1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Quotient rule integration problem

  1. May 11, 2010 #1
    [tex]\int \frac{1}{2x+3}=\frac{\ln |2x+3|}{2}+c[/tex]

    so why is [tex]\int \frac{1}{x^2+x}\neq \frac{\ln |x^2+x|}{2x+1}+c[/tex] ?

    is it because in general ,

    [tex]\int \frac{1}{x}=\ln |x|+c[/tex]

    the denominator is meant to be only linear function ?
  2. jcsd
  3. May 11, 2010 #2


    User Avatar
    Homework Helper

    Re: integration

    Yes, because to go the other way, that is, take the derivative of the result [tex]\frac{ln|x^2+x|}{2x+1}[/tex] you need to use the quotient rule. It's not as simple as treating 2x+1 as a constant, which is what you instead get if the function in the log is linear.





    [tex]\int\frac{1}{ax^2}dx \neq \frac{ln|ax^2|}{2ax}[/tex]

    [tex]\frac{d}{dx}\left(\frac{ln|ax^2|}{2ax}\right)=\frac{\frac{1}{ax^2}.2ax-2a.ln|ax^2|}{4a^2x^2} \neq \frac{1}{ax^2}[/tex] as required.
  4. May 11, 2010 #3
    Re: integration

    thanks , so it only works when the denominator is a linear function .
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook