# closed form solution?

• Oct 30th 2008, 12:47 AM
soloakewlstick
closed form solution?
Is there a closed form solution to
$\int x^2 e^{x^2} dx$?
• Oct 30th 2008, 02:05 AM
CaptainBlack
Quote:

Originally Posted by soloakewlstick
Is there a closed form solution to
$\int x^2 e^{x^2} dx$?

Because:

$2x e^{x^2}=\frac{d}{dx}e^{x^2}$

integration by parts (spliting the integrand up $(x/2)(2xe^{x^2} )$) will reduce this integral to a closed form plus a multiple of the integral:

$\int e^{x^2}\ dx$

so your question is equivalent to asking if this latter integral has a closed form representation in terms of a finite number of elementary functions and algebraic operations (it is well known not to be so expressible).

CB