Question

integrate (ln x)/x dx?

Answer 1

What's the derivative of ln x?

Answer 2

And once you know that, does that suggest a substitution to you?

Answer 3

Actually I did get that far and then the internet went away: and I still got stuck
I went with u=ln x which gives you du = 1/x dx and dx = x/1 du

the x's cancel leaving \[\int\limits_{}^{}u du = \int\limits_{}^{}\ln x \]

but apparently I'm blocking the integral for lnx or I've done something wrong...

Answer 4

After substitution of u = ln x, you have
\[ \int u \ du = \frac{1}{2}u^2 + C = \frac{1}{2} (\ln x)^2 + C \]

Answer 5

thanks...is it weird that none of my books has \[\int\limits_{}^{}\ln x\]
in the list of integral tables?