February 22nd, 2018, 04:50 PM  #1 
Senior Member Joined: Apr 2017 From: New York Posts: 165 Thanks: 6  Integration By Parts
Hi guys. Can somebody explain me only the last line ( in red frame). how did the last line shape just after the previous one. I know the topic well just didn't get that algebra part of ln transformation. appreciate it. 
February 22nd, 2018, 04:54 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,981 Thanks: 1166 Math Focus: Elementary mathematics and beyond 
Factor a 1/3 out of I. That should get you started.

February 22nd, 2018, 05:01 PM  #3 
Math Team Joined: Jul 2011 From: Texas Posts: 3,101 Thanks: 1677 
$x \color{red}{\ln(3x+1)} x+\dfrac{1}{3} \color{red}{\ln(3x+1)} + C$ factor out $\color{red}{\ln(3x+1)}$ from the two terms ... $\color{red}{\ln(3x+1)}\left[x + \dfrac{1}{3}\right] x + C$ $\color{red}{\ln(3x+1)}\left[\dfrac{3x}{3} + \dfrac{1}{3}\right] x + C$ $\color{red}{\ln(3x+1)}\left[\dfrac{3x+1}{3}\right] x + C$ $\dfrac{1}{3}\ln(3x+1) \cdot (3x+1)  x + C$ 
February 22nd, 2018, 05:17 PM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,981 Thanks: 1166 Math Focus: Elementary mathematics and beyond 
$\displaystyle x\ln(3x+1)x+\frac13\ln(3x+1)+C$ $\displaystyle \frac13(3x\ln(3x+1)+\ln(3x+1))x+C$ $\displaystyle \frac13(3x+1)\ln(3x+1)x+C$ 
February 22nd, 2018, 05:18 PM  #5 
Senior Member Joined: Apr 2017 From: New York Posts: 165 Thanks: 6 
whooops yobbaaa, I thought and tried everything but factoring out. thanks guys really appreciate. 

Tags 
integration, parts 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
integration by parts help  cookster  Calculus  4  June 2nd, 2012 06:10 AM 
Integration By Parts  aaronmath  Calculus  3  September 27th, 2011 11:36 AM 
integration by parts  oddlogic  Calculus  11  March 25th, 2011 08:59 PM 
integration by parts  jakeward123  Calculus  16  February 24th, 2011 08:34 AM 
Integration By Parts  hikagi  Calculus  3  September 24th, 2008 12:55 PM 