September 1st, 2014, 07:39 AM  #1 
Newbie Joined: Sep 2014 From: Miami Posts: 18 Thanks: 2  Integration by Parts Help
Hello everyone, This is my first time in this forum, but like other forums online I am sure there is an amazing community of people out there willing to help others; at least that's my personal experience; I know it will be similar in this forum. I am starting Integration by parts in my Calculus 2 class and it's something that I am still working on to grasp (it's tricky). I have this exercise and I cannot move forward (it might seem basic I know). $\displaystyle \int \frac{xe^{2x}}{(1+2x)^{2}}dx$ I chose: $\displaystyle u=e^{2x}$ $\displaystyle du=2e^{2x}dx$ $\displaystyle v=\frac{x}{(1+2x)^{2}}$ $\displaystyle dv=?$ But I cannot get the integral of dv to find v. Any ideas? Thanks a lot. Last edited by skipjack; September 2nd, 2014 at 02:49 PM. 
September 1st, 2014, 07:44 AM  #2 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,119 Thanks: 710 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
Before trying the integration by parts I would try substituting $\displaystyle u = 1 + 2x$. It simplifies the integral 
September 1st, 2014, 08:05 AM  #3 
Newbie Joined: Sep 2014 From: Miami Posts: 18 Thanks: 2 
Thanks for the replay Benit, I tried substituting $\displaystyle u=1+2x$ first in the original integral but the result is not that easy to work with ( or I am not seeing it) $\displaystyle \frac{1}{4}\int\frac{e^{u1}\left ( u1 \right )}{u^{2}}du$ Last edited by fredlo2010; September 1st, 2014 at 08:08 AM. 
September 1st, 2014, 12:40 PM  #4  
Global Moderator Joined: May 2007 Posts: 6,541 Thanks: 592  Quote:
It may not help. Last edited by skipjack; September 2nd, 2014 at 02:59 PM.  
September 1st, 2014, 03:45 PM  #5 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,825 Thanks: 1051 Math Focus: Elementary mathematics and beyond 
$\displaystyle u=xe^{2x},\,du=e^{2x}(1+2x)\,dx$ $\displaystyle dv=(1+2x)^{2}\,dx,\,v=\frac12(1+2x)^{1}$ 
September 1st, 2014, 05:15 PM  #6  
Newbie Joined: Sep 2014 From: Miami Posts: 18 Thanks: 2  Quote:
Thanks a lot for the reply. That did the trick. This is the final answer. I am not sure if it's correct to post all the solution? Can you guide me. In other forums we do to help other users in case they face a similar problem (programming stuff) Also I do not see a "Solved" flag. My guess is that it's not used. $\displaystyle \frac{e^{2x}}{8x+4}+C$ Thanks to all of you for the help. Last edited by skipjack; September 2nd, 2014 at 02:52 PM.  
September 1st, 2014, 05:59 PM  #7 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,825 Thanks: 1051 Math Focus: Elementary mathematics and beyond 
There's no harm in posting the solution, though we do encourage others to show some effort towards solving the problem (as you have).

September 1st, 2014, 06:18 PM  #8 
Newbie Joined: Sep 2014 From: Miami Posts: 18 Thanks: 2  
September 2nd, 2014, 12:49 PM  #9  
Banned Camp Joined: Jun 2014 From: Earth Posts: 945 Thanks: 191  Quote:
$\displaystyle \int\frac{u1}{u^2}du \ = \ \lnu \ + \ \frac{1}{u} \ + \ C$ Last edited by skipjack; September 2nd, 2014 at 02:57 PM. Reason: ln > \ln  

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