∫ e^(3x) dx = ?

Question

Please remind me how to do this. I'm forgeting stuff, and I have a test coming up.

Thank you radnee and 'I know'; most could not grasp the 'help me understand portion of the question.

Answer 1

Use the fact that ∫e^u du = e^u + C and u substitution

∫ e^(3x) dx

Let u = 3x
du/dx = 3
dx = du/3

The integral becomes
∫ [e^u du]/3
1/3 ∫ [e^u du]

Which we can integrate easily
1/3 e^u + C

put it back in terms of x
1/3 e^(3x) + C

Answer 2

Recall that the derivative of e^f(x) is e^f(x) * f'(x). Then
one can see that integrate(e^(3x)) = (1/3)e^(3x) + c where
c is some constant.

Answer 3

e to the third over 3 + c

Answer 4

I = ∫ e^(3x).dx
let u = 3x
du / dx = 3
dx = du / 3
I = (1/3).∫e^(u) du
I = (1/3).e^(u) + C
I = (1/3).e^(3x) + C

Answer 5

∫ e^(3x) dx = (1/3) e^(3x) + c

Answer 6

1/3 e^(3x)

Answer 7

1/3e^3x

Answer 8

$^u6r34967, is what that looked like to me at first...just had to tell you that. Honestly, I have no clue...good luck though.