Determine the integral

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This seems to involve the elliptical integral according to maple...

Hi,
First, separate out the easy parts; write the integrand as:

(1/e2)e1/(2x) + 4x

Integrate 4x separately, = 2x2

Lookup the integral of e1/(2x) (! I found it on Mathematica, here:

http://integrals.wolfram.com/index.jsp?expr=E^(1/(2x))&random=false"

!)

Your result will be (1/e2)[The integral you found...] + 2x2

BTW: Wolfram/Mathematica does find that the answer includes a so-called "Exponential Integral".

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Oops I meant exponential not elliptical :)

MathematicalPhysicist
Gold Member
The bigger question is how to solve an integral exp(ax^q) where q isn't null and isn't 1, I don't think there's a prescription to it.
are you sure it shouldn't be xexp(1/x), cause this can be computed by changing 1/x=u and a series change.