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Math Help - closed form solution?

  1. #1
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    closed form solution?

    Is there a closed form solution to
     \int x^2 e^{x^2} dx?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by soloakewlstick View Post
    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
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