2
$\begingroup$

I need help with evaluating the integral:

$\int x e^{-x^3}dx$

Thanks!

  • 1
    If it were a definite integral, it could be accurately approximated. If it were $\int x^2e^{-x^3}dx$, the antiderivative can be expressed in terms of [elementary functions](http://en.wikipedia.org/wiki/Elementary_function). But for this one, it cannot. See [this post](http://math.stackexchange.com/questions/155/how-can-you-prove-that-a-function-has-no-closed-form-integral) covering a relevant theorem of Liouville and the Risch algorithm for more info. If this is a homework problem, it is an error. What is the precise problem or your real need?2012-04-13

2 Answers 2

5

Typo perhaps? If it is meant to be either $\int x^2 e^{x^{3}}dx$ or $\int x e^{x^{2}} dx$ then these can be evaluated very simply.

  • 0
    @aldo: You might want to edit your question to account for this new development...2012-04-15
0
Take t = x^3  dt = 3x^2 dx and x = t^(1/3) 

and substitute x and find integration by using LIATE

  • 0
    Doesn't help...2012-04-13