rock.freak667

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**1. Homework Statement**

Find

[tex]\int \frac{1}{lnx} dx[/tex]

**3. The Attempt at a Solution**

Let [itex]t=lnx \Rightarrow \frac{dt}{dx}=\frac{1}{x} \Rightarrow dx=e^t dt[/itex]

[tex]\int \frac{1}{lnx} dx \equiv \int \frac{e^t}{t} dt[/tex]

and well

[tex]e^t= \sum _{n=o} ^{\infty} \frac{t^n}{n!}[/tex]

[tex]\frac{e^t}{t}=\sum _{n=o} ^{\infty} \frac{t^{n-1}}{n!}[/tex]

[tex]\int \frac{e^t}{t}=\int \sum _{n=o} ^{\infty} \frac{t^{n-1}}{n!}[/tex]

[tex]=\sum _{n=o} ^{\infty} \frac{t^{n}}{(n+1)!}[/tex]

Is there any easier closed form solution for this?