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[tex]\int[/tex][tex]\frac{ln(x)dx}{\sqrt[3]{x}(x+1)}[/tex] (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