**Here's my problem. [tex]\int e^{1/x} dx[/tex]**

**This was my attempt:**

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

so, [tex]x^{2} du = - e^{1/x}[/tex]

I = - [tex]\int x^{2} du , t = x , dt = (1) dx[/tex]

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

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

so, [tex]x^{2} du = - e^{1/x}[/tex]

I = - [tex]\int x^{2} du , t = x , dt = (1) dx[/tex]

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

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