Here I used integration by parts to try to solve an integral (I got it wrong, it seems), I know this has no "simple" solution, but, can anyone explain me exactly what did I do wrong? Here is what I did:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\int\frac{e^x}{x}dx=\frac{e^x}{x}-(-1)\int\frac{e^x}{x^2}dx=\frac{e^x}{x}+1(\frac{e^x}{x^2}-(-2)\int\frac{e^x}{x^3}dx)=\frac{e^x}{x}+1!(\frac{e^x}{x^2}+2!\frac{e^x}{x^3}+3!\int\frac{e^x}{x^4}dx)=...=0!\frac{e^x}{x}+1!\frac{e^x}{x^2}+2!\frac{e^x}{x^3}+3!\frac{e^x}{x^4}+...[/itex]

I just used integration by parts on the "remaining" integrals so I could produce a series, but the series is just...wrong. I would appreciate if you told me what is the error in my reasoning.

thanks.

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# Integration by parts wrong (?)

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