= t + C
= e^x sec x + C $\left(\because t=e^x\sec x\right)$