What is the Integration of (sec^2 xe^tanx)?

Question

pls note that the this is one term. I mean they are multiplied togther.
^ = to the power of.
x doesnt mean multiply, its the letter x.

Answer 1

let t = tan x
dt/dx = sec^2x
so dt = sec^2x dx
integral reduces ro

sec^2 x e^(tan x) dx = e^t dt
integral is e^t + c
or e^tan x + c

Answer 2

I = ∫ sec² x e^(tanx).dx

Let u = tan x
du = sec²x dx

so I = ∫ e^u du
I = ∫ e^u du
I = e ^ tan x + c

Answer 3

I = ∫ sec² x.e^(tanx).dx
Let u = tanx
du = sec² x.dx
I = ∫ e^(u).du
I = e^(u) + C
I = e^(tan x) + C