Solving Int e^(1/x) - Step by Step Guide

[Muzikh]

Here's my problem. $$\int e^{1/x} dx$$
This was my attempt:

$$\int e^{1/x} dx , u = e^{1/x} , du = -\frac{ e^{1/x}}{x^{2}}$$

so, $$x^{2} du = - e^{1/x}$$

I = - $$\int x^{2} du , t = x , dt = (1) dx$$

I = $$\int x^{2} [\frac{ e^{1/x}}{x^{2}}] (1) dx = \int e^{1/x} dx$$


As you can see... I've only gone full circle with this approach. Any help would be greatly appreciated. Thanks.

 

[yyat]

This integral can not be written in terms of elementary functions, only in terms of the http://en.wikipedia.org/wiki/Exponential_integral" . To do this, you will need a substitution (different from the one you did, but simple) and partial integration.