i need to integrate

x^2*e^(x^2)

i tried using parts but i still cant get an answer...

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- Nov 4th 2008, 09:29 AMlauren2988help with tricky integration
i need to integrate

x^2*e^(x^2)

i tried using parts but i still cant get an answer... - Nov 4th 2008, 10:01 AMgalactus
That's because this critter is not easily done by the means we are used to.

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

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

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

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

This can also be represented by the error function:

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

Which is complex as you can see.