# Thread: improper integral: converges/diverges before evaluation?

1. ## improper integral: converges/diverges before evaluation?

Hi. I'm a little confused about an issue in my homework problems involving improper integrals. I have problems like so:

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

$\displaystyle \int_{1}^{\infty}{\frac{ln\,x}{x}\,dx}$
How do I determine whether it converges or diverges before actually evaluating it?

2. ## Re: improper integral: converges/diverges before evaluation?

Originally Posted by infraRed
Hi. I'm a little confused about an issue in my homework problems involving improper integrals. I have problems like so:
How do I determine whether it converges or diverges before actually evaluating it?
What is the derivative of $\displaystyle \frac{(\ln(x))^2}{2}~?$

ln(x)/x

...?

4. ## Re: improper integral: converges/diverges before evaluation?

Obviously diverges.

5. ## Re: improper integral: converges/diverges before evaluation?

Originally Posted by infraRed
ln(x)/x...?

So what that tell you about the integral and why?

6. ## Re: improper integral: converges/diverges before evaluation?

$\displaystyle \frac{\ln(x)}{x} > \frac{1}{x}$. But the integral of 1/x diverges, so the integral of the original function does too.