September 12th, 2017, 05:52 PM  #1 
Newbie Joined: Sep 2017 From: Australia Posts: 2 Thanks: 0  Integration by recognition
Hi, I've been stuck on integration by recognition questions for a long time and can't get my head around them. Any help would be greatly appreciated! Thanks in advance. Here's a couple of examples: 1. Differentiate ln(32x) and hence find the antiderivative of 5/(32x) 2. Show that (32x)/(1x)=2+1/(1x) and hence find the antiderivative of (32x)/(1x) Last edited by skipjack; September 12th, 2017 at 11:48 PM. Reason: Added brackets where appropriate 
September 12th, 2017, 06:30 PM  #2 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,410 Thanks: 715 
I'm not sure what you mean by integration by recognition, but let's take a look. $\dfrac{d}{dx} \ln(32x) = \dfrac{2}{32x}$ $\dfrac{5}{32x} = \left(\dfrac{5}{2}\right) \dfrac{2}{32x}$ so $\displaystyle \int ~\dfrac{5}{32x}~dx = \left(\dfrac{5}{2}\right)\int~\dfrac{2}{32x}~dx = \left(\dfrac{5}{2}\right) \ln(32x)$ Does this make sense? See whether you can do the 2nd one. Last edited by skipjack; September 12th, 2017 at 11:49 PM. 
September 13th, 2017, 04:01 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,649 Thanks: 681 
"Integration by recognition" means to integrate by "recognizing" the integrand as being the derivative of another function. Of course, that depends upon what derivatives you know! Here, they asked you to find the derivative first so you would have to know it.


Tags 
integration, recognition 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Face Recognition  avicarpio  Math  3  May 11th, 2017 12:30 AM 
Would Anyone appreciate handwriting recognition for Maths?  cmml100  New Users  5  November 4th, 2012 07:59 PM 
LaTeX symbol recognition  mattpi  LaTex Help  2  April 28th, 2011 02:31 PM 