(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find,

[tex]\int \left( \frac{1}{x} - \frac{1}{x^2} \right)e^x ~dx[/tex]

2. Relevant equations

None

3. The attempt at a solution

I tried integrating by parts,

[tex] \]\int \left( \frac{1}{x} - \frac{1}{x^2} \right)e^x ~dx\\

Let ~\frac{dv}{dx}=\left( \frac{1}{x} - \frac{1}{x^2} \right), and ~u=e^x.\\

\therefore v=\ln{x} + \frac{1}{x}, and ~\frac{du}{dx}=e^x\\

\therefore \int \left( \frac{1}{x} - \frac{1}{x^2} \right)e^x ~dx

= e^x(\ln{x} + \frac{1}{x}) - \int{ e^x(\ln{x} + \frac{1}{x})}~dx\[ [/tex]

But I can't see what to do now; the next integral is even messier than the first!

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# Homework Help: Problematic Integral

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