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



Numerade Educator



Problem 44 Hard Difficulty

Evaluate the indefinite integral. Illustrate, and check that your answer is reasonable, by graphing both the function and its antiderivative (take $ C = 0 $).

$ \displaystyle \int x^{\frac{3}{2}} \ln x dx $


$\frac{2}{5} \cdot x^{5 / 2} \cdot\left(\ln x-\frac{2}{5}\right)$


You must be signed in to discuss.

Video Transcript

The problem is you want it. It's an indefinite, integral, illustrate and checked. Check that your mother is reasonable by graphing boss That function on this anti terror bitters Integral is zero packs to realise two times in lax Tex But this problem, we can use integration by parse the foreigner is integral off you prom the axe. It's the cultural you have swing minor internal You prime time sleeve acts now for our problem. We cannot you is the cultural Helen Axe read crime thanks to me. Homework too. Then you prom If they come to one of our acts being asleep to over of hands tax too off over too. Now, by using this farm owner, this integral is Think about you. You'd have sleaze that this is too over. Teo. Off over too. Hands on, max minus. General, you're crammed ham sleaze of this list to over of I'm specs to three over two. Max, this is equal to two over. Axe to O. R. Two has Alan necks minus. This is two over Squire Ham's tax to file over to and plus a constant number. See, this is on tired, determinative of the function, actually. Really too. Hello, Max. Stan, we use some rough Indy wise to jar the graph with this two functions. Let's see, Royal Juan is dysfunction and Wan is the anti terror votive after Lyle Cliff, when now determinative after blue on is That's right. Why? So why do you have right a curve at some point X? Is he reflect me? It's a slow post tan line have survived the blue curve at this point. Now, first I see the slope of the ten in the line of the road. Look, one x goes from zero to infinity, the tan and the slope of the tangent line of low curve goes round zero two active number and two zero to some positive remember and to infinity. Now let's say that Why do you have a lighter on X? Goes from zero to infinity while you goes from They're old Show negative two zero two positive on team friends. So he has a seam. So our results reasonable