integral of lnx / x dx

[math]

integral of lnx / x dx

I know the integral of lnx is xlnx - x + c. I know how to find that,

But when I tried to integrate lnx/x dx, I keep getting stuck.

integral of lnx * 1/x dx
Let u = lnx v' = 1/x
u' = 1/x v = ln abs(x)

ln x X ln abs(x) - integral of ln abs (x) * 1/x

Now I'm in a worse position than when I started, I think.

 

[galactus]

Try substitution instead.

Let \(\displaystyle \L\\u=ln(x), \;\ du=\frac{1}{x}dx\)

 

[math]

got it. thanks galactus!