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

1. ## 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!

2. ## Re: What is the integral of e^1/x?

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 $e^{1/x}$.

3. ## 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.

4. ## Re: What is the integral of e^1/x?

As they say, it cannot be expressed with a finite number of standard functions.

5. ## 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.

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# integral e^1/x

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