Convergence of the following integral

[Dell]

i need to prove that the following converges or diverges

\int\frac{ln(x)dx}{\sqrt[3]{x}(x+1)} (from 1-∞)

what i have been trying to do is find a function that is either:
g(x)>f(x); g(x) converges
g(x)<f(x); g(x) diverges

but i have not been able,
is there any other way to solve this, or could you please show me a similar function that is one of the 2, if possible could you show how you reached your g(x)

thank you

 

[tiny-tim]

Hi Dell!

have you tried ∫ ln(x)/x^4/3 dx ?

 

[Dell]

i thought of that, but what do i know about ln(x)/x^4/3, i would ideally liked to have taken it as my gx and said lim fx/gx=1 therefore f(x) behaves like ln(x)/x^4/3, how can i fin out if ln(x)/x^4/3 converges/diverges, do i have to integrate it? if so is there a simpler way than integration in parts? if not, is there not a simpler function you can think of

 

[tiny-tim]

how can i fin out if ln(x)/x^4/3 converges/diverges, do i have to integrate it?

D'uh!

you'd think so, wouldn't you?

get on with it!​