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



Numerade Educator



Problem 35 Hard Difficulty

Evaluate the integral.

$ \displaystyle \int_1^2 x^4 (\ln x)^2 dx $


$\frac{32}{5}(\ln 2)^{2}-\frac{64}{25} \ln 2+\frac{62}{125}\cdot 31$


You must be signed in to discuss.

Video Transcript

The problem is you wanna It's integral. Integral from one to two x two for Cam's Ellen Necks squired yaks. For this problem, we can use the integration by parts. Phoner is integral from a to B. New crime? Yes is the cultural you have speaking from a to the Linus integral from a to B you prime have sleep yaks Now for our problem, we can light. You see cultural Ellen X squire and we prom is they go to ax to force. Then you prom. It's the code to two attempts our necks over to and the movie is a cultural one. Fifth have sex two of now by using this formula our into girl This he called too. You damn species. This is two over axe too. Times out in packs. Now this is one hour five hams, Thanks to five. I'm Sal and Max Squire from wine two two and then Linus into girl. Want to too. You prime counselor. He's your promise to our next over. Max, this is two over five acts to or pounds our next. Yes. Now this is a code two. The first the term we can plug being too and one toe axe. Then we have This is thirty two cover times two score. And for the second term, this's minus to over. Off times this integral wanted to Act two or Tom's out next. Thanks. Now computer exist into girl thiss integral. We can also use integration. My parts like you is going to no in next they're from as they call to ax too. For then your crown is gone too. One over acts and wien is the culture one fifth times x through. So this dainty girl this is a one to two over How and Teo squired minus two over of on this integral If they called too one over x two. Thanks. I want to Linus into girl from wanting to your prom hams. Reasons this is one hour axe to ward the axe. This is they come true. Thirty to are off and two squire minus. For this term, this is Echo two. One hour for thirty to our file times. Alan, to this this this two over fun times thirty two over five comes out in two minus. This interview is one over twenty five times. Access to, uh, want to too on DH. This is Echo two thirty two, minus one. His answer is You called too. Thirty two over five out and to it's going minus as sixty for homer, five times out into class two over. Blind to love terms that he wants. This is a Gunther.