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# Evaluate the integral.$\displaystyle \int_1^2 \frac{(\ln x)^2}{x^3} dx$

## $-\frac{1}{2} \ln \frac{1}{2}+\left(\frac{1}{2}-1\right)=\frac{1}{2} \ln 2-\frac{1}{2}$

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Integration Techniques

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### Video Transcript

the problem is what it is. Integral. Integral from one to two. Ellen next to Squire, our thanks to Greece, Power X. For this problem, we can use my theory of the integration by parts. And the farmer is integral from a being. You have sway from the ex. It's difficult to you'd have been from a to B minus into euro from a to B. You promise has being yaks now for our problem. We cannot. You is. You go to now in choir on the way prom is they go to one over X two, raise power. Then you promise too. Two times now and necks over X here We used the changeable and we got you negative one over to X squad. Now by you having this farm owner, it's integral. It's equal to you have fleas. This's now and axe squired times connective one over to Ike's squire from one to two, minus the integral from wan t to you prime time. Sweetie, this is us two times our necks. Oh, two towns, X two three We can can thought too. This is our axe. Over. Act two three. Now this is Echo two with the first term we can plugging to and want to axe. And we have This is now and two squire hams. Negative one over eight on the for the second and minus zero for the second term. With this integral, we can also use integration. My parts on the night you is he go to island necks the way. Promise you go to one over x two, three Then your prom is equal to one. Our axe movies go to negative one over two taps sack square. So this integral. But this is a cultural with one class, you'd have sway. So this is how lax I'm still negative. One over to Max from one to two on minus and two. Girl want to too. You promise me this is This is last one over. Two times tax, too. Ring Jacks, This is Echo Two. Negative one over eight. Hands out. And to squire us this term is he got to. This is minus one over eight hands, Helen to minus zero. On this. The last tomb, this is Echo two. Make you one horse. Ham's one. No work X squared from one to two. This is the negative one. Over eight now. And two squire, minus one over age. Alan, too. On DH. This's Class one Negative. Force Tams, one of our four minus one. The answer is this one has. The answer is three hour sixteen. The answer is negative. One number eight on two squire minus one over eight Now too. Class three over sixteen.

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