# can you/how do you integrate e^2x^2?

• Feb 6th 2009, 03:30 PM
ryu991
can you/how do you integrate e^2x^2?
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?
• Feb 6th 2009, 04:25 PM
Abu-Khalil
You mean $\displaystyle \int e^{2x^2}dx$?
• Feb 6th 2009, 04:55 PM
WhoCares357
Quote:

Originally Posted by Abu-Khalil
You mean $\displaystyle \int e^{2x^2}dx$?

I'm curious myself (new to calculus).

Could you take the natural log of both sides to bring the $\displaystyle 2x^2$ down and then integrate?
• Feb 6th 2009, 05:07 PM
Chris L T521
Quote:

Originally Posted by ryu991
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 $\displaystyle \int_0^{\infty}e^{-2x^2}\,dx=\frac{1}{2}\sqrt{\frac{\pi}{2}}$