Question

How to integrate (1+1/ln(x))/x?

Answer 1

I use u-sub where u=ln(x), can this work?

Answer 2

@zepdrix @dan815 @Compassionate @SolomonZelman

Answer 3

\[\Large\rm \int\limits \frac{1}{x \ln x}dx\]Ahh the brackets are confusing, is this what we're working with?

Answer 4

\[\Large\rm \frac{1+\frac{1}{\ln x}}{x}dx\]

Answer 5

Yes, the second one.

Answer 6

u=ln x?
Hmmm that might work.. let's see.\[\Large\rm \int\limits\frac{1+\frac{1}{\ln x}}{x}dx=\int\limits\left(1+\frac{1}{\ln x}\right)\left(\frac{1}{x}dx\right)\]

\(\Large\rm du=\dfrac{1}{x}dx\), yes?

Answer 7

continue

Answer 8

Then you plug stuff in:\[\Large\rm \int\limits\left(1+\frac{1}{u}\right)\left(du\right)\]And integrate.
Looks pretty straight forward from here :)

Answer 9

I see, thank you.