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WZ

# Determine whether each integral is convergent or divergent. Evaluate those that are convergent.$\displaystyle \int_e^\infty \frac{1}{x (\ln x)^2}\ dx$

## Converges to 1

#### Topics

Integration Techniques

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##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

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### Video Transcript

the problem is determine why that this integral has cordant or that wouldn't first we can use you substitution to rewrite dysfunction for functions that are easier to integrate. We can like you is he co to our necks then the u you see Cho too one over x the axe Then this anti grow is equal to one over you, squire and the one relax T x is just to you and what Max goes toe e u goes toe on the one acts goes to infinity. You also cause Tau infinity Then, as a definition of the improper integral, this's a limit. He goes to vanity into girl from one to you of one Never your squire You. This is a two Lim. He goes to infinity It's anti derogative off one over Your square is equal to negative one over you from Tio y Tu Tio. This is the limit. He goes to infinity Negative wine over month one and he goes to infinity One hour he goes to Their answer is one this integral is converted and it's a wine You is one

WZ

#### Topics

Integration Techniques

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp