How do you use the integral test to determine whether #int dx/(x+lnx)# converges or diverges from #[2,oo)#?
1 Answer
Aug 1, 2017
The integral:
diverges.
Explanation:
As in the interval
is positive and decreasing, and:
based on the integral test the convergence of the improper integral:
is equivalent to the convergence of the series:
Consider now the harmonic series:
that we know to be divergent and apply the limit comparison test:
as the limit is finite the two series have the same character, then also the series
is divergent.