Title says it all, this isnt a question I've seen just something I'm curious about.
If you have e raised to the power of 2x, where the x is raised to the 2nd power can you integrate that? If so how?
It can't be done in terms of elementary functions.
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As an aside: If you were to find $\displaystyle \int_{-\infty}^{\infty}e^{-2x^2}\,dx$ or $\displaystyle \int_0^{\infty}e^{-2x^2}\,dx$ or $\displaystyle \int_{-\infty}^{0}e^{-2x^2}\,dx$, then it can be done, but by a conversion to a double polar integral. This way, it can be shown that $\displaystyle \int_0^{\infty}e^{-2x^2}\,dx=\frac{1}{2}\sqrt{\frac{\pi}{2}}$