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# Evaluate the integral.$\displaystyle \int_1^5 \frac{\ln R}{R^2} dR$

## $\int_{1}^{5} \frac{\ln R}{R^{2}} d R=\left[-\frac{1}{R} \ln R\right]_{1}^{5}-\int_{1}^{5}-\frac{1}{R^{2}} d R=-\frac{1}{5} \ln 5-0-\left[\frac{1}{R}\right]_{1}^{5}=-\frac{1}{5} \ln 5-\left(\frac{1}{5}-1\right)=\frac{4}{5}-\frac{1}{5} \ln 5$

#### Topics

Integration Techniques

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##### Catherine R.

Missouri State University

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

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### Video Transcript

The problem is you wanted the integral Integral from one to five. L and R or R squared D r For this problem, we can use my third of the integration by parts common. It is into girl from A to B. You have released from yaks. It's a call to you'd have screamed roommate being minus into girl from a to B you prom? Absolutely. Yaks. Now for our problem, we can like you. Is the coat too? How in and re prime is O'Toole one over. Uh, square. Then you prom this Rico to one over our arm. And we It's the code to negative. I wanna know where r now this into girl is you go to about this formula to city photo. You damn Swede! This's negative one or we are ums when are from one to five minus integral from one toe. Five. You promised me that this is negative one over our square. We are This is the coach. So for the first two term line five to one from crying foul and want Teo, are we have This is negative, Alan, Five oh five and minus zero. Second term is plus into peril of one of our squire's. This's negative one over R from one to five. This is a country negative. Our style over five class negative one over five minus Meg to Juan. The author is negative now and over a five class whom you are.

WZ

#### Topics

Integration Techniques

##### Catherine R.

Missouri State University

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp