# Determine which values of p the following integral converge. Give your answer in each case by giving an appropriate inequality sign (e.g., > or <=)  to define a range of p values for which the integral converges. If the integral never converges, enter none for the numerical value. integrate from 2 to infinity of ((dx)/(x(ln(x)))^p)

You should solve the given improper integral such that:

`int_2^oo 1/(x*(ln x)^p)dx = lim_(n->oo) int_2^n 1/(x*(ln x)^p)dx`

You need to solve the indefinite integral `int 1/(x*(ln x)^p)dx`  using the substitution `ln x = t`  such that:

`ln x = t => 1/x dx = dt`

Changing the variable yields:

`int 1/(x*(ln x)^p)dx = int (dt)/(t^p)`

Using the property of negative power yields:

`1/t^p =...

(The entire section contains 234 words.)

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