1. ## Find covergence

Find if the improper integral converges. 1 / infinity lnx/x^2

Find if the improper integral converges. 1 / infinity lnx/x^2
Consider that

$\displaystyle \frac{\ln(x)}{x^2}\leqslant\frac{\sqrt{x}}{x^2}=\f rac{1}{x^{\frac{3}{2}}}$

So what can we conclude?

3. do we have to use integration by parts? thats what my professor told us is the way to solve it.

If you are trying to actually find the value of the integral then integration by parts is the correct method. To make it a little easier first try making the substitution $\displaystyle \ln(x)=z$