How Do You Solve Integrals of the Form exp(ax^q) When q Is Not 1?

[maobadi]

Please help. How do you solve this

 

[NoMoreExams]

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

 

[BobMonahon]

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

(1/e²)e^1/(2x) + 4x

Integrate 4x separately, = 2x²

Lookup the integral of e^1/(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".

 

[NoMoreExams]

Oops I meant exponential not elliptical :)

 

[MathematicalPhysicist]

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.