# Convergence of the following integral

• Dell
In summary, the conversation is about finding a function that can prove whether the given integral converges or diverges. The person has been trying to find a function g(x) that is either greater or less than f(x), where g(x) converges and f(x) diverges, in order to solve the problem. However, they have not been successful and are looking for other ways to solve it or for a similar function that can help them. They discuss using ln(x)/x^4/3 as a possible function, but are unsure about its convergence/divergence and if it needs to be integrated.

#### Dell

i need to prove that the following converges or diverges

$$\int$$$$\frac{ln(x)dx}{\sqrt{x}(x+1)}$$ (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

Hi Dell! have you tried ∫ ln(x)/x4/3 dx ?

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

Dell said:
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!