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Math Help - help with tricky integration

  1. #1
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    help with tricky integration

    i need to integrate

    x^2*e^(x^2)

    i tried using parts but i still cant get an answer...
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  2. #2
    Eater of Worlds
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    That's because this critter is not easily done by the means we are used to.

    i.e. u-subbing, parts, etc.

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

    You could use the series for x^{2}e^{x^{2}}, \sum_{k=0}^{\infty}\frac{x^{2k+2}}{k!}

    Then, upon integrating we get \sum_{k=0}^{\infty}\frac{x^{2k+3}}{k!(2k+3)}

    This can also be represented by the error function:

    \int x^{2}e^{x^{2}}dx=\frac{1}{2}xe^{x^{2}}+\frac{1}{4}  \cdot i\cdot \sqrt{\pi}\cdot erf(ix).

    Which is complex as you can see.
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