Re: Problem with integral

On Jul 27, 9:17 am, desktop <asd...@xxxxxxx> wrote:
I am trying to solve this integral using partial integration:

(1) int(x^2* e^(x^3)) dx

I have choosen x^3 as the inner function:

u = g(x) = x^3

I isolate x and get:

x = u^(1/3)

Then I differentiate x over u:

dx = 1/3 * 1/(x^(2/3)) du

I now substitute dx and u in (1) and get:

int(x^2 * e^(u) * 1/3 * 1/(x^(2/3)) du

Is that correct so far?

I am not sure what to do next have considered partial integration or
just reducing the current expression, but I cannot seem to get the result:

> simplify(int(x^2*e^(x^3),x));
/ 3\
\x /
e
-------
3 ln(e)
which is returned my maple. Hope someone can give a hint.

Here's a hint: Instead of solving for x in terms of (x = u^(1/3)),
finding dx, and solving for du, leave your expression as u in terms of
x (u=x^3), find du, and solve for dx.

.

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