Question

integrating e^1/3dx i got 3e1/3 +c pls am i right

Answer 1

No. e^(1/3) is a constant. It's not a function of x.

The integral of a constant term (a) is:
∫ a dx = ax + C

Substitute a = e^(1/3).

Answer 2

On the other hand:

∫ e^(x/3) dx
= 3 ∫ e^u du , where x = 3u, dx = 3du
= 3 e^(u) + C
= 3 e^(x/3) + C