How to Calculate the Integral of e^{1/x}dx?

[pamoriano]

Hello everyone,

How do I to figure out the integral of e^{1/x}dx.

Thanks in advance,

 

[gb7nash]

Unfortunately, this does not have an elementary answer. However, there should be integral tables and tools available that will tell you the area under the curve.

 

[g_edgar]

If you ask Maple, you get an answer in terms of \mathrm{Ei}_1(x)

 

[TylerH]

Get the Taylor expansion and integrate that.

 

[studentstrug]

Hello everyone,

How do I to figure out the integral of e^{1/x}dx.

Thanks in advance,

What is the context of this integral? Why do you need to figure it out?

(It is straightforward to use Liouville's thereom to prove that the indefinite integral of e^{1/x} is non-elementary, that is, cannot be expressed in finite terms of elementary functions).