3.7 Improper Integrals

[STARTS AT 29:43]

Instructor: Use the comparison test to show that this diverges. So that means we need to find some function such that this one is less, or is greater than that. We need some things underneath it, that is also divergent. Well past the value of e, so this is always greater than 1 over x, on the interval e to positive infinity. 

So we can compare that to the integral of e to infinity. Of 1 over x dx x. Well, this is positive infinity, for the same reason we had earlier. So that means, the integral from us from e to infinity, of ln x over x dx also diverges.

[ENDS AT 30:37]