How Do You Solve Improper Integrals Involving Logarithms?

[ACLerok]

I am trying to find the integral of [ln(x)] / [sqrt(x)]. i tried doing it by u substitution but that failed. what is the easiest way to do it? Also, I evaulated the integral from 1 to infinity of [ln(x)]/x by treating as an improper integral.
The way i did it was by setting up lim(as t->infinity) integral(1 to t) [ln(x)]/x. This correct, i got -1 so that means it diverges right? Or is my answer wrong?

Thanks for your help!

 

[Pyrrhus]

I think you got to use integration by parts.

 

[ACLerok]

k, i will try integrating by parts but am i right about the second integral?

 

[ACLerok]

can anyone else help me out please?

 

[TenaliRaman]

lnx = 2t
x = e^2t
taking sqrt on both sides,
sqrt(x) = e^t
1/2*sqrt(x) dx = e^t dt

-- AI

 

[ACLerok]

this may be a dumb question but whre is that from?

lnx = 2t
x = e^2t
taking sqrt on both sides,
sqrt(x) = e^t
1/2*sqrt(x) dx = e^t dt

-- AI

 

[TenaliRaman]

oh i missed the word substitute ...

-- AI