💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!



Numerade Educator



Problem 22 Medium Difficulty

Determine whether each integral is convergent or divergent. Evaluate those that are convergent.

$ \displaystyle \int_1^\infty \frac{\ln x}{x^2}\ dx $


Converges to 1


You must be signed in to discuss.

Video Transcript

The problem is determined why the rich in general is converted where that wouldn't and the evaluated those that are converted. This improbability girl, by definition, this is the coach is the limit. It goes to infinity and into girl from a one way or the function on X over square DX we computed the definite integral first for this definite integral. This is going to so here we use my third off the integration by powers. It's legal tool one from one twe. The function is our necks and he make you wanna rags. This is your cut. They go to our necks. Um negative one. Iraq's from one way minus and to go one too, eh? Of the function Negative one over. Axe Ham's one over X the axe. Here we use my third of the integration by parts thiss if you call Tio ex making one arrives from want, eh? Minus off here we can run past into girl from want, eh? One over X square, The ex? Yeah, loving A and one just two functions. This is equal to l N A. Um name one over, eh? Minus zero us. Second part is next. You want over ice from one too, eh? This is ICO too. I went, eh? Make you wanna write a us? I need to find Dover. Hey, Minus Nick. Do you want? When a goes to infinity, his function goes to zero. Andi disfunction also goes to zero. The answer is one this improper integral is converted. And then why There was one.