I need to integrate

The integral is impoper because x cannot be 1. Since 1 is at the left hand, I rewrite it to...

Then I integrate and get...

Let u=lnx, du=1/x dx

Then

=

Now I do not know how to find out what the answer is. Lnt would be Ln1+, so it gets closer and closer to ln1. Ln1 = 0. Does the term (lnt)^2/3 gets zero then?

And the limit goes to 3/2((ln4)^{2/3} - 0 ?

Thanks for any help.