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

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).

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

To find the integral of e^(1/3) with respect to x, you can use the power rule for integrals. Start by rewriting e^(1/3) as (e^(1/3))^1.

Now, to integrate, use the power rule which states that if the derivative of x^n is n*x^(n-1), then the integral of x^n dx is (x^(n+1))/(n+1) + C, where C is the constant of integration.

In this case, the exponent is 1. Applying the power rule, you get:

∫ (e^(1/3))^1 dx = (e^(1/3))^2/2 + C

Simplifying, we get:

(1/2)e^(2/3) + C

So, the correct answer is (1/2)e^(2/3) + C.

Your answer of 3e^(1/3) + C is not correct.