integral question. i dont know why i'm getting it wrong when its so easy! helpp?

Question

∫ x^(2) e^(x^3) dx

Answer 1

Integral of x^2 e^(x^3) dx

Let u = x^3

Then du = 3x^2 dx, and

dx = du/3x^2

Now your integral becomes:

x^2 e^u du/3x^2

= 1/3 x^2 e^u du/x^2

= 1/3 ∫e^u du = 1/3 e^(x^3)

Answer 2

Do a change of variable: let u = x³. Then du = 3x² dx and your integral becomes

∫ x² e^(x³) dx

∫ (1/3) e^(x³) 3x²dx

(1/3) ∫ e^u du

Answer 3

I think it's 1/3 e^(x^3)

because d/dx of e^f(x) = f'(x)*e^f(x)