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

Like

Report

WZ
Numerade Educator

Like

Report

Problem 41 Hard Difficulty

First make a substitution and then use integration by parts to evaluate the integral.

$ \displaystyle \int x \ln (1 + x) dx $

Answer

$\frac{1}{2}\left(x^{2}-1\right) \ln (1+x)-\frac{1}{4} x^{2}+\frac{1}{2} x+\frac{3}{4}+C$

Discussion

You must be signed in to discuss.

Video Transcript

problem is first making a substitution on DH then used contribution. Of course to you Violet. Inventive girl. Inte grow ex terms. How in one class? Ax the ax with this problem. First we can use new substitution. But why Physical too? One plus six. Why? If you go to now is this into You know it's got you into Girl X is equal to y minus wants It is wine. One Ham's one. Why do you want? And then we can use the integration by parts to you. Violet. Just this integral the foreigner is into girl. You leave from Jax. It's the cultural you have b minus in general. You're trying? Absolutely. Yes. Now for our problem, we can last you seek ritual what is equal to how and why and re prime his future wine minus one. Then new problem. If they caught you one over. Why? And wait, Huh? Have y squared minus y. Now this girl is, don't you? New taps, please. This is yeah. And why times why? Schooling minus live, then minus into girl. Your prom times resist this. My half. Why? Minus why? Why? This is coach you, huh? Why squire months why I'm spelling. Why minus the integral is cool too. One source. Why? Squire Linus? Why? And class casting number. See? And we need to convert. Why back too? The function wax This is I have X plus Juan Squire in Ones X plus one terms. Next one. Linus, my horse X plus one squire once X plus lawn, plus past number sin. This is the answer.