Our integral is
Hint: we may use a substitution of variables.
Find the value of p for which the integral converges and evaluate the integral for those values of p
∫ 1/(x(ln x)^p)
upper limit : infinity
lower limit : e
The integral proposed by Scott H , though different from the original one, is quite interesting. First we suppose that is . In this case the integral can be devided in two parts...
(1)
Now we can set in second integral and obtain...
(2)
... so that is...
(3)
From (3) we deduct that for odd with is...
(4)
... and for even with the integral diverges...
Kind regards