- #1
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Homework Statement
Find
[tex]\int \frac{1}{lnx} dx[/tex]
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?