# What is the integral of e^1/x?

• February 17th 2013, 02:10 PM
UBCBOY
What is the integral of e^1/x?
Hi, I seem to be stumped with calculating this indefinite integral:

e^1/x6x^2dx

I'm using integration by parts, but I can't find how to take the integral of e^1/x...how does it work?

Thank you, kind sirs!

• February 17th 2013, 02:17 PM
ILikeSerena
Re: What is the integral of e^1/x?
Quote:

Originally Posted by UBCBOY
Hi, I seem to be stumped with calculating this indefinite integral:

e^1/x6x^2dx

I'm using integration by parts, but I can't find how to take the integral of e^1/x...how does it work?

Thank you, kind sirs!

Hey UBCBOY! :)

It doesn't work very well.
You won't be able to find an indefinite integral of $e^{1/x}$.
• February 17th 2013, 02:37 PM
UBCBOY
Re: What is the integral of e^1/x?
It doesn't exist? :(

I tried putting DNE on the system but it does not work.
• February 17th 2013, 02:39 PM
ILikeSerena
Re: What is the integral of e^1/x?
As they say, it cannot be expressed with a finite number of standard functions.
• February 18th 2013, 01:21 AM
JJacquelin
Re: What is the integral of e^1/x?
Hi !

The integral of exp(1/x) cannot be expressed as a combination of a finite number of elementary functions. It's formal expression requires a special function, namely Ei(x).
integrate exp(1/x) - Wolfram|Alpha
Of course, it is possible to express the integral of exp(1/x) on the form of infinite series.