Is there a closed form solution to

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

Printable View

- Oct 29th 2008, 11:47 PMsoloakewlstickclosed form solution?
Is there a closed form solution to

$\displaystyle \int x^2 e^{x^2} dx$? - Oct 30th 2008, 01:05 AMCaptainBlack
Because:

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

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

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

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